The L mode in electromagnetic proton-cyclotron waves (EPCWs) propagating
parallel
to a uniform ambient magnetic field is studied here analytically. A generalized
Lorentzian distribution function is used to model the plasma. Analytical
expressions
for the wavenumber and for both the temporal and convective growth rates
for a multi-ion plasma are obtained within the linear theory. This analytical
approach
is appropiate for β∥<1, which is the ratio of plasma
kinetic pressure to
magnetic field pressure. The characteristics of the unstable spectrum are
found to
be independent of high-energy particles. For a plasma composed of electrons
plus
hot and cold protons, it is shown that the maximum growth rates as functions
of
cold-proton concentration δ can always decrease, or can increase
until δ reaches
a certain peak value and decrease thereafter, or can always increase, depending
on the thermal anisotropy of the hot protons. This behaviour is similar
to that in
Maxwellian plasmas. However, for the convective growth rate, the expression
for the
optimum cold-proton concentration shows a significant dependence on the
spectral
index κ. Therefore, when cold protons are injected, it is more
difficult to obtain
optimum amplification in a Lorentzian plasma than in a Maxwellian plasma.
It is also
shown that the influence of the high-energy tail on the generation and
amplification
processes of the EPCWs is controlled by thermal anisotropy and cold-ion
population.
As a consequence of the latter, temporal and convective growth rates can
be
larger than, equal to or smaller than those of Maxwellian plasmas, depending
on the
anisotropy of the hot-proton distribution and on the cold-proton concentration.