LNF:Plasma Physics: Difference between revisions

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Impurity accumulation is recognized as a potential showstopper for the development of fusion energy. Particle and impurity transport are usually described empirically in terms of diffusive and convective terms, driven by neoclassical and turbulence mechanisms. In the framework of neoclassical mechanisms in tokamaks, the main ion density gradient (inwards) and the ion temperature gradient (outwards / temperature screening) are responsible for opposite convective fluxes. In non-axisymmetric devices the sign of the radial electric field plays a dominant role over the other thermodynamical forces, associated with temperature and density gradients in the convection of impurities.  
Impurity accumulation is recognized as a potential showstopper for the development of fusion energy. Particle and impurity transport are usually described empirically in terms of diffusive and convective terms, driven by neoclassical and turbulence mechanisms. In the framework of neoclassical mechanisms in tokamaks, the main ion density gradient (inwards) and the ion temperature gradient (outwards / temperature screening) are responsible for opposite convective fluxes. In non-axisymmetric devices the sign of the radial electric field plays a dominant role over the other thermodynamical forces, associated with temperature and density gradients in the convection of impurities.  


A key point in stellarator/heliotron plasmas is the empirical observation of increasing impurity confinement at high densities.<ref>R. Burhenn et al., NF 49 (2009) 065005</ref>  
A key point in stellarator/heliotron plasmas is the empirical observation of increasing impurity confinement at high densities.<ref>R. Burhenn et al., [[doi:10.1088/0029-5515/49/6/065005|Nucl. Fusion '''49''' (2009) 065005]]</ref>  
Nevertheless, effective impurity control is possible in some regimes like the HDH-mode in W7AS<ref>K. McCormick et al Phys. Rev. Lett. 89 (2002) 015001</ref> and impurity hole in LHD.<ref>T. Ido et al., PPCF 52 (2010) 124025</ref>  
Nevertheless, effective impurity control is possible in some regimes like the HDH-mode in W7AS<ref>K. McCormick et al, [[doi:10.1103/PhysRevLett.89.015001|Phys. Rev. Lett. '''89''' (2002) 015001]]</ref> and impurity hole in LHD.<ref>T. Ido et al., [[doi:10.1088/0741-3335/52/12/124025|Plasma Phys. Control. Fusion '''52''' (2010) 124025]]</ref>  


The measurement and modelling of impurity density asymmetries are considerably simpler than those of radial impurity transport and yet can provide an indirect validation of the model prediction on radial transport. The localization of impurities in a flux surface depends on the location of magnetic and electrostatic wells as well as on ion-impurity friction.<ref>J. M. García-Regaña et al., PPCF 55 (2013) 074008</ref>  
The measurement and modelling of impurity density asymmetries are considerably simpler than those of radial impurity transport and yet can provide an indirect validation of the model prediction on radial transport. The localization of impurities in a flux surface depends on the location of magnetic and electrostatic wells as well as on ion-impurity friction.<ref>J. M. García-Regaña et al., [[doi:10.1088/0741-3335/55/7/074008|Plasma Phys. Control. Fusion '''55''' (2013) 074008]]</ref>  
Centrifugal effects become important in strongly rotating plasmas.<ref>M. L. Reinke et al., 2012 Plasma Phys. Control. Fusion 54 045004</ref>  
Centrifugal effects become important in strongly rotating plasmas.<ref>M. L. Reinke et al., [[doi:10.1088/0741-3335/54/4/045004|Plasma Phys. Control. Fusion '''54''' (2012) 045004]]</ref>  
Recently, the impact of potential variation on neoclassical impurity transport has been addressed in the Large Helical Device (LHD) stellarator.  
Recently, the impact of potential variation on neoclassical impurity transport has been addressed in the Large Helical Device (LHD) stellarator.  
The first direct observations of plasma potential asymmetries on a flux surface, consistent with MC calculations, have been reported in the TJ-II stellarator.<ref>M.A. Pedrosa, A. Alonso, J.M. García-Regaña et al., NF 55 (2015) 052001</ref>
The first direct observations of plasma potential asymmetries on a flux surface, consistent with MC calculations, have been reported in the TJ-II stellarator.<ref>M.A. Pedrosa, A. Alonso, J.M. García-Regaña et al., [[doi:10.1088/0029-5515/55/5/052001|Nucl. Fusion '''55''' (2015) 052001]]</ref>


Significant progress has been reported regarding the physics understanding of empirical actuators, like ECRH heating, to avoid core impurity accumulation.  
Significant progress has been reported regarding the physics understanding of empirical actuators, like ECRH heating, to avoid core impurity accumulation.  
A reduction of the background density gradient leading to a reduction of the inward (neoclassical) convection of impurities as well as the amplification of core temperature screening can prevent core impurity accumulation has been reported in tokamaks.  
A reduction of the background density gradient leading to a reduction of the inward (neoclassical) convection of impurities as well as the amplification of core temperature screening can prevent core impurity accumulation has been reported in tokamaks.  
Furthermore, ECRH induced turbulent transport and development of plasma potential flux surface asymmetries<ref>L. C. Ingesson et al., Plasma Phys. Control. Fusion 42 (2000) 161   </ref> can play a role on impurity transport.  
Furthermore, ECRH induced turbulent transport and development of plasma potential flux surface asymmetries<ref>L. C. Ingesson et al., [[doi:10.1088/0741-3335/42/2/308|Plasma Phys. Control. Fusion '''42''' (2000) 161]]</ref> can play a role on impurity transport.  
Clarifying the role of ECRH on turbulent transport, plasma potential asymmetries and neoclassical effects remains as an open question.
Clarifying the role of ECRH on turbulent transport, plasma potential asymmetries and neoclassical effects remains as an open question.


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* Development of experimental schemes to assess the effect of edge island formation on the plasma conditions required for H-mode access and sustainment in view of W7-X: role of electromagnetic effects.
* Development of experimental schemes to assess the effect of edge island formation on the plasma conditions required for H-mode access and sustainment in view of W7-X: role of electromagnetic effects.
* Understanding the long-wavelength (neoclassical) radial electric field of stellerators in H-mode. Local neoclassical calculations usually underestimate the value and shear of the mean electric field in the H-mode of stellarators. One possible explanation that will be explored is that higher order corrections of the theory have to be included. This will be done with the code FORTEC-3D, which includes non-local effects in ion transport.
* Understanding the long-wavelength (neoclassical) radial electric field of stellerators in H-mode. Local neoclassical calculations usually underestimate the value and shear of the mean electric field in the H-mode of stellarators. One possible explanation that will be explored is that higher order corrections of the theory have to be included. This will be done with the code FORTEC-3D, which includes non-local effects in ion transport.
* It has been proven<ref>F. Parra, M. Barnes, I. Calvo, P. Catto, PoP 19 (2012) 056116</ref> that the calculation of radial transport of toroidal angular momentum in tokamaks, and equivalently the rotation profile and long-wavelength radial electric field, requires to deal with microturbulence. In particular, high-order gyrokinetic equations are needed. During the last few years, we have worked out the electrostatic gyrokinetic equations to the required order in arbitrary magnetic geometry and applied them to the tokamak. Concretely, we have given the equations that allow to compute the long-wavelength pieces entering the formula that determines the rotation profile.<ref>I. Calvo and F. Parra, PPCF 54 (2012) 115007</ref> However, the equations for the short-wavelength pieces are still lacking. We will compute them, and give all the explicit expressions that have to be implemented in a code aiming to determine tokamak intrinsic rotation. The expressions for flux-tube formulations of gyrokinetics will also be provided. A mid-term objective involves the actual code implementation and testing of the theory.
* It has been proven<ref>F. Parra, M. Barnes, I. Calvo, P. Catto, [[doi:10.1063/1.3699186|Phys. Plasmas '''19''' (2012) 056116]]</ref> that the calculation of radial transport of toroidal angular momentum in tokamaks, and equivalently the rotation profile and long-wavelength radial electric field, requires to deal with microturbulence. In particular, high-order gyrokinetic equations are needed. During the last few years, we have worked out the electrostatic gyrokinetic equations to the required order in arbitrary magnetic geometry and applied them to the tokamak. Concretely, we have given the equations that allow to compute the long-wavelength pieces entering the formula that determines the rotation profile.<ref>I. Calvo and F. Parra, [[doi:10.1088/0741-3335/54/11/115007|Plasma Phys. Control. Fusion '''54''' (2012) 115007]]</ref> However, the equations for the short-wavelength pieces are still lacking. We will compute them, and give all the explicit expressions that have to be implemented in a code aiming to determine tokamak intrinsic rotation. The expressions for flux-tube formulations of gyrokinetics will also be provided. A mid-term objective involves the actual code implementation and testing of the theory.


==== Isotope effect ====
==== Isotope effect ====
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Furthermore, considering the present ITER power capabilities, a reduction of the L-H power threshold (<math>P_{L-H}</math>) with ion mass (D vs. H) would have great impact on ITER plasma operation scenarios.  
Furthermore, considering the present ITER power capabilities, a reduction of the L-H power threshold (<math>P_{L-H}</math>) with ion mass (D vs. H) would have great impact on ITER plasma operation scenarios.  
The <math>P_{L-H}</math> power threshold deduced from empirical scaling laws is sufficient to define the minimum power required for ITER operation.  
The <math>P_{L-H}</math> power threshold deduced from empirical scaling laws is sufficient to define the minimum power required for ITER operation.  
Experimental studies have shown a reduction of the L-H power threshold by about 50% when using Deuterium and He instead of Hydrogen.<ref>F. Ryter  et al., 2013 Nuclear Fusion 53 (2012) 113003 </ref>  
Experimental studies have shown a reduction of the L-H power threshold by about 50% when using Deuterium and He instead of Hydrogen.<ref>F. Ryter  et al., [[doi:10.1088/0029-5515/53/11/113003|Nuclear Fusion '''53''' (2013) 113003]]</ref>  
Based on present ITPA scaling laws, H-mode operation is expected to be marginally feasible in H but likely in He.<ref>A. Sips et al., 25th IAEA Int. Conf. on Fusion Energy St Petersburg 2014 / EX/9-1. </ref>  
Based on present ITPA scaling laws, H-mode operation is expected to be marginally feasible in H but likely in He.<ref>A. Sips et al., 25th IAEA Int. Conf. on Fusion Energy St Petersburg 2014, EX/9-1</ref>  
Thus, better understanding of the dependence of the L-H power threshold on isotope mass is urgently needed to improve our confidence in ITER scenarios.
Thus, better understanding of the dependence of the L-H power threshold on isotope mass is urgently needed to improve our confidence in ITER scenarios.


Studies in the TEXTOR tokamak<ref>Y. Xu, C. Hidalgo, I. Shesterikov et al., PRL-2013</ref> and the TJ-II stellarator<ref>B. Liu et al., Nuclear Fusion 2015 </ref> have reported the properties of local turbulence and Long-Range-Correlations (LRC) in Hydrogen and Deuterium plasmas concluding that there is a systematic increase in the LRC amplitude during the transition from H to D dominated plasmas in the TEXTOR tokamak but not in the TJ-II stellarator.  
Studies in the TEXTOR tokamak<ref>Y. Xu, C. Hidalgo, I. Shesterikov et al., [[doi:10.1103/PhysRevLett.110.265005|Phys. Rev. Lett. '''110''' (2013) 265005]]</ref> and the TJ-II stellarator<ref>B. Liu et al., [[doi:10.1088/0029-5515/55/11/112002|Nucl. Fusion 55 (2015) 112002]]</ref> have reported the properties of local turbulence and Long-Range-Correlations (LRC) in Hydrogen and Deuterium plasmas concluding that there is a systematic increase in the LRC amplitude during the transition from H to D dominated plasmas in the TEXTOR tokamak but not in the TJ-II stellarator.  
These results suggest the role of the ion mass and viscosity on the amplitude of zonal flows and thus provide the first direct experimental evidence of the importance of multi-scale physics for unravelling the physics of the isotope effect on transport and confinement in fusion plasmas.
These results suggest the role of the ion mass and viscosity on the amplitude of zonal flows and thus provide the first direct experimental evidence of the importance of multi-scale physics for unravelling the physics of the isotope effect on transport and confinement in fusion plasmas.


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''Challenges and opportunities''
''Challenges and opportunities''


Stellarator inter-machine studies<ref>A. Dinklage et al., Nucl. Fusion 53 (2013) 063022</ref> have shown that ion energy transport significantly affects energy confinement at medium-to-high densities (<math>n_e > 4 x 10^{19} m^{-3}</math>).  
Stellarator inter-machine studies<ref>A. Dinklage et al., [[doi:10.1088/0029-5515/53/6/063022|Nucl. Fusion '''53''' (2013) 063022]]</ref> have shown that ion energy transport significantly affects energy confinement at medium-to-high densities (<math>n_e > 4 x 10^{19} m^{-3}</math>).  
Since neoclassical transport in three-dimensional devices shows unfavourable temperature scaling, it becomes more important as the temperature is increased and the validation of local neoclassical theory at reactor-relevant conditions is needed. Extensions of the standard neoclassical theory are necessary for a better assessment of collisional transport in a stellarator reactor concept, such as non-local and non flux-surface based calculations.  
Since neoclassical transport in three-dimensional devices shows unfavourable temperature scaling, it becomes more important as the temperature is increased and the validation of local neoclassical theory at reactor-relevant conditions is needed. Extensions of the standard neoclassical theory are necessary for a better assessment of collisional transport in a stellarator reactor concept, such as non-local and non flux-surface based calculations.  


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* For high ion temperatures and steep plasma gradients, non-local effects such as (i) finite radial width of trapped particle orbits and direct particle loss near the last closed ux surface and (ii) the validity of the monoenergetic approximation, used in standard local neoclassics, needs to be understood. FORTEC 3D and DKES simulations and comparison of experiment with local and non-local neoclassical theories.
* For high ion temperatures and steep plasma gradients, non-local effects such as (i) finite radial width of trapped particle orbits and direct particle loss near the last closed ux surface and (ii) the validity of the monoenergetic approximation, used in standard local neoclassics, needs to be understood. FORTEC 3D and DKES simulations and comparison of experiment with local and non-local neoclassical theories.
* The coupling of neoclassical energy and particle transport may lead to hollow density profiles in high temperature (ion and electron) plasmas, which is highly relevant for the discharge scenario development for large stellarator devices and reactor operation scenarios. The issue of particle transport therefore requires further documentation and deeper understanding in view of density control or impurity transport in three-dimensional devices. Experimental and theoretical studies of central fuelling (e.g. by pellets in operation in TJ-II) are under development supporting W7-X.
* The coupling of neoclassical energy and particle transport may lead to hollow density profiles in high temperature (ion and electron) plasmas, which is highly relevant for the discharge scenario development for large stellarator devices and reactor operation scenarios. The issue of particle transport therefore requires further documentation and deeper understanding in view of density control or impurity transport in three-dimensional devices. Experimental and theoretical studies of central fuelling (e.g. by pellets in operation in TJ-II) are under development supporting W7-X.
* The singular alteration of transport at magnetically resonant plasma regions. TJ-II offers the only experimental benchmark in Europe to evaluate their impact in deviating neoclassical predictions<ref>D. López-Bruna, Plasma Phys. Control. Fusion 55 (2013) 015001</ref> and these studies can now be pursued with improved capabilities (e.g., higher NBI power and additional microwave heating in conditions of high plasma density).
* The singular alteration of transport at magnetically resonant plasma regions. TJ-II offers the only experimental benchmark in Europe to evaluate their impact in deviating neoclassical predictions<ref>D. López-Bruna, [[doi:10.1088/0741-3335/55/1/015001|Plasma Phys. Control. Fusion '''55''' (2013) 015001]]</ref> and these studies can now be pursued with improved capabilities (e.g., higher NBI power and additional microwave heating in conditions of high plasma density).
* An important open question is the relation between neoclassical and turbulence optimization. It is seen that in LHD stellarator<ref>T H Watanabe, H Sugama and S Ferrando. PRL 100 (2008) 195002</ref> both actions go together. Effort is being carried out to understand the zonal flow relaxation in stellarator geometry and the role of neoclassical radial electric fields on ZFs and confinement.
* An important open question is the relation between neoclassical and turbulence optimization. It is seen that in LHD stellarator<ref>T H Watanabe, H Sugama and S Ferrando, [[doi:10.1103/PhysRevLett.100.195002|Phys. Rev. Lett. '''100''' (2008) 195002]]</ref> both actions go together. Effort is being carried out to understand the zonal flow relaxation in stellarator geometry and the role of neoclassical radial electric fields on ZFs and confinement.


Optimized stellarator studies:
Optimized stellarator studies:
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The demonstration of the ITER baseline scenario (i.e. H-mode operation with integrated Edge Localized Modes (ELMs) control) is progressing but its feasibility for DEMO will require full control of ELMs, which is very challenging.  
The demonstration of the ITER baseline scenario (i.e. H-mode operation with integrated Edge Localized Modes (ELMs) control) is progressing but its feasibility for DEMO will require full control of ELMs, which is very challenging.  
The full understanding needed for a confident extrapolation of new regimes as an alternative to type I ELMs to burning plasmas is not yet available, though several routes look promising.  
The full understanding needed for a confident extrapolation of new regimes as an alternative to type I ELMs to burning plasmas is not yet available, though several routes look promising.  
Clarifying the physics behind uncoupled (heat and particle) transport channels is one of the main scientific conundrums for understanding ELM control techniques (e.g. using magnetic perturbations<ref>T. E. Evans et al. Nature Phys. 2 (2006) 419.</ref>), as part of the ITER base-line scenario, and the development of plasma scenarios without ELMs (e.g. the I-mode<ref>A. Hubbard et al 25th IAEA Int. Conf. (St. Petersburg, 2014) /[EX/P6-22]</ref>).  
Clarifying the physics behind uncoupled (heat and particle) transport channels is one of the main scientific conundrums for understanding ELM control techniques (e.g. using magnetic perturbations<ref>T. E. Evans et al, [[doi:10.1038/nphys312|Nature Phys. 2 (2006) 419]]</ref>), as part of the ITER base-line scenario, and the development of plasma scenarios without ELMs (e.g. the I-mode<ref>A. Hubbard et al 25th IAEA Int. Conf. (St. Petersburg, 2014), EX/P6-22</ref>).  


''Research plan in TJ-II and related devices:''
''Research plan in TJ-II and related devices:''
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Thus, in the framework of the design and assessment of innovative plasma configurations (snowflake, Super-X), liquid metals (Li, Ga, Sn) are also being considered.  
Thus, in the framework of the design and assessment of innovative plasma configurations (snowflake, Super-X), liquid metals (Li, Ga, Sn) are also being considered.  
Lithium Capillary-Pore-system (CPS) limiters with a closed circulation loop are under development at the T11M tokamak.<ref>A. Vertkov et al., 25th IAEA Int. Conf. on Fusion (2014) / EX/P1-49. </ref>  
Lithium Capillary-Pore-system (CPS) limiters with a closed circulation loop are under development at the T11M tokamak.<ref>A. Vertkov et al., 25th IAEA Int. Conf. on Fusion (2014), EX/P1-49</ref>  
CPS experiments are also in progress at the FTU tokamak<ref>G. Mazzitelli G et al., 25th IAEA Int. Conf. on Fusion Energy St Petersburg 2014 </ref> and the TJ-II stellarator.<ref>J. Sánchez et al., Nuclear Fusion 2015 / EX/P2-46 </ref>   
CPS experiments are also in progress at the FTU tokamak<ref>G. Mazzitelli G et al., 25th IAEA Int. Conf. on Fusion Energy St Petersburg 2014 </ref> and the TJ-II stellarator.<ref>J. Sánchez et al., [[doi:10.1088/0029-5515/55/10/104014|Nucl. Fusion '''55''' (2015) 104014]] / EX/P2-46 </ref>   
CPS is a promising solution in the search for a candidate material (Li/Sn/Ga) that offers all the required properties.  
CPS is a promising solution in the search for a candidate material (Li/Sn/Ga) that offers all the required properties.  


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''Challenges and opportunities''  
''Challenges and opportunities''  


TJ-II experimental results have shown that stellarator stability is better than predicted by linear stability analyses.<ref>A. M. de Aguilera  et al., Nuclear Fusion 55 (2015) 113014</ref>  
TJ-II experimental results have shown that stellarator stability is better than predicted by linear stability analyses.<ref>A. M. de Aguilera  et al., [[doi:10.1088/0029-5515/55/11/113014|Nucl. Fusion '''55''' (2015) 113014]]</ref>  
This result strongly suggests that stability calculations, as those presently used in the optimization criteria of stellarators, might miss some stabilization mechanisms,<ref>S. Sakakibara et al., PPCF 50 (2008) 124014</ref> which could be explained by self-organization mechanisms between transport and gradients.<ref>K. Ichiguchi et al., NF 51 (2011) 053021; C. Hidalgo et al., PRL 108 (2012) 065001</ref>  
This result strongly suggests that stability calculations, as those presently used in the optimization criteria of stellarators, might miss some stabilization mechanisms,<ref>S. Sakakibara et al., [[doi:10.1088/0741-3335/50/12/124014|Plasma Phys. Control. Fusion '''50''' (2008) 124014]]</ref> which could be explained by self-organization mechanisms between transport and gradients.<ref>K. Ichiguchi et al., [[doi:10.1088/0029-5515/51/5/053021|Nucl. Fusion '''51''' (2011) 053021]]; C. Hidalgo et al., [[doi:10.1103/PhysRevLett.108.065001|Phys. Rev. Lett. '''108''' (2012) 065001]]</ref>  
Understanding this discrepancy might help to relax some optimization criteria in 3-D magnetic configurations with possible impact in engineering design and reactor technology.  
Understanding this discrepancy might help to relax some optimization criteria in 3-D magnetic configurations with possible impact in engineering design and reactor technology.  


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Alpha-particle driven Alfvénic instabilities constitute a source of major uncertainty for predicting alpha-particle transport, alpha heating profile, and He ash accumulation in burning plasmas.  
Alpha-particle driven Alfvénic instabilities constitute a source of major uncertainty for predicting alpha-particle transport, alpha heating profile, and He ash accumulation in burning plasmas.  
Moreover, Alfvén Eigenmodes (AEs) can have strong influence on the confinement of fast ions, thus making less efficient NBI heating.  
Moreover, Alfvén Eigenmodes (AEs) can have strong influence on the confinement of fast ions, thus making less efficient NBI heating.  
The observed mitigation effect of ECRH on NBI beam-driven Alfvén eigenmodes (AEs) first reported in DIII-D and later in TJ-II<ref>K. Nagaoka, T. Ido, E. Ascasibar et al., Nuclear Fusion (2013)</ref> has opened an attractive avenue for a possible control of the AEs though the physics behind this effect is yet to be understood. Fast particle can have also influence on the broadband turbulence and on several instabilities like ITGs.  
The observed mitigation effect of ECRH on NBI beam-driven Alfvén eigenmodes (AEs) first reported in DIII-D and later in TJ-II<ref>K. Nagaoka, T. Ido, E. Ascasibar et al., [[doi: 10.1088/0029-5515/53/7/072004|Nucl. Fusion '''53''' (2013) 072004]]</ref> has opened an attractive avenue for a possible control of the AEs though the physics behind this effect is yet to be understood. Fast particle can have also influence on the broadband turbulence and on several instabilities like ITGs.  


''Research plan in TJ-II''
''Research plan in TJ-II''