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Abstract

It is commonly assumed that in ultrastrong laser fields, when the strong
field parameter of the laser field $\xi$ is larger than one, the electron
radiation is well described by the local constant field approximation (LCFA).
We discuss the failure of this conjecture, considering radiation of an
ultrarelativistic electron interacting with strong counterpropagating laser
waves. A deviation from LCFA, in particular in the high-frequency domain, is
shown to occur even at $\xi\gg 1$ because of the appearance of an additional
small time scale in the trajectory. Moreover, we identify a new class of LCFA
violation, when the radiation formation length becomes smaller than the one via
LCFA. It is characterized by a broad and smooth spectrum rather than an
harmonic structure. A similar phenomenon is also demonstrated in the scenario
of an electron colliding with an ultrashort laser pulse. The relevance to
laser-plasma kinetic simulations is discussed.