Numerical modelling of focused relativistic electron-positron beams colliding with crossing angle

Abstract

We present a three-dimensional parallel algorithm for numerical modelling of self-consistent colliding beam dynamics in linear supercolliders. The thin ultrarelativistic beams are focused by quadrupole lens field and collide with a crossing angle (2-25 mrad). The small sizes of the beams are necessary for high luminosity achievement. However, their high density may be critical and the beams may significantly change their shape or even disrupt. The crossing angle between the beams and the non-linear focusing complicate the problem of the beam stability and optimization of the collider parameters.Our algorithm is based on solution of Vlasov-Liouville and Maxwell’s equations in three-dimensional case. We use the particle-in-cell method with PIC form-factor and Langdon-Lasinsky scheme on shifted Yee’s grids. We combine particle and domain decompositions for the purpose of using 109 model particles in the numerical experiments. The beam particle distribution is highly non-linear in space, and the domains with larger numbers of the model particles are computed with higher numbers of the processors. The algorithm and its components may be applied to different problems in relativistic plasma physics.