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We have developed an inversion method for determination of thecharacteristics of the acceleration mechanism directly and non-parametricallyfrom observations, in contrast to the usual forward fitting of parametric modelvariables to observations. In two recent papers (Petrosian & Chen 2010, Chen &Petrosian 2013), we demonstrate the efficacy of this inversion method by itsapplication to acceleration of electrons in solar flares based on stochasticacceleration by turbulence. Here we explore its application for determining thecharacteristics of shock acceleration in supernova remnants (SNRs) based on theelectron spectra deduced from the observed nonthermal radiation from SNRs andthe spectrum of the cosmic ray electrons observed near the Earth. These spectraare related by the process of escape of the electrons from SNRs and energy lossduring their transport in the galaxy. Thus, these observations allow us todetermine spectral characteristics of the momentum and pitch angle diffusioncoefficients, which play crucial roles in both direct acceleration byturbulence and in high Mach number shocks. Assuming that the average electronspectrum deduced from a few well known SNRs is representative of those in thesolar neighborhood we find interesting discrepancies between our deduced formsfor these coefficients and those expected from well known wave-particleinteractions. This may indicate that the standard assumptions made in treatmentof shock acceleration need revision. In particular, the escape of particlesfrom SNRs may be more complex than generally assumed.

Determination of Acceleration Mechanism Characteristics Directly and Non-Parametrically from Observations: Application to Supernova Remnants