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Abstract

Processes occurring in the strong-field regime of QED are characterized by
background electromagnetic fields of the order of the critical field
$F_{cr}=m^2c^3/\hbar|e|$ in the rest frame of participating charges. It has
been conjectured that if in their rest frame electrons/positrons experience
field strengths of the order of $F_{cr}/\alpha^{3/2}\approx 1600\,F_{cr}$, with
$\alpha\approx 1/137$ being the fine-structure constant, their effective
coupling with radiation becomes of the order of unity. Here we show that
channeling radiation by ultrarelativistic electrons with energies of the order
of a few TeV on thin tungsten crystals allows to test the predictions of QED
close to this fully non-perturbative regime by measuring the angularly resolved
single photon intensity spectrum. The proposed setup features the unique
characteristics that essentially all electrons 1) undergo at most a single
photon emission and 2) experience at the moment of emission and in the angular
region of interest the maximum allowed value of the field strength, which at
$2\;\text{TeV}$ exceeds $F_{cr}$ by more than two orders of magnitudes in their
rest frame.