This paper proposes the coupled multi-physics analysis of a S-band klystron for electron linac applications. The proposed klystron is in pulsed mode of operation and is designed to deliver average power of 24 kW with the peak power of 6 MW at the desired frequency of 2856 MHz. This paper presents the 1D/3D analysis results of the klystron with various configurations having higher order harmonic intermediate buncher cavities for improved gain and bandwidth performance. The entire model is solved for the Maxwell’s equation in time domain to arrive at the coupling factor, bunching, gain and bandwidth. The position of the cavity, interaction gap length, resonant frequency of each cavity and the number of cavities has been varied to obtain an optimal design having desired gain and bandwidth. Sub-harmonic cavities have been placed to shorten the RF interaction section and make the design compact. A study of the klystron beam wave interaction has been carried out using AJDISK. AJDISK is a one-dimensional simulation tool for round and sheet beam klystrons. As first order tool, it provides insight into the klystron design by running fast large signal design computations prior to running more accurate and time consuming 2D and/or 3D particle in cell analysis. Moreover, 1-D solutions offers a fairly good estimate of various electrical and dimensional parameters of RF section to get desired tube performance and compare reasonably with experimentally results of the klystron, particularly, 5-cell cavity klystron (SLAC-5045). The RF gain, phase and velocity profile of particles, energy distribution and RF current are plotted along the travel of the particle. Subsequently, the validation and optimization of design parameters of complete RF section using 3D CST—Particle in Cell code.