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Nonlinear Processes in Geophysics


Department of Physics and Astronomy


Mirror mode turbulence is the lowest frequency perpendicular magnetic excitation in magnetized plasma proposed already about half a century ago by Rudakov and Sagdeev (1958) and Chandrasekhar et al. (1958) from fluid theory. Its experimental verification required a relatively long time. It was early recognized that mirror modes for being excited require a transverse pressure (or temperature) anisotropy. In principle mirror modes are some version of slow mode waves. Fluid theory, however, does not give a correct physical picture of the mirror mode. The linear infinitesimally small amplitude physics is described correctly only by including the full kinetic theory and is modified by existing spatial gradients of the plasma parameters which attribute a small finite frequency to the mode. In addition, the mode is propagating only very slowly in plasma such that convective transport is the main cause of flow in it. As the lowest frequency mode it can be expected that mirror modes serve as one of the dominant energy inputs into plasma. This is however true only when the mode grows to large amplitude leaving the linear stage. At such low frequencies, on the other hand, quasilinear theory does not apply as a valid saturation mechanism. Probably the dominant processes are related to the generation of gradients in the plasma which serve as the cause of drift modes thus transferring energy to shorter wavelength propagating waves of higher nonzero frequency. This kind of theory has not yet been developed as it has not yet been understood why mirror modes in spite of their slow growth rate usually are of very large amplitudes indeed of the order of |B/B0|2~O(1). It is thus highly reasonable to assume that mirror modes are instrumental for the development of stationary turbulence in high temperature plasma. Moreover, since the magnetic field in mirror turbulence forms extended though slightly oblique magnetic bottles, low parallel energy particles can be trapped in mirror modes and redistribute energy (cf. for instance, Chisham et al. 1998). Such trapped electrons excite banded whistler wave emission known under the name of lion roars and indicating that the mirror modes contain a trapped particle component while leading to the splitting of particle distributions (see Baumjohann et al., 1999) into trapped and passing particles. The most amazing fact about mirror modes is, however, that they evolve in the practically fully collisionless regime of high temperature plasma where it is on thermodynamic reasons entirely impossible to expel any magnetic field from the plasma. The fact that magnetic fields are indeed locally extracted makes mirror modes similar to "superconducting" structures in matter as known only at extremely low temperatures. Of course, microscopic quantum effects do not play a role in mirror modes. However, it seems that all mirror structures have typical scales of the order of the ion inertial length which implies that mirrors evolve in a regime where the transverse ion and electron motions decouple. In this case the Hall kinetics comes into play. We estimate that in the marginally stationary nonlinear state of the evolution of mirror modes the modes become stretched along the magnetic field with k||=0 and that a small number the order of a few percent of the particle density is responsible only for the screening of the field from the interior of the mirror bubbles.