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Laser driven plasma accelerators promise much shorter particle acceleratorsbut their development requires detailed simulations that challenge or exceedcurrent capabilities. We report the first direct simulations of stages up to 1TeV from simulations using a Lorentz boosted calculation frame resulting in amillion times speedup, thanks to a frame boost as high as gamma=1300. Effectsof the hyperbolic rotation in Minkowski space resulting from the frame boost onthe laser propagation in the plasma is shown to be key in the mitigation of anumerical instability that was limiting previous attempts.

Effects of Hyperbolic Rotation in Minkowski Space on the Modeling of Plasma Accelerators in a Lorentz Boosted Frame