Equations of Motion of Charged Particles

At the microscopic level, in addition to the effects of the pressure gradients and gravity g, the particle motions are influenced by the electrostatic force due to their electric charges, if the medium is ionized. The collisions between particles also influence their motions by transfer of momentum; this effect is equivalent to a friction. The hydrostatic equilibrium of particles "i" with mass fraction Xi, atomic mass number Ai, electric charge Zi leads to [190]

d = -Q Xig + AQm^ZieE + £ Kij(vj - Vi)+Kie(Ve - Vi) , i u j=i

where E is the local microscopic electric field produced by the particle displacements. QXi is the partial density of particles "i" with a concentration ni = qXi/(Aimu). The coefficients Kij and Kie are the so-called resistance coefficients of particle "i" with other particles "j" and with the electrons, respectively. These coefficients in g cm-3 s-1 express the resistance force by volume unity produced by the differences of velocities between particles. These coefficients are tabulated by Paquette et al. for a number of cases [461].

Let us consider a mixture with two particle species "1" and "2". The first term on the right of (10.48) can be written as +(qXi/Q)(dP/dr) with the help of the equation for the global hydrostatic equilibrium (1.5). We thus have two equations of hydrostatic equilibrium for the two kinds of particles, dPi (qX1) d_P QXj dr q dr A1 mu

We also have two equations of continuity like (10.6) d(QX1) 1 d , 2

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