An s-Based Symplectic Spectral Space Charge Algorithm
Nathan M. Cook, Dan T. Abell, David Bruhwiler, Jonathan P. Edelen, Christopher C. Hall, Stephen D. Webb · JACOW · 2018
Traditional finite-difference particle-in-cell methods for modeling self-consistent space charge introduce non-Hamiltonian effects that make long-term tracking in storage rings unreliable. Foremost of these is so-called grid heating. Particularly for studies where the Hamiltonian invariants are critical for understanding the beam dynamics, such as nonlinear integrable optics, these spurious effects make interpreting simulation results difficult. To remedy this, we present a symplectic spectral space charge algorithm that is free of non-Hamiltonian numerical effects and, therefore, suitable for long-term tracking studies. We present initial results demonstrating the implementation of the algorithm, using a spectral representation of the fields and macro particles to preserve Hamiltonian structures. We then discuss applications to the Integrable Optics Test Accelerator (IOTA), currently under construction at Fermilab.