dorsal/arxiv
View SchemaCharged Particle Motion in a Highly Ionized Plasma
| Authors | Lowell S. Brown, Dean L. Preston, Robert L. Singleton Jr |
|---|---|
| Categories | |
| ArXiv ID | physics/0501084 |
| URL | https://arxiv.org/abs/physics/0501084 |
| DOI | 10.1016/j.physrep.2005.01.001 |
| Journal | Phys.Rept. 410 (2005) 237-333 |
Abstract
A recently introduced method utilizing dimensional continuation is employed to compute the energy loss rate for a non-relativistic particle moving through a highly ionized plasma. No restriction is made on the charge, mass, or speed of this particle. It is, however, assumed that the plasma is not strongly coupled in the sense that the dimensionless plasma coupling parameter g=e^2\kappa_D/ 4\pi T is small, where \kappa_D is the Debye wave number of the plasma. To leading and next-to-leading order in this coupling, dE/dx is of the generic form g^2 \ln[C g^2]. The precise numerical coefficient out in front of the logarithm is well known. We compute the constant C under the logarithm exactly for arbitrary particle speeds. Our exact results differ from approximations given in the literature. The differences are in the range of 20% for cases relevant to inertial confinement fusion experiments. The same method is also employed to compute the rate of momentum loss for a projectile moving in a plasma, and the rate at which two plasmas at different temperatures come into thermal equilibrium. Again these calculations are done precisely to the order given above. The loss rates of energy and momentum uniquely define a Fokker-Planck equation that describes particle motion in the plasma. The coefficients determined in this way are thus well-defined, contain no arbitrary parameters or cutoffs, and are accurate to the order described. This Fokker-Planck equation describes the longitudinal straggling and the transverse diffusion of a beam of particles. It should be emphasized that our work does not involve a model, but rather it is a precisely defined evaluation of the leading terms in a well-defined perturbation theory.
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"abstract": "A recently introduced method utilizing dimensional continuation is employed\nto compute the energy loss rate for a non-relativistic particle moving through\na highly ionized plasma. No restriction is made on the charge, mass, or speed\nof this particle. It is, however, assumed that the plasma is not strongly\ncoupled in the sense that the dimensionless plasma coupling parameter\ng=e^2\\kappa_D/ 4\\pi T is small, where \\kappa_D is the Debye wave number of the\nplasma. To leading and next-to-leading order in this coupling, dE/dx is of the\ngeneric form g^2 \\ln[C g^2]. The precise numerical coefficient out in front of\nthe logarithm is well known. We compute the constant C under the logarithm\nexactly for arbitrary particle speeds. Our exact results differ from\napproximations given in the literature. The differences are in the range of 20%\nfor cases relevant to inertial confinement fusion experiments. The same method\nis also employed to compute the rate of momentum loss for a projectile moving\nin a plasma, and the rate at which two plasmas at different temperatures come\ninto thermal equilibrium. Again these calculations are done precisely to the\norder given above. The loss rates of energy and momentum uniquely define a\nFokker-Planck equation that describes particle motion in the plasma. The\ncoefficients determined in this way are thus well-defined, contain no arbitrary\nparameters or cutoffs, and are accurate to the order described. This\nFokker-Planck equation describes the longitudinal straggling and the transverse\ndiffusion of a beam of particles. It should be emphasized that our work does\nnot involve a model, but rather it is a precisely defined evaluation of the\nleading terms in a well-defined perturbation theory.",
"arxiv_id": "physics/0501084",
"authors": [
"Lowell S. Brown",
"Dean L. Preston",
"Robert L. Singleton Jr"
],
"categories": [
"physics.plasm-ph",
"astro-ph",
"hep-ph"
],
"doi": "10.1016/j.physrep.2005.01.001",
"journal_ref": "Phys.Rept. 410 (2005) 237-333",
"title": "Charged Particle Motion in a Highly Ionized Plasma",
"url": "https://arxiv.org/abs/physics/0501084"
},
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