We present a new algorithm for mathematical modeling of colliding beams dynamics in supercolliders. A single-pass collision of the high-energy beams makes possible their strong deformation or even disruption, and the study of the beam stability is needed.
We consider the motion of the charged particle beams with the high relativistic factors of the particles and large crossing angles in self-consistent electromagnetic fields. The standard numerical models and algorithms are quasi-three-dimensional and have diffiligculties with taking into account large crossing angles (∼ 20 mrad). We present a fully three-dimensional algorithm, based on solution of the Vlasov equation and set of Maxwell equations with the particle-in-cell method. In the 3D modeling the problem is not only the computational speed, but also the insufficient memory of one processor to keep the data for the beams with highly nonuniform density distribution. The presence of the high value of the relativistic particle factor (γ ∼ 104 – 106) is a fundamental feature of the problem, due to the relativism the transversal fields grow with γ, leading to the high spatial gradients. The domain-particle parallelization enabled us to perform numerical simulations with 109 macro-particles.
We present the computational results and analysis of the beam evolution for the case of two focused colliding beams.
