skip to main content


Title: Bi-Kappa Proton Mirror and Cyclotron Instabilities in the Solar Wind
Abstract

The charged particles in the solar wind are often observed to possess a nonthermal tail in the velocity distribution function, a feature that can be fitted with the Kappa model. The anisotropic, or bi-Kappa, model of protons, electrons, and other charged particles is thus adopted in the literature for interpreting the data as well as in the context of the analysis of wave–particle interactions. The present paper develops an approximate but efficient theory of the mirror and cyclotron instabilities excited by the bi-Kappa protons in the solar wind. A velocity moment-based quasi-linear theory of these instabilities is also formulated in order to investigate the saturation behavior. Applications of the formalism are made for instabilities close to the marginally unstable state, which is typical of the solar wind near 1 au.

 
more » « less
Award ID(s):
2203321
NSF-PAR ID:
10423146
Author(s) / Creator(s):
; ;
Publisher / Repository:
DOI PREFIX: 10.3847
Date Published:
Journal Name:
The Astrophysical Journal
Volume:
950
Issue:
2
ISSN:
0004-637X
Format(s):
Medium: X Size: Article No. 131
Size(s):
["Article No. 131"]
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The quasi-steady states of collisionless plasmas in space (e.g., in the solar wind and planetary environments) are governed by the interactions of charged particles with wave fluctuations. These interactions are responsible not only for the dissipation of plasma waves but also for their excitation. The present analysis focuses on two instabilities, mirror and electromagnetic ion cyclotron instabilities, associated with the same proton temperature anisotropyT>T(where ⊥, ∥ are directions defined with respect to the local magnetic field vector). Theories relying on standard Maxwellian models fail to link these two instabilities (i.e., predicted thresholds) to the proton quasi-stable anisotropies measured in situ in a completely satisfactory manner. Here we revisit these instabilities by modeling protons with the generalized bi-Kappa (bi-κpower-law) distribution, and by a comparative analysis of a 2D hybrid simulation with the velocity-moment-based quasi-linear (QL) theory. It is shown that the two methods feature qualitative and, even to some extent, quantitative agreement. The reduced QL analysis based upon the assumption of a time-dependent bi-Kappa model thus becomes a valuable theoretical approach that can be incorporated into the present studies of solar wind dynamics.

     
    more » « less
  2. null (Ed.)
    ABSTRACT Various plasma waves and instabilities are abundantly present in the solar wind plasma, as evidenced by spacecraft observations. Among these, propagating modes and instabilities driven by temperature anisotropies are known to play a significant role in the solar wind dynamics. In situ measurements reveal that the threshold conditions for these instabilities adequately explain the solar wind conditions at large heliocentric distances. This paper pays attention to the combined effects of electron firehose instability driven by excessive parallel electron temperature anisotropy (T⊥e < T∥e) at high beta conditions, and electromagnetic ion cyclotron instability driven by excessive perpendicular proton temperature anisotropy (T⊥i > T∥i). By employing quasilinear kinetic theory based upon the assumption of bi-Maxwellian velocity distribution functions for protons and electrons, the dynamical evolution of the combined instabilities and their mutual interactions mediated by the particles is explored in depth. It is found that while in some cases, the two unstable modes are excited and saturated at distinct spatial and temporal scales, in other cases, the two unstable modes are intermingled such that a straightforward interpretation is not so easy. This shows that when the dynamics of protons and electrons are mutually coupled and when multiple unstable modes are excited in the system, the dynamical consequences can be quite complex. 
    more » « less
  3. Abstract We perform a statistical analysis of observed magnetic spectra in the solar wind at 1 au with localized power elevations above the level of the ambient turbulent fluctuations. We show that the elevations are seen only when the intensity of the ambient fluctuations is sufficiently low. Assuming that the spectral elevations are caused by thermal-ion instabilities, this suggests that on average the effect of the solar wind background is strong enough to suppress the instability or obscure it or both. We then carry out nonlinear numerical simulations with particle ions and an electron fluid to model a thermal-ion instability coexisting with an ambient turbulence. The parameters of the simulation are taken from a known solar wind interval where an instability was assumed to exist based on the linear theory and a bi-Maxwellian fit of the observed distribution with core and secondary-beam protons. The numerical model closely matches the position of the observed spectral elevation in the wavenumber space. This confirms that the thermal-ion instability is responsible for the elevation. At the same time, the magnitude of the elevation turns out to be smaller than in the real solar wind. When higher intensity of the turbulence is used in the simulation, which is typical of solar wind in general, the power elevation is no longer seen. This is in agreement with the reduced observability of the elevations at higher intensities. However, the simulations show that the turbulence does not simply obscure the instability but also lowers its saturation level. 
    more » « less
  4. Abstract

    We conduct two-dimensional particle-in-cell simulations to investigate the scattering of electron heat flux by self-generated oblique electromagnetic waves. The heat flux is modeled as a bi-kappa distribution with aT>Ttemperature anisotropy maintained by continuous injection at the boundaries. The anisotropic distribution excites oblique whistler waves and filamentary-like Weibel instabilities. Electron velocity distributions taken after the system has reached a steady state show that these instabilities inhibit the heat flux and drive the total distributions toward isotropy. Electron trajectories in velocity space show a circular-like diffusion along constant energy surfaces in the wave frame. The key parameter controlling the scattering rate is the average speed, or drift speedvd, of the heat flux compared with the electron Alfvén speedvAe, with higher drift speeds producing stronger fluctuations and a more significant reduction of the heat flux. Reducing the density of the electrons carrying the heat flux by 50% does not significantly affect the scattering rate. A scaling law for the electron scattering rate versusvd/vAeis deduced from the simulations. The implications of these results for understanding energetic electron transport during energy release in solar flares are discussed.

     
    more » « less
  5. We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modelling the turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non-Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the fluid model of Chew–Goldberger–Low (CGL) in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the fourth-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the ‘normal’ closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the ‘normal’ closure, and beyond the fourth-order moment, Landau fluid closures are required. 
    more » « less