Theoretical study of two-dimensional charge densities in intense rectangular ion beams
Beginning with its emergence from a high-aspect ratio rectangular aperture, the physics of an intense (current density [approx gt] 1 mA/cm[sup 2]), positively charged ion beam is explored in two distinct regions: an electron-free drift region, and a beam plasma containing a large density of space-charge neutralizing electrons. In the drift region, the beam expands due to the mutual inter-ion Coulomb repulsion. Energy, mass, and phase-space density conservation are combined with Poisson's equation to obtain the beam ion density and resulting potential of the diverging beam at any point in 3-dimensional space. Within the beam plasma, the divergence rate is assumed negligible and the beam ion density at the drift/plasma interface taken to be the beam ion density throughout the beam plasma. It is assumed that collisions between beam ions and residual gas molecules, producing a steady generation of electrons and slow residual gas ions, is the dominant mechanism sustaining the beam plasma. Charge is conserved and the energy balance of the plasma examined to obtain the electron and slow-ion densities. Electron, slow-ion, and beam ion densities are then introduced into Poisson's equation to produce a second order partial integro-differential equation requiring a numerical solution. This solution is obtained by expanding the density and potential functions in a complete set of orthogonal (Chebyshev) functions and reducing the differential equation to a system of linear algebraic equations. Calculations in the drift region, for beams of 50, 100 and 500 keV, indicate that all intense beams, regardless of the initial aspect ratio, ultimately relax into the same, near Gaussian profile. In the beam plasma, the theory was applied to a 100 keV, high aspect ratio arsenic beam. The electron density profile is predicted to display a shape similar to that of the beam ions, with the resulting net potential possessing substantial cylindrical symmetry.
- Research Organization:
- Arizona Univ., Tucson, AZ (United States)
- OSTI ID:
- 7271608
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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