Analytical approach to the design of RF photoinjector

The objective of this thesis is to ascertain the dimensions of an RF 2.856GHz photoinjector through a combination of analytical and computational approaches. The phase velocity within a single cavity exceeds 'c', rendering it inadequate for storing the requisite energy for beam acceleration. To surmount this limitation, we aim to devise a multi-celled cavity design. However, the alterations in electromagnetic fields and resonant frequency within the multi-celled cavity are intricate and sensitive, presenting challenges in obtaining precise dimensions solely via computer simulations. Prior to numerical methods, it is essential to analyze the photoinjector using theoretical frameworks. We employ perturbation theory and the construction of an equivalent circuit to elucidate the underlying physics of the photoinjector and the electrical oscillations within the cell structure. Detailed analytical methods for the equivalent circuit are explored. Through theoretical analysis, the dimensions and simulation outcomes can be determined quantitatively.