Scattering, during interplanetary transport in large, "gradual" solarenergetic-particle (SEP) events, can cause element abundance enhancements orsuppressions that depend upon the mass-to-charge ratio A/Q of the ions as anincreasing function early in events and a decreasing function of the residualscattered ions later. Since the Q values for the ions depend upon the sourceplasma temperature T, best fits, assuming a primarily power-law dependence ofenhancements vs. A/Q, provide a fundamentally new method to determine the mostprobable value of T for these events in the region of 3-10 MeV/amu. Complicatedvariations in the grouping of element enhancements or suppressions matchsimilar variations in A/Q at the best-fit temperature. We find that fits to thetimes of increasing and decreasing powers give similar values of T, mostcommonly in the range of 0.8-1.6 MK for 69% of the events, consistent with theacceleration of ambient coronal plasma by shock waves driven out from the Sunby coronal mass ejections (CMEs). However, 24% of the SEP events studied showedplasma of 2.5-3.2 MK, typical of that previously determined for the smallerimpulsive SEP events; these particles may be reaccelerated preferentially byquasi-perpendicular shock waves that require a high injection threshold thatthe impulsive-event ions exceed or simply by high intensities of impulsivesuprathermal ions at the shock. The source-temperature distribution of tenhigher-energy ground-level events (GLEs) in the sample is similar to that ofthe other gradual events. Some events show evidence that a portion of the ionshave been further stripped of electrons; such events are smaller and tend tocluster late in the solar cycle.
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