Simulation of space-charge effects using a quantum Schrödinger approach

Abstract

Space-charge effects play an important role in high intensity and high brightness particle accelerators. These effects were generally studied self-consistently by solving the Vlasov-Poisson equations using a particle-in-cell method in the accelerator community. In this paper, we propose an alternative method to simulate the space-charge effects in the accelerator. Instead of solving the Vlasov-Poisson equations, the proposed approach solves the Schr\"odinger-Poisson equations to study the space-charge effects in accelerators. Using a quantum Schr\"odinger approach reduces the original problem from six- or four-dimensional phase space down to three or two spatial dimensions. It also provides a possibility to simulate accelerator beam physics on quantum computers by evolving the wave function through quantum gates. Benchmarks of a coasting proton beam through a focusing drift defocusing drift lattice show excellent agreement between the quantum Schr\"odinger method and the particle-in-cell method.