Abstract
A kinetic description is proposed for the dynamics of vortex lattices in rigid superconductors located in a magnetic field whose direction varies. The collision integral in the kinetic equation for the vortex density includes the crossing and successive regeneration of vortex filaments. The second equation of the theory expresses force balance: the equality of the magnetic force to the pinning force. It is shown that the magnetic force contains a collective term which depends on the vortex distribution function. The model is used as a basis for the electrodynamic equations of the critical state for the case of crossed magnetic fields. The transition from the proposed theory to the previously developed two-velocity quasihydrodynamic model is discussed.
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