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66 Chapter 3 μi + μe where Da is the ambipolar diffusion coefficient given by E=Di–De n. μi+μe n Da=μiDe+μeDi . μi + μe (3.6-53) (3.6-54) (3.6-55) Substituting E into Eq. (3.6-29) for the ion flux, =–μiDe+μeDi n=–Da n, Equation (3.6-54) was expressed in the form of Fick’s law, but with a new diffusion coefficient reflecting the impact of ambipolar flow on the particle mobilities. Substituting Eq. (3.6-54) into the continuity equation without sources or sinks gives the diffusion equation for ambipolar flow: n – Da 2n = 0 . t Since the electron and ion mobilities depend on the mass μe= e >>μi= e , m M (3.6-56) (3.6-57) it is usually possible to neglect the ion mobility. In this case, Eq. (3.6-55) combined with Eq. (3.6-28) gives D D + μi D = D 1+ Te . (3.6-58) a i μe e i Ti Since the electron temperature in thrusters is usually significantly higher than the ion temperature ( Te >> Ti ), ambipolar diffusion greatly enhances the ion diffusion coefficient. Likewise, the smaller ion mobility significantly decreases the ambipolar electron flux leaving the plasma. 3.6.3 Diffusion Across Magnetic Fields Charged particle transport across magnetic fields is described by what is called classical diffusion theory and non-classical or anomalous diffusion. Classical diffusion, which will be presented below, includes both the case of particles of one species moving across the field due to collisions with another species ofPDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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