Numerical simulations of colliding beams dynamics with nonzero crossing angle

The work is devoted to the problem of charged particle beam dynamics in self‐consistent electromagnetic fields in the modern colliders. The colliding beams move in vacuum with highly relativistic speeds (γ∼103 − 105). The achievement of the high luminosities for the high energy beams finds difficulties due to the beam disruption under the strong electromagnetic fields. We present our first results on the numerical simulations for the beams with the nonzero crossing angle with our parallel fully three‐dimensional algorithm. The results of the numerical modelling demonstrate qualitative and quantitative coincidence with theory for noncritical beam parameters.