Obtaining the complete distribution of a beam in high-dimensional phase space is crucial for predicting and controlling beam evolution. Based on the theory of maximum entropy tomography, we developed an algorithm for reconstructing the four-dimensional (4D) transverse phase space distribution. Our algorithm can take any number of 2D linear projections as constraints, and iteratively converges to the unique numerical solution which is the maximum-entropy distribution satisfying the constraints. Having verified the algorithm with simulation experiments, we plan to use it to conduct 4D phase space tomography in the MEBT and HEBT of the heavy ion linac CAFe II.

Quantifying the difference between two beam distributions in high-dimensional phase space is crucial for interpreting experimental or simulation results. This study aims to analyze and compare several common statistical divergences that quantify the differences in high-dimensional distributions, and to determine which of them are suitable for beam physics applications. We tested these divergences with common kinds of initial distributions by computing how the difference values vary when the mismatch factor and emittance change, between the same and different kinds of distributions. These results, along with similar comparisons after extended beam transport, provided guidance on the use and choice of statistical divergences for beam phase space distributions.