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60 Chapter 3 current in the plasma, this equation reduces to Eq. (3.5-7), which was used to derive the Boltzmann relationship for plasma electrons. In Eq. (3.6-20), the total resistivity of a partially ionized plasma is given by = m ( e i + v e n ) = 1 , ( 3 . 6 - 2 1 ) e 2 n o e 2p where the total collision time for electrons, accounting for both electron–ion and electron–neutral collisions, is given by e = 1 . (3.6-22) ei + en By neglecting the electron–neutral collision terms in Eq. (3.6-19), the well- known expression for the resistivity of a fully ionized plasma [1,9] is recovered: ei = m ei = 1 . (3.6-23) e 2 n o e i 2p In ion and Hall thrusters, the ion current in the plasma is typically much smaller than the electron current due to the large mass ratio, so the ion current term in Ohm’s law, Eq. (3.6-20), is sometimes neglected. 3.6.2 Diffusion and Mobility Without a Magnetic Field The simplest case of diffusion in a plasma is found by neglecting the magnetic field and writing the equation of motion for any species as mndv=qnE– p–mn (v–vo), (3.6-24) dt where m is the species mass and the collision frequency is taken to be a constant. Assume that the velocity of the particle species of interest is large compared to the slow species ( v >> vo ), the plasma is isothermal ( p = kT n ), and the diffusion is steady state and occurring with a sufficiently high velocity that the convective derivative can be neglected. Equation (3.6-24) can then be solved for the particle velocity:PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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