The initial distribution function of particle beams has been shown to have a significant impact on downstream beam dynamics. Accurate knowledge of the initial phase space at beam creation is crucial for understanding and predicting beam dynamics, enabling the production of beams with minimal emittance growth.
( https://doi.org/10.1063/5.0280429 )
High-dimensional phase space measurements provide valuable information about the beam dynamics in an accelerator; however, conventional diagnostics can only measure the distribution’s low-dimensional projections. Reconstructing the phase space distribution from these projections is referred to as phase space tomography.
( https://doi.org/10.1103/PhysRevAccelBeams.27.122802 )
Tomography is the reconstruction of a multidimensional distribution from its lower-dimensional projections. In the context of beam diagnostics, where the number of measured projections ≈10, tomographic reconstruction of the beam phase space distribution is typically an inverse problem with nonunique solutions. One commonly adopted approach in solving such an underdetermined problem is to invoke the principle of maximum entropy (MENT), which states that, among the many possible solutions, one should select the solution that maximizes the entropy of the resulting distribution.
( https://doi.org/10.1103/PhysRevAccelBeams.25.042801 )
Predicting halo formation in linear hadron accelerators is complicated by incomplete knowledge of the beam’s initial distribution in six-dimensional phase space.
( https://proceedings.jacow.org/hb2023/papers/tuc1c2.pdf )
Ion beams extracted from ion sources often exhibit complex structures in the full four-dimensional (4D) transverse phase space. Even when the rms emittances in individual planes are equal, the beams are typically strongly correlated upon extraction. Such interplane correlations contribute to an increase in the projected emittances. Eliminating these correlations can significantly reduce the effective emittance without relying on beam loss mechanisms such as scraping. However, to remove unknown correlations, they must first be accurately quantified through dedicated measurement techniques. Therefore, 4D diagnostic techniques play a crucial role, enabling the identification and elimination of interplane coupling in the beam.
( https://doi.org/10.1038/s41598-025-24550-2 )
In plasma and beam physics, tomographic methods may be used to infer the distribution of particles in 2D, 4D, or 6D phase space from measured 1D or 2D projections. While 2D tomography is an established technique, 4D and 6D tomography introduce several challenges. The first challenge is to fit the data: searching the space of high-dimensional distribution functions is not straightforward. The second challenge is to regularize the solution and quantify the reconstruction uncertainty: increasing the phase space dimension can generate an ill-posed inverse problem.
( https://journals.aps.org/prab/abstract/10.1103/zl2h-3v32 )
