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Basic Plasma Physics 59 where Z is the ion charge number. Collisions between like particles and between separate species tend to equilibrate the energy and distribution functions of the particles. This effect was analyzed in detail by Spitzer [9] in his classic book. In thrusters, there are several equilibration time constants of interest. First, the characteristic collision times between the different charged particles is just one over the average collision frequencies given above. Second, equilibration times between the species and between different populations of the same species were calculated by Spitzer. The time for a monoenergetic electron (sometimes called a primary electron) to equilibrate with the Maxwellian population of the plasma electrons is called the slowing time, s . Finally, the time for one Maxwellian population to equilibrate with another Maxwellian population is called the equilibration time, eq . Expressions for these equilibration times, and a comparison of the rates of equilibration by these two effects, are found in Appendix F. Collisions of electrons with other species in the plasma lead to resistivity and provide a mechanism for heating. This mechanism is often called ohmic heating or joule heating. In steady state and neglecting electron inertia, the electron momentum equation, taking into account electron–ion collisions and electron- neutral collisions, is 0= en(E+ve B)– pe –mn ei(ve vi)+ en(ve vn) . (3.6-18) The electron velocity is very large with respect to the neutral velocity, and Eq. (3.6-18) can be written as 0=–en E+ pe –env B–mn( +v )v +mn v . (3.6-19) en e eieneeii Since charged particle current density is given by J = qnv, Eq. (3.6-19) can be written as Je =E+ p Je B eiJi, (3.6-20) en where Je is the electron current density, Ji is the ion current density, and ei is the plasma resistivity. Equation (3.6-20) is commonly known as Ohm’s law for partially ionized plasmas and is a variant of the well-known generalized Ohm’s law, which usually is expressed in terms of the total current density, J = en(vi – ve ) , and the ion fluid velocity, vi . If there are no collisions or netPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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