Electron pitch angle diffusion by electrostatic electron cyclotron harmonic waves: The origin of pancake distributions

It has been suggested that highly anisotropic electron pancake distribution s are the result of pitch angle diffusion by electrostatic electron cyclotr on harmonic (ECH) and whistler mode waves in the equatorial region. Here we present pitch angle diffusion rates for ECH wave spectra centered at diffe rent frequencies with respect to the electron gyrofrequency Omega(e), corre sponding to spacecraft observations. The wave spectra are carefully mapped to the correct resonant electron velocities. We show that previous diffusio n calculations of ECH waves at 1.5 Omega(e), driven by the loss cone instab ility, result in large diffusion rates confined to a small range of pitch a ngles near the loss cone and therefore cannot account for pancake distribut ions. However, when the wave spectrum is centered at higher frequencies in the band (> 1.6 Omega(e)), the diffusion rates become very small inside the loss cone, peak just outside, and remain large over a wide range of pitch angles up to 60 degrees or more. When the upper hybrid resonance frequency (UHR)-U-omega is several times Omega(e), ECH waves excited in higher bands also contribute significantly to pitch angle diffusion outside the loss con e up to very large pitch angles. We suggest that ECH waves driven by a loss cone could form pancake distributions as they grow if the wave spectrum ex tends from the middle to the upper part of the first (and higher) gyroharmo nic bands. Alternatively we suggest that pancake distributions can be forme d by outward propagation in a nonhomogeneous medium, so that resonant absor ption occurs at higher frequencies between (n + 1\2) and (n + 1)Omega(e) in regions where waves are also growing locally at < 1.5 Omega(e). The calcul ated diffusion rates suggest that ECH waves with amplitudes of the order of 1 mV m(-1) can form pancake distributions from an initially isotropic dist ribution on a timescale of a few hours. This is consistent with recent CRRE S observations of ECH wave amplitudes following substorm injections near ge ostationary orbit and the timescales for pancake formation. Persistent but much weaker ECH waves can further intensify and maintain pancake distributi ons during magnetically quiet periods.