6 Cold plasma waves in a magnetized plasma
Chapter 4 showed that finite temperature is responsible for the lowest order dispersive
terms in both electron plasma waves [dispersionω^2 =ω^2 p+3k^2 κTe/me] and ion acoustic
waves [dispersionω^2 =k^2 c^2 s/(1+k^2 λ^2 De)]. Furthermore, finite temperature was shown
in Chapter 5 to be essential to Landau damping and instability.
Chapter 4 also contained a derivation of the electromagnetic plasma wave [dispersion
ω^2 =ωpe^2 +k^2 c^2 ] and of the inertial Alfvén wave [dispersionω^2 =kz^2 vA^2 /(1+k^2 xc^2 /ω^2 pe)],
both of which had no dependence on temperature. To distinguish waves which depend
on temperature from waves which do not, the terminology “cold plasma wave” and “hot
plasma wave” is used. A cold plasma wave is a wave having a temperature-independent
dispersion relation so that the temperature could be set to zero without changing the wave,
whereas a hot plasma wave has a temperature-dependent dispersion relation. Thus hot
and cold do not refer to a ‘temperature’ of the wave, but rather to the wave’s dependence
or lack thereof on plasma temperature. Generally speaking, cold plasma waves are just
the consequence of a large number of particles having identical Hamiltonian-Lagrangian
dynamics whereas hot plasma waves involve different groups of particleshaving different
dynamics because they have different initial velocities. Thus hot plasma waves involve
statistical mechanical or thermodynamic considerations. The generaltheory of cold plasma
waves in a uniformly magnetized plasma is presented in this chapter and hot plasma waves
will be discussed in later chapters.
6.1 Redundancy of Poisson’s equation in electromagnetic mode analysis
When electrostatic waves were examined in Chapter 4 it was seen thatthe plasma response
to the wave electric field could be expressed as a sum of susceptibilities where the sus-
ceptibility of each species was proportional to the density perturbation of that species.
Combining the susceptibilities with Poisson’s equation gave a dispersion relation. How-
ever, because electric fields can also be generated inductively, electrostatic waves are not
the only type of wave. Inductive electric fields result from time-dependent currents, i.e.,
from charged particle acceleration, and do not involve density perturbations. As an exam-
ple, the electromagnetic plasma wave involved inductive rather thanelectrostatic electric
fields. The inertial Alfvén wave involved inductive electric fields in the parallel direction
and electrostatic electric fields in the perpendicular direction.