Authors: Michael Glen
The properties of a resonant half wavelength mode, sometimes called a 4pi mode, is investigated in a toroidal cavity of large aspect ratio. No dividing wall is used but instead the field is given a poloidal (in the direction of the smaller circumference) twist. The toroidal cavity resonator equations are derived by bending a length of cylindrical waveguide into a toroid and changing the field equations from cylindrical to local toroidal. If the toroid aspect ratio is large the errors are small but the equations must still be considered to be approximate and so in order to confirm the stability and form of the resonant modes a finite difference time domain (FDTD) program was written to model the propagation of the fields. This also confirms that no false assumptions have been made, particularly regarding how the fields behave where the two ends of the half wave join. This is believed to be the first confirmation of the existence of a half wave toroidal mode without a dividing wall. FDTD simulations of both a toroidal (in the direction of the larger circumference) and a poloidal spinning 4pi mode were also carried out. It was observed that the presence of twist would prevent either a pure toroidal or poloidal spinning mode being produced and that the poloidally spinning field produced a stable mode with both spin and angular momentum.
Comments: 28 Pages. 19 figures
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[v1] 2023-10-19 21:48:58
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