Six-Dimensional Beam-Envelope Equations: An Ultrafast Computational Approach for Interactive Modeling of Accelerator Structures

The design and implementation of accelerators capable providing high-quality bunches require precise efficient online modeling tools. Current comprehensive beam dynamics studies are prohibitively costly challenging to use for interactive system design. A high-speed method analysis in accelerator components is presented compared the results conventional particle-in-cell codes. Using powerful mathematical techniques, suggested evaluates temporal evolution a bunch shape six-dimensional (6D) phase space along accelerators. moment equations that govern envelope 6D introduced. three-dimensional space-charge, external, emittance forces calculated be fully analytically insensitive different envelopes. Substituting obtained into beam-envelope establishes set six modified describing using simple algebraic expressions. whole solution considers energy spread inherent an electron beam. model accuracy demonstrated by studying transport through various accelerator. Applying this analytical approach not only forms style physical thinking indicating factors affect behavior charged particle but also has ultrafast computational speed at least 3 orders magnitude faster than tracking codes designing today's linear Finally, model's feasibility benchmarked successfully photoinjector advanced proton driven plasma wakefield acceleration experiment.