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II Electromagnetic Fields in a Toroidal Cavity
The Fields Expressed as Two Index Sums
5 other sections not shown
applied voltage approximation azimuthal azimuthal distribution Bessel functions Bevatron bottom surfaces boundary condition circulating current circulation frequency considered constant curve density distribution of particles effect electric field electromagnetic fields energy loss evaluated expression Fourier coefficients Fourier components FREQUENCY MODULATION Graph h cosh Hamiltonian induced voltage joule heating kz g machine magnetic fields Maxwell's equations n p n p n s n s ns n ns number of particles numerical obtain order of magnitude parameters particle accelerator particle circulation particle distribution phase velocity Poynting vector radiation ratio resonance is possible result rf cavity scalar potential shunt impedance solution space-charge stable-phase surface integrals synchronous particle synchrotron phase space tangential component TM modes top and bottom toroidal cavity total number total voltage transverse vacuum chamber vacuum tank valid values variable vector potential Vlasov equation zero