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Basic Plasma Physics 71 The transverse velocity of each species is then v =v = μe E+kTe n . (3.6-81) i e 1+μ2B2– ei e n In this case, the electron mobility is reduced by the magnetic field (the first term on the right-hand side of this equation), and so an electric field E is generated in the plasma to actually slow down the ion transverse velocity in order to balance the pressure term and maintain ambipolarity. This is exactly the opposite of the normal ambipolar diffusion without magnetic fields or along the magnetic field lines covered in Section 3.6.2, where the electric field slowed the electrons and accelerated the ions to maintain ambipolarity. Equation (3.6-81) can be written in terms of the transverse flux as = μe (enE + kTe n). (3.6-82) ( 1 + μ e2 B 2 – e i e ) 3.7 Sheaths at the Boundaries of Plasmas While the motion of the various particles in the plasma is important in understanding the behavior and performance of ion and Hall thrusters, the boundaries of the plasma represent the physical interface through which energy and particles enter and leave the plasma and the thruster. Depending on the conditions, the plasma will establish potential and density variations at the boundaries in order to satisfy particle balance or the imposed electrical conditions at the thruster walls. This region of potential and density change is called the sheath, and understanding sheath formation and behavior is also very important in understanding and modeling ion and Hall thruster plasmas. Consider the generic plasma in Fig. 3-2, consisting of quasi-neutral ion and electron densities with temperatures given by Ti and Te , respectively. The ion current density to the boundary “wall” for singly charged ions, to first order, is given by nievi , where vi is the ion velocity. Likewise, the electron flux to the boundary wall, to first order, is given by neeve, where ve is the electron velocity. The ratio of the electron flux to the ion current density going to the boundary, assuming quasi-neutrality, is Je = neeve = ve . (3.7-1) Ji nievi vi e ePDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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