689 research outputs found
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><sub>⊥</sub>/<I>T</I><sub>∥</sub>>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
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