Qingrong Chen, Vahé Petrosian
Abridged. Following our recent paper, we have developed an inversion method to determine the basic characteristics for the model of stochastic acceleration (SA) by plasma wave turbulence directly and non-parametrically from observations in the framework of the leaky box version of the Fokker-Planck kinetic equation. In particular, we show that by inverting the Fokker-Planck equation to its integral form, one can derive the energy diffusion coefficient and direct acceleration rate by turbulence in terms of the accelerated and escaping particle spectra. We apply the analytic formulas to solar flare suprathermal electrons, which produce HXR emission at the coronal loop top (LT) and two thick target footpoints. Using the spatially resolved electron spectra from regularized electron flux images, we determine the electron escape time (related to pitch angle scattering rate), and the energy diffusion coefficient at the LT accelerator. Results obtained from two intense RHESSI events indicate that the escape time increases with energy and the energy diffusion (acceleration) time and scattering time have dramatically different energy dependences. Such behaviors may be difficult to explain by existing SA modeling, and may indicate that a different acceleration mechanism is at work or imply a breakdown of the interpretation of the electron escape being a random walk process. The discrepant energy dependences can be alleviated somewhat by a much steeper than the Kolmogorov-type turbulence spectrum. A more likely explanation could be that the escape of electrons out of the LT acceleration region is governed by converging fields in a magnetic mirror geometry. The results demonstrate the critical importance of combined modeling of electron acceleration by plasma wave turbulence and the large scale magnetic field variations in a reconnection environment.
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http://arxiv.org/abs/1307.1837
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