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Title: Saturation of Alfvén modes in tokamaks

Abstract

Here, the growth of Alfvén modes driven unstable by a distribution of high energy particles up to saturation is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and a numerical high energy particle distribution, in order to make detailed comparison with experiment and with models for saturation amplitudes and the modification of beam profiles. Two innovations are introduced. First, a very noise free means of obtaining the mode-particle energy and momentum transfer is introduced, and secondly, a spline representation of the actual beam particle distribution is used.

Authors:
 [1];  [1];  [1];  [1];  [1];  [2]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Univ. of Colorado, Boulder, CO (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1328851
Report Number(s):
5257
Journal ID: ISSN 0741-3335
Grant/Contract Number:
AC02-09CH11466
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Plasma Physics and Controlled Fusion
Additional Journal Information:
Journal Volume: 58; Journal Issue: 11; Journal ID: ISSN 0741-3335
Publisher:
IOP Science
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Alfven modes; tokamaks; saturation; beam particles

Citation Formats

White, Roscoe, Gorelenkov, Nikolai, Gorelenkova, Marina, Podesta, Mario, Ethier, Stephane, and Chen, Yang. Saturation of Alfvén modes in tokamaks. United States: N. p., 2016. Web. doi:10.1088/0741-3335/58/11/115007.
White, Roscoe, Gorelenkov, Nikolai, Gorelenkova, Marina, Podesta, Mario, Ethier, Stephane, & Chen, Yang. Saturation of Alfvén modes in tokamaks. United States. doi:10.1088/0741-3335/58/11/115007.
White, Roscoe, Gorelenkov, Nikolai, Gorelenkova, Marina, Podesta, Mario, Ethier, Stephane, and Chen, Yang. 2016. "Saturation of Alfvén modes in tokamaks". United States. doi:10.1088/0741-3335/58/11/115007. https://www.osti.gov/servlets/purl/1328851.
@article{osti_1328851,
title = {Saturation of Alfvén modes in tokamaks},
author = {White, Roscoe and Gorelenkov, Nikolai and Gorelenkova, Marina and Podesta, Mario and Ethier, Stephane and Chen, Yang},
abstractNote = {Here, the growth of Alfvén modes driven unstable by a distribution of high energy particles up to saturation is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and a numerical high energy particle distribution, in order to make detailed comparison with experiment and with models for saturation amplitudes and the modification of beam profiles. Two innovations are introduced. First, a very noise free means of obtaining the mode-particle energy and momentum transfer is introduced, and secondly, a spline representation of the actual beam particle distribution is used.},
doi = {10.1088/0741-3335/58/11/115007},
journal = {Plasma Physics and Controlled Fusion},
number = 11,
volume = 58,
place = {United States},
year = 2016,
month = 9
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 1work
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  • Saturation of Alfvén modes driven unstable by a distribution of high energy particles as a function of collisionality is investigated with a guiding center code, using numerical eigenfunctions produced by linear theory and numerical high energy particle distributions. The most important resonance is found and it is shown that when the resonance domain is bounded, not allowing particles to collisionlessly escape, the saturation amplitude is given by the balance of the resonance mixing time with the time for nearby particles to collisionally diffuse across the resonance width. Finally, saturation amplitudes are in agreement with theoretical predictions as long as themore » mode amplitude is not so large that it produces stochastic loss from the resonance domain.« less
  • We present a series of numerical simulation experiments set up to illustrate the fundamental physics processes underlying the nonlinear dynamics of Alfvénic modes resonantly excited by energetic particles in tokamak plasmas and of the ensuing energetic particle transports. These phenomena are investigated by following the evolution of a test particle population in the electromagnetic fields computed in self-consistent MHD-particle simulation performed by the HMGC code. Hamiltonian mapping techniques are used to extract and illustrate several features of wave-particle dynamics. The universal structure of resonant particle phase space near an isolated resonance is recovered and analyzed, showing that bounded orbits andmore » untrapped trajectories, divided by the instantaneous separatrix, form phase space zonal structures, whose characteristic non-adiabatic evolution time is the same as the nonlinear time of the underlying fluctuations. Bounded orbits correspond to a net outward resonant particle flux, which produces a flattening and/or gradient inversion of the fast ion density profile around the peak of the linear wave-particle resonance. The connection of this phenomenon to the mode saturation is analyzed with reference to two different cases: a Toroidal Alfvén eigenmode in a low shear magnetic equilibrium and a weakly unstable energetic particle mode for stronger magnetic shear. It is shown that, in the former case, saturation is reached because of radial decoupling (resonant particle redistribution matching the mode radial width) and is characterized by a weak dependence of the mode amplitude on the growth rate. In the latter case, saturation is due to resonance detuning (resonant particle redistribution matching the resonance width) with a stronger dependence of the mode amplitude on the growth rate.« less
  • The spectral code BETAS computes plasma equilibrium in a toroidal magnetic field B = {nabla}s {times} {nabla}{psi} with remarkable accuracy because the finite difference scheme employed in the radial direction allows for discontinuities of the flux function {psi} across the nested surfaces s = const. Instability of higher modes in stellarators like the Heliotron E can be detected in roughly an hour on the best supercomputers by calculating bifurcated equilibria that are defined over just one field period. The method has been validated by comparing results about nonlinear saturation of ballooning modes in tokamaks with numerical data from the PESTmore » code.« less