  Scattering, during interplanetary transport in large, "gradual" solar
energetic-particle (SEP) events, can cause element abundance enhancements or
suppressions that depend upon the mass-to-charge ratio A/Q of the ions as an
increasing function early in events and a decreasing function of the residual
scattered ions later. Since the Q values for the ions depend upon the source
plasma temperature T, best fits, assuming a primarily power-law dependence of
enhancements vs. A/Q, provide a fundamentally new method to determine the most
probable value of T for these events in the region of 3-10 MeV/amu. Complicated
variations in the grouping of element enhancements or suppressions match
similar variations in A/Q at the best-fit temperature. We find that fits to the
times of increasing and decreasing powers give similar values of T, most
commonly in the range of 0.8-1.6 MK for 69% of the events, consistent with the
acceleration of ambient coronal plasma by shock waves driven out from the Sun
by coronal mass ejections (CMEs). However, 24% of the SEP events studied showed
plasma of 2.5-3.2 MK, typical of that previously determined for the smaller
impulsive SEP events; these particles may be reaccelerated preferentially by
quasi-perpendicular shock waves that require a high injection threshold that
the impulsive-event ions exceed or simply by high intensities of impulsive
suprathermal ions at the shock. The source-temperature distribution of ten
higher-energy ground-level events (GLEs) in the sample is similar to that of
the other gradual events. Some events show evidence that a portion of the ions
have been further stripped of electrons; such events are smaller and tend to
cluster late in the solar cycle.
