dorsal/arxiv
View SchemaNegative-Energy Perturbations in Circularly Cylindrical Equilibria within the Framework of Maxwell-Drift Kinetic Theory
| Authors | G. N. Throumoulopoulos, D. Pfirsch |
|---|---|
| Categories | |
| ArXiv ID | plasm-ph/9602002 |
| URL | https://arxiv.org/abs/plasm-ph/9602002 |
| DOI | 10.1103/PhysRevE.53.2767 |
Abstract
The conditions for the existence of negative-energy perturbations (which could be nonlinearly unstable and cause anomalous transport) are investigated in the framework of linearized collisionless Maxwell-drift kinetic theory for the case of equilibria of magnetically confined, circularly cylindrical plasmas and vanishing initial field perturbations. For wave vectors with a non-vanishing component parallel to the magnetic field, the plane equilibrium conditions (derived by Throumoulopoulos and Pfirsch [Phys Rev. E {\bf 49}, 3290 (1994)]) are shown to remain valid, while the condition for perpendicular perturbations (which are found to be the most important modes) is modified. Consequently, besides the tokamak equilibrium regime in which the existence of negative-energy perturbations is related to the threshold value of 2/3 of the quantity $\eta_\nu = \frac {\partial \ln T_\nu} {\partial \ln N_\nu}$, a new regime appears, not present in plane equilibria, in which negative-energy perturbations exist for {\em any} value of $\eta_\nu$. For various analytic cold-ion tokamak equilibria a substantial fraction of thermal electrons are associated with negative-energy perturbations (active particles). In particular, for linearly stable equilibria of a paramagnetic plasma with flat electron temperature profile ($\eta_e=0$), the entire velocity space is occupied by active electrons. The part of the velocity space occupied by active particles increases from the center to the plasma edge and is larger in a paramagnetic plasma than in a diamagnetic plasma with the same pressure profile. It is also shown that, unlike in plane equilibria, negative-energy perturbations exist in force-free reversed-field pinch equilibria with a substantial fraction of active particles.
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"abstract": "The conditions for the existence of negative-energy perturbations (which\ncould be nonlinearly unstable and cause anomalous transport) are investigated\nin the framework of linearized collisionless Maxwell-drift kinetic theory for\nthe case of equilibria of magnetically confined, circularly cylindrical plasmas\nand vanishing initial field perturbations. For wave vectors with a\nnon-vanishing component parallel to the magnetic field, the plane equilibrium\nconditions (derived by Throumoulopoulos and Pfirsch [Phys Rev. E {\\bf 49}, 3290\n(1994)]) are shown to remain valid, while the condition for perpendicular\nperturbations (which are found to be the most important modes) is modified.\nConsequently, besides the tokamak equilibrium regime in which the existence of\nnegative-energy perturbations is related to the threshold value of 2/3 of the\nquantity $\\eta_\\nu = \\frac {\\partial \\ln T_\\nu} {\\partial \\ln N_\\nu}$, a new\nregime appears, not present in plane equilibria, in which negative-energy\nperturbations exist for {\\em any} value of $\\eta_\\nu$. For various analytic\ncold-ion tokamak equilibria a substantial fraction of thermal electrons are\nassociated with negative-energy perturbations (active particles). In\nparticular, for linearly stable equilibria of a paramagnetic plasma with flat\nelectron temperature profile ($\\eta_e=0$), the entire velocity space is\noccupied by active electrons. The part of the velocity space occupied by active\nparticles increases from the center to the plasma edge and is larger in a\nparamagnetic plasma than in a diamagnetic plasma with the same pressure\nprofile. It is also shown that, unlike in plane equilibria, negative-energy\nperturbations exist in force-free reversed-field pinch equilibria with a\nsubstantial fraction of active particles.",
"arxiv_id": "plasm-ph/9602002",
"authors": [
"G. N. Throumoulopoulos",
"D. Pfirsch"
],
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"doi": "10.1103/PhysRevE.53.2767",
"title": "Negative-Energy Perturbations in Circularly Cylindrical Equilibria within the Framework of Maxwell-Drift Kinetic Theory",
"url": "https://arxiv.org/abs/plasm-ph/9602002"
},
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