*Astron. Astrophys. 337, 887-896 (1998)*
## 3. Basic equations
We start from the equations of three-fluid plasma
magnetohydrodynamics for electrons, ions, and neutral atoms. Let us
introduce the bulk plasma velocity in the
laboratory reference frame
where *k* = e, i, a, and **v** _{k} are the
velocities of the species in the laboratory reference system. Denote
the velocities of the species in the reference frame connected with
bulk plasma (diffusion velocities) as . When the
diffusion velocities, as well as their derivatives, are small compared
with the velocity and acceleration of the bulk plasma (this allows us
to consider dt), and the dependence of the
friction force due to collisions vs. velocity is linear, the equation
of motion for *k*-th component can be written as
Here = +
is the electric field in the reference frame
moving with the bulk plasma, =
, =
for *k* = i, e, a, and is the momentum
losses of the *k*-type particles, due to collisions with
particles of *l*-types. After summing all three equations (1) for
each *k* = e, i, a, and taking the relations
into account one can get the equation of motion for the bulk plasma
where = +
+ is the density of
partially ionized plasma and =
+ +
.
Excluding from Eq. (1) velocities , after
neglecting the terms as small as in comparison
with the units, one can obtain the generalized Ohm's law
Here =
/((+))
is conductivity, and *F* =
/ is the relative density
of neutrals. Eqs. (2) and (3) together with the Maxwell equations and
the mass conservation law
describe self-consistently the behavior of the plasma and the
electromagnetic fields.
© European Southern Observatory (ESO) 1998
Online publication: August 27, 1998
helpdesk.link@springer.de |