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