Design of a Relativistic Magnetron for 2π-Mode to TE11 in X-Band

High power microwaves (HPM) are energy-dense waves that can be used to disrupt or destroy electronics from a distance. Relativistic magnetrons can generate HPM from the interaction between fast electrons and an electromagnetic field. With output powers on a scale of 100 MW, they have a large effective range. The aim of this project was to create a relativistic magnetron that first excites the 2𝜋-mode, axially extracts it and then converts it into a TE11-mode, with a frequency in the X-band (8−12 GHz). The starting point was the magnetron developed by the Swedish Defence Research Agency

(FOI), which in its original form excites a 𝜋-mode in the interaction region.

Which wave mode that is excited depends on the dimensions of the interaction region, the applied voltage and the magnetic field strength. The problem of exciting the 2𝜋-mode was approached by calculating the orbit and velocity of a single electron in a coaxial gap. Using the Hamiltonian mechanics for electrons in electromagnetic fields, new expressions were derived for the radial position of the orbit apex, along with the magnitude of the electron velocity along the orbit. These were validated against numerical calculations using COMSOL Multiphysics.

The diffraction output transforms the excited wave mode into a suitable output mode. The original diffraction output of the FOI-magnetron did not produce TE11 when fed with a 2𝜋-mode. An asymmetric variation did produce TE11, but not without strong parasitic modes. A more efficient conversion was discovered using a simpler, smooth-walled diffraction output that produced an intermediate TE01. An added mode converter then transformed TE01 into a linearly polarized TE11.

The efficiency of the entire magnetron was calculated through Particlein-Cell simulations. The smooth-walled diffraction output was joined with several variations of the interaction region. The 2𝜋-mode appeared in one variation at 7.1 GHz, which was lower than the expected cutoff frequency 8.3 GHz, with an efficiency of 0.3%. This is a partial success and a step towards a fully functioning magnetron. The analytical orbit model provides new insight into the interaction region and the successful conversion to TE11 makes the 2𝜋-mode a promising option for HPM.