We study the trident process in laser pulses. We provide exact numerical results for all contributions, including the difficult exchange term. We show that all terms are in general important for a short pulse. For a long pulse we identify a term that gives the dominant contribution even if the intensity is only moderately high, $a_0gtrsim1$, which is an experimentally important regime where the standard locally-constant-field (LCF) approximation cannot be used. We show that the spectrum has a richer structure at $a_0sim1$, compared to the LCF regime $a_0gg1$. We study the convergence to LCF as $a_0$ increases and how this convergence depends on the momentum of the initial electron. We also identify the terms that dominate at high energy.
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