A statistical study of diffuse energetic ion events and their related
waves upstream of the Earth's bow shock was performed using data from
the Active Mapetospheric Particle Tracer Explorers/Ion Release Module
satellite over two 5-month periods in 1984 and 1985. The data set was
used to test the assumption in the self-consistent model of the upstre
am wave and particle populations by Lee (1982) that the particle accel
eration through hydromagnetic waves and the wave generation are direct
ly coupled. The comparison between the observed wave power and the wav
e power predicted on the observed energetic particle energy density an
d solar wind parameters results in a high correlation coefficient of a
bout 0.89. The intensity of diffuse ions falls off approximately expon
entially with the distance upstream from the bow shock parallel to the
magnetic field with e-folding distances which vary from approximately
3.3 R(E) to approximately 11.7 R(E) over the energy range from 10 keV
/e to 67.3 keV/e for both protons and alpha particles. After normalizi
ng the upstream particle densities to zero bow shock distance by using
these exponential variations, a good correlation (0.7) of the density
of the diffuse ions with the solar wind density was found. This suppo
rts the suggestion that the solar wind is the source of the diffuse io
ns. Furthermore, the spectral slope of the diffuse ions correlates wel
l with the solar wind velocity component in the direction of the inter
planetary magnetic field (0.68 and 0.66 for protons and alpha particle
s) which concurs with the notion that the solar wind plays an importan
t role in the acceleration of the upstream particles.