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Title: Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

Abstract

The resonant interaction of shear Alfvén waves with energetic particles is investigated numerically in tokamak and stellarator geometry using a non-perturbative MHD-kinetic hybrid approach. The focus lies on toroidicity-induced Alfvén eigenmodes (TAEs), which are most easily destabilized by a fast-particle population in fusion plasmas. While the background plasma is treated within the framework of an ideal-MHD theory, the drive of the fast particles, as well as Landau damping of the background plasma, is modelled using the drift-kinetic Vlasov equation without collisions. Building on analytical theory, a fast numerical tool, STAE-K, has been developed to solve the resulting eigenvalue problem using a Riccati shooting method. The code, which can be used for parameter scans, is applied to tokamaks and the stellarator Wendelstein 7-X. High energetic-ion pressure leads to large growth rates of the TAEs and to their conversion into kinetically modified TAEs and kinetic Alfvén waves via continuum interaction. To better understand the physics of this conversion mechanism, the connections between TAEs and the shear Alfvén wave continuum are examined. It is shown that, when energetic particles are present, the continuum deforms substantially and the TAE frequency can leave the continuum gap. The interaction of the TAE with the continuum leadsmore » to singularities in the eigenfunctions. To further advance the physical model and also to eliminate the MHD continuum together with the singularities in the eigenfunctions, a fourth-order term connected to radiative damping has been included. The radiative damping term is connected to non-ideal effects of the bulk plasma and introduces higher-order derivatives to the model. Thus, it has the potential to substantially change the nature of the solution. For the first time, the fast-particle drive, Landau damping, continuum damping, and radiative damping have been modelled together in tokamak- as well as in stellarator geometry.« less

Authors:
; ;  [1]
  1. Max-Planck-Institut für Plasmaphysik, D-17491 Greifswald (Germany)
Publication Date:
OSTI Identifier:
22599864
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 9; Other Information: (c) 2016 EURATOM; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOLTZMANN-VLASOV EQUATION; EIGENFUNCTIONS; EIGENVALUES; GEOMETRY; INTERACTIONS; LANDAU DAMPING; MAGNETOHYDRODYNAMICS; NUMERICAL SOLUTION; PARTICLES; PLASMA; SINGULARITY; STELLARATORS; TAIL IONS; TOKAMAK DEVICES

Citation Formats

Slaby, Christoph, Könies, Axel, and Kleiber, Ralf. Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators. United States: N. p., 2016. Web. doi:10.1063/1.4961916.
Slaby, Christoph, Könies, Axel, & Kleiber, Ralf. Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators. United States. doi:10.1063/1.4961916.
Slaby, Christoph, Könies, Axel, and Kleiber, Ralf. 2016. "Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators". United States. doi:10.1063/1.4961916.
@article{osti_22599864,
title = {Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators},
author = {Slaby, Christoph and Könies, Axel and Kleiber, Ralf},
abstractNote = {The resonant interaction of shear Alfvén waves with energetic particles is investigated numerically in tokamak and stellarator geometry using a non-perturbative MHD-kinetic hybrid approach. The focus lies on toroidicity-induced Alfvén eigenmodes (TAEs), which are most easily destabilized by a fast-particle population in fusion plasmas. While the background plasma is treated within the framework of an ideal-MHD theory, the drive of the fast particles, as well as Landau damping of the background plasma, is modelled using the drift-kinetic Vlasov equation without collisions. Building on analytical theory, a fast numerical tool, STAE-K, has been developed to solve the resulting eigenvalue problem using a Riccati shooting method. The code, which can be used for parameter scans, is applied to tokamaks and the stellarator Wendelstein 7-X. High energetic-ion pressure leads to large growth rates of the TAEs and to their conversion into kinetically modified TAEs and kinetic Alfvén waves via continuum interaction. To better understand the physics of this conversion mechanism, the connections between TAEs and the shear Alfvén wave continuum are examined. It is shown that, when energetic particles are present, the continuum deforms substantially and the TAE frequency can leave the continuum gap. The interaction of the TAE with the continuum leads to singularities in the eigenfunctions. To further advance the physical model and also to eliminate the MHD continuum together with the singularities in the eigenfunctions, a fourth-order term connected to radiative damping has been included. The radiative damping term is connected to non-ideal effects of the bulk plasma and introduces higher-order derivatives to the model. Thus, it has the potential to substantially change the nature of the solution. For the first time, the fast-particle drive, Landau damping, continuum damping, and radiative damping have been modelled together in tokamak- as well as in stellarator geometry.},
doi = {10.1063/1.4961916},
journal = {Physics of Plasmas},
number = 9,
volume = 23,
place = {United States},
year = 2016,
month = 9
}
  • The stability of high-[ital n] toroidicity-induced shear Alfven eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated. The TAE modes are discrete in nature, and thus can easily tap the free energy associated with energetic particle pressure gradient through wave particle resonant interaction. A quadratic form is derived for the high-[ital n] TAE modes using gyrokinetic equation. The kinetic effects of energetic particles are calculated perturbatively using the ideal magnetohydrodynamic (MHD) solution as the lowest-order eigenfunction. The finite Larmor radius (FLR) effects and the finite drift orbit width (FDW) effects are included formore » both circulating and trapped energetic particles. It is shown that, for circulating particles, FLR and FDW effects have two opposite influences on the stability of the high-[ital n] TAE modes. First, they have the usual stabilizing effects by reducing the wave particle interaction strength. Second, they also have destabilizing effects by allowing more particles to resonate with the TAE modes. It is found that the growth rate induced by the circulating alpha particles increases linearly with the toroidal mode number [ital n] for small [ital k][sub [theta]][rho][sub [alpha]], and decreases as 1/[ital n] for [ital k][sub [theta]][rho][sub [alpha]][much gt]1. The maximum growth rate is obtained at [ital k][sub [theta]][rho][sub [alpha]] on the order of unity, and is nearly constant for the range of 0.7[le][ital v][sub [alpha]]/[ital v][sub A][le]2.5. On the other hand, the trapped particle response is dominated by the precessional drift resonance. The bounce resonant contribution is negligible. The growth rate peaks sharply at the value of [ital k][sub [theta]][rho][sub [alpha]], such that the precessional drift resonance occurs for the most energetic trapped particles.« less
  • This work reports on linear global gyrokinetic particle simulations of the excitation of toroidicity-induced Alfvén eigenmodes (TAE) and energetic particle modes (EPM), and the comparison between these two modes. The TAE excitation by antenna clarifies the magnetohydrodynamic (MHD) mode structure and the discrete eigenmode exists in the gap between the upper and lower accumulation points. The TAE excitation by fast ions modifies the MHD mode structure because of radial symmetry breaking and the eigenmode frequency moves towards the lower accumulation point. The phase space structure of fast ions shows that both passing and trapped particles contribute to the TAE excitationmore » and that trapped particles dominate the wave-particle resonance in our simulations. The growth rate of TAE is sensitive to the fast ion energy, density, and density gradient, which are also important factors contributing to the transition of the TAE to the EPM. The gyrokinetic particle simulations also confirm the excitation of EPM when the drive is stronger. The frequency of the EPM is determined by the characteristic frequencies of fast ion motion in toroidal geometry.« less
  • The anisotropy instability of global Alfven eigenmodes induced by toroidicity driven by trapped thermonuclear {alpha} particles having an anisotropic distribution in velocity space is studied. The anisotropy arises in a nonuniform plasma when the finite width of the {alpha}-particle orbits is treated. The growth rate of the anisotropy instability is comparable with the growth rate of the instability due to the {alpha}-particle density gradient. The threshold values of the ratio of the {alpha}-particle density to the density of the bulk plasma are obtained, taking into account the toroidicity-induced Alfven eigenmodes associated with trapped electrons. 23 refs.
  • The first linear global electromagnetic gyrokinetic particle simulation on the excitation of toroidicity induced Alfven eigenmode (TAE) by energetic particles is reported. It is shown that the long wavelength magnetohydrodynamic instabilities can be studied by the gyrokinetic particle simulation. With an increase in the energetic particle pressure, the TAE frequency moves down into the lower continuum together with an increase in the linear growth rate.
  • The stability of high-n toroidicity-induced shear Alfven eigenmodes (TAE) in the presence of fusion alpha particles or energetic ions in tokamaks is investigated. The TAE modes are discrete in nature and thus can easily tap the free energy associated with energetic particle pressure gradient through wave particle resonant interaction. A quadratic form is derived for the high-n TAE modes using gyro-kinetic equation. The kinetic effects of energetic particles are calculated perturbatively using the ideal MHD solution as the lowest order eigenfunction. The finite Larmor radius (FLR) effects and the finite drift orbit width (FDW) effects are included for both circulatingmore » and trapped energetic particles. It is shown that, for circulating particles, FLR and FDW effects have two opposite influences on the stability of the high-n TAE modes. First, they have the usual stabilizing effects by reducing the wave particle interaction strength. Second, they also have destabilizing effects by allowing more particles to resonate with the TAE modes. It is found that the growth rate induced by the circulating alpha particles increase linearly with toroidal mode number n for small {kappa}{sub {theta}}{rho}{sub {alpha}}, and decreases as 1/n for {kappa}{sub {theta}}{rho}{sub {alpha}} {much gt} 1. The maximum growth rate is obtained at {kappa}{sub {theta}}{rho}{sub {alpha}} on the order of unity and is nearly constant for the range of 0.7 < {upsilon}{sub {alpha}}/{upsilon}{sub A} < 2.5. On the other hand, the trapped particle response is dominated by the precessional drift resonance. The bounce resonant contribution is negligible. The growth rate peaks sharply at the value of {kappa}{sub {theta}}{rho}{sub {alpha}} such that the precessional drift resonance occurs for the most energetic trapped particles. The maximum growth rate due to the energetic trapped particles is comparable to that of circulating particles.« less