MULTIPLE-TIMESCALES ANALYSIS OF IDEAL POLOIDAL ALFVEN WAVES

Time-dependent analytic solutions for the evolution of undriven ideal standing poloidal Alfven waves are considered in a box model magnetosp here. Assuming an ''aximuthal'' variation of exp i lambda y, where lam bda is large, we use the asymptotic method of multiple timescales to d etermine analytic solutions over the long timescale a defined by sigma = epsilon t, where epsilon 1/lambda. Our asymptotic poloidal Alfven w ave solutions (with lambda >> k(x), k(z)) accurately reproduce the und riven ideal wave polarization rotation from poloidal to toroidal in ti me determined numerically by Mann and Wright [1995]. Using the same as ymptotic method, we further consider the evolution of radially localiz ed large lambda Alfven waves. We find that undriven waves having k(x), lambda >> k(z), oscillating in a radially inhomogeneous plasma remain incompressible to leading order and experience similar asymptotically toroidal behavior as t --> infinity. Consequently, undriven poloidal Alfven waves and, in general, transversally localized large lambda ide al Alfven wave disturbances have a finite lifetime before they evolve into purely decoupled toroidal Alfven waves. This polarization rotatio n may be apparent in waves driven by the drift-bounce resonance mechan ism in situations where the wave evolution occurs more rapidly than io nospheric damping. This can be possible on the dayside of the magnetos phere, with the evolution more likely to be observable toward the end of a temporal wave packet when the driving mechanism is no longer oper ative.