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The functions tex2html_wrap_inline10242 (k=1,2) are stored in a 5-dimensional array FF(k,n,i,j,l) (n=1,MPH), (i=0,MY), (j=0,MXI), (l=0,MLM). The integral over y from 0 to tex2html_wrap_inline11200 is stored in FINT(k,n,i,j,l). The integral over the full range tex2html_wrap_inline11086 is then FINT(k,n,MY,j,l) For integration, the trapezondal rule is used, which means the function tex2html_wrap_inline10242 is approximated by a piecewise linear function. The sum of FINT(k,n,MY,j,l) over n is stored in FALL(k,j,l).

For a given initial condition, calculate the parameters tex2html_wrap_inline11240 and tex2html_wrap_inline7928 and find FALL(*) by 2-dimensional interpolation. (The asterisk * indicates the appropriate sum over the initial polarization, i,e., FALL(*)=FALLtex2html_wrap_inline11250FALLtex2html_wrap_inline11252). Then, calculate the total probability P (eq.(131) times the time interval DT):
Generate a uniform random number tex2html_wrap_inline9572 in the interval (0,1). If tex2html_wrap_inline11260, decide to emit a photon and, otherwise reject.

If rejected, the helicity of the electron should be changed, according to eq.(12), to

If accepted, decide how many laser photons to absorb. To do so, sum up FINT(*,n,MY,j,l) from n=1 to tex2html_wrap_inline11272 until the sum becomes larger than tex2html_wrap_inline9572. Then, tex2html_wrap_inline8380 will be the number of photons.

Once tex2html_wrap_inline8380 is determined, the photon energy is determined by
where tex2html_wrap_inline9574 is another uniform random number. The left hand side is known for the mesh point of y (i.e., FINT(k,n,MY,j,l)). Since we approximate tex2html_wrap_inline10242 by a piecewise linear function of y, the left hand side is a quadratic function between successive y's. Thus, inverse interpolation with respect to i by solving a quadratic equation gives the photon energy to be emitted.

The helicities of the final photon and electron are calculated from


for tex2html_wrap_inline11272. This is done by directly calling a Bessel function routine.

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