The work proposes an analytical theory of nonlinear generation of large-scale magnetic turbulence in collisionless plasma with an anisotropic velocity distribution of particle in the presence of an external magnetic field. Based on the results of the dispersion analysis of the Weibel-type instability in magnetoactive collisional plasma, and with use of the quasilinear approach, a system of equations describing the evolution of the mean-square magnetic-field energy density of small- and large-scale components of the turbulent field is obtained.

It is shown that, even in the absence of interparticle collisions, anomalous collisions of particles due to scattering on small-scale magnetic fluctuations lead to instability of long-wave harmonics, which are stable in the linear approximation. The non-linear growth of such harmonics at a given anisotropy of the particle velocity distribution, consistent with the dynamics of short-wave perturbations at the saturation stage and possible anisotropic particle injection, occurs in the superexponential regime and corresponds to an explosive-type instability (Fig. 1).

The growth law of the large-scale magnetic field is found analytically and the critical time of explosive instability is estimated. This type of fundamental plasma process is expected in a number of transient phenomena in laboratory and astrophysics, e.g., in accretion disks and jets, in stellar winds and coronal flares, in collisionless shock waves and laser ablation processes.

Fig.1 Time dependence of the mean-square magnetic-field energy density $w$. The dotted and dash-dotted lines are numerical solutions for small- and large-scale components of the turbulent field, and the blue and red solid lines are analytical solutions, respectively. A formal explosion takes place at a normalized time $\tau_c$.

N.Emel’yanov and V.V.Kocharovskii
JETP Letters 122, issue 2 (2025)