The nonlinear space-charge effects are an important topic in high intensity accelerator beam dynamics and have been extensively studied using macroparticle tracking simulations. In this paper, we report on recent advances in the simulation of space-charge effects using a symplectic multiparticle space-charge model. The transverse space-charge limit was explored for a periodic focusing and defocusing lattice. The artificial numerical emittance growth in the macroparticle space-charge simulation was analyzed using a one-dimensional model.

In Refs. Qiang (2019) and Kesting (2015), the authors showed that the emittance growth rate due to the force error of macroparticle sampling will be proportional to the step size of simulation. In this note, we show that for the random force error, the emittance growth rate will be independent of the step size, which is consistent with the simulation observation.

Symplectic tracking is important in accelerator beam dynamics simulation. So far, to the best of our knowledge, there is no self-consistent symplectic space-charge tracking model available in the accelerator community. In this paper, we present a two-dimensional and a three-dimensional symplectic multiparticle spectral model for space-charge tracking simulation. This model includes both the effect from external fields and the effect of self-consistent space-charge fields using a split-operator method. Such a model preserves the phase space structure and shows much less numerical emittance growth than the particle-in-cell model in the illustrative examples.

The long-term macroparticle tracking simulation is computationally challenging but needed in order to study space-charge effects in high intensity circular accelerators. To address the challenge, in this paper, we proposed using a fully symplectic particle-in-cell model for the long-term space-charge simulation. We analyzed the artificial numerical emittance growth in the simulation and suggested using threshold numerical filtering in frequency domain to mitigate the emittance growth in the simulation. We also explored alternative frozen space-charge simulations and observed qualitative agreement with the self-consistent simulations.

The space-charge driven envelope instability can be of great danger in high intensity accelerators. Linear accelerators were designed to avoid this instability by keeping the zero current phase advance per lattice period below 90 degrees. In this paper, we studied the acceleration effects on the instability in a periodic solenoid and radio-frequency (rf) focusing channel and a periodic quadrupole and rf focusing channel using a three-dimensional envelope model and self-consistent macroparticle simulations. Our results suggest that the envelope instability might be dramatically mitigated with a reasonable accelerating gradient in both channels. This suggests that the zero current phase advance without acceleration might be above 90 degrees in linear accelerators where the accelerating gradient is sufficiently high.

Space-charge effects play an important role in high intensity accelerators. These effects can be studied self-consistently by solving the Poisson equation with the dynamically evolved charge density distribution subject to appropriate boundary conditions. In this paper, two computationally efficient methods are proposed to solve the Poisson equation inside an elliptical perfectly conducting pipe. One method uses a spectral method and the other uses a spectral finite difference method. The former method has a high accuracy and the latter one has a computational complexity of O(Nlog(N)), where N is the total number of unknowns. These methods implemented in a beam dynamics tracking code enable the fast simulation of space-charge effects in an accelerator with an elliptical conducting pipe.

In this paper, we report on recent advances in terascale simulations of the beam-beam interaction in Tevatron, RHIC and LHC. Computational methods for selfconsistent calculation of beam-beam forces are reviewed. New method for solving the two-dimensional Poisson equation with open boundary conditions is proposed and tested. This new spectral-finite difference method is a factor of four faster than the widely used FFT based Green function method for beam-beam interaction on axis. We also present applications to the study of antiproton losses during the injection stage at Tevatron, to the study of multiple bunch coherent beam-beam modes at RHIC, and to the study of beam-beam driven emittance growth at LHC.

A high peak current, flat longitudinal phase space electron beam is desirable for efficient X-ray free electron laser (FEL) radiation in next generation light sources. To attain such a beam requires the extensive design of the linear accelerator (linac) including both linear and nonlinear effects. In this paper, we propose a lumped longitudinal beam dynamics model for fast optimization of the electron beam longitudinal phase space through the accelerator. This model is much faster than available tracking programs and also shows good agreement with the fully three-dimensional element-by-element multiparticle simulations. We applied this model in a parallel multiobjective differential evolution optimization program to an existing LCLS-II superconducting linac design and obtained an optimal solution with significantly higher core peak current than the original design.

X-ray streak cameras (XSC) have been known to be one of the fastest detectors for ultrafast X-ray science. A number of applications in material science, biochemistry, accelerator physics, require sub-picosecond resolution to study new phenomena. In this paper, we report on a new method which can potentially improve the temporal resolution of a streak camera down to 100 femtoseconds. This method uses a time-dependent acceleration field to lengthen the photoelectron bunch, significantly improving the time resolution as well as reducing the time dispersion caused by initial energy spread and the effects from the space charge forces. A computer simulation of an XSC using this method shows significant improvement in the resolution.

A three-dimensional (3D) Poisson solver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of O(Nu(logNmode)), where Nu is the total number of unknowns and Nmode is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage of using an artificial boundary condition in a large extended computational domain. The new 3D Poisson solver is parallelized using a message passing interface (MPI) on multi-processor computers and shows a reasonable parallel performance up to hundreds of processor cores.