We investigate the propagation, growth, and decay of fast magnetosonic wave
s in the Earth's magnetosphere which are believed to contribute to proton h
eating up to energies of a few hundred eV near the magnetic equator. We con
struct a model of the proton and electron distribution functions from space
craft data and use the HOTRAY code to calculate the path-integrated growth
and decay of the waves over a range of L shells from L = 2 to L = 7. instab
ility calculations show that the waves are excited at very large angles of
propagation with respect to the magnetic field, psi approximate to 89 degre
es, at the harmonics of the proton gyrofrequency Omega (H+) up to the lower
hybrid resonance frequency omega (LHR) by a proton ring distribution at en
ergies of the order of 10 keV. As a "rule of thumb", we find that growth is
possible for omega > 30 Omega (H+) when the ring velocity exceeds the Alfv
en speed nu (R) > nu (A), and for omega < 30<Omega>(H+) when nu (R) > 2 nu
(A) For propagation in the meridian plane, waves generated just outside the
plasmapause grow with large amplification as they propagate away from the
Earth but eventually lose energy to plasma sheet electrons at energies of a
few keV by Landau damping. The waves grow to large amplification at freque
ncies just below omega (LHR) For inward propagation we find that waves gene
rated just outside the plasmapause can propagate to L approximate to 2 with
very little attenuation, suggesting that waves observed well inside the pl
asmasphere could originate from a source region just outside the plasmapaus
e. Strong wave growth only occurs for large angles of propagation, and thus
the waves are confined to within a few degrees of the magnetic equator. Wa
ves generated near geostationary orbit and which propagate toward the Earth
are absorbed by Doppler-shifted cyclotron resonance when they propagate in
to a region where nu (R) < <nu>(A). Cyclotron resonant absorption causes pi
tch angle scattering and heating transverse to the ambient magnetic held. T
he amount of absorption, and hence transverse proton heating, increases sig
nificantly as the thermal proton temperature is increased up to 100 eV, sug
gesting a feedback process. Ray tracing shows that transverse heating of th
e thermal proton distribution is most likely to occur just outside the plas
mapause where nu (A) is large. Since proton ring distributions are formed d
uring magnetic storms at ring current energies, we suggest that fast magnet
osonic waves provide an additional energy loss process for ring current dec
ay.