Speaker
Vladimir Kocharovsky
Description
See the full Abstract at http://ocs.ciemat.es/EPS2018ABS/pdf/P5.4010.pdf
Practical criteria for the Weibel instability and its saturation
Vl. V. Kocharovsky1 , V.V. Kocharovsky2 , V.Yu. Martyanov3
1 1Institute of Applied Physics RAS, Nizhny Novgorod, Russia
2 Texas A&M University, College Station, USA
3 Intel Corp., Chandler, USA
We consider the Weibel, purely aperiodic instability in a collisionless plasma, relativistic or
not, for the important in practice case when the particle distribution function exhibits mirror
symmetry with respect to a certain plane and a wave vector of an ordinary wave perturbation is
parallel to this plane. In this case, we obtain a novel analytical criterion for the Weibel instability
using its analogy with a long-wavelength soft-mode instability which is well known in the solid
state physics. It facilitates an analysis of the Weibel instability and agrees with the results which
have been known for the certain particle distributions, including the bi-Maxwellian, power-law,
and parallelepiped ones as well as various variants of the so-called waterbag distributions. Also,
for a series of the special cylindrically-symmetric particle distributions we find the analytical
dependence of the Weibel-instability growth rate on the wavenumber of perturbation and show
that it agrees well with the criterion presented [1]. We compare in detail the various known
estimates of a magnetic field saturating the Weibel instability and, in particular, point to the
case when this field cannot achieve an equipartition value due to a weak anisotropy of the initial
particle distribution. In the latter, poorly studied case, a relatively large-scale magnetic field is
generated and, during the inverse growth-rate time, most particles follow the diffusive transport
law and undergo displacements over many wavelengths of this field. We estimate a number of
particles which are subject to bounce-oscillations under these conditions and come to a general
criterion of the saturation of the Weibel instability [1]. We show that it is consistent with the
analytical results obtained previously for the case of a strong anisotropy as well as with the
numerical simulations carried out for the particular examples of a weak anisotropy of particle
distribution. Finally, we present the practical examples of an implementation of both criteria for
the typical situations in the space and laboratory collisionless plasmas with anisotropic particle
distributions.
References
[1] V.V. Kocharovsky, Vl.V. Kocharovsky, V.Yu. Martyanov, S.V. Tarasov, Phys. Uspekhi, 59, 1165 (2016)
