Abstract
The Courant—Friedrichs—Lewy (CFL) stability condition limits the size of time step that may be used by conventional explicit finite-difference time-domain particle-in-cell (FDTD-PIC) codes in proportion to the grid cell size. In slow-wave vacuum electronic devices with non-relativistic electron beams, the typical scale length for fields in the beam region is L ≅ βλ b /c is the normalized beam velocity and λ is the vacuum wavelength. This dictates a very small cell size h << L << λ for PIC simulation which via the CFL condition imposes extremely small time steps compared to the RF period. Consequently explicit methods require long simulation times to model slow-wave devices.
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