Cluster observations of trapped ions interacting with magnetosheath mirror modes

Mirror modes are among the most intense low frequency plasma wave phenomena observed in the magnetosheaths of magnetized planets. They appear as large amplitude non-propagating fluctuations in the magnetic field magnitude and plasma density. These structures are widely accepted to represent a non-linear stage of the mirror instability, dominant in plasmas with large ion beta and a significant ion temperature anisotropy <I>T</I>_&perp;/<I>T</I>_&parallel;&gt;1. It has long been recognized that the mirror instability both in the linear and non-linear stage is a kinetic process and that the behavior of resonant particles at small parallel velocities is crucial for its development and saturation. While the dynamics of the instability and the effect of trapped particles have been studied extensively in theoretical models and numerical simulations, only spurious observations of the trapped ions were published to date. In this work we used data from the Cluster spacecraft to perform the first detailed experimental study of ion velocity distribution associated with mirror mode oscillations. We show a conclusive evidence for the predicted cooling of resonant ions at small parallel velocities and heating of trapped ions at intermediate pitch angles

Dunkl operators and a family of realizations of osp(1|2)

In this paper, a family of radial deformations of the realization of the Lie superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads to a Dirac operator depending on 3 parameters. Several function theoretical aspects of this operator are studied, such as the associated measure, the related Laguerre polynomials and the related Fourier transform. For special values of the parameters, it is possible to construct the kernel of the Fourier transform explicitly, as well as the related intertwining operator.Comment: 28 pages, some small changes, accepted in Trans. Amer. Math. So