Non-linear evolution of synchrotron thermal instabilities

We present a time-dependent, nonlinear study of thermal instability in a magnetized plasma whose relativistic component supports the pressure and undergoes synchrotron losses while the thermal matter provides the inertia of the medium. We follow the temporal evolution of the instability in the nonlinear regime by means of a 1D finite-difference MHD numerical code employing either free or periodic boundary conditions. We find that, in a plasma subject to constant heating, after an initial phase in which the instability growth rate follows the linear model, the instability reaches a quasi-equilibrium state on timescales of the order of several synchrotron timescales. An essential condition for this instability to be efficient is that the plasma is out of equipartition with the relativistic particle energy exceeding the magnetic field energy. The mechanism considered can interpret the formation of filaments of enhanced emission observed at high resolution in lobes and jets of several extragalactic radio sources.