Analytical calculations of wake field generated by microwave pulses in a plasma filled waveguide for electron acceleration

Abstract

Analytical expressions are obtained for the longitudinal field (wake field), density perturbation, and the potential behind microwave pulse propagating in a plasma filled rectangular waveguide with the pulse duration half of the electron plasma period. A feasibility study on wake field is carried out with rectangular pulse and its combination with Gaussian and triangular pulses under the effects of microwave pulse parameters and waveguide dimensions. It is inferred that the wake field in the waveguide cannot be attained when the length of rectangular microwave pulse is exactly equal to the plasma wavelength. A 1 ns short rectangular pulse with intensity of 250 kW/cm2 at the frequency of 5.03 GHz can excite the wake field of 1.0 MV/m in a waveguide with width of 6 cm and height of 4 cm. However, enhanced field is obtained when rectangular-triangular pulse (combination of rectangular and triangular pulses) is used. The field of wake gets weakened at higher microwave frequency and larger dimensions of the waveguide for other fixed parameters. However, a larger field is achieved when the pulse length of the microwave pulses is made shorter and/or intensity of the pulses is increased. A comparative study of the pulses shows that better results can be obtained with rectangular pulse (rectangular-Gaussian pulse: combination of rectangular and Gaussian pulses) if the microwave of shorter pulse duration (higher intensity) is available.