Nonlinear Growth of Firehose and Mirror Fluctuations in Astrophysical Plasmas

In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, $\delta B/B\sim 1$, on a time scale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.

Figure 1

Evolution of $\delta B_{\perp }^2(t)/B_0^2$ and $\Delta (t)$ (inset) obtained by numerically solving Eqs. (9) and (8) for a single Fourier mode. Here ${\gamma }_0/{\nu }_{ii}=0.01$, ${\beta }_i=1000$, and $k_{\parallel }{v}_{\mathrm{th}i}/\sqrt{2}{\nu }_{ii}=10$.