Abstract
The present paper formulates a weak turbulence theory in which electromagnetic perturbations are assumed to propagate in directions perpendicular to the ambient magnetic field. By assuming that all wave vectors lie in one direction transverse to the ambient magnetic field, the linear solution and second-order nonlinear solutions to the equation for the perturbed distribution function are obtained. Nonlinear perturbed current from the second-order nonlinearity is derived in general form, but the limiting situation of cold plasma temperature is taken in order to derive an explicit nonlinear wave kinetic equation that describes three-wave decay/coalescence interactions among X and Z modes. A potential application of the present formalism is also discussed.
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