Nonstationary driven oscillations of a magnetic cavity

The problem of transition to the steady state of driven oscillations in a m agnetic cavity in a cold resistive plasma is addressed. The foot point driv ing polarized in the inhomogeneous direction is considered, and it is assum ed that the cavity length in the direction of the equilibrium magnetic fiel d is much larger than the cavity width in the inhomogeneous direction. The latter assumption enables one to neglect the variation of the magnetic pres sure in the inhomogeneous direction, which strongly simplifies the analysis . The explicit solution describing the nonstationary behavior of the magnet ic pressure and the velocity is obtained. This solution is used to study th e properties of the transition to the steady state of oscillation. The main conclusion is that, in general, there are two different characteristic tra nsitional times. The first time is inversely proportional to the decrement of the global mode. It characterizes the transition to the steady state of the global motion, which is the coherent oscillation of the cavity in the i nhomogeneous direction. The second time is the largest of the two times, th e first transitional time and the phase-mixing time, which is proportional to the magnetic Reynolds number in 1/3 power. It characterizes the transiti on to the steady state of the local motion, which is oscillations at the lo cal Alfven frequencies, and the saturation of the energy damping rate. An e xample from solar physics shows that, in applications, the second transitio nal time can be much larger than the first one. (C) 2000 American Institute of Physics. [S1070-664X(00)04509-2].