THE SELF-SIMILAR, NONLINEAR EVOLUTION OF ROTATING MAGNETIC-FLUX ROPES

We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their sy mmetry axis. Our force balance consists of inertial terms, which inclu de the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We emp loy the ''separable'' class of self-similar magnetic fields, defined r ecently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillat ion. We investigate the specific effect rotation has on these two mode s of evolution. We focus on critical values of the flux rope parameter s and show that rotation can suppress the oscillatory mode. We estimat e the critical value of the angular velocity Omega(cvit), above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. B y setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation omega is inversely proportional to the a ngular velocity of rotating Omega; the product omega Omega being propo rtional to the inverse square of the Alfven time. The period of large- amplitude oscillations of a rotating flux rope of low beta increases e xponentially with the energy of the equivalent 1D oscillator. With res pect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This m ultiplicative factor depends on the ratio of the azimuthal speed to th e Alfven speed. Finally, considering interplanetary magnetic clouds as cylindrical flux ropes, we inquire whether they rotate. We find that a 1 AU only a minority do. We discuss data on two magnetic clouds wher e we interpret the presence in each of vortical plasma motion about th e symmetry axis as a sign of rotation. Our estimates for the angular v elocities suggest that the parameters of the two magnetic clouds are b elow critical values. The two clouds differ in may respects (such as a ge, bulk flow speed, size, handedness of the magnetic field, etc.), an d we find that their rotational parameters reflect some of these diffe rences, particularly the difference in age. In both clouds, a rough es timate of the radial electric field in the rigidly rotating core, calc ulated in a non-rotating frame, yields values of the order mV m(-1).