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ABSTRACT This paper formulates a velocity moment-based quasi-linear theory that combines the impacts of weakly unstable proton–cyclotron- (or, equivalently, electromagnetic ion cyclotron) and proton-mirror instabilities on the solar wind plasma initially characterized by an excessive perpendicular proton temperature anisotropy. The present formalism is an alternative to the existing model in that the weakly unstable modes are characterized by analytical formalism that involves the assumption of weak growth rate and/or fluid-theoretical dispersion relation, in place of numerical root-finding method based on the transcendental plasma dispersion function. This results in an efficient numerical platform for analyzing the quasi-linear development of the said instabilities. Such a formalism may be useful in the larger context of global solar wind modelling effort where an efficient calculation of self-consistent wave–particle interaction process is called for. A direct comparison with spacecraft observations of solar wind proton data distribution shows that the present weak growth rate formalism of quasi-linear calculation produces results that are consistent with the observation.
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Quasi-linear Analysis of Proton-cyclotron Instability
Abstract The proton-cyclotron (PC) instability operates in various space plasma environments. In the literature, the so-called velocity moment-based quasi-linear theory is employed to investigate the physical process of PC instability that takes place after the onset of early linear exponential growth. In this method, the proton velocity distribution function (VDF) is assumed to maintain a bi-Maxwellian form for all time, which substantially simplifies the analysis, but its validity has not been rigorously examined by comparing against the actual solution of the kinetic equation. The present paper relaxes the assumption of the velocity moment-based quasi-linear theory by actually solving for the velocity space diffusion equation under the assumption of separable perpendicular and parallel VDFs, and upon comparison with the simplified velocity moment theory, it demonstrates that the simplified method is largely valid, despite the fact that the method slightly overemphasizes the relaxation of temperature anisotropy when the system is close to the marginally stable state. The overall validation is further confirmed with the results of particle-in-cell and hybrid-code simulations. The present paper thus provides a justification for making use of the velocity moment-based quasi-linear theory as an efficient first-cut theoretical tool for the PC instability.
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- Award ID(s):
- 2203321
- PAR ID:
- 10556174
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 976
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 173
- Size(s):
- Article No. 173
- Sponsoring Org:
- National Science Foundation
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