Usually in explicit time-integrator methods such as Boris Method, the maximum timestep is imposed by the Courant criterion due to the EM counterpart method (eg FDTD). Is there any empirical rule to calculate the maximum timestep related to cyclotron frequency ωc for motion in a magnetic field and not plasma frequency as is known (Δt
The formal stability analysis of the Boris scheme is presented in
https://arxiv.org/pdf/1409.5677.pdf
The direct answer to your question is in the left part of Fig 2 depicting stability regions for the single-particle system.
In most practical applications, the Boris method is used with a time step of about 1/20 of the gyro period. For reference, see
https://bp.pppl.gov/pub_report/2013/PPPL-4872.pdf
After my general review of the problem, I would like to suggest the use of implicit method described in section 2.3 of the paper “A fully implicit numerical integration of the relativistic particle equation of motion”
https://arxiv.org/pdf/1612.04563.pdf
The third, even better way to solve the equations of charged particle motion is to use exponential integration schemes, which are not subject to the time step limitation imposed in Boris scheme.
But take care about simulations due time shift propagation of EM waves. The problem is that influence in a point of space due moving charged particle and fields has a time delay due the time lag due EM finite speed.
Thank you for your answers. Given that conventional FDTD is an explicit method, 1/20 of the gyroperiod should also be lower than the corresponding timestep imposed by the CFL criterion.
- Badges
- Science topic