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Ion Thruster Plasma Generators 149 coil. Typical frequencies used in rf ion thrusters are in the range of 1 MHz. At these frequencies, the penetration of the fields from the coil at the boundary is limited by the skin depth in the plasma [24], which is on the order of or slightly less than the radius of most rf ion thrusters at the plasma densities required to produce xenon ion current densities in excess of 1 mA/cm2. This produces an attenuation of the electric and magnetic fields toward the axis, and the majority of plasma interaction with the fields occurs off axis closer to the boundary. The axial magnetic field inside the coil induced by the rf current, neglecting end effects, is Bz = NI ei t, (4.5-1) μo where I is the rf current in the coil, μo is the permeability of the vacuum, is the cyclic frequency ( 2 f ) of the rf, and t is the time. From Maxwell’s equation, the time-varying magnetic field creates a time-varying electric field: E = – B . (4.5-2) t The induced rf electric field in the rf thruster geometry is then in the azimuthal direction: E =–i r Bzoei t, (4.5-3) 2 where r is the distance from the axis and Bzo is the peak axial rf magnetic field from Eq. (4.5-1). A finite electric field is generated spatially off axis inside the thruster. The induced electric field exists in one direction (± direction) for roughly half a period, which for a 1-MHz frequency is 0.5 microseconds. The electrons, however, don’t see the oscillating component of the electric field because they transit the interaction region close to the antenna in a time much less than this value. For example, a 5-eV electron will travel a distance of about 1 meter in 1 microsecond, and so can traverse the electric field region many times within a half cycle. Therefore, electrons traversing the induced electric field region “see” a DC electric field and are accelerated. If they make a collision prior to leaving the region, they can then retain some or all of the velocity imparted by the electric field and are heated.PDF Image | Fundamentals of Electric Propulsion: Ion and Hall Thrusters
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