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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38 Chapter 3 intended to provide the basic plasma physics necessary to understand the operation of ion and Hall thrusters. The units used throughout the book are based on the International System (SI). However, by convention we will occasionally revert to other metric units (such as A/cm2, mg/s, etc.) commonly used in the literature describing these devices. 3.2 Maxwell’s Equations The electric and magnetic fields that exist in electric propulsion plasmas obey Maxwell’s equations formulated in a vacuum that contains charges and currents. Maxwell’s equations for these conditions are E = o E = B t B = 0 B=μ J+ E, (3.2-1) o o t where is the charge density in the plasma, J is the current density in the plasma, and o and μo are the permittivity and permeability of free space, respectively. Note that and J comprise all the charges and currents for all the particle species that are present in the plasma, including multiply charged ions. The charge density is then =qsns =e(Zni ne), (3.2-5) s where qs is the charge state of species s, Z is the charge state, ni is the ion number density, and ne is the electron number density. Likewise, the current density is J = qsnsvs = e(Znivi neve ), (3.2-6) s where vs is the velocity of the charge species, vi is the ion velocity, and ve is the electron velocity. For static magnetic fields (B t = 0), the electric field can be expressed as the gradient of the electric potential, (3.2-2) (3.2-3) (3.2-4)

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