Dynamics of quasilinear relaxation of fast particles in a plasma at the presence of sources and sinks of particles and waves

Features of quasilinear relaxation of fast particles in plasma under conditions when fast particles ingress rate (due to injection or acceleration) is comparable with wave attenuation decrement are analyzed. In one-dimensional approximation the system dynamics are reduced to the establishment of the steady state within the period equal to several specific times of fast particles accumulation. Under certain conditions the establishment of the steady state is accompanied by relaxation oscillations of wave energy density. Steady state instability is possible in case of inhomogeneous medium or multidimentional phase space; selfoscillating mode of wave generation is realized under such instability. Such a mode is investigated for the systems of equations which describe the cyclotron instability of whistle waves in an inhomogeneous magnetic trap and beam instability in a weak magnetic field. The results of numeric solution of these systems are considered; the results confirm a possibility of the establishment of auto-oscillations