Thermal conduction in a mirror-unstable plasma

Abstract

The ICM plasma is subject to firehose and mirror instabilities at scales of order the ion Larmor radius. The mirror instability generates fluctuations of magnetic-field strength $\delta B / B \sim 1$. These fluctuations act as magnetic traps for the heat-conducting electrons, suppressing their transport. We calculate the effective parallel thermal conductivity in the ICM in the presence of the mirror fluctuations for different stages of the evolution of the instability. The mirror fluctuations are limited in amplitude by the maximum and minimum values of the field strength, with no large deviations from the mean value. This key property leads to a finite suppression of thermal conduction at large scales. We find suppression down to $\approx 0.2$ of the Spitzer value for the secular phase of the perturbations' growth, and $\approx 0.3$ for their saturated phase. The effect operates in addition to other suppression mechanisms and independently of them. Globally, fluctuations $\delta B / B \sim 1$ can be present on much larger scales, of the order of the scale of turbulent motions. However, we do not expect large suppression of thermal conduction by these, because their scale is considerably larger than the collisional mean free path of the ICM electrons. The obtained suppression of thermal conduction by a factor of $\sim 5$ appears to be characteristic and potentially universal for a weakly collisional mirror-unstable plasma.