When the orbit of a high energy electron(positron)
with energy is bent
by a magnetic field B or by an electric field
with the curvature radius ,
the critical energy of synchrotron radiation is given by
where is the Compton wavelength,
Tesla is Schwinger's critical
field and
V/m.
The energy spectrum of emitted photons is given by the
Sokolov-Ternov formula .
(Radiation angle is not included in CAIN.
All the photons are emitted forward.) The number of photons per unit time
in the interval (x,x+dx) of the energy fraction is
Here, is the fine structure constant and
is the final electron energy,
the modified Bessel function and is its integral: