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Basic formulas

When the orbit of a high energy electron(positron) with energy tex2html_wrap_inline10274 is bent by a magnetic field B or by an electric field tex2html_wrap_inline10278 with the curvature radius tex2html_wrap_inline10280, the critical energy of synchrotron radiation is given by
where tex2html_wrap_inline10282 is the Compton wavelength, tex2html_wrap_inline10284Tesla is Schwinger's critical field  and tex2html_wrap_inline10286V/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 tex2html_wrap_inline10290 is
Here, tex2html_wrap_inline7492 is the fine structure constant and
tex2html_wrap_inline10294 is the final electron energy, tex2html_wrap_inline10296 the modified Bessel function and tex2html_wrap_inline10298 is its integral:

Toshiaki Tauchi
Thu Dec 3 17:27:26 JST 1998