The generalized Balescu-Lenard collision Operator

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Abstract
The generalization of the Balescu-Lenard collision operator to its fully electromagnetic counterpart in Kaufman's action-angle formalism is derived and its properties investigated. The general form may be specialized to any particular geometry where the unperturbed particle motion is integrable, and thus includes cylindrical plasmas, inhomogeneous slabs with non-uniform magnetic fields, tokamaks and the particularly simple geometry of the standard operator as special cases. The general form points to the commonality between axisymmetric, turbulent and ripple transport, and implies properties (e.g. intrinsic ambipolarity) that should be shared by them, under appropriate conditions. Along with a turbulent ‘anomalous diffusion coefficient’ calculated for tokamaks in previous work, an ‘anomalous pinch’ term of closely related structure and scaling is also implied by the generalized operator.