Engineering topics

Mitchell, Chad

Publications and source records attributed to Mitchell, Chad.

4 records

DOE OSTI2026

The Memory Scaling of Reverse-Mode Differentiation in Particle Accelerator Simulations with Space Charge

The recent development of differentiable simulation codes for particle accelerators has enabled gradient-based workflows that promise finer control and more realistic modeling of accelerator facilities. However, when using reverse-mode automatic differentiation, the memory usage continuously increases during the simulation, and can potentially exceed the available hardware memory - especially when costly space charge computation is included. To study the memory requirements for differentiable simulations, we have implemented space charge in Cheetah, a PyTorch-based beam tracking code that supports reverse-mode differentiation. We find that the memory usage for reverse-mode differentiation grows linearly with the number of macroparticles and cells, and that it is proportional to the number of space charge kicks involved in the simulation. This general scaling can be used to evaluate whether a given differentiable simulation is feasible given hardware memory constraints.

Dhamrait, Arjun↗

DOE OSTI2025

Chromatic Transport Models for ImpactX

This note describes the basic levels of Hamiltonian approximation (for straight-axis elements) that are used in the symplectic beam dynamics modeling code ImpactX. These include: purely linear models, models based on a paraxial (chromatic) expansion of the Hamiltonian, and models based on the exact nonlinear Hamiltonian. The focus here is on paraxial (chromatic) models.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Poisson Equation for a (General) Homogeneous d-Dimensional Ellipsoid with Applications to Beam Envelope Tracking

This note describes the solution of the free-space Poisson equation in the interior of a $d$-dimensional homogeneous ellipsoid, and the associated space charge fields. An explicit formula (\ref{Sformula}) is provided that relates the $d\times d$ matrix describing the space charge (quadratic) potential to the $d\times d$ covariance matrix of the ellipsoid. For the cases $d=2$ and $d=3$, this result is used to determine the linear map corresponding to a space charge kick, that may be used to push the beam $6\times 6$ covariance matrix during envelope tracking. The treatment of upright ellipsoids for $d=2$ and $d=3$ is well-represented in the literature. However, the approach taken here emphasizes a general ellipsoid with arbitrary correlations in any dimension. The Appendix provides a general solution of the free-space Poisson equation in dimension $d$ for a source distribution with ellipsoidal symmetry.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Elliptic multipoles and the modeling of narrow-gap bend magnets in accelerators

We highlight the virtues of 2D elliptic-multipole field expansions in modeling the magnetic fields of narrow-aperture, straight-axis bending magnets with parallel faces, addressing the limitations of the conventional circular multipole series when the beam-orbit sagitta exceeds the magnet's vertical half-gap. The elliptic multipoles provide a convenient way to represent the field in all aspects of the magnet development (design, particle-tracking simulations, measurements). We propose a numerically robust method of data analysis to determine the elliptic (or circular) multipoles from stretched-wire measurements with the wire moving on an arbitrary path.

Venturini, Marco↗