Abstract
Two-dimensional hydrodynamics of ion extraction from quasi-neutral plasmas has been calculated numerically for non-parallel ion extractors, and the results compared with those for the parallel case. The ions were assumed to be initially uniform with a very steep density profile at the boundaries, and held between two non-parallel metal plates as cathode and anode with fixed potentials. Experimentally, tunable pulsed lasers through stepwise photo-excitation and photo-ionization or multi-photo-ionization processes can produce such plasma. Poisson's equation was solved simultaneously with the equations of mass and momentum, assuming the Maxwell–Boltzmann distribution for electrons. Ordinary Cartesian co-ordinates are not suitable for the rotated extractor geometry; therefore using the `algebraic method' a transformation from the physical domain into the computational rectangular plane is applied for analysing the irregular boundaries. Such a technique provides adequate resolution for the boundary layer. Using a first-order explicit upwind differencing in an appropriate transformed Cartesian co-ordinate system, the hydrodynamics of the plasma ions between the two non-parallel electrodes was evaluated. In these calculations electric potential, ion density between the two electrodes, and the extraction time were assessed, considering three separate regions for the plasma, i.e. the ion sheath where (ni≫ne≈0), the transition region (pre-sheath) (ni = ne), and the quasi-neutral plasma (ni−ne≪ni). The results were compared with those for parallel electrodes. A significant discrepancy was found between the two results. From the calculation, the non-uniform asymmetric potential contour, and the ion density contour across the plasma, were obtained for the non-parallel electrodes. For comparison with the parallel extractors, we have also obtained almost the same extraction time for the non-parallel extractors.
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