Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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46 Chapter 3 temperature and density are known. The electrons tend to be relatively hot (compared to the ions and atoms) in ion and Hall thrusters because they typically are injected into the plasma or heated by external mechanisms to provide sufficient energy to produce ionization. In the presence of electric and magnetic fields in the plasma and at the boundaries, the electron motion will no longer be purely random, and the flux described by Eq. (3.4-12) must be modified as described in the remainder of this chapter. The ions in thrusters, on the other hand, are usually relatively cold in temperature (they may have high directed velocities after being accelerated, but they usually have low random velocities and temperatures). This occurs because the ions are not well confined in the plasma generators because they must be extracted to form the thrust beam, and so they leave the plasma after perhaps only a single pass. The ions are also not heated efficiently by the various mechanisms used to ionize the gas. Therefore, the plasmas in ion and Hall thrusters are usually characterized as having cold ions and Maxwellian electrons with a high electron-to-ion temperature ratio (Te /Ti 10). As a result, the velocity of the ions in the plasma and the fluxes to the boundaries tend to be determined by the electric fields generated inside the plasma to conserve charge, and to be different from the expressions derived here for the electron velocity and fluxes. This effect will be described in more detail in Section 3.6. 3.5 Plasma as a Fluid The behavior of most of the plasma effects in ion and Hall thrusters can be described by simplified models in which the plasma is treated as a fluid of neutral particles and electrical charges with Maxwellian distribution functions, and the interactions and motion of only the fluid elements must be considered. Kinetic effects that consider the actual velocity distribution of each species are important in some instances, but will not be addressed here. 3.5.1 Momentum Conservation In constructing a fluid approach to plasmas, there are three dominant forces on the charged particles in the plasma that transfer momentum that are considered here. First, charged particles react to electric and magnetic field by means of the Lorentz force, which was given by Eq. (3.3-1): FL =m dv =q(E+vB). (3.5-1) dt Next, there is a pressure gradient force,

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