A relativistic magnetron (RM) is a high-power microwave (HPM) source. The main objective of the RM is to generate directed electromagnetic pulses with high power, which can be used in e.g. HPM weapons and for electromagnetic compatibility testing. These pulses can disturb or damage electronic equipment. One of the main challenges when designing an RM is to generate the advantageous TE11 wave mode to the circular waveguide and antenna with high efficiency and peak power. This thesis investigates a new design of the RM, developed at the Swedish Defence Research Agency (FOI), referred to as the FOI magnetron. This design is based on the A6-magnetron and employs four large and two small cavities in the diffraction output of the RM, compared to the conventional design that has six identical cavities. The FOI magnetron has previously shown results that indicate the possibility of generating the TE11 wave mode. In this thesis, a literature study was performed to better understand the governing physical laws of the RM. This was followed by parametric studies using the ​​particle-in-cell code MAGIC3D for simulating the RM. To validate the simulation models, a model of a conventional RM was constructed and the results were compared against the published simulation results by Daimon and Jiang (2008).  Lastly, different geometrical properties, applied magnetic field, and applied voltage of the FOI magnetron were studied to see how they impacted the RM performance. Apart from the diffraction output, the geometry of the interaction region was studied to investigate the effect on frequency and power. The goal was to generate a clean TE11 mode in the waveguide of the RM with high efficiency. The validation yielded results that were in good agreement with the ones obtained by Daimon and Jiang (beam-to-microwave efficiencies of 37% and 36% respectively). The parameter studies of the FOI magnetron gave results that indicate a clean TE11 mode with a beam-to-microwave efficiency of ∼35% and peak powers up to 1 GW at frequencies of approximately 2.5 GHz. The studies on the interaction region showed that a shift of approximately 0.12 GHz was possible when making the rear part of the interaction region 4.5 cm longer. It was found that the length of the front of the interaction region can to some extent affect the output power. Lastly, it was found that a fraction of the output power (∼10−17%) that leaves the interaction region propagates back toward the input region and the voltage source.