Magnetic island: Difference between revisions
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A magnetic island is a closed magnetic flux tube (cf. [[Flux surface]]), bounded by a [[Separatrix|separatrix]], isolating it from the rest of space. | 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. | 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 [[ | 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> | <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. | Subsidiary islands can appear within an island. | ||
== Island birth == | == Island birth == | ||
The rupture of the | 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>[ | <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 == | == Island rotation == | ||
| Line 17: | Line 25: | ||
The detection of such modes is possible by measuring perturbations of the magnetic field, or the electron density, temperature, or pressure. | 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. | If the ambient magnetic field (produced by external coils) has an appropriate structure, the island can also lock onto that structure. | ||
<ref> | <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 == | == 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. | 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> | <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, | However, it is possible to qualify this statement somewhat by taking into account the ratio between parallel and perpendicular transport within an island. | ||
<ref> | <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> | <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 == | == See also == | ||
* [[MHD equilibrium]] | * [[MHD equilibrium]] | ||
* [[Island Divertor]] | |||
== References == | == References == | ||
<references /> | <references /> | ||
Latest revision as of 08:19, 6 April 2023
A magnetic island is a closed magnetic flux tube (cf. Flux surface), bounded by a 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 surfaces, while each flux surface is characterised by a certain value of the rotational transform or safety factor q. Magnetic islands can appear at flux surfaces with a rational value of the safety factor q = m/n. [1] 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. [2] Stellarators 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 Tearing Mode (NTM) theory. This theory has been developed to a considerable level of sophistication, although discrepancies with experimental observations remain. [3]
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. [4] Locked islands often lead to a disruption (complete loss of confinement) in 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. [5] However, it is possible to qualify this statement somewhat by taking into account the ratio between parallel and perpendicular transport within an island. [6]
The interaction of neighbouring island chains causes the magnetic field to become stochastic (according to the Chirikov criterion [7]), resulting in enhanced (anomalous) radial transport. [8]
Island control
Island control is possible by tailoring the q-profile, external magnetic fields, [9] and the pressure profile, or by spinning up the plasma. [10] Pressure effects can lead to 'island healing'. [11] Active control of islands by external means - in particular, Electron Cyclotron Heating and Current Drive - is also possible. [12] [13] [14]
See also
References
- ↑ 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, Ann. Phys. Fr. 28 (2003) 1
- ↑ F.L. Waelbroeck, Theory and observations of magnetic islands, Nucl. Fusion 49 (2009) 104025
- ↑ H. Lütjens and J.-F. Luciani, Saturation levels of neoclassical tearing modes in International Thermonuclear Experimental Reactor plasmas, Phys. Plasmas 12 (2005) 080703
- ↑ F.L. Waelbroeck and R. Fitzpatrick, Rotation and Locking of Magnetic Islands, Phys. Rev. Lett. 78 (1997) 1703–1706
- ↑ ITER Physics Expert Group on Confinement and Transport et al, Chapter 2: Plasma confinement and transport, Nucl. Fusion 39 (1999) 2175-2249
- ↑ 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, Nucl. Fusion 33 (1993) 1119
- ↑ B.V. Chirikov, A universal instability of many-dimensional oscillator systems, Phys. Rep. 52, Issue 5 (1979) 263
- ↑ C.W. Horton, Y.H. Ichikawa, Chaos and structures in nonlinear plasmas, World Scientific, 1996 ISBN 9789810226367
- ↑ S.R. Hudson et al, Free-boundary full-pressure island healing in stellarator equilibria: coil-healing, Plasma Phys. Control. Fusion 44 (2002) 1377
- ↑ H. Zohm et al,MHD limits to tokamak operation and their control, Plasma Phys. Control. Fusion 45 (2003) A163
- ↑ R. Kanno et al, Formation and healing of n = 1 magnetic islands in LHD equilibrium, Nucl. Fusion 45 (2005) 588
- ↑ Seek and Destroy System for magnetic island control
- ↑ A. Isayama et al, Neoclassical tearing mode control using electron cyclotron current drive and magnetic island evolution in JT-60U, Nucl. Fusion 49 (2009) 055006
- ↑ B. Ayten et al., Modelling of tearing mode suppression experiments in TEXTOR based on the generalized Rutherford equation, Nucl. Fusion 51 (2011) 043007