Quantum effects of the interaction of elementary particles with an intense electromagnetic field

Streaking at high energies with electrons and positrons

“…The condition of Eq. (2) is usually fulfilled when ξ i 1 which corresponds to the quasi-static limit in which the probability of strong field QED processes in laser fields coincides with the one in the crossed field with the same value of χ [32]. For χ 8/3, the pair production process becomes very efficient, and the number of produced pairs via Eq.…”

“…(10) αξ i χ 1, while only in the opposite limit αξ i χ 1, the radiation dominated regime of multiphoton Compton scattering is entered [36,37]. Similarly, a cascade of pair production [38,39] can only be initiated for χ 1 if the interaction time τ i = 2πN i /ω i is much larger than the pair creation time τ e + e − ∼ ω t /αm 2 χ 2/3 [32], which yields αξ i N i /χ 1/3 1. But the opposite condition is fulfilled in the streaking regime and thus the pair production cascade is suppressed [40].…”

“…Therefore, the fields of the SP and IP in the center-of-mass frame of the electron-positron pairs, hypothetically produced via the SP and IP, should be negligible with respect to the Schwinger critical field E cr = m 2 /e [32]. The center-of-mass frame is determined by the equality of the Doppler-shifted frequencies of the SP and IP, 2γ cm ω i = ω s /2γ cm , with the Lorentz-factor of the center-of-mass frame γ cm .…”

“…The first requirement for SHEEP is that a sufficient number of electron-positron pairs is created by the laser fields. The strong field pair production process is governed by two relativistic invariant parameters ξ = e A µ A µ /m and χ = e (F µν k ν t ) 2 /m 3 [32], where A µ and F µν are the vector potential and the field tensor of the laser fields, respectively, and e and m are the absolute value of the charge and the mass of the electron. The number of pairs (averaged by the photon polarization) produced during the interaction time τ i of the TP photons with IP is given by [32] …”

“…The number of absorbed IP photons at the threshold is n i0 = m 2 * /ω t ω i [33]. The width of variation of the absorbed laser photons (n i ) from the threshold value (n i0 ) is of order δn i ∼ n i0 [32]. Absorbing n i photons from the laser field, the particles in the center-of-mass frame are born with an energy E cm = √ n i ω i ω t [34] and with the polar emission angles θ, φ for the positron.…”