  In this paper, we present experimental results and numerical simulations of
trident production, $e^-\rightarrow e^-e^+e^-$, in a strong electromagnetic
field. The experiment was conducted at CERN for the purpose of probing the
strong-field parameter $\chi$ up to 2.4, using a 200 GeV electron beam
penetrating a 400 $\mu$m thick germanium crystal oriented along the $\langle
110\rangle$ axis. For the current experimental parameters we found that the
trident process is primarily a two-step process, and show remarkable agreement
between theoretical predictions and experimental data. This paper is an
extension of the previously published paper (Phys. Rev. Lett. 130, 071601
(2023)) and features new analysis differential in the energy of the produced
positron and electron in the trident process. Even for the more demanding
differential analysis, we find good agreement between theoretical predictions
and experimental data, while a slight discrepancy is found in the high energy
tail of the trident spectrum. This discrepancy could be an indication of the
direct process, but further investigation is needed due to the large
uncertainties in this part of the spectrum. Finally we present a suggestion for
a future experiment, aiming to probe the direct process using thin crystals.
