Differentiable self-consistent space-charge simulation for accelerator design

The nonlinear space-charge effects in a high intensity or high brightness accelerator can have a significant impact on the beam properties through the accelerator. These effects are included in the accelerator design via self-consistent multiparticle tracking simulations. In order to study the sensitivity of the final beam’s properties with respect to the accelerator design parameters, one has to carry out the time-consuming space-charge simulation multiple times. In this paper, we propose a differentiable self-consistent space-charge simulation model that enables the study of such sensitivity through only one simulation. This model differs from previous applications of the truncated power series algebra by connecting the beam properties directly with the accelerator design parameters in the presence of collective space-charge effects so that the local derivative of the beam properties with respect to the design parameters can be computed during the simulation. Such a model can also be used with gradient-based numerical optimizers for accelerator design optimizations including the self-consistent space-charge effects.

Figure 1

Schematic plot of a FODO lattice in the first application example.

Figure 2

Derivatives of final horizontal and vertical emittances with respect to seven lattice parameters from the single differentiable self-consistent space-charge simulation and from the finite difference approximation to the first derivative.

Figure 3

Derivatives of final horizontal and vertical emittance with respect to eight beam parameters.

Figure 4

Schematic plot of a FODO lattice used in the second application example. The four quadrupoles inside the dashed line box were used to match the initial distribution to the periodic FODO lattice.

Figure 5

Transverse rms size evolution without the quadrupole matching (left) and with the quadrupole matching including the space-charge effects (right) through the FODO lattice.