dorsal/arxiv
View SchemaA sharp stability criterion for the Vlasov-Maxwell system
| Authors | Zhiwu Lin, Walter Strauss |
|---|---|
| Categories | |
| ArXiv ID | physics/0702023 |
| URL | https://arxiv.org/abs/physics/0702023 |
| DOI | 10.1007/s00222-008-0122-1 |
Abstract
We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria.
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"abstract": "We consider the linear stability problem for a 3D cylindrically symmetric\nequilibrium of the relativistic Vlasov-Maxwell system that describes a\ncollisionless plasma. For an equilibrium whose distribution function decreases\nmonotonically with the particle energy, we obtained a linear stability\ncriterion in our previous paper. Here we prove that this criterion is sharp;\nthat is, there would otherwise be an exponentially growing solution to the\nlinearized system. Therefore for the class of symmetric Vlasov-Maxwell\nequilibria, we establish an energy principle for linear stability. We also\ntreat the considerably simpler periodic 1.5D case. The new formulation\nintroduced here is applicable as well to the nonrelativistic case, to other\nsymmetries, and to general equilibria.",
"arxiv_id": "physics/0702023",
"authors": [
"Zhiwu Lin",
"Walter Strauss"
],
"categories": [
"physics.plasm-ph",
"math.AP"
],
"doi": "10.1007/s00222-008-0122-1",
"title": "A sharp stability criterion for the Vlasov-Maxwell system",
"url": "https://arxiv.org/abs/physics/0702023"
},
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