Fundamentals of Electric Propulsion: Ion and Hall Thrusters

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Fundamentals of Electric Propulsion: Ion and Hall Thrusters ( fundamentals-electric-propulsion-ion-and-hall-thrusters )

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70 Chapter 3 two species and equate them, the resulting equation cannot be easily solved because it depends on the behavior both in the plasma and at the boundaries conditions. A special case in which only the ambipolar diffusion toward a wall in the presence of a transverse magnetic field is now considered. In this situation, charge balance is conserved separately along and across the magnetic field lines. The transverse electron equation of motion for isothermal electrons, including electron–neutral and electron–ion collisions, can be written as mnve+(v )v =–en(E+v B)–kTn t e e e e (3.6-76) –mnen(ve –vo)–mnei(ve –vi), where vo is the neutral particle velocity. Taking the magnetic field to be in the z-direction, and assuming the convective derivative to be negligibly small, then in steady-state this equation can be separated into the two transverse electron velocity components: vx+μeEx+ e vyB+ kTe n–eivi=0 (3.6-77) me mnex e vy+μeEy– e vxB+ kTe n–eivi=0, (3.6-78) me mney e where e = en + ei is the total collision frequency, μe = e / mve is the electron mobility including both ion and neutral collisional effects, and vo is neglected as being small compared to the electron velocity ve . Solving for vy and eliminating the E B and diagmagnetic drift terms in the x-direction, the transverse electron velocity is given by v (1+μ2B2)=μ E+kTen+eiv, (3.6-79) e e e enei Since ambipolar flow and quasi-neutrality are assumed everywhere in the plasma, the transverse electron and ion transverse velocities must be equal, which gives v1+μ2B2–ei=μ E+kTen. (3.6-80) i e e e e n

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