Plasma properties inside a hydrogen-filled capillary discharge waveguide were modeled with dissipative magnetohydrodynamic simulations to enable analysis of capillaries of circular and square cross-sections implying that square capillaries can be used to guide circularly-symmetric laser beams. When the quasistationary stage of the discharge is reached, the plasma and temperature in the vicinity of the capillary axis has almost the same profile for both the circular and square capillaries. The effect of cross-section on the electron beam focusing properties were studied using the simulation-derived magnetic field map. Particle tracking simulations showed only slight effects on the electron beam symmetry in the horizontal and diagonal directions for square capillary.
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