Effect of plasma density on proton acceleration in a rectangular waveguide

Analytical studies are made for the proton acceleration during its motion in the fields of the fundamental mode excited by a high-intensity microwave in a rectangular waveguide, when the proton is injected along the propagating direction of the mode. The trajectory of the proton is calculated and the expressions are obtained for the energy gain and acceleration gradient together with the effects of plasma density, microwave frequency and waveguide width. Energy gain of 181 keV is attained by a 50 keV proton in a 0.015m x 0.020 m evacuated waveguide when 0.5 x 10(10) W/m(2) microwave intensity is used. However, this gain increases to 1387 keV when the waveguide is filled with a plasma having a density of 1.0 x 10(19) m(-3). Higher acceleration gradients are achieved when the proton is injected with a higher initial energy and also when the microwave intensity increases. The effects of the microwave frequency and width of the waveguide are found to decrease the acceleration gradient.