Simulation of space-charge effects using a quantum Schrödinger approach

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 Schrödinger-Poisson equations to study the space-charge effects in accelerators. Using a quantum Schrödinger 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 Schrödinger method and the particle-in-cell method.

Figure 1

Schematic plot of the FODO lattice used in the benchmark examples.

Figure 2

Horizontal (x) and vertical (y) rms size (top left), rms momentum (top right), and beam Twiss alpha parameter (bottom) evolution through a five period FODO lattice from the quantum Schrödinger method (red and green) and from the PIC method (blue and magenta) without including the space-charge effects.

Figure 3

Horizontal (x) and vertical (y) rms emittance evolution through a five period FODO lattice from the quantum Schrödinger method (red and green) and from the PIC method (blue and magenta) without including the space-charge effects.

Figure 4

Horizontal (x) and vertical (y) rms size (top left), rms momentum (top right), and beam Twiss alpha parameter (bottom) evolution through a five period FODO lattice from the quantum Schrödinger method (red and green) and from the PIC method (blue and magenta) with the space-charge effects.

Figure 5

Four-dimensional normalized rms emittance evolution through a five period FODO lattice from the quantum Schrödinger method (red and green) and from the PIC method (blue and magenta) with the space-charge effects.

Figure 6

Horizontal (x) and vertical (y) rms size (top left), rms momentum (top right), and beam Twiss alpha parameter (bottom) evolution through a five period FODO lattice from the quantum Schrödinger method (red and green) and from the PIC method (blue and magenta) with the mismatched space-charge effects.

Figure 7

Horizontal (x) and vertical (y) rms emittance evolution through a five period FODO lattice from the quantum Schrödinger method (red and green) and from the PIC method (blue and magenta) with the mismatched space-charge effects.