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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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Ion Thruster Accelerator Grids 201 trajectories and charge exchange reactions between beam ions and un-ionized propellant gas in two [4] and three [17] dimensions. The CEX-2D code solves Poisson’s equation, given in Eq. (3.7-8) in Chapter 3, on a regular mesh in cylindrical geometry. The code models a single set of screen and accel grid holes and assumes cylindrical symmetry. The computational space is divided into a grid of rectangular cells with up to 400 increments radially and 600 axially. The radial grid spacing is uniform; the axial spacing is allowed to increase in the downstream direction. The computational region is typically a few millimeters radially and up to 5 centimeters along the axis downstream of the final grid. With a few exceptions, the code uses a combination of algorithms used in earlier optics codes for ion thrusters [11–15]. Upstream of the accelerator grid, the electron density is obtained analytically from the barometric law assuming a Maxwellian distribution: n (V)=n (0)expo. (5.3-1) e e Te The upstream reference electron density, ne(0), is set equal to the input discharge chamber ion density. Downstream of the accelerator grid, the electron population is also assumed to be a Maxwellian distribution with a different reference potential: n (V)=n ()exp, (5.3-2) e e Te where the downstream reference electron density, ne(), is set equal to the calculated average downstream ion beam density. As a result, downstream potentials are determined self consistently; there is no need to assume a neutralization plane. These codes include focusing effects and the fact that the aperture dimensions are usually significantly larger than the gap size such that the electric fields are reduced from the ideal maximum. The potential distributions are calculated using an optimized pre-conditioned least-square conjugate gradient sparse matrix solver. Results for a given upstream plasma number density, n, are found by starting from zero density and iterating. At each iteration, i, a fraction, , of the desired discharge chamber ion density is blended into the code:

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