next up previous contents index
Next: Polarization Up: Beamstrahlung Previous: Basic formulas

Algorithm of event generation

The random number generation using the acception-rejection method is applicable when the distribution function is everywhere finite and is most efficient when the function is flat.

Since the function tex2html_wrap_inline10300 is infinite at tex2html_wrap_inline10302, the following variable y is introduced in CAIN instead of the photon energy fraction x in order to make the distribution function finite and relatively flat.gif
 equation4602

The number of photons during a time interval tex2html_wrap_inline8540 in the photon energy range (y,y+dy) is then given by
equation4607
where
 equation4609

 equation4614
The function tex2html_wrap_inline10316 is less than or equal to unity for any tex2html_wrap_inline9648 and y. It is plotted in Fig.7.

  figure4431
Figure 7: Function tex2html_wrap_inline10316 for various values of tex2html_wrap_inline9648. Unpolarized case only.

The photon generation in CAIN proceeds in the following way.

The cases when accepted in (3) but rejected in (6) cause a waste of time because the calculation of tex2html_wrap_inline10316 is the most time consuming. The probability to be accepted in (6) is plotted in Fig.8 is given by tex2html_wrap_inline10362 and is plotted as a function of tex2html_wrap_inline9648. One finds the probability is very high for any tex2html_wrap_inline9648 owing to the choice of the variable y.

  figure4447
Figure 8: The acception probability in the step (6) as a function of tex2html_wrap_inline9648. The solid line is the unpolarized case The dot-dash and dotted lines are polarized cases with tex2html_wrap_inline10372 = 1 and -1, respectively.


next up previous contents index
Next: Polarization Up: Beamstrahlung Previous: Basic formulas

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