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A Scattered-Field Formulation for Coupled Geometric Wakefield and Space Charge Field Simulations in Particle Accelerators

J. Christ, E. Gjonaj, H. De Gersem

Abstract

We propose a self-consistent simulation model for particle beams in accelerators, which includes the impact of electromagnetic wakefields caused by the geometry of the accelerator chamber. The method is based on a scattered-field formulation for the beam-driven Maxwell's equations. The total electromagnetic field seen by the particles is obtained as the solution of two coupled problems: a purely wakefield problem and a space charge field problem, where for each of these problems, specialized and numerically efficient approaches can be used. To assess the accuracy of the method, we compare simulation results with the analytical solution for a relativistic beam in a uniform accelerator pipe. The numerical efficiency of the method is, furthermore, demonstrated in the beam dynamics study of the multi-cell RF photo-gun installed at the SuperKEK collider facility. We show that electromagnetic wakefields have a non-negligible impact on the quality of the generated beam and, therefore, should be taken into account in the design of high-brilliance electron sources.

A Scattered-Field Formulation for Coupled Geometric Wakefield and Space Charge Field Simulations in Particle Accelerators

Abstract

We propose a self-consistent simulation model for particle beams in accelerators, which includes the impact of electromagnetic wakefields caused by the geometry of the accelerator chamber. The method is based on a scattered-field formulation for the beam-driven Maxwell's equations. The total electromagnetic field seen by the particles is obtained as the solution of two coupled problems: a purely wakefield problem and a space charge field problem, where for each of these problems, specialized and numerically efficient approaches can be used. To assess the accuracy of the method, we compare simulation results with the analytical solution for a relativistic beam in a uniform accelerator pipe. The numerical efficiency of the method is, furthermore, demonstrated in the beam dynamics study of the multi-cell RF photo-gun installed at the SuperKEK collider facility. We show that electromagnetic wakefields have a non-negligible impact on the quality of the generated beam and, therefore, should be taken into account in the design of high-brilliance electron sources.
Paper Structure (20 sections, 22 equations, 12 figures, 1 table)

This paper contains 20 sections, 22 equations, 12 figures, 1 table.

Table of Contents

  1. Introduction
  2. Beam-driven electromagnetic fields
  3. Solution of the wakefield problem
  4. Discretization of Maxwell's equations by FIT
  5. Discrete scattered-field formulation
  6. Boundary conformal approximation
  7. Solution of the space charge field problem
  8. Particle field computation
  9. Boundary field computation
  10. Fully relativistic case
  11. Putting the pieces together
  12. Numerical verification and accuracy
  13. Particle beam in a uniform pipe
  14. Model setup
  15. Steady-state solution
  16. ...and 5 more sections

Figures (12)

  • Figure 1: Primal FIT face in free space (a) and partially filled with a PEC material (b). The edge lengths and face areas used in the definition of the FIT degrees of freedom for the boundary conformal approximation are shown.
  • Figure 2: Schematic view of the coupling procedure depicting a particle bunch, an accelerator structure and the two meshes used for the SCF and wakefield computations, respectively.
  • Figure 3: Longitudinal electric field on-axis within the computational window at different bunch traveling distances $z_0$. The red curve is simulated; the black-dotted one is the analytical solution \ref{['eq_validation_EzTotal']}.
  • Figure 4: Contributions of the free-space SCF (blue) and scattered field (black-dotted) to the total longitudinal electric field along the axis (red) in a rectangular beam pipe.
  • Figure 5: Relative rms error vs. mesh step size in the rectangular pipe case for two different pipe heights $h$.
  • ...and 7 more figures