Speaker
Description
Accurate evaluation of space-charge effects and their parameter sensitivities is essential for the design and optimization of high-intensity accelerators. We present the construction of a differentiable self-consistent space-charge map by combining Differential Algebra (DA) with an FFT-based Poisson solver using a truncated Green’s function. In this approach, the charge density, electrostatic potential, and electric field are represented as truncated multivariate power series with respect to selected initial-beam and accelerator parameters. Because the truncated Green’s-function convolution is linear, each DA coefficient is propagated efficiently through batched Fourier transforms, enabling direct calculation of first- and higher-order derivatives without repeated finite-difference simulations. The resulting DA space-charge map can be integrated with external lattice maps to propagate parameter sensitivities through self-consistent multiparticle tracking. A Hamiltonian split-operator formulation is also considered so that the space-charge kick is derived from a discrete interaction potential, supporting symplectic tracking. The proposed framework provides a systematic basis for sensitivity analysis, nonlinear map generation, tolerance studies, and gradient-based optimization of accelerator systems with collective space-charge effects.