LEOPARD: A grid‐based dispersion relation solver for arbitrary gyrotropic distributions

Abstract

Particle velocity distributions measured in collisionless space plasmas often show strong deviations from idealized model distributions. Despite this observational evidence, linear wave analysis in space plasma environments such as the solar wind or Earth's magnetosphere is still mainly carried out using dispersion relation solvers based on Maxwellians or other parametric models. To enable a more realistic analysis, we present the new grid‐based kinetic dispersion relation solver LEOPARD (Linear Electromagnetic Oscillations in Plasmas with Arbitrary Rotationally‐symmetric Distributions) which no longer requires prescribed model distributions but allows for arbitrary gyrotropic distribution functions. In this work, we discuss the underlying numerical scheme of the code and we show a few exemplary benchmarks. Furthermore, we demonstrate a first application of LEOPARD to ion distribution data obtained from hybrid simulations. In particular, we show that in the saturation stage of the parallel fire hose instability, the deformation of the initial bi‐Maxwellian distribution invalidates the use of standard dispersion relation solvers. A linear solver based on bi‐Maxwellians predicts further growth even after saturation, while LEOPARD correctly indicates vanishing growth rates. We also discuss how this complies with former studies on the validity of quasilinear theory for the resonant fire hose. In the end, we briefly comment on the role of LEOPARD in directly analyzing spacecraft data, and we refer to an upcoming paper which demonstrates a first application of that kind.

On the Quasi‐linear Saturation of the Parallel Proton Firehose Instability Using a Full‐f Approach

“…Finally, our findings also confirm the results of Astfalk and Jenko (), namely, that for , strong cyclotron‐resonant scattering is a main driver for the firehose stabilization, which is why the moment‐kinetic approach fails in this regime since it cannot properly account for the distribution deformation due to the resonant diffusion. At the same time, the reduction of the macroscopic temperature anisotropy is relatively weak, which indicates that in the solar wind the PFHI may not be the dominant player in constraining the anisotropy when .…”

“…And since in Figure 8 the single wave characteristics roughly follow the bi-Maxwellian contours only weakly non-Maxwellian deformation occurs, which justifies a good applicability of the moment-kinetic approach. A clear signature of cyclotron-resonant diffusion is also observed in the hybrid Vlasov-Maxwell simulations, as has already been demonstrated for setup (V) in Astfalk and Jenko (2017).…”

“…In light of the fact that Seough et al (2015) report significant dumbbell-like deformation of the velocity distribution in particle-in-cell simulations which, in line with the findings of Matteini et al (2006), gets more pronounced for decreasing ∥,p , and accounting for the results of Astfalk and Jenko (2017) that anomalous cyclotron-resonant diffusion can play a crucial role in the growth suppression, we conclude that the latter of the two explanations asks for a careful inspection. To address this point, we embedded Linear Electromagnetic Oscillations in Plasmas with Arbitrary Rotationally-symmetric Distributions (LEOPARD), a linear kinetic dispersion relation solver for arbitrary gyrotropic distributions (Astfalk & Jenko, 2017), in the kinetic quasi-linear framework, which allows us to relax the assumption of bi-Maxwellian preservation in the moment-kinetic approach. This new full-f approach enables the inclusion of effects due to distribution deformation caused by linear wave-particle interactions.…”

The multi-scale nature of the solar wind

“…If the underlying distribution has a shape other than bi-Maxwellian -e.g., if the particles have a κ-distribution according to Equation (62) or a bi-κ-distribution according to Equation (63) -these threshold curves can be significantly different (Summers and Thorne, 1991;Xue et al, 1993;Summers et al, 1994;Xue et al, 1996;Astfalk et al, 2015;Astfalk and Jenko, 2016). The exploration of more general phase-space densities requires direct numerical integration of the dispersion relation (Dum et al, 1980;Matsuda and Smith, 1992;Astfalk and Jenko, 2017;.…”

Kinetic instabilities in the solar wind driven by temperature anisotropies

“…However, for the parallel proton firehose instability, the wave phase speed is defined only over a very narrow range such that all particles pitch-angle scatter about the nearly identical paths defined in the wave frame. This contributes to the distortion of the initial biMaxwellian form into a dumb-bell shape distribution (Astfalk and Jenko 2017), and leads to the premature quenching of the instability. The time evolution of the initially bi-Maxwellian distribution in PIC code runs is discussed in Seough et al ( , 2015a, and shows that indeed, for EMIC case, the quasi-bi-Maxwellian shape is maintained throughout most of the simulation time.…”