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368 Chapter 7 cathode across the transverse field lines and into the channel to support the discharge current. Two mechanisms have been proposed in an attempt to describe “enhanced” cross-field electron transport and explain the observed Hall thruster operation. Morozov [12] postulated that electron-wall interactions in the channel region will scatter electron momentum and introduce secondary electrons, which can increase the effective cross-field transport. This effect is introduced into the effective collision frequency by a wall-scattering frequency w : m = ei + en + w . (7.4-10) The wall-scattering frequency is either given by 107 per second [53], with an adjustable parameter used to match the experimental data, or the wall collision frequency of electrons is calculated directly in the code [59]. While this effect does increase the electron transport in the channel, it is sometimes found to provide insufficient enhancement of the electron transport. In addition, in the plume of the thruster there are no walls and the neutral density is very low, which precludes the use of Eq. (7.4-10) to increase the cross-field transport sufficiently to explain the experimental data. Additional cross-field transport has been added in the codes by invoking Bohm diffusion both inside and outside the thruster channel. As discussed in Chapter 3, Bohm diffusion likely arises from E B driven drift instabilities, which can naturally occur in these thrusters due to the Hall current. Using the Bohm diffusion coefficient from Eq. (3.6-72) and the Einstein relationship of Eq. (3.6-28), a Bohm mobility can be defined as μB = 1 = e , (7-4-11) B m c where is an adjustable coefficient changed to make the code predictions of the thruster parameters fit the experimental data. If full Bohm diffusion is required by the code to match the data, such as is often the case in the plume, then = 16. The effective Bohm collision frequency is then B = c . (7-4-12) The total “anomalous” collision frequency used in the codes is m = ei + en + w + B, (7.4-13)PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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