When the laser field is strong, the simple formulas
of Compton/Breit-Wheeler can nolonger be used. The laser strength is
characterized by the parameter
where is the laser wavelength in meter, m the electron rest mass in eV/, c the velocity of light in m/s, , and P the power density in Watt/m. When , the simple formas are enough but as becomes large, the probability of absorbing more than one photon in the laser field cannot be ignored. When , the constant-field approximation becomes good. If , the expansion in terms of the number of absorbed photons, n, shows good convergence. The expansion takes a relatively simple form when the laser is circularly polarized by 100%. The present version accepts such case only.
In the case of the nonlinear Compton process
the number of emitted photons per unit time
can be expanded in the form
The formula for the nonlinear Breit-Wheeler process
can be written in a similar form.
The total number of pair electrons per unit time summed over the positron
When NPH is specified in LASERQED command, the above formulas are used with the terms upto n=NPH. See Sec.A for the algorithm of the event generation.