Authors: Garyfallia Strus (University of Colorado Boulder), Steven Cranmer (University of Colorado Boulder)

The accurate modeling of the energy exchange between waves and particles in the solar wind depends sensitively on the expression for the diffusion tensor for quasilinear wave-particle resonances. To our knowledge, the form of the electromagnetic diffusion tensor most commonly used in the literature corresponds to the limiting case where the growth and damping rates of waves are assumed to be small compared to the real frequencies. However, this approximation is not always valid: the ratios of the imaginary to real parts of the frequency can sometimes reach values of order unity. These cases require generalized expressions for the diffusion tensor and are the focus of this work. We begin by writing the solution to the equations of the electromagnetic third-order closure of the Vlasov Cumulant (collisionless BBGKY) Hierarchy by using an operator formulation first introduced by Davidson (1972) for the electrostatic case. This allows us to derive a quasilinear equation for the evolution of the background distribution function for arbitrary dispersion relations with arbitrarily large growth/damping rates. These expressions reduce to the standard forms (i.e., Dirac delta functions consistent with the Plemelj formula) in the limit of small growth/damping rates, and they also differ from the idealized Lorentzian forms presented by Cranmer (2014). Our primary goal is to explore changes in the shapes of “resonant shells” in velocity space due to these new expressions. Also, we find that the generalized diffusion tensor is no longer symmetric and that its antisymmetric part may give rise to substantial advection in velocity space in addition to the standard diffusion. We aim to illustrate these new expressions with example parameters relevant to the corona and inner heliosphere, and we hope to show how the use of these new expressions will affect calculations of particle heating rates.