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Basic Plasma Physics 55 To evaluate diffusion-driven particle motion in ion and Hall thruster plasmas, the equation of motion for any species can be written as mndv =qn(E+v B)– p–mn (v–vo), (3.6-1) dt where the terms in this equation have been previously defined and is the collision frequency between two species in the plasma. In order to apply and solve this equation, it is first necessary to understand the collisional processes between the different species in the plasma that determine the applicable collision frequency. 3.6.1 Collisions Charged particles in a plasma interact with each other primarily by coulomb collisions and also can collide with neutral atoms present in the plasma. These collisions are very important when describing diffusion, mobility, and resistivity in the plasma. When a charged particle collides with a neutral atom, it can undergo an elastic or an inelastic collision. The probability that such a collision will occur can be expressed in terms of an effective cross-sectional area. Consider a thin slice of neutral gas with an area A and a thickness dx containing essentially stationary neutral gas atoms with a density na . Assume that the atoms are simple spheres of cross-sectional area . The number of atoms in the slice is given by na Adx . The fraction of the slice area that is occupied by the spheres is na A dx = na dx . (3.6-2) A If the incident flux of particles is o , then the flux that emerges without making a collision after passing through the slice is (x)= o (1– na dx). The change in the flux as the particles pass through the slice is (3.6-3) (3.6-4) The solution to Eq. (3.6-4) is d = – na . dxPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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