3D Numerical Modeling of Ultrarelativistic Particle Beams with Crossing Angle

We present a new algorithm for numerical simulation of beam dynamics in the modern supercolliders, where the beams move with ultrarelativistic speeds and collide with crossing angle (~20 mrad). In case of critical charge densities the colliding beams may disrupt and the problem of beam stability arises. We consider the fully three-dimensional dynamics of charged particle beams in self-consistent electromagnetic-fields in vacuum. We solve Vlasov-Liouville equation and Maxwell equations with the particle-in-cell method. The algorithm is parallel and is based on a mixed decomposition to achieve the effective performance in case of strongly focused thin beams. We present the numerical results for single-passage beam interaction with different beam configurations. Comparison with analytical solutions in case of their existence is shown.