  In solar energetic particle (SEP) events, the physical processes of both
shock acceleration and scattering during transport can cause energy-spectral
indices to be correlated with enhancement or suppression of element abundances
versus mass-to-charge ratios A/Q. We observe correlations for those "gradual"
SEP events where shock waves accelerate ions from the ambient coronal plasma,
but there are no such correlations for "impulsive" SEP events produced by
magnetic reconnection in solar jets, where abundance enhancement in different
events vary from (A/Q)^+2 to (A/Q)^+8, nor are there correlations when shock
waves reaccelerate these residual impulsive ions. In these latter events the
abundances are determined separately, prior to the accelerated spectra. Events
with correlated spectra and abundances show a wide variety of interesting
behavior that has not been described previously. Small and moderate gradual SEP
events, with relative abundances typically depending approximately upon
(A/Q)^-1 and the spectra upon energy E^-2.5, vary little with time. Large SEP
events show huge temporal variations skirting the correlation line; in one case
O spectra vary with time from E^-1 to E^-5 while abundances vary from (A/Q)^+1
to (A/Q)^-2 during the event. In very large events, streaming-limited transport
through proton-generated resonant Alfve'n waves flattens the spectra and
enhances heavy ion abundances prior to local shock passage, then steepens the
spectra and reduces enhancements afterward, recapturing the typical
correlation. Systematic correlation of spectra and element abundances provide a
new perspective on the "injection problem" of ion selection by shocks and on
the physics of SEP acceleration and transport.
