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Title: Excitation of high-n toroidicity-induced shear Alfven eigenmodes by energetic particles and fusion alpha particles in tokamaks

Abstract

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 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-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 atmore » {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

Authors:
;
Publication Date:
Research Org.:
Princeton Univ., NJ (United States). Plasma Physics Lab.
Sponsoring Org.:
USDOE; USDOE, Washington, DC (United States)
OSTI Identifier:
5077248
Report Number(s):
PPPL-2852
ON: DE92016804
DOE Contract Number:
AC02-76CH03073
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ALFVEN WAVES; EXCITATION; ALPHA PARTICLES; TRAPPED-PARTICLE INSTABILITY; DISTRIBUTION FUNCTIONS; KINETIC EQUATIONS; LANDAU DAMPING; MAGNETIC FIELDS; MHD EQUILIBRIUM; SHEAR; TOKAMAK DEVICES; CHARGED PARTICLES; CLOSED PLASMA DEVICES; DAMPING; ENERGY-LEVEL TRANSITIONS; EQUATIONS; EQUILIBRIUM; FUNCTIONS; HYDROMAGNETIC WAVES; INSTABILITY; PLASMA INSTABILITY; PLASMA MACROINSTABILITIES; THERMONUCLEAR DEVICES; 700310* - Plasma Confinement- (1992-); 700340 - Plasma Waves, Oscillations, & Instabilities- (1992-)

Citation Formats

Fu, G.Y., and Cheng, C.Z.. Excitation of high-n toroidicity-induced shear Alfven eigenmodes by energetic particles and fusion alpha particles in tokamaks. United States: N. p., 1992. Web. doi:10.2172/5077248.
Fu, G.Y., & Cheng, C.Z.. Excitation of high-n toroidicity-induced shear Alfven eigenmodes by energetic particles and fusion alpha particles in tokamaks. United States. doi:10.2172/5077248.
Fu, G.Y., and Cheng, C.Z.. Wed . "Excitation of high-n toroidicity-induced shear Alfven eigenmodes by energetic particles and fusion alpha particles in tokamaks". United States. doi:10.2172/5077248. https://www.osti.gov/servlets/purl/5077248.
@article{osti_5077248,
title = {Excitation of high-n toroidicity-induced shear Alfven eigenmodes by energetic particles and fusion alpha particles in tokamaks},
author = {Fu, G.Y. and Cheng, C.Z.},
abstractNote = {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 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-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.},
doi = {10.2172/5077248},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Jul 01 00:00:00 EDT 1992},
month = {Wed Jul 01 00:00:00 EDT 1992}
}

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  • 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
  • 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
  • The structure of toroidicity-induced Alfven eigenmodes (TAE) and kinetic TAE (KTAE) with large mode numbers is analyzed and the linear power transfer from energetic particles to these modes is calculated in the low shear limit when each mode is localized near a single gap within an interval whose total width {Delta}{sup out} is much smaller than the radius r{sub m} of the mode location. Near its peak where most of the mode energy is concentrated, the mode has an inner scalelength {Delta}{sup in}, which is much smaller than {Delta}{sup out}. The scale {Delta}{sup in} is determined by toroidicity and kineticmore » effects, which eliminate the singularity of the potential at the resonant surface. This work examines the case when the drift orbit width of energetic particles {Delta}{sub b} is much larger than the inner scalelength {Delta}{sup in}, but arbitrary compared to the total width of the mode. It is shown that the particle-to-wave linear power transfer is comparable for the TAE and KTAE modes in this case. The ratio of the energetic particle contributions to the growth rates of the TAE and KTAE modes is then roughly equal to the inverse ratio of the mode energies. It is found that, in the low shear limit the growth rate of the KTAE modes can be larger than that for the TAE modes.« 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.
  • High-n WKB-ballooning mode equation is employed to study toroidicity-induced shear Alfven eigenmodes (TAE) in the /delta/ /minus/ /alpha/ space, where /delta/ = (r/q)(dq/dr) is the magnetic shear, and /alpha/ = /minus/(2Rq/sup 2//B/sup 2/)(dp/dr) is the normalized pressure gradient for tokamak plasmas. In the ballooning mode first stability region, TAE modes are found to exist only for /alpha/ less than some critical value /alpha//sub c/. We also find that these TAE modes reappear in the ballooning mode second stability region for bands of /alpha/ values. The global envelope structures of these TAE modes are studied by WKB method and are foundmore » to be bounded radially if the local mode frequency has a maximum in radius. 15 refs., 14 figs.« less