FusionWiki - User contributions [en]

Island Divertor

2023-04-25T03:42:28Z

Rkba39f8:

The Island Divertor is a concept in magnetic confinement fusion devices that utilizes inherent low-order [[magnetic island|magnetic islands]] to manage power and particle exhaust. Developed for advanced low-shear [[stellarator|stellarators]] in the Wendelstein-7 family, the island divertor was first tested on [[W7-AS|W7-AS]] before its shutdown in 2002<ref>[[doi:10.1088/0029-5515/46/8/006|Y. Feng et al, Nucl. Fusion '''46''' (2006) 807]]</ref>. The concept has since been investigated in more detail and at a larger scale in [[W7-X|Wendelstein 7-X]] (W7-X).

One major challenge magnetic confinement fusion devices face is managing power and particle exhaust. In future reactors, hundreds of MWs of power will stream out from the confined plasma region (core) and must be dissipated before reaching the plasma-facing components (PFCs). Excessive heat and erosion can lead to short lifetimes of the PFCs, as well as the release of impurities and subsequent contamination of the confined plasma.

[[Divertor|Divertors]] are dedicated plasma-wall interaction zones where particles and heat stream to, moving parallel to the open magnetic field lines in the scrape-off layer (SOL). However, the fast parallel heat transport leads to localized heat deposition on the targets. In stellarators, several edge topologies have been proposed and used to form a divertor for particle and heat exhaust (e.g., helical divertor, non-resonant divertor).<ref>http://www.jspf.or.jp/jspf_annual2018/JSPF35/pdf/S8-4.pdf</ref> The island divertor is one such concept, using intrinsic magnetic islands in the SOL to set up a divertor volume.

The first W7-X island divertor experiments and 3D modeling studies with [[EMC3-EIRENE|EMC3-EIRENE]] have found a strong dependence of the divertor heat fluxes on the magnetic configurations and island geometry. Local heat load profiles showed offsets and varying peak fluxes, complicating the matching between experiments and 3D modeling<ref>[[doi:10.1016/j.nme.2019.01.006|F. Effenberg, et al, Nucl. Mater. Energy '''18''' (2019) 262-267]]</ref><ref>[[doi:10.1088/1741-4326/ab18d1|J.D. Lore et al, Nucl. Fusion '''59''' (2019) 066041]]</ref>.

The island divertor has shown great success in accessing and stabilizing detached scenarios<ref>[[doi:10.1088/1741-4326/ab280f|T. Sunn Pedersen et al, Nucl. Fusion '''59''' (2019) 096014]]</ref>. During the first island divertor operation at W7-X, a stable operation regime had been achieved with reduced heat load on all divertor targets. This regime was maintained over several energy confinement times, and the plasma scenario proved reproducible and robust under various conditions. The plasma radiation, primarily due to oxygen, was located at the plasma edge<ref>[[doi:10.1063/1.5026324|D. Zhang et al, Phys. Rev. Lett. '''123''' (2019) 025002]]</ref>. Island divertor detachment has been achieved since then for different plasma parameters and magnetic configurations<ref>[[doi:10.1088/1741-4326/abb51e|O. Schmitz et al, Nucl. Fusion '''61''' (2021) 016026]]</ref><ref>[[doi:10.1088/1741-4326/ac1b68|M. Jakubowski et al, Nucl. Fusion '''61''' (2021) 106003]]</ref><ref>[[doi:10.1088/1741-4326/ac0772|Y. Feng et al, Nucl. Fusion '''61''' (2021) 086012]]</ref>.

A particular feature of the island divertor topology is the existence of multiple, adjacent counter-streaming flow regions at the plasma edge<ref>[[doi:10.1088/1741-4326/ab4320|V. Perseo et al, Nucl. Fusion '''59''' (2019) 124003]]</ref>. Strong counter-streaming flows can lead to frictional dissipation of momentum, causing a reduction of the flow speed parallel to the magnetic field lines. This is likely to have played a role in substantial heat flux mitigation at the targets.

Radiative power exhaust by impurity seeding was demonstrated during the first island divertor experiments at the Wendelstein 7-X stellarator<ref>[[doi:10.1088/1741-4326/ab32c4|F. Effenberg et al, Nucl. Fusion '''59''' (2019) 106020]]</ref>. Stable plasma operation was shown during seeding with both neon (Ne) and nitrogen (N2). High radiative power losses (80%) were found to reduce the divertor heat loads globally by 2/3 with both seeding gases injected at a single toroidal location into one of five magnetic islands.

The island divertor concept has shown reliable heat flux control with hydrogen gas puffing and impurity seeding, making it a promising solution for future [[Detachment control|detachment control]] in high-performance scenarios and upgrades towards a metal divertor. Feedback-controlled divertor detachment has been achieved with hydrogen gas injection in W7-X<ref>[[doi:10.1016/j.nme.2023.101363|M. Krychowiak, et al, Nucl. Mater. Energy '''34''' (2023) 101363]]</ref> and may be extended to impurity seeding in the future.

The edge magnetic structure in helically symmetric stellarators, such as the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X), has been shown to have a significant impact on particle fueling and exhaust of the main plasma species (hydrogen) and impurity helium. The magnetic island chain in the plasma edge can control the plasma fueling from the recycling source and active gas injection, a basic requirement for a divertor system<ref>[[doi:10.1063/1.5026324|L. Stephey et al, Phys. Plasmas '''25''' (2018) 062501]]</ref>.

== References ==
<references />

EIRENE

2023-04-16T20:44:17Z

Rkba39f8: dead link

The EIRENE neutral gas transport code (...) resorts to a combinatorial discretisation of general 3 dimensional computational domains. It is a multi-species code solving simultaneously a system of time dependent (optional) or stationary (default) linear kinetic transport equations of almost arbitrary complexity. A crude model for transport of ionized particles along magnetic field lines is also included. EIRENE is coupled to external databases for atomic and molecular data and for surface reflection data, and it calls various user supplied routines, e.g. for exchange of data with other (fluid-) transport codes. The main goal of code development was to provide a tool to investigate neutral gas transport in magnetically confined plasmas. But, due to its flexibility, it also can be used to solve more general linear kinetic transport equations, by applying a stochastic rather than a numerical or analytical method of solution. In particular, options are retained to reduce the model equations to the theoretically important case of the one speed transport problem. Major applications of EIRENE are in connection with plasma fluid codes, in particular with the various versions of the B2 code. The semi-implicit iterative coupling method of B2- EIRENE and it’s implementation (code segment: EIRCOP) are also described. (Extracted from [http://www.eirene.de The Eirene Code User Manual]).

Extensive documentation about the code can be found in the EIRENE Code [http://www.eirene.de EIRENE home] page, including the manual and [http://www.eirene.de/cgi-bin/eirene/write_temp.cgi?temp_dat=Publications/publications&sort_attrib=authors&asc_desc=asc reports] on its coupling to transport codes.

== References ==
<references/>

* [http://www.eirene.de D. Reiter, The Eirene Code User Manual, Version: 11/2005]
* B. Braams. Computational Studies in Tokamak Equilibrium and Transport. PhD thesis, Rijksuniversiteit Utrecht, June 1986
* [http://iopscience.iop.org/0741-3335/33/13/008 D. Reiter, H. Kever, G.H. Wolf, et al. Helium removal from tokamaks. Plasma Phys. and Contr. Fus., 33:1579, 1991]
* [http://www.sciencedirect.com/science/article/pii/S0022311506800140 D. Reiter. Progress in 2-dimensional plasma edge modelling. J. Nucl. Mat., 196– 198:241, 1992]

[[Category:Software]]

Plasma simulation

2023-04-16T20:41:03Z

Rkba39f8: /* Fluid codes */

The complexity of fusion-grade plasmas and the increased computational power that has become available in recent years has made the simulation of plasmas a prime object of study in the field of fusion research. Although the basic equations governing the behaviour of magnetised plasmas are known, approximations are always necessary in any code of practical interest; e.g. the extreme disparity of the transport timescales (seconds) and turbulent timescales (microseconds) make it hard to perform detailed turbulence simulations for the whole three-dimensional plasma volume and for several transport timescales.

This page discusses plasma transport calculations, not the [[MHD equilibrium]].

== Projects ==

* [http://www.lehigh.edu/~infusion/ Fusion Simulation Project] (USA)

== Codes ==

Codes can either be interpretative (taking some input from experiment) or predictive.
They can be full-[[Tokamak|tokamak]] (or full-[[Stellarator|stellarator]]), or simulate only a small portion of plasma (a [[Flux tube|flux tube]], the edge, or the [[Scrape-Off Layer]]). They can be fluid models for one (electrons), two (electrons + ions) or more ([[impurities]]) fluid species, Monte Carlo type (particle tracing) codes, or gyro-kinetic codes. The latter are again subdivided into full-f or delta-f codes (delta-f referring to the fact that only the deviation from a background Maxwellian particle velocity distribution function is simulated).

Recent years have seen an increased effort in the field of cross code benchmarking.
<ref>Nevins W.M. et al, [[doi:10.1063/1.2402510|Phys. Plasmas '''13''' (2006) 122306]]</ref>
<ref>A.M. Dimits et al, [[doi:10.1088/0029-5515/47/8/012|Nucl. Fusion '''47''' (2007) 817-824]]</ref>
<ref>G L Falchetto et al, [[doi:10.1088/0741-3335/50/12/124015|Plasma Phys. Control. Fusion '''50''' (2008) 124015]]</ref>
<ref>[http://w3.pppl.gov/ntcc/ National Transport Code Collaboration]</ref>

=== Fluid codes ===

In the fluid model approach, equations are derived for the moments of the distribution function f. This approach requires making several more or less strong assumptions regarding the relative importance of physical phenomena and closing the infinite set of moment equations, thus possibly losing some interesting physics.

* [[CUTIE]] (predictive, 3-D, full-tokamak)
* [[PRETOR]]
* [[PROCTR]] (1-D)
* [[TRANSP]]
* [[JETTO]]
* [[MMM95]]
* [[EDGE2D-NIMBUS]] (edge)
* [[UEDGE]]
* [[SOLPS]]
* [[EMC3-EIRENE]]<ref>[[doi:10.1002/ctpp.201410092|Y. Feng et al, Contrib. Plasma Phys. '''54''' (2014) 426-431]]</ref>
* [[FINDIF]] <ref>https://hsx.wisc.edu/wp-content/uploads/sites/747/2022/10/Findif_nvTT_3.19-G.Pelka_.pdf</ref>

=== Monte Carlo codes ===

The Monte Carlo or single particle approach solves the kinetic single-particle equations (the Lorentz force equation) in a fixed background.

* [[MOCA]]
* [[EIRENE]] (edge)

=== Gyrokinetic codes ===

The gyrokinetic treatment simplifies the [[:Wikipedia:Vlasov_equation|Vlasov equation]] for the evolution of the single-particle distribution function <math>f(\vec{x},\vec{v},t)</math> by averaging over the gyration angle, resulting in an evolution equation for the particle guiding centre.
See [[Gyrokinetic simulations]].

* [[GYRO]] <ref>[http://fusion.gat.com/theory/Gyro Gyro homepage]</ref>
* [[GS2]] ([[Flux tube|flux tube]])
* [[GENE]] ([[Flux tube|flux tube]])
* [[GEM]] (delta f) <ref>[http://cips.colorado.edu/simulation/gem.htm Plasma Simulation Group]</ref>
* [[EUTERPE]]
* [[SUMMIT/PG3EQ_NC]]

== Validation ==

See [[Model validation]]

== References ==
<references />

Island Divertor

2023-04-16T20:37:11Z

Rkba39f8:

The Island Divertor is a concept in magnetic confinement fusion devices that utilizes inherent low-order [[magnetic island|magnetic islands]] to manage power and particle exhaust. Developed for advanced low-shear [[stellarator|stellarators]] in the Wendelstein-7 family, the island divertor was first tested on [[W7-AS|W7-AS]] before its shutdown in 2002<ref>[[doi:10.1088/0029-5515/46/8/006|Y. Feng et al, Nucl. Fusion '''46''' (2006) 807]]</ref>. The concept has since been investigated in more detail and at a larger scale in [[W7-X|Wendelstein 7-X]] (W7-X).

One major challenge magnetic confinement fusion devices face is managing power and particle exhaust. In future reactors, hundreds of MWs of power will stream out from the confined plasma region (core) and must be dissipated before reaching the plasma-facing components (PFCs). Excessive heat and erosion can lead to short lifetimes of the PFCs, as well as the release of impurities and subsequent contamination of the confined plasma.

[[Divertor|Divertors]] are dedicated plasma-wall interaction zones where particles and heat stream to, moving parallel to the open magnetic field lines in the scrape-off layer (SOL). However, the fast parallel heat transport leads to localized heat deposition on the targets. In stellarators, several edge topologies have been proposed and used to form a divertor for particle and heat exhaust (e.g., helical divertor, non-resonant divertor).<ref>http://www.jspf.or.jp/jspf_annual2018/JSPF35/pdf/S8-4.pdf</ref> The island divertor is one such concept, using intrinsic magnetic islands in the SOL to set up a divertor volume.

The first W7-X island divertor experiments and 3D modeling studies with [[EMC3-EIRENE|EMC3-EIRENE]] have found a strong dependence of the divertor heat fluxes on the magnetic configurations and island geometry. Local heat load profiles showed offsets and varying peak fluxes, complicating the matching between experiments and 3D modeling<ref>[[doi:10.1016/j.nme.2019.01.006|F. Effenberg, et al, Nucl. Mater. Energy '''18''' (2019) 262-267]]</ref><ref>[[doi:10.1088/1741-4326/ab18d1|J.D. Lore et al, Nucl. Fusion '''59''' (2019) 066041]]</ref>.

The island divertor has shown great success in accessing and stabilizing detached scenarios<ref>[[doi:10.1088/1741-4326/ab280f|T. Sunn Pedersen et al, Nucl. Fusion '''59''' (2019) 096014]]</ref>. During the first island divertor operation at W7-X, a stable operation regime had been achieved with reduced heat load on all divertor targets. This regime was maintained over several energy confinement times, and the plasma scenario proved reproducible and robust under various conditions. The plasma radiation, primarily due to oxygen, was located at the plasma edge<ref>[[doi:10.1063/1.5026324|D. Zhang et al, Phys. Rev. Lett. '''123''' (2019) 025002]]</ref>. Island divertor detachment has been achieved since then for different plasma parameters and magnetic configurations<ref>[[doi:10.1088/1741-4326/abb51e|O. Schmitz et al, Nucl. Fusion '''61''' (2021) 016026]]</ref><ref>[[doi:10.1088/1741-4326/ac1b68|M. Jakubowski et al, Nucl. Fusion '''61''' (2021) 106003]]</ref><ref>[[doi:10.1088/1741-4326/ac0772|Y. Feng et al, Nucl. Fusion '''61''' (2021) 086012]]</ref>.

A particular feature of the island divertor topology is the existence of multiple, adjacent counter-streaming flow regions at the plasma edge<ref>[[doi:10.1088/1741-4326/ab4320|V. Perseo et al, Nucl. Fusion '''59''' (2019) 124003]]</ref>. Strong counter-streaming flows can lead to frictional dissipation of momentum, causing a reduction of the flow speed parallel to the magnetic field lines. This is likely to have played a role in substantial heat flux mitigation at the targets.

Radiative power exhaust by impurity seeding was demonstrated for the first time in island divertor configurations at the Wendelstein 7-X stellarator<ref>[[doi:10.1088/1741-4326/ab32c4|F. Effenberg et al, Nucl. Fusion '''59''' (2019) 106020]]</ref>. Stable plasma operation was shown during seeding with both neon (Ne) and nitrogen (N2). High radiative power losses (80%) were found to reduce the divertor heat loads globally by 2/3 with both seeding gases injected at a single toroidal location into one of five magnetic islands.

The island divertor concept has demonstrated reliable heat flux control with impurity seeding, making it a promising solution for future [[Detachment control|detachment control]] in high-performance scenarios and upgrades towards a metal divertor. Feedback-controlled divertor detachment has been achieved with hydrogen gas injection in W7-X<ref>[[doi:10.1016/j.nme.2023.101363|M. Krychowiak, et al, Nucl. Mater. Energy '''34''' (2023) 101363]]</ref> and may be extended to impurity seeding in the future.

The edge magnetic structure in helically symmetric stellarators, such as the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X), has been shown to have a significant impact on particle fueling and exhaust of the main plasma species (hydrogen) and impurity helium. The magnetic island chain in the plasma edge can control the plasma fueling from the recycling source and active gas injection, a basic requirement for a divertor system<ref>[[doi:10.1063/1.5026324|L. Stephey et al, Phys. Plasmas '''25''' (2018) 062501]]</ref>.

== References ==
<references />

Heat flux width

2023-04-10T20:46:15Z

Rkba39f8:

The [[Scrape-Off Layer]] (SOL) heat flux width <math>\lambda_q</math> is the length scale of the decaying exponential heat flux profile on the open flux surfaces.
Here, there is a competition between heat transport parallel to the field, which conducts heat to the divertors, and perpendicular diffusion.
Since parallel conduction is much faster than perpendicular diffusion, heat flux widths (<math>\lambda_q</math>) are fairly narrow—usually a few mm to a cm.
<math>\lambda_q</math> is assumed to be set at or near the outboard midplane,<ref name="eich_2013">[[doi:10.1016/j.jnucmat.2013.01.011|T. Eich, et al., J. Nucl. Mater. '''438''' (2013) S72-S77]]</ref> which is where the dominant heat source from the core into the SOL is located.
So when <math>\lambda_q</math> is quoted, it should be understood that the value at the outboard midplane is given unless otherwise stated.

As heat flows through the SOL to the divertor, the profile is broadened by [[magnetic flux expansion]].
After passing the [[Divertor|X-point]], perpendicular diffusion can go in both directions; outboard and deeper into the SOL as before, and inward to the [[Divertor|private flux region]] (PFR).<ref name=eich_2011>[[doi:10.1103/PhysRevLett.107.215001|T. Eich, et al., Phys. Rev. Lett. '''107''' (2011) 215001]]</ref>
This has the effect of smoothing the profile.

The heat flux <math>q</math> profile at the divertor (neglecting dissipation in the SOL, such as in the case of detachment) is then<ref name="eich_2013" />
:<math>q(\bar{s})=\frac{q_0}{2} \exp\left(\left(\frac{S}{2\lambda_q}\right)^2-\frac{\bar{s}}{\lambda_q f_x}\right) \cdot \mathrm{erfc}\left(\frac{S}{2\lambda_q}-\frac{\bar{s}}{S f_x}\right) +q_{BG}</math>
where <math>\bar{s}=s-s_0</math>, <math>s</math> is distance along the divertor plate, <math>s_0</math> is the [[magnetic strike point]] position, <math>S</math> is the width of the Gaussian blur effect that is convoluted with the exponential profile, <math>f_x</math> is the flux expansion (distance between flux surfaces at the divertor / distance between the same surfaces at the midplane), and <math>q_{BG}</math> is a background heat flux (which could come from radiated heat, for example).
An equation for the heat flux at the divertor is useful because the divertor heat flux profile can be measured by infrared thermography, Langmuir probes, or surface thermocouples.

This functional form was fit to heat flux profiles from several devices, and the resulting <math>\lambda_q</math> values were regressed versus several important parameters, such as field, power, safety factor, and device size.<ref name=eich_2013_nf>[[doi:10.1088/0029-5515/53/9/093031|T. Eich, et al., Nucl. Fusion '''53''' (2013) 093031]]</ref>
The regression analysis had several variants with different subsets of available devices and different parameters.
An example is
:<math>\lambda_q = C B_T^{\alpha_B} q_{cyl}^{\alpha_q} P_{SOL}^{\alpha_P} R_{geo}^{\alpha_R}</math>
with a fit to [[:Wikipedia:Joint European Torus|JET]], [[:Wikipedia:DIII-D (fusion reactor)|DIII-D]], and [[:Wikipedia:ASDEX Upgrade|ASDEX Upgrade]] resulting in

<math>C=0.86\pm 0.25</math> mm, <math>\alpha_B=-0.80\pm 0.21</math>, <math>\alpha_q=1.11\pm 0.15</math>, <math>\alpha_P=0.11 \pm 0.09</math>, <math>\alpha_R=-0.13 \pm 0.16</math>,

where <math>B_T</math> is the toroidal magnetic field, <math>q_cyl</math> is the cylindrical safety factor, <math>P_{SOL}</math> is the power flowing into the SOL, and <math>R_{geo}</math> is the geometric major radius of the plasma.

There have been other regression fits by different researchers using different subsets of devices and different parameters.<ref>[[doi:10.1016/j.jnucmat.2013.01.028|M.A. Makowski, et al., J. Nucl. Mater. '''438''' (2013) S208-S211]]</ref><ref>[[doi:10.1088/1741-4326/ab472c|H. Niemann et al 2020 Nucl. Fusion '''60''' (2020) 016014]]</ref>

== References ==
<references />

Stellarator

2023-04-10T20:42:08Z

Rkba39f8: /* Operational stellarators */

A stellarator is a [[Magnetic confinement|magnetic confinement]] device. The [[Rotational transform|rotational transform]] is predominantly generated by external coils - as opposed to a [[Tokamak|tokamak]], in which the poloidal field is generated by plasma currents. Hybrid concepts (including the concepts known as quasi-[[axisymmetry]] and quasi-[[omnigeneity]]) employ both external coils and self-generated ([[Bootstrap current|bootstrap]]) currents (e.g. NCSX).

[[File:NCSX_plasmaVessel.jpg|200px|thumb|right|NCSX plasma vessel.]]

== Classification of stellarators ==

Somewhat arbitrarily, stellarators may be classified according to the type of magnetic configuration.
* Torsatron / Heliotron: the [[rotational transform]] is produced by an external helical coil surrounding the plasma.
* Heliac: a stellarator with a toroidally helical magnetic axis.
* Helias: advanced stellarator with [[modular coil]]s.

== Defunct stellarators ==
* ATF (Oak Ridge, TN, USA)
* CHS (Japan)
* [http://prl.anu.edu.au/H-1NF H-1NF] (Canberra, Australia)
* [http://ncsx.pppl.gov/ NCSX] (Princeton, NJ, USA) - cancelled before construction was completed
* [[W7-AS]] (Garching, Germany, 1988-2002)

== Operational stellarators ==

* [http://fusion.auburn.edu/ CAT/CTH] (Auburn, USA)
* [http://www.center.iae.kyoto-u.ac.jp/plasma/index.html Heliotron-J] (Kyoto, Japan)
* [[HSX]] (Madison, WI, USA)
* [http://www.lhd.nifs.ac.jp/en/ LHD] (Toki, Japan)
* [[Wikipedia:SCR-1|SCR-1]] (Cartago, Costa Rica)
* [[TJ-II]] (Madrid, Spain)
* [[TJ-K]] (Stuttgart, Germany)
* [http://tsubaki.qse.tohoku.ac.jp/study/heliac/index.html TU Heliac] (Tohoku Univ., Sendai, Japan)
* [http://www.fusionvic.org/ UST-1] (Spain) - tabletop experiment
* [http://www.ipp.mpg.de/ippcms/eng/for/bereiche/e3/projekte/wega.html WEGA] (Greifswald, Germany)
* [[W7-X|Wendelstein 7-x (W7-X)]] (Greifswald, Germany)

== Future stellarators ==
* [http://web.utk.edu/~qps/ QPS] (in design phase, TN, USA)
* [http://estell.blog.uhp-nancy.fr STELL] (in design phase, University of Lorraine, France, in collaboration with IPP Greifswald)

== See also ==

* [[Stellarator reactor]]
* [[Stellarator optimization]]
* [[International Stellarator and Heliotron Workshop]]
* [[Coordinated Working Group Meeting]]
* [[Stellarator symmetry]]
* [http://www.ornl.gov/sci/fed/stelnews/ Stellarator News]
* [http://aries.ucsd.edu/ARIES/ ARIES Project] (conceptual design of a compact stellarator)
* [http://www.highfactor.com/ss/ Spherical Stellarator] design study

== References ==

* M. Wakatani, Stellarator and Heliotron devices, Oxford University Press, New York and Oxford (1998) {{ISBN|0-19-507831-4}}
* P. Helander, ''Theory of plasma confinement in non-axisymmetric magnetic fields'', [[doi:10.1088/0034-4885/77/8/087001|Rep. Prog. Phys. 77 (2014) 087001]]

W7-X

2023-04-10T06:37:24Z

Rkba39f8:

[[File:W7X.png|400px|thumb|right|W7-X model]]
Wendelstein 7-X (W7-X) is an experimental stellarator currently being operated in Greifswald, Germany by the [[:Wikipedia:Max-Planck-Institut_f%C3%BCr_Plasmaphysik|Max-Planck-Institut für Plasmaphysik]] (IPP). W7-X is an [[Stellarator optimization|optimized stellarator]], i.e. the magnetic field has been tailored to meet several physical optimization criteria.

== Background ==

The Wendelstein 7-X (W7-X) is a fusion research device that uses the [[stellarator]] concept to confine plasma in a magnetic field. As of 2023, it is the world's largest stellarator device, and its main goal is to demonstrate the feasibility of continuous operation in a fusion power plant. The W7-X is located in Greifswald, Germany, and is an independent partner project of the Max-Planck Institute for Plasma Physics with the University of Greifswald.

The W7-X is based on a five-field-period Helias configuration and consists of 50 non-planar and 20 planar superconducting magnetic coils. These coils induce a magnetic field that prevents the plasma from colliding with the reactor walls, allowing it to be confined for longer periods. The plasma vessel, built of 20 parts, is on the inside and adjusted to the complex shape of the magnetic field, and it has 254 ports for plasma heating and observation diagnostics. The heating system includes high power gyrotrons for electron cyclotron resonance heating (ECRH), which can deliver up to 15 MW of heating to the plasma. Additionally, neutral beam injection and ion cyclotron resonance heating (ICRH) systems are also available for physics operation.

The W7-X has undergone several operational phases, each with its specific objectives. During Operational Phase 1 (OP1.1), the W7-X produced helium plasma for about 0.1 seconds, followed by hydrogen plasma with gradually increasing discharge power and duration. More than 2,000 pulses were conducted before the shutdown. Five poloidal graphite limiters served as the main plasma-facing components during this first campaign (instead of the divertor modules). Experimental observations confirmed 3D modeling predictions that showed heat and particle flux deposition patterns on the limiters in clear correlation with the lengths of the open magnetic field lines in the plasma boundary.

Operational Phase 1 continued (OP1.2) in 2017 to test the uncooled divertor. During the last experiments of 2018, the density reached 2 × 1020 particles/m3 at a temperature of 20 million degrees. With good plasma values, long-lasting plasmas with long discharge times of 100 seconds were obtained, and energy content exceeded 1 megajoule. In 2018, a record ion temperature of about 40 million degrees, a density of 0.8 × 1020 particles/m3, and a confinement time of 0.2 seconds yielded a record fusion product of 6 × 1026 degree-seconds per cubic metre.

The limiter and divertor experimental campaigns aimed to test plasma-wall interactions in the complex 3D geometry of the W7-X. The limiter campaign presented the first-time characterization of the limiter heat loads, confirming major geometry effects of the connection length on heat transport predicted by 3D modeling. The divertor experimental campaign tested the [[Island Divertor|island divertor]] concept, which plays a central role in the device mission to demonstrate reactor relevant plasma confinement for steady-state time scales of up to 30 minutes in the high-performance campaign (OP2). During the first campaign with the inertially cooled island divertor, a large step in the experimental qualification of this divertor concept was made.

{| class="wikitable" align="center" border="1"
!''Parameter'' !!''Value''!!''Unit''
|-
|Major radius, ''R0'': || 5.5 || m
|-
|Minor radius, ''a'': || 0.53 || m
|-
|Plasma volume, ''V'': || 30 || m3
|-
|Non-planar coils: || 50 ||
|-
|Planar coils: || 20 ||
|-
|Number of ports: || 254 ||
|-
|Rotational transform, ''ι/2π'': || 5/6-5/4 ||
|-
|Magnetic field on axis, ''B0'': || <3 || T
|-
|Stored energy, ''W'': || 600 || MJ
|-
|Heating power, ''P'': || 15-30 || MW
|-
|Pulse length: || 30 || min
|-
|Machine height: || 4.5 || m
|-
|Machine diameter: || 16 || m
|-
|Machine mass: || 725 || t
|}

== Optimization criteria ==

* Feasible [[modular coil]]s
* Good, nested [[Flux surface|magnetic surfaces]]
* Good finite-[[Beta|β]] equilibria
* Good MHD [[Plasma instability|stability]]
* Small [[neoclassical transport]]
* Small [[bootstrap current]]
* Good confinement of fast particles

== See also ==

* [https://www.ipp.mpg.de/16900/w7x Wendelstein 7-X]
* [[Island Divertor]]

== References ==
* H. Wobig, ''The theoretical basis of a drift-optimized stellarator reactor'', [[doi:10.1088/0741-3335/35/8/001|Plasma Phys. Control. Fusion '''35''' (1993) 903]]
* J. Nührenberg et al., Trans. Fusion Technology '''27''' (1995) 71
* C. Nührenberg, ''Global ideal magnetohydrodynamic stability analysis for the configurational space of Wendelstein 7–X'', [[doi:10.1063/1.871924|Phys. Plasmas '''3''' (1996) 2401]]
* V. Erckmann et al, ''The W7-X project: scientific basis and technical realization'', [[doi:10.1109/FUSION.1997.685662|Fusion Engineering '''6-10''' (1997) 40]]
* M. Wanner and the W7-X Team, ''Design goals and status of the WENDELSTEIN 7-X project'', [[doi:10.1088/0741-3335/42/11/304|Plasma Phys. Control. Fusion '''42''' (2000) 1179]]
* M. Wanner et al, ''Design and construction of WENDELSTEIN 7-X'', [[doi:10.1016/S0920-3796(01)00239-3|Fusion Engineering and Design '''56-57''' (2001) 155-162]]
* M. Wanner et al, ''Status of WENDELSTEIN 7-X construction'', [[doi:10.1088/0029-5515/43/6/304|Nucl. Fusion '''43''' (2003) 416]]
* M. Wanner and the W7-X Team, ''Construction and assembly of WENDELSTEIN 7-X'', [[doi:10.1016/j.fusengdes.2006.07.013|Fusion Engineering and Design '''81''', 20-22 (2006) 2305-2313]]
* L. Wegener, ''Status of Wendelstein 7-X construction'', [[doi:10.1016/j.fusengdes.2009.01.106|Fusion Engineering and Design '''84''', 2-6 (2009) 106-112]]
* H.-S. Bosch et al, ''Construction of Wendelstein 7-X; Engineering a Steady-State Stellarator'', [[doi:10.1109/TPS.2009.2036918|IEEE Trans. Plasma Science '''38''', 3 (2010) 265]]
* H.-S. Bosch et al, ''Technical challenges in the construction of the steady-state stellarator Wendelstein 7-X'', [[doi:10.1088/0029-5515/53/12/126001|Nucl. Fusion '''53''' (2013) 126001]]
* D. Clery, ''Feature: The bizarre reactor that might save nuclear fusion'', [[doi:10.1126/science.aad4746|Science, 21 October 2015]]
* O. Neubauer et al, ''Diagnostic setup for investigation of plasma wall interactions at Wendelstein 7-X'', [[doi:10.1016/j.fusengdes.2015.06.102|Fusion Engineering and Design '''96-97''' (2015) 891-894]]
* T. Sunn Pedersen et al, ''Plans for the first plasma operation of Wendelstein 7-X'', [[doi:10.1088/0029-5515/55/12/126001|Nucl. Fusion '''55''' (2015) 126001]]
* M. Krychowiak et al, ''Overview of diagnostic performance and results for the first operation phase in Wendelstein 7-X'', [[doi:10.1063/1.4964376|Review of Scientific Instruments '''87''' (2016) 11D304]]
* R.C. Wolf et al, ''Major results from the first plasma campaign of the Wendelstein 7-X stellarator'', [[doi:10.1088/1741-4326/aa770d|Nucl. Fusion '''57''' (2017) 102020]]
* D. Hathiramani et al, ''Upgrades of edge, divertor and scrape-off layer diagnostics of W7‐X for OP1.2'', [[doi:10.1016/j.fusengdes.2018.02.013|Fusion Engineering and Design '''136A''' (2018) 304-308]]
* A. Dinklage et al, ''Magnetic configuration effects on the Wendelstein 7-X stellarator'', [[doi:10.1038/s41567-018-0141-9|Nature Phys '''14''' (2018) 855–860]]
* R.C. Wolf et al, ''Performance of Wendelstein 7-X stellarator plasmas during the first divertor operation phase'', [[doi:10.1063/1.5098761|Physics of Plasmas '''26''' (2019) 082504]]

[[Category:Toroidal confinement devices]]

HSX

2023-04-10T06:01:44Z

Rkba39f8:

The Helically Symmetric Experiment (HSX) at the University of Wisconsin-Madison is a unique modular coil [[stellarator|stellarator]] that is optimized for quasi-helical symmetry. The device is designed to investigate plasma transport, turbulence, and confinement in a quasi-helically symmetric magnetic field, with the aim of advancing fusion reactor technology. The HSX began operation in 1999 and has since made significant contributions to the physics of [[Quasisymmetry|quasisymmetric]] stellarators.<ref>[[doi:10.13182/FST95-A11947086|F.S.B. Anderson et al, Fusion Technol. '''27''' (1995) 273–277]]</ref>

The HSX uses a set of 48 twisted coils arranged in four field periods to generate a magnetic field for plasma containment. The vacuum vessel is made of stainless steel and is helically shaped to follow the magnetic geometry. Plasma formation and heating are achieved using 28 GHz, 100 kW electron cyclotron resonance heating (ECRH). The device also features a second 100 kW gyrotron for heat pulse modulation studies.

Experiments at HSX have shown that edge magnetic islands can affect particle fueling and exhaust. The presence of a magnetic island chain at the plasma edge can increase the plasma sourcing to exhaust ratio but reduces fueling efficiency by 25%. Moving the island radially inward decreases both the effective and global particle confinement times, which can effectively control plasma fueling and helium exhaust times. These findings suggest that the magnetic island chain in the plasma edge can be a crucial element in the design of a [[Island Divertor|divertor]] system.<ref>[[doi:10.1063/1.5026324|L. Stephey et al, Phys. Plasmas '''25''' (2018) 062501]]</ref>

HSX has also shown significant improvements over conventional stellarator designs. The device has measured large ion flows in the direction of quasisymmetry, reduced flow damping, reduced passing particle deviation from a flux surface, reduced direct loss orbits, reduced neoclassical transport, and reduced equilibrium parallel currents due to the high effective transform.<ref>[[doi:10.1088/0029-5515/53/8/082001|J.C. Schmitt et al, Nucl. Fusion '''53''' (2013) 082001]]</ref>

Ongoing experiments at HSX include investigations into plasma flows<ref>[[doi:10.1088/0741-3335/58/8/084002|A R Akerson et al, Plasma Phys. Control. Fusion '''58''' (2016) 084002]]</ref>, impurity transport, radio frequency heating, supersonic plasma fueling and the neutral population, heat pulse propagation experiments to study thermal transport, and more. These experiments are being conducted by students, staff, and faculties, often in collaboration with other universities and national laboratories in the USA and abroad.

== See also ==

* [https://hsx.wisc.edu/ HSX Fusion Energy Device Website]

== References ==
<references />

Quasisymmetry

2023-04-10T05:57:57Z

Rkba39f8:

Quasisymmetric (quasihelically symmetric) [[MHD equilibrium|plasma equilibria]] are non-[[axisymmetry|axisymmetric]] configurations in which the magnetic field strength depends only on one angular coordinate within the magnetic [[flux surface]]s.
<ref>D.A. Garren and A.H. Boozer, ''Existence of quasihelically symmetric stellarators'', [[doi:10.1063/1.859916|Phys. Fluids B 3 (1991) 2822]]</ref>
This concept is part of the program of [[stellarator optimization]] (designing stellarators to have reduced transport, i.e., heat and particle losses).
<ref>Iván Calvo et al, ''Stellarators close to quasisymmetry'', [[doi:10.1088/0741-3335/55/12/125014|Plasma Phys. Control. Fusion '''55''' (2013) 125014]]</ref>

Types of quasisymmetry:
* Quasihelical (QH) symmetry, on which the design of the [[HSX]] stellarator (operational) is based.<ref>J.N. Talmadge, F.S.B. Anderson, D.T. Anderson, C. Deng, W. Guttenfelder, K.M. Likin, J. Lore, J.C. Schmitt, K. Zhai, ''Experimental Tests of Quasisymmetry in HSX'', [[doi:10.1585/pfr.3.S1002|Plasma and Fusion Research '''3''' (2008) S1002]]</ref>
* Quasipoloidal (QP) symmetry, on which the design of the [http://web.utk.edu/~qps/ QPS stellarator] (under construction) is based.<ref>D.A. Spong, S.P. Hirshman, J.F. Lyon, L.A. Berry and D.J. Strickler, ''Recent advances in quasi-poloidal stellarator physics issues'', [[doi:10.1088/0029-5515/45/8/020|Nucl. Fusion '''45''' (2005) 918]]</ref>
* Quasi-axisymmetry (QA), on which the design of the [http://ncsx.pppl.gov/ NCSX stellarator] was based<ref>M.Yu. Isaev et al, ''The pseudo-symmetric optimization of the National Compact Stellarator Experiment'', [[doi:10.1063/1.873557|Phys. Plasmas '''6''', 8 (1999) 3174]]</ref>

== See also ==
* [[Stellarator]]
* [[Omnigeneity]]

== References ==
<references />

Stellarator

2023-04-10T05:56:19Z

Rkba39f8: /* Operational stellarators */

A stellarator is a [[Magnetic confinement|magnetic confinement]] device. The [[Rotational transform|rotational transform]] is predominantly generated by external coils - as opposed to a [[Tokamak|tokamak]], in which the poloidal field is generated by plasma currents. Hybrid concepts (including the concepts known as quasi-[[axisymmetry]] and quasi-[[omnigeneity]]) employ both external coils and self-generated ([[Bootstrap current|bootstrap]]) currents (e.g. NCSX).

[[File:NCSX_plasmaVessel.jpg|200px|thumb|right|NCSX plasma vessel.]]

== Classification of stellarators ==

Somewhat arbitrarily, stellarators may be classified according to the type of magnetic configuration.
* Torsatron / Heliotron: the [[rotational transform]] is produced by an external helical coil surrounding the plasma.
* Heliac: a stellarator with a toroidally helical magnetic axis.
* Helias: advanced stellarator with [[modular coil]]s.

== Defunct stellarators ==
* ATF (Oak Ridge, TN, USA)
* CHS (Japan)
* [http://prl.anu.edu.au/H-1NF H-1NF] (Canberra, Australia)
* [http://ncsx.pppl.gov/ NCSX] (Princeton, NJ, USA) - cancelled before construction was completed
* [[W7-AS]] (Garching, Germany, 1988-2002)

== Operational stellarators ==

* [http://fusion.auburn.edu/ CAT/CTH] (Auburn, USA)
* [http://www.center.iae.kyoto-u.ac.jp/plasma/index.html Heliotron-J] (Kyoto, Japan)
* [[HSX]] (Madison, WI, USA)
* [http://www.lhd.nifs.ac.jp/en/ LHD] (Toki, Japan)
* [[Wikipedia:SCR-1|SCR-1]] (Cartago, Costa Rica)
* [[TJ-II]] (Madrid, Spain)
* [[TJ-K]] (Stuttgart, Germany)
* [http://tsubaki.qse.tohoku.ac.jp/study/heliac/index.html TU Heliac] (Tohoku Univ., Sendai, Japan)
* [http://www.fusionvic.org/ UST-1] (Spain) - tabletop experiment
* [http://www.ipp.mpg.de/ippcms/eng/for/bereiche/e3/projekte/wega.html WEGA] (Greifswald, Germany)
* [[:Wikipedia:Wendelstein_7-X|W7-X]] (Greifswald, Germany)

== Future stellarators ==
* [http://web.utk.edu/~qps/ QPS] (in design phase, TN, USA)
* [http://estell.blog.uhp-nancy.fr STELL] (in design phase, University of Lorraine, France, in collaboration with IPP Greifswald)

== See also ==

* [[Stellarator reactor]]
* [[Stellarator optimization]]
* [[International Stellarator and Heliotron Workshop]]
* [[Coordinated Working Group Meeting]]
* [[Stellarator symmetry]]
* [http://www.ornl.gov/sci/fed/stelnews/ Stellarator News]
* [http://aries.ucsd.edu/ARIES/ ARIES Project] (conceptual design of a compact stellarator)
* [http://www.highfactor.com/ss/ Spherical Stellarator] design study

== References ==

* M. Wakatani, Stellarator and Heliotron devices, Oxford University Press, New York and Oxford (1998) {{ISBN|0-19-507831-4}}
* P. Helander, ''Theory of plasma confinement in non-axisymmetric magnetic fields'', [[doi:10.1088/0034-4885/77/8/087001|Rep. Prog. Phys. 77 (2014) 087001]]

HSX

2023-04-10T05:55:10Z

Rkba39f8: Created page with "The Helically Symmetric Experiment (HSX) at the University of Wisconsin-Madison is a unique modular coil stellarator that is optimized for quasi-helical symmet..."

Heat flux width

2023-04-10T05:18:28Z

Rkba39f8:

Island Divertor

2023-04-06T07:55:08Z

Rkba39f8:

The Island Divertor is a concept in magnetic confinement fusion devices that utilizes inherent low-order [[magnetic island|magnetic islands]] to manage power and particle exhaust. Developed for advanced low-shear [[stellarator|stellarators]] in the Wendelstein-7 family, the island divertor was first tested on [[W7-AS|W7-AS]] before its shutdown in 2002<ref>[[doi:10.1088/0029-5515/46/8/006|Y. Feng et al, Nucl. Fusion '''46''' (2006) 807]]</ref>. The concept has since been investigated in more detail and at a larger scale in [[W7-X|Wendelstein 7-X]] (W7-X).

One major challenge magnetic confinement fusion devices face is managing power and particle exhaust. In future reactors, hundreds of MWs of power will stream out from the confined plasma region (core) and must be dissipated before reaching the plasma-facing components (PFCs). Excessive heat and erosion can lead to short lifetimes of the PFCs, as well as the release of impurities and subsequent contamination of the confined plasma.

[[Divertor|Divertors]] are dedicated plasma-wall interaction zones where particles and heat stream to, moving parallel to the open magnetic field lines in the scrape-off layer (SOL). However, the fast parallel heat transport leads to localized heat deposition on the targets. In stellarators, several edge topologies have been proposed and used to form a divertor for particle and heat exhaust. The island divertor is one such concept, using intrinsic magnetic islands in the SOL to set up a divertor volume.

The first W7-X island divertor experiments and 3D modeling studies with [[EMC3-EIRENE|EMC3-EIRENE]] have found a strong dependence of the divertor heat fluxes on the magnetic configurations and island geometry. Local heat load profiles showed offsets and varying peak fluxes, complicating the matching between experiments and 3D modeling<ref>[[doi:10.1016/j.nme.2019.01.006|F. Effenberg, et al, Nucl. Mater. Energy '''18''' (2019) 262-267]]</ref><ref>[[doi:10.1088/1741-4326/ab18d1|J.D. Lore et al, Nucl. Fusion '''59''' (2019) 066041]]</ref>.

The island divertor has shown great success in accessing and stabilizing detached scenarios<ref>[[doi:10.1088/1741-4326/ab280f|T. Sunn Pedersen et al, Nucl. Fusion '''59''' (2019) 096014]]</ref>. During the first island divertor operation at W7-X, a stable operation regime had been achieved with reduced heat load on all divertor targets. This regime was maintained over several energy confinement times, and the plasma scenario proved reproducible and robust under various conditions. The plasma radiation, primarily due to oxygen, was located at the plasma edge<ref>[[doi:10.1063/1.5026324|D. Zhang et al, Phys. Rev. Lett. '''123''' (2019) 025002]]</ref>. Island divertor detachment has been achieved since then for different plasma parameters and magnetic configurations<ref>[[doi:10.1088/1741-4326/abb51e|O. Schmitz et al, Nucl. Fusion '''61''' (2021) 016026]]</ref><ref>[[doi:10.1088/1741-4326/ac1b68|M. Jakubowski et al, Nucl. Fusion '''61''' (2021) 106003]]</ref><ref>[[doi:10.1088/1741-4326/ac0772|Y. Feng et al, Nucl. Fusion '''61''' (2021) 086012]]</ref>.

A particular feature of the island divertor topology is the existence of multiple, adjacent counter-streaming flow regions at the plasma edge<ref>[[doi:10.1088/1741-4326/ab4320|V. Perseo et al, Nucl. Fusion '''59''' (2019) 124003]]</ref>. Strong counter-streaming flows can lead to frictional dissipation of momentum, causing a reduction of the flow speed parallel to the magnetic field lines. This is likely to have played a role in substantial heat flux mitigation at the targets.

Radiative power exhaust by impurity seeding was demonstrated for the first time in island divertor configurations at the Wendelstein 7-X stellarator<ref>[[doi:10.1088/1741-4326/ab32c4|F. Effenberg et al, Nucl. Fusion '''59''' (2019) 106020]]</ref>. Stable plasma operation was shown during seeding with both neon (Ne) and nitrogen (N2). High radiative power losses (80%) were found to reduce the divertor heat loads globally by 2/3 with both seeding gases injected at a single toroidal location into one of five magnetic islands.

The island divertor concept has demonstrated reliable heat flux control with impurity seeding, making it a promising solution for future [[Detachment control|detachment control]] in high-performance scenarios and upgrades towards a metal divertor. Feedback-controlled divertor detachment has been achieved with hydrogen gas injection in W7-X<ref>[[doi:10.1016/j.nme.2023.101363|M. Krychowiak, et al, Nucl. Mater. Energy '''34''' (2023) 101363]]</ref> and may be extended to impurity seeding in the future.

The edge magnetic structure in helically symmetric stellarators, such as the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X), has been shown to have a significant impact on particle fueling and exhaust of the main plasma species (hydrogen) and impurity helium. The magnetic island chain in the plasma edge can control the plasma fueling from the recycling source and active gas injection, a basic requirement for a divertor system<ref>[[doi:10.1063/1.5026324|L. Stephey et al, Phys. Plasmas '''25''' (2018) 062501]]</ref>.

== References ==
<references />

Plasma simulation

2023-04-06T07:53:03Z

Rkba39f8: /* Fluid codes */

The complexity of fusion-grade plasmas and the increased computational power that has become available in recent years has made the simulation of plasmas a prime object of study in the field of fusion research. Although the basic equations governing the behaviour of magnetised plasmas are known, approximations are always necessary in any code of practical interest; e.g. the extreme disparity of the transport timescales (seconds) and turbulent timescales (microseconds) make it hard to perform detailed turbulence simulations for the whole three-dimensional plasma volume and for several transport timescales.

This page discusses plasma transport calculations, not the [[MHD equilibrium]].

== Projects ==

* [http://www.lehigh.edu/~infusion/ Fusion Simulation Project] (USA)

== Codes ==

Codes can either be interpretative (taking some input from experiment) or predictive.
They can be full-[[Tokamak|tokamak]] (or full-[[Stellarator|stellarator]]), or simulate only a small portion of plasma (a [[Flux tube|flux tube]], the edge, or the [[Scrape-Off Layer]]). They can be fluid models for one (electrons), two (electrons + ions) or more ([[impurities]]) fluid species, Monte Carlo type (particle tracing) codes, or gyro-kinetic codes. The latter are again subdivided into full-f or delta-f codes (delta-f referring to the fact that only the deviation from a background Maxwellian particle velocity distribution function is simulated).

Recent years have seen an increased effort in the field of cross code benchmarking.
<ref>Nevins W.M. et al, [[doi:10.1063/1.2402510|Phys. Plasmas '''13''' (2006) 122306]]</ref>
<ref>A.M. Dimits et al, [[doi:10.1088/0029-5515/47/8/012|Nucl. Fusion '''47''' (2007) 817-824]]</ref>
<ref>G L Falchetto et al, [[doi:10.1088/0741-3335/50/12/124015|Plasma Phys. Control. Fusion '''50''' (2008) 124015]]</ref>
<ref>[http://w3.pppl.gov/ntcc/ National Transport Code Collaboration]</ref>

=== Fluid codes ===

In the fluid model approach, equations are derived for the moments of the distribution function f. This approach requires making several more or less strong assumptions regarding the relative importance of physical phenomena and closing the infinite set of moment equations, thus possibly losing some interesting physics.

* [[CUTIE]] (predictive, 3-D, full-tokamak)
* [[PRETOR]]
* [[PROCTR]] (1-D)
* [[TRANSP]]
* [[JETTO]]
* [[MMM95]]
* [[EDGE2D-NIMBUS]] (edge)
* [[UEDGE]]
* [[SOLPS]]
* [[EMC3-EIRENE]]<ref>[[doi:10.1002/ctpp.201410092|Y. Feng et al, Contrib. Plasma Phys. '''54''' (2014) 426-431]]</ref>

=== Monte Carlo codes ===

The Monte Carlo or single particle approach solves the kinetic single-particle equations (the Lorentz force equation) in a fixed background.

* [[MOCA]]
* [[EIRENE]] (edge)

=== Gyrokinetic codes ===

The gyrokinetic treatment simplifies the [[:Wikipedia:Vlasov_equation|Vlasov equation]] for the evolution of the single-particle distribution function <math>f(\vec{x},\vec{v},t)</math> by averaging over the gyration angle, resulting in an evolution equation for the particle guiding centre.
See [[Gyrokinetic simulations]].

* [[GYRO]] <ref>[http://fusion.gat.com/theory/Gyro Gyro homepage]</ref>
* [[GS2]] ([[Flux tube|flux tube]])
* [[GENE]] ([[Flux tube|flux tube]])
* [[GEM]] (delta f) <ref>[http://cips.colorado.edu/simulation/gem.htm Plasma Simulation Group]</ref>
* [[EUTERPE]]
* [[SUMMIT/PG3EQ_NC]]

== Validation ==

See [[Model validation]]

== References ==
<references />

Plasma simulation

2023-04-06T07:52:41Z

Rkba39f8: /* Fluid codes */

The complexity of fusion-grade plasmas and the increased computational power that has become available in recent years has made the simulation of plasmas a prime object of study in the field of fusion research. Although the basic equations governing the behaviour of magnetised plasmas are known, approximations are always necessary in any code of practical interest; e.g. the extreme disparity of the transport timescales (seconds) and turbulent timescales (microseconds) make it hard to perform detailed turbulence simulations for the whole three-dimensional plasma volume and for several transport timescales.

This page discusses plasma transport calculations, not the [[MHD equilibrium]].

== Projects ==

* [http://www.lehigh.edu/~infusion/ Fusion Simulation Project] (USA)

== Codes ==

Codes can either be interpretative (taking some input from experiment) or predictive.
They can be full-[[Tokamak|tokamak]] (or full-[[Stellarator|stellarator]]), or simulate only a small portion of plasma (a [[Flux tube|flux tube]], the edge, or the [[Scrape-Off Layer]]). They can be fluid models for one (electrons), two (electrons + ions) or more ([[impurities]]) fluid species, Monte Carlo type (particle tracing) codes, or gyro-kinetic codes. The latter are again subdivided into full-f or delta-f codes (delta-f referring to the fact that only the deviation from a background Maxwellian particle velocity distribution function is simulated).

Recent years have seen an increased effort in the field of cross code benchmarking.
<ref>Nevins W.M. et al, [[doi:10.1063/1.2402510|Phys. Plasmas '''13''' (2006) 122306]]</ref>
<ref>A.M. Dimits et al, [[doi:10.1088/0029-5515/47/8/012|Nucl. Fusion '''47''' (2007) 817-824]]</ref>
<ref>G L Falchetto et al, [[doi:10.1088/0741-3335/50/12/124015|Plasma Phys. Control. Fusion '''50''' (2008) 124015]]</ref>
<ref>[http://w3.pppl.gov/ntcc/ National Transport Code Collaboration]</ref>

=== Fluid codes ===

In the fluid model approach, equations are derived for the moments of the distribution function f. This approach requires making several more or less strong assumptions regarding the relative importance of physical phenomena and closing the infinite set of moment equations, thus possibly losing some interesting physics.

* [[CUTIE]] (predictive, 3-D, full-tokamak)
* [[PRETOR]]
* [[PROCTR]] (1-D)
* [[TRANSP]]
* [[JETTO]]
* [[MMM95]]
* [[EDGE2D-NIMBUS]] (edge)
* [[UEDGE]]
* [[SOLPS]]
* [[EMC3-EIRENE]]<ref>[[doi:10.1002/ctpp.201410092|Y. Feng et al., Contrib. Plasma Phys. '''54''' (2014) 426-431]]</ref>

=== Monte Carlo codes ===

The Monte Carlo or single particle approach solves the kinetic single-particle equations (the Lorentz force equation) in a fixed background.

* [[MOCA]]
* [[EIRENE]] (edge)

=== Gyrokinetic codes ===

The gyrokinetic treatment simplifies the [[:Wikipedia:Vlasov_equation|Vlasov equation]] for the evolution of the single-particle distribution function <math>f(\vec{x},\vec{v},t)</math> by averaging over the gyration angle, resulting in an evolution equation for the particle guiding centre.
See [[Gyrokinetic simulations]].

* [[GYRO]] <ref>[http://fusion.gat.com/theory/Gyro Gyro homepage]</ref>
* [[GS2]] ([[Flux tube|flux tube]])
* [[GENE]] ([[Flux tube|flux tube]])
* [[GEM]] (delta f) <ref>[http://cips.colorado.edu/simulation/gem.htm Plasma Simulation Group]</ref>
* [[EUTERPE]]
* [[SUMMIT/PG3EQ_NC]]

== Validation ==

See [[Model validation]]

== References ==
<references />

Plasma simulation

2023-04-06T07:51:09Z

Rkba39f8: /* Fluid codes */

The complexity of fusion-grade plasmas and the increased computational power that has become available in recent years has made the simulation of plasmas a prime object of study in the field of fusion research. Although the basic equations governing the behaviour of magnetised plasmas are known, approximations are always necessary in any code of practical interest; e.g. the extreme disparity of the transport timescales (seconds) and turbulent timescales (microseconds) make it hard to perform detailed turbulence simulations for the whole three-dimensional plasma volume and for several transport timescales.

This page discusses plasma transport calculations, not the [[MHD equilibrium]].

== Projects ==

* [http://www.lehigh.edu/~infusion/ Fusion Simulation Project] (USA)

== Codes ==

Codes can either be interpretative (taking some input from experiment) or predictive.
They can be full-[[Tokamak|tokamak]] (or full-[[Stellarator|stellarator]]), or simulate only a small portion of plasma (a [[Flux tube|flux tube]], the edge, or the [[Scrape-Off Layer]]). They can be fluid models for one (electrons), two (electrons + ions) or more ([[impurities]]) fluid species, Monte Carlo type (particle tracing) codes, or gyro-kinetic codes. The latter are again subdivided into full-f or delta-f codes (delta-f referring to the fact that only the deviation from a background Maxwellian particle velocity distribution function is simulated).

Recent years have seen an increased effort in the field of cross code benchmarking.
<ref>Nevins W.M. et al, [[doi:10.1063/1.2402510|Phys. Plasmas '''13''' (2006) 122306]]</ref>
<ref>A.M. Dimits et al, [[doi:10.1088/0029-5515/47/8/012|Nucl. Fusion '''47''' (2007) 817-824]]</ref>
<ref>G L Falchetto et al, [[doi:10.1088/0741-3335/50/12/124015|Plasma Phys. Control. Fusion '''50''' (2008) 124015]]</ref>
<ref>[http://w3.pppl.gov/ntcc/ National Transport Code Collaboration]</ref>

=== Fluid codes ===

In the fluid model approach, equations are derived for the moments of the distribution function f. This approach requires making several more or less strong assumptions regarding the relative importance of physical phenomena and closing the infinite set of moment equations, thus possibly losing some interesting physics.

* [[CUTIE]] (predictive, 3-D, full-tokamak)
* [[PRETOR]]
* [[PROCTR]] (1-D)
* [[TRANSP]]
* [[JETTO]]
* [[MMM95]]
* [[EDGE2D-NIMBUS]] (edge)
* [[UEDGE]]
* [[SOLPS]]
* [[EMC3-EIRENE]]<ref>[[doi:10.1002/ctpp.201410092|Y. Feng et al., Contributions to Plasma Physics '''54''' (2014) 426-431]]</ref>

=== Monte Carlo codes ===

The Monte Carlo or single particle approach solves the kinetic single-particle equations (the Lorentz force equation) in a fixed background.

* [[MOCA]]
* [[EIRENE]] (edge)

=== Gyrokinetic codes ===

The gyrokinetic treatment simplifies the [[:Wikipedia:Vlasov_equation|Vlasov equation]] for the evolution of the single-particle distribution function <math>f(\vec{x},\vec{v},t)</math> by averaging over the gyration angle, resulting in an evolution equation for the particle guiding centre.
See [[Gyrokinetic simulations]].

* [[GYRO]] <ref>[http://fusion.gat.com/theory/Gyro Gyro homepage]</ref>
* [[GS2]] ([[Flux tube|flux tube]])
* [[GENE]] ([[Flux tube|flux tube]])
* [[GEM]] (delta f) <ref>[http://cips.colorado.edu/simulation/gem.htm Plasma Simulation Group]</ref>
* [[EUTERPE]]
* [[SUMMIT/PG3EQ_NC]]

== Validation ==

See [[Model validation]]

== References ==
<references />

EMC3-EIRENE

2023-04-06T07:47:19Z

Rkba39f8:

EMC3-EIRENE is a state-of-the-art computational tool that combines the EMC3 (Edge Monte Carlo 3D) code with the [[EIRENE]] code to simulate plasma fluid and kinetic neutral edge transport in non-axisymmetric configurations. Developed for the study of [[stellarator]] and [[tokamak]] configurations, the code can model the full torus plasma and impurity transport, including the effects of 3D fields, such as [[Resonant Magnetic Perturbation|resonant magnetic perturbations]] (RMPs).
EMC3 is a 3D plasma fluid code that solves a set of reduced Braginskii fluid equations for particles, parallel momentum, and energies for electrons and ions. The code models parallel electron and ion heat conductivity using classical assumptions. Perpendicular transport is determined by coefficients for anomalous particle transport (<math>D_\bot</math>) and anomalous electron and ion heat transport (<math>\chi_\bot</math>), which are free model parameters. EIRENE is a kinetic edge transport code that solves the transport equations for neutral atoms and molecules, accounting for collisional processes. The code calculates ionization sources, momentum sources/losses, and energy sources/losses due to atomic/molecular processes, such as charge exchange and ionization. EMC3-EIRENE models impurity transport using a fluid approach, causing energy losses to the main plasma through excitation and ionization. The trace fluid approach assumes that impurities only cause small density perturbations and impacts the main plasma species through ionization and excitation via an energy loss term in the energy balance equation.

Several improvements have been made to the EMC3-EIRENE code to enhance its performance and capabilities:

* Implicit coupling to a 1D core model, eliminating ad hoc boundary conditions for intrinsic impurities at the SOL-core interface.
* Allowing non-uniform cross-field transport coefficients.
* Implementing a particle splitting technique to improve Monte Carlo statistics in low-temperature ranges.
* Enabling domain splitting in all three directions for mesh optimization in various divertor configurations.
* Relaxing stellarator-specific constraints on mesh construction.
* Moving axisymmetric neutral-facing components to cylindrical coordinates.

EMC3-EIRENE has been widely used to analyze 3D effects in stellarator and tokamak configurations. The code's ability to model plasma and neutral transport in inherently non-axisymmetric magnetic field configurations and its compatibility with various limiter designs make it a suitable tool for self-consistent 3D modeling of plasma and neutral transport in fusion devices.

The current version of EMC3-EIRENE does not include self-consistent treatment of magnetic or electric drift effects and volumetric recombination. Future developments may address these limitations and expand the code's capabilities.

== References ==

* Y. Feng et al, ''Recent Improvements in the EMC3-Eirene Code'', [[doi:10.1002/ctpp.201410092|Contributions to Plasma Physics '''54''' (2014) 426-431]]
* T. Lunt et al, ''EMC3-Eirene simulations of particle- and energy fluxes to main chamber- and divertor plasma facing components in ASDEX Upgrade compared to experiments'', [[doi:10.1016/j.jnucmat.2014.09.020|Journal of Nuclear Materials '''463''' (2015) 744-747]]
* H. Frerichs et al, ''Synthetic plasma edge diagnostics for EMC3-EIRENE, highlighted for Wendelstein 7-X'', [[doi:10.1063/1.4959910|Review of Scientific Instruments '''87''' (2016) 11D441]]
* A. Bader et al, ''Modeling of helium transport and exhaust in the LHD edge'', [[doi:10.1088/0741-3335/58/12/124006|Plasma Phys. Control. Fusion '''58''' (2016) 124006]]
* F. Effenberg et al, ''Investigation of 3D effects on heat fluxes in performance-optimized island divertor configurations at Wendelstein 7-X'', [[doi:10.1016/j.nme.2019.01.006|Nuclear Materials and Energy '''18''' (2019) 262-267]]
* J.D. Lore et al, ''Measurement and modeling of magnetic configurations to mimic overload scenarios in the W7-X stellarator'', [[doi:10.1088/1741-4326/ab18d1|Nucl. Fusion '''59''' (2019) 066041]]
* K. Schmid et al, ''Integrated modelling: Coupling of surface evolution and plasma-impurity transport'', [[doi:10.1016/j.nme.2020.100821|Nuclear Materials and Energy '''25''' (2020) 100821]]

W7-X

2023-04-06T07:28:52Z

Rkba39f8: /* See also */

W7-AS

2023-04-06T07:28:16Z

Rkba39f8: /* See also */

{| border="0" style="width:450px;" position="right"
|- valign="top"
| [[File:Garching Experiment Wendelstein 7-AS.jpg|400px|thumb|right|Wendelstein 7-AS]]
| [[File:W7as.gif|right|Wendelstein 7-AS]]
|}

The Wendelstein 7-AS (Advanced Stellarator) was located at the [http://www.ipp.mpg.de/ Max Planck Institut für Plasmaphysik (IPP)] in Garching, Germany.
The denomination 'advanced' refers to the use of [[Modular coil|modular]] (non-planar) coils.
It has been operated from 1988 to July, 2002. <ref>M. Hirsch, J. Baldzuhn, C. Beidler, et al., ''Major results from the stellarator Wendelstein 7-AS'', [[doi:10.1088/0741-3335/50/5/053001|Plasma Phys. Control. Fusion '''50''' (2008) 053001]]</ref>
Its successor is the [[W7-X]] stellarator.

== Main parameters ==

{| class="wikitable" align="center" border="1"
!''Parameter'' !!''Value''
|-
|Major radius, R0 || 2 m
|-
|Minor radius, a || ≤ 0.18 m
|-
|Periodicity || 5
|-
|Nr. of coils || 45
|-
|Plasma volume || 1 m3
|-
|Toroidal field, BT || ≤ 3 T
|-
|[[Rotational transform]] || 0.25 ≤ ι(a)/2π ≤ 0.7
|-
|Heating || 5.6 MW
|-
|Pulse length || 5 s
|}

== See also ==

* [http://www.ipp.mpg.de/ippcms/eng/for/bereiche/e3/projekte/w7as.html W7-AS page at IPP]
* [[Island Divertor]]

== References ==
<references />

[[Category:Toroidal confinement devices]]

Island Divertor

2023-04-06T07:27:18Z

Rkba39f8:

The Island Divertor is a concept in magnetic confinement fusion devices that utilizes inherent low-order [[magnetic island|magnetic islands]] to manage power and particle exhaust. Developed for advanced low-shear [[stellarator|stellarators]] in the Wendelstein-7 family, the island divertor was first tested on [[W7-AS|W7-AS]] before its shutdown in 2002<ref>[[doi:10.1088/0029-5515/46/8/006|Y. Feng et al ., Nucl. Fusion '''46''' (2006) 807]]</ref>. The concept has since been investigated in more detail and at a larger scale in [[W7-X|Wendelstein 7-X]] (W7-X).

One major challenge magnetic confinement fusion devices face is managing power and particle exhaust. In future reactors, hundreds of MWs of power will stream out from the confined plasma region (core) and must be dissipated before reaching the plasma-facing components (PFCs). Excessive heat and erosion can lead to short lifetimes of the PFCs, as well as the release of impurities and subsequent contamination of the confined plasma.

[[Divertor|Divertors]] are dedicated plasma-wall interaction zones where particles and heat stream to, moving parallel to the open magnetic field lines in the scrape-off layer (SOL). However, the fast parallel heat transport leads to localized heat deposition on the targets. In stellarators, several edge topologies have been proposed and used to form a divertor for particle and heat exhaust. The island divertor is one such concept, using intrinsic magnetic islands in the SOL to set up a divertor volume.

The first W7-X island divertor experiments and 3D modeling studies with [[EMC3-EIRENE|EMC3-EIRENE]] have found a strong dependence of the divertor heat fluxes on the magnetic configurations and island geometry. Local heat load profiles showed offsets and varying peak fluxes, complicating the matching between experiments and 3D modeling<ref>[[doi:10.1016/j.nme.2019.01.006|F. Effenberg, et al., Nucl. Mater. Energy '''18''' (2019) 262-267]]</ref><ref>[[doi:10.1088/1741-4326/ab18d1|J.D. Lore et al., Nucl. Fusion '''59''' (2019) 066041]]</ref>.

The island divertor has shown great success in accessing and stabilizing detached scenarios<ref>[[doi:10.1088/1741-4326/ab280f|T. Sunn Pedersen et al., Nucl. Fusion '''59''' (2019) 096014]]</ref>. During the first island divertor operation at W7-X, a stable operation regime had been achieved with reduced heat load on all divertor targets. This regime was maintained over several energy confinement times, and the plasma scenario proved reproducible and robust under various conditions. The plasma radiation, primarily due to oxygen, was located at the plasma edge<ref>[[doi:10.1063/1.5026324|D. Zhang et al ., Phys. Rev. Lett. '''123''' (2019) 025002]]</ref>. Island divertor detachment has been achieved since then for different plasma parameters and magnetic configurations<ref>[[doi:10.1088/1741-4326/abb51e|O. Schmitz et al., Nucl. Fusion '''61''' (2021) 016026]]</ref><ref>[[doi:10.1088/1741-4326/ac1b68|M. Jakubowski et al., Nucl. Fusion '''61''' (2021) 106003]]</ref><ref>[[doi:10.1088/1741-4326/ac0772|Y. Feng et al ., Nucl. Fusion '''61''' (2021) 086012]]</ref>.

A particular feature of the island divertor topology is the existence of multiple, adjacent counter-streaming flow regions at the plasma edge<ref>[[doi:10.1088/1741-4326/ab4320|V. Perseo et al., Nucl. Fusion '''59''' (2019) 124003]]</ref>. Strong counter-streaming flows can lead to frictional dissipation of momentum, causing a reduction of the flow speed parallel to the magnetic field lines. This is likely to have played a role in substantial heat flux mitigation at the targets.

Radiative power exhaust by impurity seeding was demonstrated for the first time in island divertor configurations at the Wendelstein 7-X stellarator<ref>[[doi:10.1088/1741-4326/ab32c4|F. Effenberg et al., Nucl. Fusion '''59''' (2019) 106020]]</ref>. Stable plasma operation was shown during seeding with both neon (Ne) and nitrogen (N2). High radiative power losses (80%) were found to reduce the divertor heat loads globally by 2/3 with both seeding gases injected at a single toroidal location into one of five magnetic islands.

The island divertor concept has demonstrated reliable heat flux control with impurity seeding, making it a promising solution for future [[Detachment control|detachment control]] in high-performance scenarios and upgrades towards a metal divertor. Feedback-controlled divertor detachment has been achieved with hydrogen gas injection in W7-X<ref>[[doi:10.1016/j.nme.2023.101363|M. Krychowiak, et al., Nucl. Mater. Energy '''34''' (2023) 101363]]</ref> and may be extended to impurity seeding in the future.

The edge magnetic structure in helically symmetric stellarators, such as the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X), has been shown to have a significant impact on particle fueling and exhaust of the main plasma species (hydrogen) and impurity helium. The magnetic island chain in the plasma edge can control the plasma fueling from the recycling source and active gas injection, a basic requirement for a divertor system<ref>[[doi:10.1063/1.5026324|L. Stephey et al ., Phys. Plasmas '''25''' (2018) 062501]]</ref>.

== References ==
<references />

Magnetic island

2023-04-06T07:19:53Z

Rkba39f8: /* See also */

A magnetic island is a closed magnetic [[Flux tube|flux tube]] (cf. [[Flux surface]]), bounded by a [[Separatrix|separatrix]], isolating it from the rest of space.
Its topology is toroidal.

In the context of magnetic confinement fusion, the basic magnetic field configuration consists of toroidally nested [[Flux surface|flux surfaces]], while each flux surface is characterised by a certain value of the [[Rotational transform|rotational transform]] or safety factor ''q''. Magnetic islands can appear at flux surfaces with a rational value of the safety factor ''q = m/n''.
<ref>J.H. Misguich, J.-D. Reuss, D. Constantinescu, G. Steinbrecher, M. Vlad, F. Spineanu, B. Weyssow, R. Balescu, ''Noble internal transport barriers and radial subdiffusion of toroidal magnetic lines'', [[doi:10.1051/anphys:2004001|Ann. Phys. Fr. '''28''' (2003) 1]]</ref>
Subsidiary islands can appear within an island.

== Island birth ==

The rupture of the assumed initial topology of toroidally nested flux surfaces needed to produce the island requires the [[reconnection]] of magnetic field lines, which can only occur with finite resistivity.
<ref>F.L. Waelbroeck, ''Theory and observations of magnetic islands'', [[doi:10.1088/0029-5515/49/10/104025|Nucl. Fusion '''49''' (2009) 104025]]</ref>
[[Stellarator]]s may have a vacuum magnetic field structure that already contains some islands (so-called 'natural islands').
Since these are completely determined by the external magnetic field, they are static.

== Island growth and saturation ==

The prediction of the non-linear saturated state of islands is the goal of [[Neoclassical transport|Neoclassical]] Tearing Mode (NTM) theory.
This theory has been developed to a considerable level of sophistication, although discrepancies with experimental observations remain.
<ref>H. Lütjens and J.-F. Luciani, ''Saturation levels of neoclassical tearing modes in International Thermonuclear Experimental Reactor plasmas'', [[doi:10.1063/1.2001667|Phys. Plasmas '''12''' (2005) 080703]]</ref>

== Island rotation ==

Islands can rotate within and/or with respect to the ambient plasma.
The observation of such rotating 'MHD modes' is ubiquitous in fusion plasmas with typical frequencies of the order of several tens of kHz.
The detection of such modes is possible by measuring perturbations of the magnetic field, or the electron density, temperature, or pressure.
If the ambient magnetic field (produced by external coils) has an appropriate structure, the island can also lock onto that structure.
<ref>F.L. Waelbroeck and R. Fitzpatrick, ''Rotation and Locking of Magnetic Islands'', [[doi:10.1103/PhysRevLett.78.1703|Phys. Rev. Lett. '''78''' (1997) 1703–1706]]</ref>
Locked islands often lead to a [[Disruption|disruption]] (complete loss of confinement) in [[Tokamak|tokamaks]].

== Transport effects ==

It is generally assumed that the temperature is rapidly equilibrated along the magnetic field lines inside the island, so that radial transport is effectively short-circuited across the islands, decreasing the effective size of the main plasma.
<ref>ITER Physics Expert Group on Confinement and Transport et al, ''Chapter 2: Plasma confinement and transport'', [[doi:10.1088/0029-5515/39/12/302|Nucl. Fusion '''39''' (1999) 2175-2249]]</ref>
However, it is possible to qualify this statement somewhat by taking into account the ratio between parallel and perpendicular transport within an island.
<ref>B.Ph. van Milligen, A.C.A.P. van Lammeren, N.J. Lopes Cardozo, F.C. Schüller, and M. Verreck, ''Gradients of electron temperature and density across m=2 islands in RTP'', [[doi:10.1088/0029-5515/33/8/I03|Nucl. Fusion '''33''' (1993) 1119]]</ref>

The interaction of neighbouring island chains causes the magnetic field to become stochastic (according to the Chirikov criterion <ref>B.V. Chirikov, ''A universal instability of many-dimensional oscillator systems'', [[doi:10.1016/0370-1573(79)90023-1|Phys. Rep. '''52''', Issue 5 (1979) 263]]</ref>), resulting in enhanced (anomalous) radial transport.
<ref>C.W. Horton, Y.H. Ichikawa, ''Chaos and structures in nonlinear plasmas'', World Scientific, 1996 {{ISBN|9789810226367}}</ref>

== Island control ==

Island control is possible by tailoring the ''q''-profile, external magnetic fields,
<ref>S.R. Hudson et al, ''Free-boundary full-pressure island healing in stellarator equilibria: coil-healing'', [[doi:10.1088/0741-3335/44/7/323|Plasma Phys. Control. Fusion '''44''' (2002) 1377]]</ref>
and the pressure profile, or by spinning up the plasma.
<ref>H. Zohm et al,''MHD limits to tokamak operation and their control'', [[doi:10.1088/0741-3335/45/12A/012|Plasma Phys. Control. Fusion '''45''' (2003) A163]]</ref>
Pressure effects can lead to 'island healing'.
<ref>R. Kanno et al, ''Formation and healing of n = 1 magnetic islands in LHD equilibrium'', [[doi:10.1088/0029-5515/45/7/006|Nucl. Fusion '''45''' (2005) 588]]</ref>
Active control of islands by external means - in particular, Electron Cyclotron Heating and Current Drive - is also possible.
<ref>[http://www.rijnhuizen.nl/en/node/195 Seek and Destroy System for magnetic island control]</ref>
<ref>A. Isayama et al, ''Neoclassical tearing mode control using electron cyclotron current drive and magnetic island evolution in JT-60U'', [[doi:10.1088/0029-5515/49/5/055006|Nucl. Fusion '''49''' (2009) 055006]]</ref>
<ref>B. Ayten et al., ''Modelling of tearing mode suppression experiments in TEXTOR based on the generalized Rutherford equation'', [[doi:10.1088/0029-5515/51/4/043007|Nucl. Fusion '''51''' (2011) 043007]]</ref>

== See also ==
* [[MHD equilibrium]]
* [[Island Divertor]]

== References ==
<references />

Island Divertor

2023-04-06T07:14:37Z

Rkba39f8:

The Island Divertor is a concept in magnetic confinement fusion devices that utilizes inherent low-order [[magnetic island|magnetic islands]] to manage power and particle exhaust. Developed for advanced low-shear [[stellarator|stellarators]] in the Wendelstein-7 family, the island divertor was first tested on W7-AS before its shutdown in 2002<ref>[[doi:10.1088/0029-5515/46/8/006|Y. Feng et al ., Nucl. Fusion '''46''' (2006) 807]]</ref>. The concept has since been investigated in more detail and at a larger scale in Wendelstein 7-X (W7-X).

One major challenge magnetic confinement fusion devices face is managing power and particle exhaust. In future reactors, hundreds of MWs of power will stream out from the confined plasma region (core) and must be dissipated before reaching the plasma-facing components (PFCs). Excessive heat and erosion can lead to short lifetimes of the PFCs, as well as the release of impurities and subsequent contamination of the confined plasma.

Divertors are dedicated plasma-wall interaction zones where particles and heat stream to, moving parallel to the open magnetic field lines in the scrape-off layer (SOL). However, the fast parallel heat transport leads to localized heat deposition on the targets. In stellarators, several edge topologies have been proposed and used to form a divertor for particle and heat exhaust. The island divertor is one such concept, using intrinsic magnetic islands in the SOL to set up a divertor volume.

The first W7-X island divertor experiments and 3D modeling studies have found a strong dependence of the divertor heat fluxes on the magnetic configurations and island geometry. Local heat load profiles showed offsets and varying peak fluxes, complicating the matching between experiments and 3D modeling<ref>[[doi:10.1016/j.nme.2019.01.006|F. Effenberg, et al., Nucl. Mater. Energy '''18''' (2019) 262-267]]</ref><ref>[[doi:10.1088/1741-4326/ab18d1|J.D. Lore et al., Nucl. Fusion '''59''' (2019) 066041]]</ref>.

The island divertor has shown great success in accessing and stabilizing detached scenarios<ref>[[doi:10.1088/1741-4326/ab280f|T. Sunn Pedersen et al., Nucl. Fusion '''59''' (2019) 096014]]</ref>. During the first island divertor operation at W7-X, a stable operation regime had been achieved with reduced heat load on all divertor targets. This regime was maintained over several energy confinement times, and the plasma scenario proved reproducible and robust under various conditions. The plasma radiation, primarily due to oxygen, was located at the plasma edge<ref>[[doi:10.1063/1.5026324|D. Zhang et al ., Phys. Rev. Lett. '''123''' (2019) 025002]]</ref>. Island divertor detachment has been achieved since then for different plasma parameters and magnetic configurations<ref>[[doi:10.1088/1741-4326/abb51e|O. Schmitz et al., Nucl. Fusion '''61''' (2021) 016026]]</ref><ref>[[doi:10.1088/1741-4326/ac1b68|M. Jakubowski et al., Nucl. Fusion '''61''' (2021) 106003]]</ref><ref>[[doi:10.1088/1741-4326/ac0772|Y. Feng et al ., Nucl. Fusion '''61''' (2021) 086012]]</ref>.

A particular feature of the island divertor topology is the existence of multiple, adjacent counter-streaming flow regions at the plasma edge<ref>[[doi:10.1088/1741-4326/ab4320|V. Perseo et al., Nucl. Fusion '''59''' (2019) 124003]]</ref>. Strong counter-streaming flows can lead to frictional dissipation of momentum, causing a reduction of the flow speed parallel to the magnetic field lines. This is likely to have played a role in substantial heat flux mitigation at the targets.

Radiative power exhaust by impurity seeding was demonstrated for the first time in island divertor configurations at the Wendelstein 7-X stellarator<ref>[[doi:10.1088/1741-4326/ab32c4|F. Effenberg et al., Nucl. Fusion '''59''' (2019) 106020]]</ref>. Stable plasma operation was shown during seeding with both neon (Ne) and nitrogen (N2). High radiative power losses (80%) were found to reduce the divertor heat loads globally by 2/3 with both seeding gases injected at a single toroidal location into one of five magnetic islands.

The island divertor concept has demonstrated reliable heat flux control with impurity seeding, making it a promising solution for future detachment control in high-performance scenarios and upgrades towards a metal divertor. Feedback-controlled divertor detachment has been achieved with hydrogen gas injection in W7-X<ref>[[doi:10.1016/j.nme.2023.101363|M. Krychowiak, et al., Nucl. Mater. Energy '''34''' (2023) 101363]]</ref> and may be extended to impurity seeding in the future.

The edge magnetic structure in helically symmetric stellarators, such as the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X), has been shown to have a significant impact on particle fueling and exhaust of the main plasma species (hydrogen) and impurity helium. The magnetic island chain in the plasma edge can control the plasma fueling from the recycling source and active gas injection, a basic requirement for a divertor system<ref>[[doi:10.1063/1.5026324|L. Stephey et al ., Phys. Plasmas '''25''' (2018) 062501]]</ref>.

== References ==
<references />

Divertor

2023-04-06T07:12:59Z

Rkba39f8:

[[File:Divertors.png|300px|thumb|right|Sketch of divertor types: single and double null tokamak divertors (toroidally symmetric), and island divertor. From <ref name="Feng">[http://dx.doi.org/10.1088/0029-5515/46/8/006 Y. Feng, F. Sardei, P. Grigull, K. McCormick, J. Kisslinger and D. Reiter, ''Physics of island divertors as highlighted by the example of W7-AS'', Nucl. Fusion '''46''' (2006) 807]</ref>.]]
A divertor configuration is a magnetic field configuration in which the toroidally confined (plasma) region is separated from the outside world by a [[Separatrix|separatrix]] -
as opposed to a limiter configuration in which the plasma's Last Closed Magnetic Surface is determined by the intersection of field lines by a material object.

One can distinguish '[[Tokamak|tokamak]] divertors' (characterised by toroidal symmetry and one or two X-points or 'nulls') and '[[Island Divertor|island divertors]]' (for [[Stellarator|stellarators]]).
<ref name="Feng"></ref>

The term 'divertor' can refer to:
* the magnetic field structure beyond the X-point and in contact with material surfaces, or
* the material structure intersecting the 'outgoing legs' of the magnetic separatrix surface.

The divertor region between the 'outgoing legs' - the region between the material divertor and the X-point, up to the separatrix - is known as the private flux region (PFR).

== See also ==

* [[Flux surface]]

== References ==
<references />

Island Divertor

2023-04-06T07:09:54Z

Rkba39f8: Created page with "The Island Divertor is a concept in magnetic confinement fusion devices that utilizes inherent low-order magnetic islands to manage power and particle exhaust. Developed for a..."

The Island Divertor is a concept in magnetic confinement fusion devices that utilizes inherent low-order magnetic islands to manage power and particle exhaust. Developed for advanced low-shear stellarators in the Wendelstein-7 family, the island divertor was first tested on W7-AS before its shutdown in 2002<ref>[[doi:10.1088/0029-5515/46/8/006|Y. Feng et al ., Nucl. Fusion '''46''' (2006) 807]]</ref>. The concept has since been investigated in more detail and at a larger scale in Wendelstein 7-X (W7-X).

One major challenge magnetic confinement fusion devices face is managing power and particle exhaust. In future reactors, hundreds of MWs of power will stream out from the confined plasma region (core) and must be dissipated before reaching the plasma-facing components (PFCs). Excessive heat and erosion can lead to short lifetimes of the PFCs, as well as the release of impurities and subsequent contamination of the confined plasma.

Divertors are dedicated plasma-wall interaction zones where particles and heat stream to, moving parallel to the open magnetic field lines in the scrape-off layer (SOL). However, the fast parallel heat transport leads to localized heat deposition on the targets. In stellarators, several edge topologies have been proposed and used to form a divertor for particle and heat exhaust. The island divertor is one such concept, using intrinsic magnetic islands in the SOL to set up a divertor volume.

The first W7-X island divertor experiments and 3D modeling studies have found a strong dependence of the divertor heat fluxes on the magnetic configurations and island geometry. Local heat load profiles showed offsets and varying peak fluxes, complicating the matching between experiments and 3D modeling<ref>[[doi:10.1016/j.nme.2019.01.006|F. Effenberg, et al., Nucl. Mater. Energy '''18''' (2019) 262-267]]</ref><ref>[[doi:10.1088/1741-4326/ab18d1|J.D. Lore et al., Nucl. Fusion '''59''' (2019) 066041]]</ref>.

The island divertor has shown great success in accessing and stabilizing detached scenarios<ref>[[doi:10.1088/1741-4326/ab280f|T. Sunn Pedersen et al., Nucl. Fusion '''59''' (2019) 096014]]</ref>. During the first island divertor operation at W7-X, a stable operation regime had been achieved with reduced heat load on all divertor targets. This regime was maintained over several energy confinement times, and the plasma scenario proved reproducible and robust under various conditions. The plasma radiation, primarily due to oxygen, was located at the plasma edge<ref>[[doi:10.1063/1.5026324|D. Zhang et al ., Phys. Rev. Lett. '''123''' (2019) 025002]]</ref>. Island divertor detachment has been achieved since then for different plasma parameters and magnetic configurations<ref>[[doi:10.1088/1741-4326/abb51e|O. Schmitz et al., Nucl. Fusion '''61''' (2021) 016026]]</ref><ref>[[doi:10.1088/1741-4326/ac1b68|M. Jakubowski et al., Nucl. Fusion '''61''' (2021) 106003]]</ref><ref>[[doi:10.1088/1741-4326/ac0772|Y. Feng et al ., Nucl. Fusion '''61''' (2021) 086012]]</ref>.

A particular feature of the island divertor topology is the existence of multiple, adjacent counter-streaming flow regions at the plasma edge<ref>[[doi:10.1088/1741-4326/ab4320|V. Perseo et al., Nucl. Fusion '''59''' (2019) 124003]]</ref>. Strong counter-streaming flows can lead to frictional dissipation of momentum, causing a reduction of the flow speed parallel to the magnetic field lines. This is likely to have played a role in substantial heat flux mitigation at the targets.

Radiative power exhaust by impurity seeding was demonstrated for the first time in island divertor configurations at the Wendelstein 7-X stellarator<ref>[[doi:10.1088/1741-4326/ab32c4|F. Effenberg et al., Nucl. Fusion '''59''' (2019) 106020]]</ref>. Stable plasma operation was shown during seeding with both neon (Ne) and nitrogen (N2). High radiative power losses (80%) were found to reduce the divertor heat loads globally by 2/3 with both seeding gases injected at a single toroidal location into one of five magnetic islands.

The island divertor concept has demonstrated reliable heat flux control with impurity seeding, making it a promising solution for future detachment control in high-performance scenarios and upgrades towards a metal divertor. Feedback-controlled divertor detachment has been achieved with hydrogen gas injection in W7-X<ref>[[doi:10.1016/j.nme.2023.101363|M. Krychowiak, et al., Nucl. Mater. Energy '''34''' (2023) 101363]]</ref> and may be extended to impurity seeding in the future.

The edge magnetic structure in helically symmetric stellarators, such as the Helically Symmetric eXperiment (HSX) and Wendelstein 7X (W7-X), has been shown to have a significant impact on particle fueling and exhaust of the main plasma species (hydrogen) and impurity helium. The magnetic island chain in the plasma edge can control the plasma fueling from the recycling source and active gas injection, a basic requirement for a divertor system<ref>[[doi:10.1063/1.5026324|L. Stephey et al ., Phys. Plasmas '''25''' (2018) 062501]]</ref>.

== References ==
<references />

EMC3-EIRENE

2023-04-03T06:58:51Z

Rkba39f8: /* References */

EMC3-EIRENE is a state-of-the-art computational tool that combines the EMC3 (Edge Monte Carlo 3D) code with the EIRENE code to simulate plasma fluid and kinetic neutral edge transport in non-axisymmetric configurations. Developed for the study of stellarator and tokamak configurations, the code can model the full torus plasma and impurity transport, including the effects of 3D fields, such as resonant-magnetic perturbations (RMPs).
EMC3 is a 3D plasma fluid code that solves a set of reduced Braginskii fluid equations for particles, parallel momentum, and energies for electrons and ions. The code models parallel electron and ion heat conductivity using classical assumptions. Perpendicular transport is determined by coefficients for anomalous particle transport (<math>D_\bot</math>) and anomalous electron and ion heat transport (<math>\chi_\bot</math>), which are free model parameters. EIRENE is a kinetic edge transport code that solves the transport equations for neutral atoms and molecules, accounting for collisional processes. The code calculates ionization sources, momentum sources/losses, and energy sources/losses due to atomic/molecular processes, such as charge exchange and ionization. EMC3-EIRENE models impurity transport using a fluid approach, causing energy losses to the main plasma through excitation and ionization. The trace fluid approach assumes that impurities only cause small density perturbations and impacts the main plasma species through ionization and excitation via an energy loss term in the energy balance equation.

Several improvements have been made to the EMC3-EIRENE code to enhance its performance and capabilities:

* Implicit coupling to a 1D core model, eliminating ad hoc boundary conditions for intrinsic impurities at the SOL-core interface.
* Allowing non-uniform cross-field transport coefficients.
* Implementing a particle splitting technique to improve Monte Carlo statistics in low-temperature ranges.
* Enabling domain splitting in all three directions for mesh optimization in various divertor configurations.
* Relaxing stellarator-specific constraints on mesh construction.
* Moving axisymmetric neutral-facing components to cylindrical coordinates.

EMC3-EIRENE has been widely used to analyze 3D effects in stellarator and tokamak configurations. The code's ability to model plasma and neutral transport in inherently non-axisymmetric magnetic field configurations and its compatibility with various limiter designs make it a suitable tool for self-consistent 3D modeling of plasma and neutral transport in fusion devices.

The current version of EMC3-EIRENE does not include self-consistent treatment of magnetic or electric drift effects and volumetric recombination. Future developments may address these limitations and expand the code's capabilities.

== References ==

* Y. Feng et al, ''Recent Improvements in the EMC3-Eirene Code'', [[doi:10.1002/ctpp.201410092|Contributions to Plasma Physics '''54''' (2014) 426-431]]
* T. Lunt et al, ''EMC3-Eirene simulations of particle- and energy fluxes to main chamber- and divertor plasma facing components in ASDEX Upgrade compared to experiments'', [[doi:10.1016/j.jnucmat.2014.09.020|Journal of Nuclear Materials '''463''' (2015) 744-747]]
* H. Frerichs et al, ''Synthetic plasma edge diagnostics for EMC3-EIRENE, highlighted for Wendelstein 7-X'', [[doi:10.1063/1.4959910|Review of Scientific Instruments '''87''' (2016) 11D441]]
* A. Bader et al, ''Modeling of helium transport and exhaust in the LHD edge'', [[doi:10.1088/0741-3335/58/12/124006|Plasma Phys. Control. Fusion '''58''' (2016) 124006]]
* F. Effenberg et al, ''Investigation of 3D effects on heat fluxes in performance-optimized island divertor configurations at Wendelstein 7-X'', [[doi:10.1016/j.nme.2019.01.006|Nuclear Materials and Energy '''18''' (2019) 262-267]]
* J.D. Lore et al, ''Measurement and modeling of magnetic configurations to mimic overload scenarios in the W7-X stellarator'', [[doi:10.1088/1741-4326/ab18d1|Nucl. Fusion '''59''' (2019) 066041]]
* K. Schmid et al, ''Integrated modelling: Coupling of surface evolution and plasma-impurity transport'', [[doi:10.1016/j.nme.2020.100821|Nuclear Materials and Energy '''25''' (2020) 100821]]

Tokamak

2023-04-03T06:49:32Z

Rkba39f8: /* Defunct tokamaks */

A tokamak is a [[Magnetic confinement|magnetic confinement]] device in which the poloidal component of the magnetic field is generated mainly by currents flowing in the plasma.
The relative simplicity of the tokamak design has led to an initial headway of this design with respect to other prospective designs for a [[Nuclear fusion|fusion]] reactor, and the top performance among current fusion experiments has been achieved in tokamaks. As a consequence, next-step devices are based on this design.
However, the intrinsic limitations of tokamaks when operated at high values of the operational parameters may lead to an eventual preference for the [[Stellarator reactor|stellarator]] design, in spite of its increased complexity.

== Defunct tokamaks ==
* Alcator A (USA)
* Alcator C (USA)
* CASTOR (Prague, Czech Republic)
* [[:Wikipedia:Electric Tokamak|Electric Tokamak]] (USA)
* LT-1 (Australia)
* [[:Wikipedia:Mega_Ampere_Spherical_Tokamak|MAST]] (Culham, UK)
* PBX-M (Princeton, NJ, USA)
* RTP (Rijnhuizen, The Netherlands)
* [[:Wikipedia:Small_Tight_Aspect_Ratio_Tokamak|START]] (UK)
* T-3 (Russia)
* T-4 (Russia)
* T-15 (Russia)
* TEXT (USA)
* [https://www.fz-juelich.de/en/iek/iek-4/forschung/textor TEXTOR] (Jülich, Germany)
* [[:Wikipedia:TFTR|TFTR]] (USA)
* [[TJ-I]] (Spain)
* Tokamak de Varennes (Canada)
* [[:Wikipedia:Tokamak à Chauffage Alfvén|Tokamak à Chauffage Alfvén]] (CH)

== Operational tokamaks ==
* [http://www.ipr.res.in/aboutaditya.html Aditya] (Gujarat, India)
* [[:Wikipedia:Alcator C-Mod|Alcator C-Mod]] (Cambridge, USA)
* [[:Wikipedia:ASDEX Upgrade|ASDEX Upgrade]] (Garching, Germany)
* [http://www.ipp.cas.cz/Tokamak/ COMPASS] (Prague, Czech Republic - previously in Culham, UK)
* [[:Wikipedia:DIII-D|DIII-D]] (San Diego, USA)
* [[:Wikipedia:EAST|EAST]] (HT-7U) (Hefei, China)
* [[:Wikipedia:Frascati_Tokamak_Upgrade|FTU]] (Frascati, Italy)
* [[:Wikipedia:HT-7|HT-7]] (Hefei, China)
* [http://www.cfn.ist.utl.pt/eng/Prj_Tokamak_main.html ISTTOK] (Lisbon, Portugal)
* [[:Wikipedia:Joint_European_Torus|JET]] (UK - European)
* [[:Wikipedia:JT-60|JT-60]] (Naka, Japan)
* [[:Wikipedia:KSTAR|KSTAR]] (Daejon, South Korea)
* KTM (Kazakhstan)
* [http://plasma47.energy.kyoto-u.ac.jp/index_e.html LATE] Low Aspect ratio Torus Experiment (Kyoto, Japan)
* [http://pst.pppl.gov/ltx/ LTX] Lithium Tokamak Experiment (USA)
* [https://ccfe.ukaea.uk/research/mast-upgrade/ MAST Upgrade]] (Culham, UK)
* [[:Wikipedia:National Spherical Torus Experiment|NSTX-U]] (Princeton, NJ, USA)
* [https://www.dtu.dk/english/news/2019/08/dtus-own-tokamak-for-fusion-energy-research?id=69f514ed-2ad4-4a34-98a5-81e3d0ace6cd NORTH] (Copenhagen, Danemark)
* [[:Wikipedia:Pegasus_Toroidal_Experiment|Pegasus]] (Madison, USA)
* [http://plasma.usask.ca/storm/index.php STOR-M] (Canada)
* T-10 (Russia)
* TCABR (Sao Paulo, Brazil - previously in Switzerland)
* [[:Wikipedia:Tokamak_%C3%A0_configuration_variable|TCV]] (Switzerland)
* [[:Wikipedia:Tore Supra|Tore Supra]] (Cadarache, France)
* VEST (Seoul, Korea)

== Future tokamaks ==

* [[ITER]] (under construction, France - International)
* [http://www.ipr.res.in/sst1/SST-1.html SST-1] (India)
* [[DEMO]] (in design phase)

== See also ==

* [[Stellarator]]
* [[:Wikipedia:Tokamak]]
* [http://www.tokamak.info www.tokamak.info] - comprehensive list of tokamaks
* [https://www.google.com/maps/d/viewer?mid=z74xNCoUPT3o.klOHFNk4lzac Map: All the world's tokamaks]

Tokamak

2023-04-03T06:47:18Z

Rkba39f8: /* Operational tokamaks */

A tokamak is a [[Magnetic confinement|magnetic confinement]] device in which the poloidal component of the magnetic field is generated mainly by currents flowing in the plasma.
The relative simplicity of the tokamak design has led to an initial headway of this design with respect to other prospective designs for a [[Nuclear fusion|fusion]] reactor, and the top performance among current fusion experiments has been achieved in tokamaks. As a consequence, next-step devices are based on this design.
However, the intrinsic limitations of tokamaks when operated at high values of the operational parameters may lead to an eventual preference for the [[Stellarator reactor|stellarator]] design, in spite of its increased complexity.

== Defunct tokamaks ==
* Alcator A (USA)
* Alcator C (USA)
* CASTOR (Prague, Czech Republic)
* [[:Wikipedia:Electric Tokamak|Electric Tokamak]] (USA)
* LT-1 (Australia)
* [[:Wikipedia:Mega_Ampere_Spherical_Tokamak|MAST]] (Culham, UK)
* PBX-M (Princeton, NJ, USA)
* RTP (Rijnhuizen, The Netherlands)
* [[:Wikipedia:Small_Tight_Aspect_Ratio_Tokamak|START]] (UK)
* T-3 (Russia)
* T-4 (Russia)
* T-15 (Russia)
* TEXT (USA)
* [[:Wikipedia:TFTR|TFTR]] (USA)
* [[TJ-I]] (Spain)
* Tokamak de Varennes (Canada)
* [[:Wikipedia:Tokamak à Chauffage Alfvén|Tokamak à Chauffage Alfvén]] (CH)

== Operational tokamaks ==
* [http://www.ipr.res.in/aboutaditya.html Aditya] (Gujarat, India)
* [[:Wikipedia:Alcator C-Mod|Alcator C-Mod]] (Cambridge, USA)
* [[:Wikipedia:ASDEX Upgrade|ASDEX Upgrade]] (Garching, Germany)
* [http://www.ipp.cas.cz/Tokamak/ COMPASS] (Prague, Czech Republic - previously in Culham, UK)
* [[:Wikipedia:DIII-D|DIII-D]] (San Diego, USA)
* [[:Wikipedia:EAST|EAST]] (HT-7U) (Hefei, China)
* [[:Wikipedia:Frascati_Tokamak_Upgrade|FTU]] (Frascati, Italy)
* [[:Wikipedia:HT-7|HT-7]] (Hefei, China)
* [http://www.cfn.ist.utl.pt/eng/Prj_Tokamak_main.html ISTTOK] (Lisbon, Portugal)
* [[:Wikipedia:Joint_European_Torus|JET]] (UK - European)
* [[:Wikipedia:JT-60|JT-60]] (Naka, Japan)
* [[:Wikipedia:KSTAR|KSTAR]] (Daejon, South Korea)
* KTM (Kazakhstan)
* [http://plasma47.energy.kyoto-u.ac.jp/index_e.html LATE] Low Aspect ratio Torus Experiment (Kyoto, Japan)
* [http://pst.pppl.gov/ltx/ LTX] Lithium Tokamak Experiment (USA)
* [https://ccfe.ukaea.uk/research/mast-upgrade/ MAST Upgrade]] (Culham, UK)
* [[:Wikipedia:National Spherical Torus Experiment|NSTX-U]] (Princeton, NJ, USA)
* [https://www.dtu.dk/english/news/2019/08/dtus-own-tokamak-for-fusion-energy-research?id=69f514ed-2ad4-4a34-98a5-81e3d0ace6cd NORTH] (Copenhagen, Danemark)
* [[:Wikipedia:Pegasus_Toroidal_Experiment|Pegasus]] (Madison, USA)
* [http://plasma.usask.ca/storm/index.php STOR-M] (Canada)
* T-10 (Russia)
* TCABR (Sao Paulo, Brazil - previously in Switzerland)
* [[:Wikipedia:Tokamak_%C3%A0_configuration_variable|TCV]] (Switzerland)
* [[:Wikipedia:Tore Supra|Tore Supra]] (Cadarache, France)
* VEST (Seoul, Korea)

== Future tokamaks ==

* [[ITER]] (under construction, France - International)
* [http://www.ipr.res.in/sst1/SST-1.html SST-1] (India)
* [[DEMO]] (in design phase)

== See also ==

* [[Stellarator]]
* [[:Wikipedia:Tokamak]]
* [http://www.tokamak.info www.tokamak.info] - comprehensive list of tokamaks
* [https://www.google.com/maps/d/viewer?mid=z74xNCoUPT3o.klOHFNk4lzac Map: All the world's tokamaks]

EMC3-EIRENE

2023-04-03T06:45:40Z

Rkba39f8: /* References */

EMC3-EIRENE is a state-of-the-art computational tool that combines the EMC3 (Edge Monte Carlo 3D) code with the EIRENE code to simulate plasma fluid and kinetic neutral edge transport in non-axisymmetric configurations. Developed for the study of stellarator and tokamak configurations, the code can model the full torus plasma and impurity transport, including the effects of 3D fields, such as resonant-magnetic perturbations (RMPs).
EMC3 is a 3D plasma fluid code that solves a set of reduced Braginskii fluid equations for particles, parallel momentum, and energies for electrons and ions. The code models parallel electron and ion heat conductivity using classical assumptions. Perpendicular transport is determined by coefficients for anomalous particle transport (<math>D_\bot</math>) and anomalous electron and ion heat transport (<math>\chi_\bot</math>), which are free model parameters. EIRENE is a kinetic edge transport code that solves the transport equations for neutral atoms and molecules, accounting for collisional processes. The code calculates ionization sources, momentum sources/losses, and energy sources/losses due to atomic/molecular processes, such as charge exchange and ionization. EMC3-EIRENE models impurity transport using a fluid approach, causing energy losses to the main plasma through excitation and ionization. The trace fluid approach assumes that impurities only cause small density perturbations and impacts the main plasma species through ionization and excitation via an energy loss term in the energy balance equation.

Several improvements have been made to the EMC3-EIRENE code to enhance its performance and capabilities:

* Implicit coupling to a 1D core model, eliminating ad hoc boundary conditions for intrinsic impurities at the SOL-core interface.
* Allowing non-uniform cross-field transport coefficients.
* Implementing a particle splitting technique to improve Monte Carlo statistics in low-temperature ranges.
* Enabling domain splitting in all three directions for mesh optimization in various divertor configurations.
* Relaxing stellarator-specific constraints on mesh construction.
* Moving axisymmetric neutral-facing components to cylindrical coordinates.

EMC3-EIRENE has been widely used to analyze 3D effects in stellarator and tokamak configurations. The code's ability to model plasma and neutral transport in inherently non-axisymmetric magnetic field configurations and its compatibility with various limiter designs make it a suitable tool for self-consistent 3D modeling of plasma and neutral transport in fusion devices.

The current version of EMC3-EIRENE does not include self-consistent treatment of magnetic or electric drift effects and volumetric recombination. Future developments may address these limitations and expand the code's capabilities.

== References ==

* Y. Feng et al, ''Recent Improvements in the EMC3-Eirene Code'', [[doi:10.1002/ctpp.201410092|Contributions to Plasma Physics '''54''' (2014) 426-431]]
* T. Lunt et al, ''EMC3-Eirene simulations of particle- and energy fluxes to main chamber- and divertor plasma facing components in ASDEX Upgrade compared to experiments'', [[doi:10.1016/j.jnucmat.2014.09.020|Journal of Nuclear Materials '''463''' (2015) 744-747]]
* H. Frerichs et al, ''Synthetic plasma edge diagnostics for EMC3-EIRENE, highlighted for Wendelstein 7-X'', [[doi:10.1063/1.4959910|Review of Scientific Instruments '''87''' (2016) 11D441]]
* A. Bader et al, ''Modeling of helium transport and exhaust in the LHD edge'', [[doi:10.1088/0741-3335/58/12/124006|Plasma Phys. Control. Fusion '''58''' (2016) 124006]]
* J.D. Lore et al, ''Measurement and modeling of magnetic configurations to mimic overload scenarios in the W7-X stellarator'', [[doi:10.1088/1741-4326/ab18d1|Nucl. Fusion '''59''' (2019) 066041]]
* F. Effenberg et al, ''Investigation of 3D effects on heat fluxes in performance-optimized island divertor configurations at Wendelstein 7-X'', [[doi:10.1016/j.nme.2019.01.006|Nuclear Materials and Energy '''18''' (2019) 262-267]]
* K. Schmid et al, ''Integrated modelling: Coupling of surface evolution and plasma-impurity transport'', [[doi:10.1016/j.nme.2020.100821|Nuclear Materials and Energy '''25''' (2020) 100821]]

Plasma simulation

2023-04-03T05:58:12Z

Rkba39f8: /* Fluid codes */

The complexity of fusion-grade plasmas and the increased computational power that has become available in recent years has made the simulation of plasmas a prime object of study in the field of fusion research. Although the basic equations governing the behaviour of magnetised plasmas are known, approximations are always necessary in any code of practical interest; e.g. the extreme disparity of the transport timescales (seconds) and turbulent timescales (microseconds) make it hard to perform detailed turbulence simulations for the whole three-dimensional plasma volume and for several transport timescales.

This page discusses plasma transport calculations, not the [[MHD equilibrium]].

== Projects ==

* [http://www.lehigh.edu/~infusion/ Fusion Simulation Project] (USA)

== Codes ==

Codes can either be interpretative (taking some input from experiment) or predictive.
They can be full-[[Tokamak|tokamak]] (or full-[[Stellarator|stellarator]]), or simulate only a small portion of plasma (a [[Flux tube|flux tube]], the edge, or the [[Scrape-Off Layer]]). They can be fluid models for one (electrons), two (electrons + ions) or more ([[impurities]]) fluid species, Monte Carlo type (particle tracing) codes, or gyro-kinetic codes. The latter are again subdivided into full-f or delta-f codes (delta-f referring to the fact that only the deviation from a background Maxwellian particle velocity distribution function is simulated).

Recent years have seen an increased effort in the field of cross code benchmarking.
<ref>Nevins W.M. et al, [[doi:10.1063/1.2402510|Phys. Plasmas '''13''' (2006) 122306]]</ref>
<ref>A.M. Dimits et al, [[doi:10.1088/0029-5515/47/8/012|Nucl. Fusion '''47''' (2007) 817-824]]</ref>
<ref>G L Falchetto et al, [[doi:10.1088/0741-3335/50/12/124015|Plasma Phys. Control. Fusion '''50''' (2008) 124015]]</ref>
<ref>[http://w3.pppl.gov/ntcc/ National Transport Code Collaboration]</ref>

=== Fluid codes ===

In the fluid model approach, equations are derived for the moments of the distribution function f. This approach requires making several more or less strong assumptions regarding the relative importance of physical phenomena and closing the infinite set of moment equations, thus possibly losing some interesting physics.

* [[CUTIE]] (predictive, 3-D, full-tokamak)
* [[PRETOR]]
* [[PROCTR]] (1-D)
* [[TRANSP]]
* [[JETTO]]
* [[MMM95]]
* [[EDGE2D-NIMBUS]] (edge)
* [[UEDGE]]
* [[SOLPS]]
* [[EMC3-EIRENE]]

=== Monte Carlo codes ===

The Monte Carlo or single particle approach solves the kinetic single-particle equations (the Lorentz force equation) in a fixed background.

* [[MOCA]]
* [[EIRENE]] (edge)

=== Gyrokinetic codes ===

The gyrokinetic treatment simplifies the [[:Wikipedia:Vlasov_equation|Vlasov equation]] for the evolution of the single-particle distribution function <math>f(\vec{x},\vec{v},t)</math> by averaging over the gyration angle, resulting in an evolution equation for the particle guiding centre.
See [[Gyrokinetic simulations]].

* [[GYRO]] <ref>[http://fusion.gat.com/theory/Gyro Gyro homepage]</ref>
* [[GS2]] ([[Flux tube|flux tube]])
* [[GENE]] ([[Flux tube|flux tube]])
* [[GEM]] (delta f) <ref>[http://cips.colorado.edu/simulation/gem.htm Plasma Simulation Group]</ref>
* [[EUTERPE]]
* [[SUMMIT/PG3EQ_NC]]

== Validation ==

See [[Model validation]]

== References ==
<references />

EMC3-EIRENE

2023-04-03T05:55:36Z

Rkba39f8: /* References */

EMC3-EIRENE is a state-of-the-art computational tool that combines the EMC3 (Edge Monte Carlo 3D) code with the EIRENE code to simulate plasma fluid and kinetic neutral edge transport in non-axisymmetric configurations. Developed for the study of stellarator and tokamak configurations, the code can model the full torus plasma and impurity transport, including the effects of 3D fields, such as resonant-magnetic perturbations (RMPs).
EMC3 is a 3D plasma fluid code that solves a set of reduced Braginskii fluid equations for particles, parallel momentum, and energies for electrons and ions. The code models parallel electron and ion heat conductivity using classical assumptions. Perpendicular transport is determined by coefficients for anomalous particle transport (<math>D_\bot</math>) and anomalous electron and ion heat transport (<math>\chi_\bot</math>), which are free model parameters. EIRENE is a kinetic edge transport code that solves the transport equations for neutral atoms and molecules, accounting for collisional processes. The code calculates ionization sources, momentum sources/losses, and energy sources/losses due to atomic/molecular processes, such as charge exchange and ionization. EMC3-EIRENE models impurity transport using a fluid approach, causing energy losses to the main plasma through excitation and ionization. The trace fluid approach assumes that impurities only cause small density perturbations and impacts the main plasma species through ionization and excitation via an energy loss term in the energy balance equation.

Several improvements have been made to the EMC3-EIRENE code to enhance its performance and capabilities:

* Implicit coupling to a 1D core model, eliminating ad hoc boundary conditions for intrinsic impurities at the SOL-core interface.
* Allowing non-uniform cross-field transport coefficients.
* Implementing a particle splitting technique to improve Monte Carlo statistics in low-temperature ranges.
* Enabling domain splitting in all three directions for mesh optimization in various divertor configurations.
* Relaxing stellarator-specific constraints on mesh construction.
* Moving axisymmetric neutral-facing components to cylindrical coordinates.

EMC3-EIRENE has been widely used to analyze 3D effects in stellarator and tokamak configurations. The code's ability to model plasma and neutral transport in inherently non-axisymmetric magnetic field configurations and its compatibility with various limiter designs make it a suitable tool for self-consistent 3D modeling of plasma and neutral transport in fusion devices.

The current version of EMC3-EIRENE does not include self-consistent treatment of magnetic or electric drift effects and volumetric recombination. Future developments may address these limitations and expand the code's capabilities.

== References ==

* Y. Feng et al, ''Recent Improvements in the EMC3-Eirene Code'', [[doi:10.1002/ctpp.201410092|Contributions to Plasma Physics '''54''' (2014) 426-431]]
* H. Frerichs et al, ''Synthetic plasma edge diagnostics for EMC3-EIRENE, highlighted for Wendelstein 7-X'', [[doi:10.1063/1.4959910|Review of Scientific Instruments '''87''' (2016) 11D441]]
* K. Schmid et al, ''Integrated modelling: Coupling of surface evolution and plasma-impurity transport'', [[doi:10.1016/j.nme.2020.100821|Nuclear Materials and Energy '''25''' (2020) 100821]]

EMC3-EIRENE

2023-04-03T05:24:08Z

Rkba39f8: Created page with "EMC3-EIRENE is a state-of-the-art computational tool that combines the EMC3 (Edge Monte Carlo 3D) code with the EIRENE code to simulate plasma fluid and kinetic neutral edge t..."

W7-X

2023-04-03T04:41:50Z

Rkba39f8:

W7-X

2023-04-03T04:40:50Z

Rkba39f8:

[[File:W7X.png|400px|thumb|right|W7-X model]]
Wendelstein 7-X (W7-X) is an experimental stellarator currently being in operation in Greifswald, Germany by the [[:Wikipedia:Max-Planck-Institut_f%C3%BCr_Plasmaphysik|Max-Planck-Institut für Plasmaphysik]] (IPP). W7-X is an [[Stellarator optimization|optimized stellarator]], i.e. the magnetic field has been tailored to meet several physical optimization criteria.

{| class="wikitable" align="center" border="1"
!''Parameter'' !!''Value''!!''Unit''
|-
|Major radius, ''R0'': || 5.5 || m
|-
|Minor radius, ''a'': || 0.53 || m
|-
|Plasma volume, ''V'': || 30 || m3
|-
|Non-planar coils: || 50 ||
|-
|Planar coils: || 20 ||
|-
|Number of ports: || 254 ||
|-
|Rotational transform, ''ι/2π'': || 5/6-5/4 ||
|-
|Magnetic field on axis, ''B0'': || <3 || T
|-
|Stored energy, ''W'': || 600 || MJ
|-
|Heating power, ''P'': || 15-30 || MW
|-
|Pulse length: || 30 || min
|-
|Machine height: || 4.5 || m
|-
|Machine diameter: || 16 || m
|-
|Machine mass: || 725 || t
|}

== Optimization criteria ==

* Feasible [[modular coil]]s
* Good, nested [[Flux surface|magnetic surfaces]]
* Good finite-[[Beta|β]] equilibria
* Good MHD [[Plasma instability|stability]]
* Small [[neoclassical transport]]
* Small [[bootstrap current]]
* Good confinement of fast particles

== See also ==

* [https://www.ipp.mpg.de/16900/w7x Wendelstein 7-X]

== References ==
* H. Wobig, ''The theoretical basis of a drift-optimized stellarator reactor'', [[doi:10.1088/0741-3335/35/8/001|Plasma Phys. Control. Fusion '''35''' (1993) 903]]
* J. Nührenberg et al., Trans. Fusion Technology '''27''' (1995) 71
* C. Nührenberg, ''Global ideal magnetohydrodynamic stability analysis for the configurational space of Wendelstein 7–X'', [[doi:10.1063/1.871924|Phys. Plasmas '''3''' (1996) 2401]]
* V. Erckmann et al, ''The W7-X project: scientific basis and technical realization'', [[doi:10.1109/FUSION.1997.685662|Fusion Engineering '''6-10''' (1997) 40]]
* M. Wanner and the W7-X Team, ''Design goals and status of the WENDELSTEIN 7-X project'', [[doi:10.1088/0741-3335/42/11/304|Plasma Phys. Control. Fusion '''42''' (2000) 1179]]
* M. Wanner et al, ''Design and construction of WENDELSTEIN 7-X'', [[doi:10.1016/S0920-3796(01)00239-3|Fusion Engineering and Design '''56-57''' (2001) 155-162]]
* M. Wanner et al, ''Status of WENDELSTEIN 7-X construction'', [[doi:10.1088/0029-5515/43/6/304|Nucl. Fusion '''43''' (2003) 416]]
* M. Wanner and the W7-X Team, ''Construction and assembly of WENDELSTEIN 7-X'', [[doi:10.1016/j.fusengdes.2006.07.013|Fusion Engineering and Design '''81''', 20-22 (2006) 2305-2313]]
* L. Wegener, ''Status of Wendelstein 7-X construction'', [[doi:10.1016/j.fusengdes.2009.01.106|Fusion Engineering and Design '''84''', 2-6 (2009) 106-112]]
* H.-S. Bosch et al, ''Construction of Wendelstein 7-X; Engineering a Steady-State Stellarator'', [[doi:10.1109/TPS.2009.2036918|IEEE Trans. Plasma Science '''38''', 3 (2010) 265]]
* H.-S. Bosch et al, ''Technical challenges in the construction of the steady-state stellarator Wendelstein 7-X'', [[doi:10.1088/0029-5515/53/12/126001|Nucl. Fusion '''53''' (2013) 126001]]
* D. Clery, ''Feature: The bizarre reactor that might save nuclear fusion'', [[doi:10.1126/science.aad4746|Science, 21 October 2015]]
* O. Neubauer et al, ''Diagnostic setup for investigation of plasma wall interactions at Wendelstein 7-X'', [[doi:10.1016/j.fusengdes.2015.06.102|Fusion Engineering and Design '''96-97''' (2015) 891-894]]
* T. Sunn Pedersen et al, ''Plans for the first plasma operation of Wendelstein 7-X'', [[doi:10.1088/0029-5515/55/12/126001|Nucl. Fusion '''55''' (2015) 126001]]
* M. Krychowiak et al, ''Overview of diagnostic performance and results for the first operation phase in Wendelstein 7-X'', [[doi:10.1063/1.4964376|Review of Scientific Instruments '''87''' (2016) 11D304]]
* R.C. Wolf et al, ''Major results from the first plasma campaign of the Wendelstein 7-X stellarator'', [[doi:10.1088/1741-4326/aa770d|Nucl. Fusion '''57''' (2017) 102020]]
* D. Hathiramani et al, ''Upgrades of edge, divertor and scrape-off layer diagnostics of W7‐X for OP1.2'', [[doi:10.1016/j.fusengdes.2018.02.013|Fusion Engineering and Design '''136A''' (2018) 304-308]]
* A. Dinklage et al, ''Magnetic configuration effects on the Wendelstein 7-X stellarator'', [[doi:10.1038/s41567-018-0141-9|Nature Phys '''14''' (2018) 855–860]]
* R.C. Wolf et al, ''Performance of Wendelstein 7-X stellarator plasmas during the first divertor operation phase'', [[doi:10.1063/1.5098761|Physics of Plasmas '''26''' (2019) 082504]]

[[Category:Toroidal confinement devices]]

W7-X

2023-04-03T04:39:00Z

Rkba39f8: /* References */

[[File:W7X.png|400px|thumb|right|W7-X model]]
Wendelstein 7-X (W7-X) is an experimental stellarator currently being built in Greifswald, Germany by the [[:Wikipedia:Max-Planck-Institut_f%C3%BCr_Plasmaphysik|Max-Planck-Institut für Plasmaphysik]] (IPP). W7-X is an [[Stellarator optimization|optimized stellarator]], i.e. the magnetic field has been tailored to meet several physical optimization criteria.

{| class="wikitable" align="center" border="1"
!''Parameter'' !!''Value''!!''Unit''
|-
|Major radius, ''R0'': || 5.5 || m
|-
|Minor radius, ''a'': || 0.53 || m
|-
|Plasma volume, ''V'': || 30 || m3
|-
|Non-planar coils: || 50 ||
|-
|Planar coils: || 20 ||
|-
|Number of ports: || 254 ||
|-
|Rotational transform, ''ι/2π'': || 5/6-5/4 ||
|-
|Magnetic field on axis, ''B0'': || <3 || T
|-
|Stored energy, ''W'': || 600 || MJ
|-
|Heating power, ''P'': || 15-30 || MW
|-
|Pulse length: || 30 || min
|-
|Machine height: || 4.5 || m
|-
|Machine diameter: || 16 || m
|-
|Machine mass: || 725 || t
|}

== Optimization criteria ==

* Feasible [[modular coil]]s
* Good, nested [[Flux surface|magnetic surfaces]]
* Good finite-[[Beta|β]] equilibria
* Good MHD [[Plasma instability|stability]]
* Small [[neoclassical transport]]
* Small [[bootstrap current]]
* Good confinement of fast particles

== See also ==

* [https://www.ipp.mpg.de/16900/w7x Wendelstein 7-X]

== References ==
* H. Wobig, ''The theoretical basis of a drift-optimized stellarator reactor'', [[doi:10.1088/0741-3335/35/8/001|Plasma Phys. Control. Fusion '''35''' (1993) 903]]
* J. Nührenberg et al., Trans. Fusion Technology '''27''' (1995) 71
* C. Nührenberg, ''Global ideal magnetohydrodynamic stability analysis for the configurational space of Wendelstein 7–X'', [[doi:10.1063/1.871924|Phys. Plasmas '''3''' (1996) 2401]]
* V. Erckmann et al, ''The W7-X project: scientific basis and technical realization'', [[doi:10.1109/FUSION.1997.685662|Fusion Engineering '''6-10''' (1997) 40]]
* M. Wanner and the W7-X Team, ''Design goals and status of the WENDELSTEIN 7-X project'', [[doi:10.1088/0741-3335/42/11/304|Plasma Phys. Control. Fusion '''42''' (2000) 1179]]
* M. Wanner et al, ''Design and construction of WENDELSTEIN 7-X'', [[doi:10.1016/S0920-3796(01)00239-3|Fusion Engineering and Design '''56-57''' (2001) 155-162]]
* M. Wanner et al, ''Status of WENDELSTEIN 7-X construction'', [[doi:10.1088/0029-5515/43/6/304|Nucl. Fusion '''43''' (2003) 416]]
* M. Wanner and the W7-X Team, ''Construction and assembly of WENDELSTEIN 7-X'', [[doi:10.1016/j.fusengdes.2006.07.013|Fusion Engineering and Design '''81''', 20-22 (2006) 2305-2313]]
* L. Wegener, ''Status of Wendelstein 7-X construction'', [[doi:10.1016/j.fusengdes.2009.01.106|Fusion Engineering and Design '''84''', 2-6 (2009) 106-112]]
* H.-S. Bosch et al, ''Construction of Wendelstein 7-X; Engineering a Steady-State Stellarator'', [[doi:10.1109/TPS.2009.2036918|IEEE Trans. Plasma Science '''38''', 3 (2010) 265]]
* H.-S. Bosch et al, ''Technical challenges in the construction of the steady-state stellarator Wendelstein 7-X'', [[doi:10.1088/0029-5515/53/12/126001|Nucl. Fusion '''53''' (2013) 126001]]
* D. Clery, ''Feature: The bizarre reactor that might save nuclear fusion'', [[doi:10.1126/science.aad4746|Science, 21 October 2015]]
* O. Neubauer et al, ''Diagnostic setup for investigation of plasma wall interactions at Wendelstein 7-X'', [[doi:10.1016/j.fusengdes.2015.06.102|Fusion Engineering and Design '''96-97''' (2015) 891-894]]
* T. Sunn Pedersen et al, ''Plans for the first plasma operation of Wendelstein 7-X'', [[doi:10.1088/0029-5515/55/12/126001|Nucl. Fusion '''55''' (2015) 126001]]
* M. Krychowiak et al, ''Overview of diagnostic performance and results for the first operation phase in Wendelstein 7-X'', [[doi:10.1063/1.4964376|Review of Scientific Instruments '''87''' (2016) 11D304]]
* R.C. Wolf et al, ''Major results from the first plasma campaign of the Wendelstein 7-X stellarator'', [[doi:10.1088/1741-4326/aa770d|Nucl. Fusion '''57''' (2017) 102020]]
* D. Hathiramani et al, ''Upgrades of edge, divertor and scrape-off layer diagnostics of W7‐X for OP1.2'', [[doi:10.1016/j.fusengdes.2018.02.013|Fusion Engineering and Design '''136A''' (2018) 304-308]]
* A. Dinklage et al, ''Magnetic configuration effects on the Wendelstein 7-X stellarator'', [[doi:10.1038/s41567-018-0141-9|Nature Phys '''14''' (2018) 855–860]]
* R.C. Wolf et al, ''Performance of Wendelstein 7-X stellarator plasmas during the first divertor operation phase'', [[doi:10.1063/1.5098761|Physics of Plasmas '''26''' (2019) 082504]]

[[Category:Toroidal confinement devices]]

Detachment control

2023-04-03T04:09:31Z

Rkba39f8: /* Advanced techniques */

== Summary and motivation ==

[[file:1_problems_schematic.png|400px|thumb|right|Trade off between problems for the divertor and problems for the core.]]

Detachment and heat exhaust control systems aim to meet the requirements of prolonging the lifetime of plasma facing components, particularly in the divertor, while avoiding excessive use of the actuators used to achieve and maintain detachment, which can have harmful side effects.
That is, there is an optimal degree of [[detachment]] or heat dissipation that protects the plasma facing components while minimizing problems in the core.

'''Possible problems associated with insufficient detachment and heat dissipation:'''
* Thermal stress on plasma facing components due to high heat flux
* Melting due to high heat flux
* Sputtering of wall material due to high electron temperature <math>T_e</math> next to wall

'''Possible problems associated with excessive detachment / impurity content:'''
* Reduced performance due to suboptimal scenario properties / excess density
* Reduced [[energy confinement time]] due to excess core radiation
* Fuel dilution due to extrinsic impurity seeding used to promote detachment
* Excitation of various MHD instabilities, reducing fusion performance further
* Increased [[effective charge state|effective charge state <math>Z_{eff}</math>]] and resistivity and therefore more difficult current drive and potentially shorter pulse length
* H-L back transitions due to higher H-mode power threshold at high density and/or power loss via core radiation
* [[Greenwald limit|Density limit]] [[disruption|disruptions]]
* [[MARFE]]s
* Radiative collapse [[disruption|disruptions]]

== Basic technique ==
The problem with an attached plasma with low radiation is that heat and particle exhaust out of the core plasma becomes concentrated in a narrow part of the chamber wall, usually in the divertor.
In a tokamak, this takes the form of a narrow annulus next to the [[magnetic strike point]].
To avoid this concentration and distribute the heat exhaust load over a larger area, the flow of energy and particles through the [[Scrape-Off Layer]] (SOL) is interrupted by activating dissipation processes like radiation and charge exchange.
Low <math>Z</math> impurities like neon, nitrogen, and carbon are efficient radiators at low <math>T_e</math> but less so at high <math>T_e</math>, which reduces their ability to cool the core plasma.<ref name="kallenbach_2013_ppcf">[[doi:10.1088/0741-3335/55/12/124041|A. Kallenbach, et al., Plasma Phys. Control. Fusion '''55''' (2013) 124041]]</ref>
To ensure that the SOL is cold enough for low Z impurities to radiate, edge density can be increased by puffing in additional hydrogenic (H,D, or T) gas.
With an appropriate combination of density and impurity content, [[detachment]] can begin.

The plasma state is measured with some set of sensors connected to the Plasma Control System (PCS) to transmit data in real-time.
For example, Langmuir probes can be used to estimate [[detachment|degree of detachment]],<ref name=eldon_2022_ppcf>[[doi:10.1088/1361-6587/ac6ff9|D. Eldon, et al., Plasma Phys. Control. Fusion '''64''' (2022) 075002]]</ref> triple-tipped Langmuir probes<ref name=eldon_2021_nme>[[doi:10.1016/j.nme.2021.100963|D. Eldon, et al., Nucl. Mater. Energy '''27''' (2021) 100963]]</ref> or divertor Thomson scattering<ref name=eldon_2017_nf>[[doi:doi.org/10.1088/1741-4326/aa6b16|D. Eldon, et al., Nucl. Fusion '''57''' (2017) 066039]]</ref> can be used to measure <math>T_e</math>, or bolometers can measure radiated power.<ref name=kallenbach_2012_nf>[[doi:10.1088/0029-5515/52/12/122003|A. Kallenbach, et al., Nucl. Fusion '''52''' (2012) 122003]]</ref><ref name="eldon_2019_nme">[[doi:10.1016/j.nme.2019.01.010|D. Eldon, et al., Nucl. Mater. Energy '''18''' (2019) 285]]</ref>
Data from the chosen sensor(s) is formulated into one or more control variables.
A target or reference value is set for each control variable in the PCS, and a control policy such as [[:Wikipedia:PID_controller|PID]] compares the measurement to the reference to decide on a command to one more actuators.

Possible actuators are gas valves for adding fuel or impurities, impurity powder droppers, or pellet launchers. Tests so far have used gas valves.

== Advanced techniques ==

Detachment control is fundamentally a tool for integrating core and edge scenarios.
Thus, it is natural to try to combine basic detachment control with other requirements of an integrated scenario, such as ELM removal and wall conditioning.

At ASDEX-Upgrade, a detachment control system to also control impurity-induced ELM suppression.<ref name="bernert_2021_nf">[[doi:10.1088/1741-4326/abc936|M. Bernert, et al., Nucl. Fusion '''61''' (2021) 024001]]</ref> In this case, the control variable is the the height of a local radiation centroid above (in a lower null plasma) the magnetic X-point.
It was found that this is first of all a viable control variable that is useful even when measurements at the divertor plate are saturated at low levels in deep detachment, and furthermore that positioning the radiator a specific distance above the X-point results in ELM suppression.
Somewhat related work at DIII-D has achieved ELM mitigation by impurity seeding, but without the sophisticated X-point radiator height controller.<ref name=eldon_2023_nme>[[doi:10.1016/j.nme.2022.101332|D. Eldon, et al., Nucl. Mater. Energy '''34''' (2023) 101332]]</ref>

Another promising discovery is that injection of low-Z powdered materials such as lithium, boron, and boron nitride powders are not only useful for wall conditioning but also can result in heat flux mitigation, detachment, and ELM removal.<ref name=gilson_2021_nme>[[doi:10.1016/j.nme.2021.101043|E.P. Gilson, et al., Nucl. Mater. Energy '''28''' (2021) 101043]]</ref><ref name=effenberg_2022_nf>[[doi:10.1088/1741-4326/ac899d|F. Effenberg, et al., Nucl. Fusion '''62''' (2022) 106015]]</ref>

== History ==

Radiated power control is the most commonly deployed control system related to dissipation and heat exhaust handling. These systems use foil or UV photodiode bolometers to measure radiated power. The first prototype was demonstrated and published in 1995 at ASDEX Upgrade,<ref>[[doi:10.1088/0029-5515/35/10/I07|A. Kallenbach, et al., Nucl. Fusion '''35''' (1995) 1231]]</ref>
with a demonstration at DIII-D reported in 1997.<ref>[[doi:10.1016/S0022-3115(97)80110-9|G.L. Jackson, et al., J. Nucl. Mater. '''241''' (1997) 618]]</ref>
Radiated power controllers have been demonstrated on
CMOD<ref>[[doi:10.1063/1.873447|J.A. Goetz, et al., Phys. Plasmas '''6''' (1999) 1899]]</ref>
JT-60U<ref>[[doi:10.1088/0029-5515/49/11/115010|N. Asakura, et al., Nucl. Fusion '''49''' (2009) 115010]]</ref>
JET,<ref>[[doi:10.1088/0029-5515/51/8/082001|G.P. Maddison, et al., Nucl. Fusion '''51''' (2011) 082001]]</ref>
and EAST,<ref>[[doi:10.1088/1741-4326/aab506|K. Wu, et al., Nucl. Fusion '''58''' (2018) 056019]]</ref>
and progress has continued on ASDEX Upgrade<ref name="kallenbach_2012_nf" /><ref name="kallenbach_2013_ppcf" /><ref name="kallenbach_2015_nf">[[doi:10.1088/0029-5515/55/5/053026|A. Kallenbach, et al., Nucl. Fusion '''55''' (2015) 053026]]</ref><ref name="kallenbach_2016_ppcf">[[doi:10.1088/0741-3335/58/4/045013|A. Kallenbach, Plasma Phys. Control. Fusion '''58''' (2016) 045013]]</ref> and DIII-D<ref name="eldon_2019_nme" />.

Divertor power loads assessed with shunt resistors have been used as a control variable at ASDEX Upgrade and reported in 2010.<ref>[[doi:10.1088/0741-3335/52/5/055002|A. Kallenbach, et al., Plasma Phys. Control. Fusion '''52''' (2010) 055002]]</ref>

Electron temperature <math>T_e</math> measured with divertor Thomson scattering was used as a control variable at DIII-D,<ref>[[doi:10.1016/j.jnucmat.2014.11.099|E. Kolemen, et al., J. Nucl. Mater. '''463''' (2015) 1186]]</ref><ref name="eldon_2017_nf" />
and <math>T_e</math> from triple-tipped Langmuir probes was used for detachment control at EAST.<ref name="eldon_2021_nme" />

Heat flux from surface thermocouples was used for feedback control at Alcator CMOD,<ref>[[doi:10.1088/1741-4326/aa7923|D. Brunner, et al., Nucl. Fusion '''57''' (2017) 086030]]</ref>
heat flux as calculated from Langmuir probes was used at COMPASS,<ref>[[doi:10.1088/1361-6587/abf03e|I. Khodunov, et al., Plasma Phys. Control. Fusion '''63''' (2021) 065012]]</ref>
and a model for heatflux was used for control at DIII-D.<ref>[[doi:10.1016/j.fusengdes.2021.112560|H. Anand, et al., Fus. Eng. Design '''171''' (2021) 112560]]</ref>

Attachment fraction, based on ion saturation current <math>I_{sat}</math> measurements from Langmuir probes, has been used as a control variable at
JET,<ref>[[doi:10.1088/1361-6587/aa5951|C. Guillemaut, et al., Plasma Phys. Control. Fusion '''59''' (2017) 045001]]</ref>
EAST,<ref>[[doi:10.1016/j.fusengdes.2020.111557|Q.P. Yuan, Fus. Eng. Design '''154''' (2020) 111557]]</ref>
DIII-D,<ref name="eldon_2021_nme" />
and KSTAR.<ref name="eldon_2022_ppcf" />
While many other control systems have developed semi-independently, the JET design was the direct basis for the successors at EAST and DIII-D. The KSTAR implementation was also a result of this lineage, but with modifications resulting from lessons learned while operating with the JET design.

The position of the detachment front along the divertor leg (between the X-point and the divertor target plate) has been controlled on TCV using the MANTIS camera to view C-III emission (peaks at about 8-10 eV).<ref>[[doi:10.1038/s41467-021-21268-3|T. Ravensbergen, et al., Nature Communications '''12''' (2021) 1105]]</ref>

The position of a radiation centroid relative to the magnetic X-point has been controlled at ASDEX Upgrade.<ref name="bernert_2021_nf" />

In 2020, ITPA DSOL 43 was formed to coordinate global efforts to develop detachment control systems.

== References ==

Detachment control

2023-04-03T04:02:12Z

Rkba39f8: /* References */

== Summary and motivation ==

[[file:1_problems_schematic.png|400px|thumb|right|Trade off between problems for the divertor and problems for the core.]]

Detachment and heat exhaust control systems aim to meet the requirements of prolonging the lifetime of plasma facing components, particularly in the divertor, while avoiding excessive use of the actuators used to achieve and maintain detachment, which can have harmful side effects.
That is, there is an optimal degree of [[detachment]] or heat dissipation that protects the plasma facing components while minimizing problems in the core.

'''Possible problems associated with insufficient detachment and heat dissipation:'''
* Thermal stress on plasma facing components due to high heat flux
* Melting due to high heat flux
* Sputtering of wall material due to high electron temperature <math>T_e</math> next to wall

'''Possible problems associated with excessive detachment / impurity content:'''
* Reduced performance due to suboptimal scenario properties / excess density
* Reduced [[energy confinement time]] due to excess core radiation
* Fuel dilution due to extrinsic impurity seeding used to promote detachment
* Excitation of various MHD instabilities, reducing fusion performance further
* Increased [[effective charge state|effective charge state <math>Z_{eff}</math>]] and resistivity and therefore more difficult current drive and potentially shorter pulse length
* H-L back transitions due to higher H-mode power threshold at high density and/or power loss via core radiation
* [[Greenwald limit|Density limit]] [[disruption|disruptions]]
* [[MARFE]]s
* Radiative collapse [[disruption|disruptions]]

== Basic technique ==
The problem with an attached plasma with low radiation is that heat and particle exhaust out of the core plasma becomes concentrated in a narrow part of the chamber wall, usually in the divertor.
In a tokamak, this takes the form of a narrow annulus next to the [[magnetic strike point]].
To avoid this concentration and distribute the heat exhaust load over a larger area, the flow of energy and particles through the [[Scrape-Off Layer]] (SOL) is interrupted by activating dissipation processes like radiation and charge exchange.
Low <math>Z</math> impurities like neon, nitrogen, and carbon are efficient radiators at low <math>T_e</math> but less so at high <math>T_e</math>, which reduces their ability to cool the core plasma.<ref name="kallenbach_2013_ppcf">[[doi:10.1088/0741-3335/55/12/124041|A. Kallenbach, et al., Plasma Phys. Control. Fusion '''55''' (2013) 124041]]</ref>
To ensure that the SOL is cold enough for low Z impurities to radiate, edge density can be increased by puffing in additional hydrogenic (H,D, or T) gas.
With an appropriate combination of density and impurity content, [[detachment]] can begin.

The plasma state is measured with some set of sensors connected to the Plasma Control System (PCS) to transmit data in real-time.
For example, Langmuir probes can be used to estimate [[detachment|degree of detachment]],<ref name=eldon_2022_ppcf>[[doi:10.1088/1361-6587/ac6ff9|D. Eldon, et al., Plasma Phys. Control. Fusion '''64''' (2022) 075002]]</ref> triple-tipped Langmuir probes<ref name=eldon_2021_nme>[[doi:10.1016/j.nme.2021.100963|D. Eldon, et al., Nucl. Mater. Energy '''27''' (2021) 100963]]</ref> or divertor Thomson scattering<ref name=eldon_2017_nf>[[doi:doi.org/10.1088/1741-4326/aa6b16|D. Eldon, et al., Nucl. Fusion '''57''' (2017) 066039]]</ref> can be used to measure <math>T_e</math>, or bolometers can measure radiated power.<ref name=kallenbach_2012_nf>[[doi:10.1088/0029-5515/52/12/122003|A. Kallenbach, et al., Nucl. Fusion '''52''' (2012) 122003]]</ref><ref name="eldon_2019_nme">[[doi:10.1016/j.nme.2019.01.010|D. Eldon, et al., Nucl. Mater. Energy '''18''' (2019) 285]]</ref>
Data from the chosen sensor(s) is formulated into one or more control variables.
A target or reference value is set for each control variable in the PCS, and a control policy such as [[:Wikipedia:PID_controller|PID]] compares the measurement to the reference to decide on a command to one more actuators.

Possible actuators are gas valves for adding fuel or impurities, impurity powder droppers, or pellet launchers. Tests so far have used gas valves.

== Advanced techniques ==

Detachment control is fundamentally a tool for integrating core and edge scenarios.
Thus, it is natural to try to combine basic detachment control with other requirements of an integrated scenario, such as ELM removal and wall conditioning.

At ASDEX-Upgrade, a detachment control system to also control impurity-induced ELM suppression.<ref name="bernert_2021_nf">[[doi:10.1088/1741-4326/abc936|M. Bernert, et al., Nucl. Fusion '''61''' (2021) 024001]]</ref> In this case, the control variable is the the height of a local radiation centroid above (in a lower null plasma) the magnetic X-point.
It was found that this is first of all a viable control variable that is useful even when measurements at the divertor plate are saturated at low levels in deep detachment, and furthermore that positioning the radiator a specific distance above the X-point results in ELM suppression.
Somewhat related work at DIII-D has achieved ELM mitigation by impurity seeding, but without the sophisticated X-point radiator height controller.<ref name=eldon_2023_nme>[[doi:10.1016/j.nme.2022.101332|D. Eldon, et al., Nucl. Mater. Energy '''34''' (2023) 101332]]</ref>

Another promising discovery is that dropping boron nitride powder is not only useful for boron wall conditioning, but also can result in ELM removal.<ref name=gilson_2021_nme>[[doi:10.1016/j.nme.2021.101043|E.P. Gilson, et al., Nucl. Mater. Energy '''28''' (2021) 101043]]</ref>

== History ==

Radiated power control is the most commonly deployed control system related to dissipation and heat exhaust handling. These systems use foil or UV photodiode bolometers to measure radiated power. The first prototype was demonstrated and published in 1995 at ASDEX Upgrade,<ref>[[doi:10.1088/0029-5515/35/10/I07|A. Kallenbach, et al., Nucl. Fusion '''35''' (1995) 1231]]</ref>
with a demonstration at DIII-D reported in 1997.<ref>[[doi:10.1016/S0022-3115(97)80110-9|G.L. Jackson, et al., J. Nucl. Mater. '''241''' (1997) 618]]</ref>
Radiated power controllers have been demonstrated on
CMOD<ref>[[doi:10.1063/1.873447|J.A. Goetz, et al., Phys. Plasmas '''6''' (1999) 1899]]</ref>
JT-60U<ref>[[doi:10.1088/0029-5515/49/11/115010|N. Asakura, et al., Nucl. Fusion '''49''' (2009) 115010]]</ref>
JET,<ref>[[doi:10.1088/0029-5515/51/8/082001|G.P. Maddison, et al., Nucl. Fusion '''51''' (2011) 082001]]</ref>
and EAST,<ref>[[doi:10.1088/1741-4326/aab506|K. Wu, et al., Nucl. Fusion '''58''' (2018) 056019]]</ref>
and progress has continued on ASDEX Upgrade<ref name="kallenbach_2012_nf" /><ref name="kallenbach_2013_ppcf" /><ref name="kallenbach_2015_nf">[[doi:10.1088/0029-5515/55/5/053026|A. Kallenbach, et al., Nucl. Fusion '''55''' (2015) 053026]]</ref><ref name="kallenbach_2016_ppcf">[[doi:10.1088/0741-3335/58/4/045013|A. Kallenbach, Plasma Phys. Control. Fusion '''58''' (2016) 045013]]</ref> and DIII-D<ref name="eldon_2019_nme" />.

Divertor power loads assessed with shunt resistors have been used as a control variable at ASDEX Upgrade and reported in 2010.<ref>[[doi:10.1088/0741-3335/52/5/055002|A. Kallenbach, et al., Plasma Phys. Control. Fusion '''52''' (2010) 055002]]</ref>

Electron temperature <math>T_e</math> measured with divertor Thomson scattering was used as a control variable at DIII-D,<ref>[[doi:10.1016/j.jnucmat.2014.11.099|E. Kolemen, et al., J. Nucl. Mater. '''463''' (2015) 1186]]</ref><ref name="eldon_2017_nf" />
and <math>T_e</math> from triple-tipped Langmuir probes was used for detachment control at EAST.<ref name="eldon_2021_nme" />

Heat flux from surface thermocouples was used for feedback control at Alcator CMOD,<ref>[[doi:10.1088/1741-4326/aa7923|D. Brunner, et al., Nucl. Fusion '''57''' (2017) 086030]]</ref>
heat flux as calculated from Langmuir probes was used at COMPASS,<ref>[[doi:10.1088/1361-6587/abf03e|I. Khodunov, et al., Plasma Phys. Control. Fusion '''63''' (2021) 065012]]</ref>
and a model for heatflux was used for control at DIII-D.<ref>[[doi:10.1016/j.fusengdes.2021.112560|H. Anand, et al., Fus. Eng. Design '''171''' (2021) 112560]]</ref>

Attachment fraction, based on ion saturation current <math>I_{sat}</math> measurements from Langmuir probes, has been used as a control variable at
JET,<ref>[[doi:10.1088/1361-6587/aa5951|C. Guillemaut, et al., Plasma Phys. Control. Fusion '''59''' (2017) 045001]]</ref>
EAST,<ref>[[doi:10.1016/j.fusengdes.2020.111557|Q.P. Yuan, Fus. Eng. Design '''154''' (2020) 111557]]</ref>
DIII-D,<ref name="eldon_2021_nme" />
and KSTAR.<ref name="eldon_2022_ppcf" />
While many other control systems have developed semi-independently, the JET design was the direct basis for the successors at EAST and DIII-D. The KSTAR implementation was also a result of this lineage, but with modifications resulting from lessons learned while operating with the JET design.

The position of the detachment front along the divertor leg (between the X-point and the divertor target plate) has been controlled on TCV using the MANTIS camera to view C-III emission (peaks at about 8-10 eV).<ref>[[doi:10.1038/s41467-021-21268-3|T. Ravensbergen, et al., Nature Communications '''12''' (2021) 1105]]</ref>

The position of a radiation centroid relative to the magnetic X-point has been controlled at ASDEX Upgrade.<ref name="bernert_2021_nf" />

In 2020, ITPA DSOL 43 was formed to coordinate global efforts to develop detachment control systems.

== References ==