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A six-dimensional symplectic tracking approach exploiting the periodicityproperties of Dielectric Laser Acceleration (DLA) gratings is presented. Thelongitudinal kick is obtained from the spatial Fourier harmonics of the laserfield within the structure, and the transverse kicks are obtained using thePanofsky-Wenzel theorem. Additionally to the usual, strictly longitudinallyperiodic gratings, our approach is also applicable to periodicity chirped(sub-relativistic) and tilted (deflection) gratings. In the limit of smallkicks and short periods we obtain the 6D Hamiltonian, which allows, forexample, to obtain matched beam distributions in DLAs. The scheme is applied tobeam and grating parameters similar to recently performed experiments. Thepaper concludes with an outlook to laser based focusing schemes, which arepromising to overcome fundamental interaction length limitations, in order tobuild an entire microchip-sized laser driven accelerator.

Beam Dynamics Analysis of Dielectric Laser Acceleration using a Fast 6D Tracking Scheme