Charged Particle Diffusion by Violation of the Third Adiabatic Invariant

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Abstract
An equation which describes statistically the motion of charged particles in response to fluctuating electric and magnetic fields is derived. The particles are assumed to be moving in a mirror‐type magnetic geometry. In addition to a static magnetic field there are small superposed fields fluctuating randomly on such a time scale that the first and second adiabatic invariants, M and J, are conserved, but the third or flux invariant φ is violated. By using second adiabatic theory a two dimensional diffusion equation is obtained valid on a much longer time scale than that of the fluctuations. Elements of the diffusion tensor are time—space correlations of fluctuation‐induced perturbations in the guiding center drifts. These drift perturbations are systematically derived and shown to reduce simply in various special cases.

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