J. Steinacker et al., THE HELIUM VALLEY - COMPARISON OF IMPULSIVE SOLAR-FLARE ION ABUNDANCES AND GYRORESONANT ACCELERATION WITH OBLIQUE TURBULENCE IN A HOT MULTIION PLASMA, The Astrophysical journal, 476(1), 1997, pp. 403-427
We present a detailed interpretation of the heavy ion abundance enhanc
ements observed in impulsive flare energetic particles, in terms of th
e conditions for gyroresonant acceleration by moderately oblique waves
in a hot solar coronal plasma. On the basis of a realistic coronal pl
asma containing its complete set of minor ions, we analyze first all p
arallel wave modes in terms of their dispersion relation, damping time
scale, and condition for gyroresonant acceleration of thermal ions, as
a function of temperature. We identify the ''Helium Valley,'' the reg
ion in the frequency-wavenumber plane of strong wave damping by therma
l He-4(+2) ions, as crucial for explaining the observed abundances: an
y ions with charge-to-mass ratio in the neighborhood of 0.5 cannot be
accelerated preferentially, relative to He-4(+2). Then solving the dis
persion relation equation for oblique waves in a hot e-p-He plasma, we
discuss this general class of waves in terms of polarization and damp
ing timescale. For waves propagating at moderate angles to the magneti
c held (theta not approximate to 90 degrees), our calculations indicat
e that the first harmonic n = 1 gyroresonance is dominant, and that th
e corresponding He valley narrows down for increasing angle theta. Usi
ng this analysis, we calculate the limits of the He valley and investi
gate the preferential gyroresonant acceleration of heavy ions by moder
ately oblique waves (theta not approximate to 90 degrees) in a solar c
oronal plasma. Only for nearly perpendicular waves (theta approximate
to 90 degrees), are higher order resonances important and regions of w
ave damping by interaction with thermal particles vanishingly narrow i
n frequency. We estimate the fraction of ions of each element outside
the He valley as a function of temperature and compare the resulting e
nhanced abundances with the observed enhancements, for the case of a s
pectrum of non-quasi-perpendicular waves, as produced by a cascading o
f the general turbulence. The results allow us to specify the range of
possible temperatures for the source plasma of the accelerated partic
les to between similar to 2.4 and similar to 4.5 x 10(6) K, i.e., comp
arable to active region (AR), but not to flaring gas, temperatures. Th
is points to an acceleration of the ions taking place, either in the A
R gas surrounding the flare itself or within the flaring loop but befo
re it became heated. Constraints are set on the typical time At over w
hich the ions are accelerated preferentially. We find times between si
milar to 5 x 10(-4) and similar to 3 x 10(-2) s (for our nominal plasm
a with density and field of n(e) = 10(10) cm(-3) and B = 100 G); it co
uld be similar to 10 times larger, if the typical conditions in quiesc
ent ARs (n(e) similar to 2 x 10(9) cm(-3) and B similar to 200 G) appl
y also to the bulk similar to 3 x 10(6) K gas of flaring ARs. We discu
ss another physical interpretation of At, if wave cascading is effecti
ve. Preliminary calculations have shown that the proposed selective ac
celeration mechanism can be applied in underdense (omega(p)/Omega(e) <
1) as well as in overdense plasmas (our nominal case), provided that
quasi-perpendicular waves (generated, e.g., by an electron beam) are n
ot dominant.