the turbulent plasma of the current sheet) opens a new approach, where the elastic particle-plasmon interaction and direct energy change in the DC electric field are combined in a natural way. This approach leads both to the observed power-law energy spectrum and high energy limits (Pustil'nik, 1978).
According to Pustil'nik (1978), the physical reason for the formation of the spectrum in the model (ii) is the universal power-law dependence of the scattering probability on the particle energy: P(EE"3. This leads to different free path lengths for particles with opposite velocity directions relative to the electric field. The result is that two diffusion fluxes are formed: the first is the standard flux caused by the density or potential gradient, and the second is the specific flux caused by variation of kinetic parameters in the medium, similar to thermodiffusion. It was found for the second flux that the energy of particles E = ZeEx and also their number n(E) depends only on the distance x from the point of injection of the particles into the acceleration state to the space boundary where particles escape. This general connection leads to a direct "leakage-lifetime" relation with a power-law character for the energy spectrum. The resulting spectrum can be estimated from conservation of the diffusion flux (Pustil'nik, 1978):
which, for a current sheet with the simplest geometry, leads naturally to a power-law energy spectrum for the ejected particles:
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