I am trying to calculate classical trajectories for a single positive ion and a single electron inside an RF trap. Therefore, I am dealing with a two-body system that possesses:
- Coulomb potential with a singularity
- time-dependent potential that is periodic in time and quadratic in space (smooth, relatively weak - compared to the Coulomb). However, asymptotically it becomes dominant.
I would like to calculate the classical trajectories that start from an arbitrary point in the phase space. The time interval I am interested in, is up to 10 periods of the trap field.
I've had some limited success with Tao's symplectic integrator for charged particle in electromagnetic fields (J. Comp. Phys. 327, 245 (2016)). However, the number of time steps necessary to get converged trajectories, is quite large and I would need to perform some systematic scan of the parameter space.
There are several ideas I have in mind but I am afraid that I am going to reinvent a wheel with them. Some of them:
- When the particles approach each other, the time-dependent field can be perhaps neglected or treated perturbatively. So using different integrators in different regions of the phase space could help. However, it seems from the classical references that it would take away the symplecticity.
- I could regularize the COulomb singularity, add an additional degree of freedom and make the Hamiltonian non-separable. Then I could try to solve it in the extended phase space.
- Maybe it would be worth trying some existing simulation software (LAMMPS?). However, how is the singularity treated there?
Is there "canonically" appropriate integrator for this kind of situations please? Is any of the strategy mentioned above worth the shot? Thanks for any hint.