The aperiodic firehose instability of counter-beaming electrons in space plasmas

¹ Centre for mathematical Plasma Astrophysics/Dept. of Mathematics, Celestijnenlaan 200B, 3001 Leuven, Belgium
e-mail: marian.lazar@kuleuven.be
² Institute for Theoretical Physics IV, Faculty for Physics and Astronomy, Ruhr-University Bochum, 44780 Bochum, Germany
e-mail: mlazar@tp4.rub.de
³ Departamento de Física, Universidad de Santiago de Chile, Usach, 9170124 Santiago, Chile
⁴ Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Ñuñoa, Santiago 7800003, Chile
⁵ Institute of Physics, University of Maria Curie-Skłodowska, Pl. M. Curie-Skłodowska 5, 20-031 Lublin, Poland
⁶ Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt

Received: 7 October 2022
Accepted: 10 December 2022

Abstract

Context. Recent studies have revealed new unstable regimes of the counter-beaming electrons specific to hot and dilute plasmas from astrophysical scenarios: an aperiodic firehose-like instability is induced for highly oblique angles of propagation relative to the magnetic field, resembling the fast growing and aperiodic mode triggered by the temperature anisotropy T_∥ > T_⊥ (where ∥, ⊥ denote directions relative to the magnetic field).

Aims. The counter-beaming electron firehose instability is investigated here for space plasma conditions, which include not only a specific plasma parameterization but, in particular, the influence of an embedding background plasma of electrons and ions (protons).

Methods. We applied fundamental plasma kinetic theory to prescribe the unstable regimes, characterize the wave-number dispersion of the growth rates, and differentiate from the regimes of interplay with other instabilities. We also used numerical particle-in-cell (PIC) simulations to confirm the instability of these aperiodic modes, and their effects on the relaxation of counter-beaming electrons.

Results. Linear theory predicts a systematic inhibition of the (counter-)beaming electron firehose instability (BEFI) by reduction of the growth rates and the range of unstable wave-number with increasing relative density of the background electrons. To obtain finite and reasonably high values of the growth rate, the (relative) beam speed does not need to be very high (just comparable to the thermal speed), but the (counter-)beams must be dense enough, with a relative density of at least 15%–20% of the total density. Quantified in terms of the beam speed and the beta parameter, the plasma parametric conditions favorable to this instability are also markedly reduced under the influence of background electrons. Numerical simulations confirm not only that BEFI can be excited in the presence of background electrons, but also the inhibiting effect of this population, especially when this latter is cooler. In the regimes of transition to electrostatic (ES) instabilities, BEFI is still robust enough to develop as a secondary instability, after the relaxation of beams under a quick interaction with ES fluctuations.

Conclusions. To the features presented in previous studies, we can add that BEFI resembles the properties of solar wind firehose heat-flux instability triggered along the magnetic field by the anti-sunward electron strahl. However, BEFI is driven by a double (counter-beaming) electron strahl, and develops at highly oblique angles, which makes it potentially effective in the regularization and relaxation of the electron counter-beams observed in expanding coronal loops (with closed magnetic field topology) and in interplanetary shocks.