IRES: A Code to Calculate the Beamlet-Beamlet Interaction for Multiaperture Electrostatic Accelerators

The beamlet-beamlet interaction is an important process which has a relevant impact on the design of the grids for a multiaperture electrostatic accelerator. Space-charge effect leads to beamlet deflection, increasing the divergence of the whole beamlet group. According to the beamlet deflection, the grid apertures have to be properly aligned in order to provide the correct aiming of the beamlets and to avoid excessive thermal load on the grids. A new tool called Ion Relativistic Equation Solver (IRES) has been developed in Matlab to simulate the 3-D trajectories of a whole group of beamlets by integrating the relativistic equation of motion; the benchmark between this simple code and the results calculated by other tools can be useful to address the electrostatic accelerator design toward a reliable solution. The IRES code starts from a 3-D map of magnetic and electric fields evaluated by other software packages (e.g., ANSYS or Comsol Multiphysics), and it determines iteratively the central particle trajectory of each beamlet. The field map is then updated by taking into account the effect of the spatial charge due to the negative-ion beamlets; the process is repeated until a self-consistent solution is reached both for the field maps and the trajectories. The code has been validated in the case of a simple beamlet-beamlet interaction by comparing the results with those obtained using an analytical formula. IRES has then been applied to study the trajectories of negative ions in the 1-MV ITER neutral-beam injector with a single-gap configuration. It is expected that the advantage of using IRES will be apparent when evaluating the beam divergence in the presence of a large number of beamlets, due to the 1-D approximation used in the code.