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
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