Synergia Particle-in-Cell Accelerator Simulations
Simulations of beam dynamics in particle accelerators have a wide range of computational requirements. The simplest calculations involve independent-particle tracking of a few thousand particles -which can easily be accomplished on modern desktop computers. Calculations involving collective effects may require millions or even billions of particles and push the limits of modern supercomputers. Synergia is an accelerator simulation package capable of running the gamut from independent-particle simulations on desktop machines to multi-bunch, multi-billion particle simulations with collective effects utilizing over 100k cores on supercomputers.
The animation shows a beam bunch with self-field interactions moving through a canonical accelerator focusing-defocusing lattice. It takes place in the rest frame of the beam, i.e., the camera is moving along with the beam centroid. The displayed elements are a sample subset of particles (green) and field contours (purple) representing the scalar electric potential generated by the electromagnetic interactions between the particles (space charge in accelerator physics terminology.) The simulation also includes external magnetic fields generated by focusing and defocusing quadrupoles, but these are not shown. Only 1000 particles are shown; actual simulations require millions to billions of particles.
This is a particle-in-cell simulation — the particles are really macroparticles, each of which represents (roughly) 1 million real particles. The fields are calculated by depositing charge on a finite grid, typically of a size of 128^3 (3-D rectangular grid with 128 segments on each direction), solving the field equations on that grid, and then interpolating to the particle positions for electromagnetic kicks.
The external focusing magnets are responsible for the transverse breathing motion exhibited by the particles. The self-fields form a small perturbation, which modifies the frequency of transverse oscillation for each particle. In this example, there are no external fields constraining the longitudinal motion. The particles expand longitudinally primarily due to the electromagnetic repulsion of the self-fields. This sort of phenomenon is present, for example, in the early phase of the Fermilab Booster, where the particle bunches injected from the Fermilab Linac are allowed to debunch before being rebunched by the radiofrequency cavities that are turned on later in the Booster cycle.