Partially Ionized Plasma - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 2

is

d N α = f α ( r , V ,t )d r d V .

From the definition of f α ( r , V ,t ), the concentration of particles of the sort α
can be written as

N α ( r ,t )= f α ( r , V ,t )d V .

(1.1)

The products

ρ mα = m α N α ( r ,t ) , α = Z α eN α ( r ,t ) (1.2)

are the mass density and charge density of particles of the type α ; Z e = 1

for electrons and Z α = 0 for neutrals. Total concentration, charge density and
mass density are determined as
N =
α

−

ρ =
α

m =
α

N α , Z α eN α ( r ,t ) , m α N α ( r ,t ) .

The summation is taken over all plasma species.

The Boltzmann-Vlasov Equation

As for the non-ionized gases, the kinetic equation method is applicable only
for low-density plasma in which the mean energy of the interaction of two
particles is low in comparison with their mean kinetic energy. In this case, it
is possible to consider the plasma as a gas. Neglecting at the first step the
existence of the multi-charged ions, the energy of the interaction between two
charged particles is e 2 /

r , where r

is a mean distance between the particles.

N − 1 / 3 .
Under these simplifying assumptions, we write the condition of applicability
of the gas approximation in the form

If N is the total number of particles in a unit volume, then r ∼

e 2 / e 2 N 1 / 3 ,

kT r ∼ (1.3)

10 − 16 erg where k is the Boltzmann constant ( k =1 . 38 K), T is the plasma

temperature (in Kelvins, K). This condition can be expressed in terms of the
Debye radius

× ·

r D = kT

8 πNe 2 .

(1.4)

r D determines the distance of screening of the Coulomb fields in the plasma.
Taking into account (1.4), the condition (1.3) can be rewritten as

2 / 8 π

r 2 D , r (1.5)