Darwin model in plasma physics revisited

Xie, Huasheng; Zhu, Jia; W., Z.

doi:10.1088/0031-8949/89/10/105602

Cited by 3 publications

(6 citation statements)

References 13 publications

(18 reference statements)

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“…The results show that Darwin model is a good approximate model in this case, and the slight deviations agree with the theoretical expectation in Ref. [16].…”

Section: ! I /! Cesupporting

confidence: 89%

“…To extend the application range, we will also given the Darwin model [16] version. In Darwin mode, all field variables can be divided into two parts: the transverse (T, divergence free) part and the longitudinal (L, curl free) part, i.e.,…”

Section: Starting Equationsmentioning

confidence: 99%

“…3 is for the Darwin model in Ref. [16], which is the same as the one solved using accurate Z function with conventional iterative root finding in Fig. 5 of Ref.…”

Section: Benchmarkmentioning

confidence: 99%

“…The tool is largely benefit from the powerful matrix approach of PDRK solver [1], which is the first algorithm can yield all the important kinetic solutions without initial guess for root finding. The new tool is named as PASS (Plasma wAve and inStability analySis), which includes the present work be kinetic version PASS-K succeed from PDRK [1] (hereafter 'PASS-K' is refered equivalent to 'PDRK'), the fluid version PASS-F succeed from PDRF [16], and possibly more.…”

Section: Introductionmentioning

confidence: 99%

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A Unified Numerically Solvable Framework for Complicated Kinetic Plasma Dispersion Relations

Xie

2019

Preprint

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A unified numerically solvable framework for dispersion relations with arbitrary number of species drifting at arbitrary directions and with Krook collision is derived for linear uniform/homogenous kinetic plasma, which largely extended the standard one [say, T. Stix, Waves in Plasmas, AIP Press, 1992]. The purpose of this work is to provide a kinetic plasma dispersion relation tool not only the physical model but also the numerical approach be as general/powerful as possible. As a very general application example, we give the final dispersion relations which assume further the equilibrium distribution function be bi-Maxwellian and including parallel drift, two directions of perpendicular drift (i.e., drift across magnetic field), ring beam and loss-cone. Both electromagnetic and electrostatic versions are provided, with also the Darwin (a.k.a., magnetoinductive or magnetostatic) version. The species can be treated either magnetized or unmagnetized. Later, the equations are transformed to the matrix form be solvable by using the powerful matrix algorithm [H. S. Xie and Y. Xiao, Plasma Science and Technology, 18, 2, 97, 2016], which is the first approach can give all the important solutions of a linear kinetic plasma system without requiring initial guess for root finding and thus can be extremely useful to the community. To our knowledge, the present model would be the most comprehensive one in literature for the distribution function constructed bases on Maxwellian, which thus can be applied widely for study waves and instabilities in space, astrophysics, fusion and laser plasma. We limit the present work to non-relativistic case.

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“…The results show that Darwin model is a good approximate model in this case, and the slight deviations agree with the theoretical expectation in Ref. [16].…”

Section: ! I /! Cesupporting

confidence: 89%

Section: Starting Equationsmentioning

confidence: 99%

“…3 is for the Darwin model in Ref. [16], which is the same as the one solved using accurate Z function with conventional iterative root finding in Fig. 5 of Ref.…”

Section: Benchmarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Unified Numerically Solvable Framework for Complicated Kinetic Plasma Dispersion Relations

Xie

2019

Preprint

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“…The other two branches are given by Eqs. (1) and (13) are solved by root finding with the original Z function [19] and comparing with PDRK. A typical result is shown in Fig.7.…”

Section: Parallel Propagation Kinetic Modesmentioning

confidence: 99%

PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma

Xie

Xiao

2016

Plasma Sci. Technol.

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A general, fast, and effective approach is developed for numerical calculation of kinetic plasma dispersion relations. The plasma dispersion function is approximated by J-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. The result is accurate for J = 8 except the solutions that are the little interesting heavily damped modes. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial guess. It is also free from convergent problems. The approach is demonstrated from electrostatic one-dimensional and three-dimensional dispersion relations, to electromagnetic kinetic magnetized plasma dispersion relation for bi-Maxwellian distribution with parallel velocity drift.

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BO: A unified tool for plasma waves and instabilities analysis

Xie

2019

Computer Physics Communications

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Darwin model in plasma physics revisited

Cited by 3 publications

References 13 publications

A Unified Numerically Solvable Framework for Complicated Kinetic Plasma Dispersion Relations

A Unified Numerically Solvable Framework for Complicated Kinetic Plasma Dispersion Relations

PDRK: A General Kinetic Dispersion Relation Solver for Magnetized Plasma

BO: A unified tool for plasma waves and instabilities analysis

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