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Usage

tex2html_wrap_inline10268 are 3-argument functions. In order to avoid discontinuities due to the n-photon threshold, following variables (in addition to tex2html_wrap_inline11240) are used as the independent variables instead of (tex2html_wrap_inline7924, tex2html_wrap_inline7944, x):

q
Defined by tex2html_wrap_inline11402. The n-photon threshold is given by tex2html_wrap_inline11406.
y
Defined by tex2html_wrap_inline11410. tex2html_wrap_inline11086 represents electrons with energy tex2html_wrap_inline11414 and tex2html_wrap_inline11416 those tex2html_wrap_inline11418. Since tex2html_wrap_inline11420 and tex2html_wrap_inline11422 are even functions of y, only the part tex2html_wrap_inline11426 is tabulated.

Now, the initialization is done by

C ALL NLBWST(MY,MPH,MXI,MQ,XIMAX,ETAMAX,LENHBW,ENHBWF,IRTN)

    MY
    Number of y's. (i-th y point is tex2html_wrap_inline11094, tex2html_wrap_inline11096)
    MPH
    Maximum number of laser photons. (tex2html_wrap_inline11098)
    MXI
    Number of tex2html_wrap_inline7924's. (tex2html_wrap_inline11102, tex2html_wrap_inline11104)
    MQ
    Number of q's. Non-equally-spaced MQ points are selected in tex2html_wrap_inline11448.
    XIMAX
    Maximum tex2html_wrap_inline7924.
    ETAMAX
    Maximum tex2html_wrap_inline7944. Must satisfy tex2html_wrap_inline11454. Otherwise, no pair creation is possible.
    LENHBW
    Flag to apply a rate enhancement function.
    ENHBWF
    Enhancement function name declared external. Used when LENHCPtex2html_wrap_inline72481. 
    IRTN
    Return code.
The parameters MY, MPH, MXI can be different from those for nlcpst. A second call of NLBWST will replace the parameters and the arrays created in the first call.

The enhancement function, if needed, has to be defined as

            FUNCTION ENHBWF(Y)
            REAL*8 ENHBWF,Y
            ENHBWF=......
            RETURN
            END
The enhancement function has to be a function of tex2html_wrap_inline11458 (tex2html_wrap_inline11460) only and it must be an even function of y and tex2html_wrap_inline7900 for all y. (Actually, only the part tex2html_wrap_inline11086 is used.) The probability functions tex2html_wrap_inline10268 are multiplied by ENHBWF(y). Note that tex2html_wrap_inline11474 close to 1 represents events with a large unbalance of energy between final electron and positron. See NLBWGN for how the weight should be treated in the simulation.

Possible errors 1ex

    IRTN=1000
    Memory insufficient. You have to reduce MYtex2html_wrap_inline9166MPHtex2html_wrap_inline9166MXItex2html_wrap_inline9166MQ or increase the parameter MW in the FORTRAN source.
    IRTN=1001 to 1004
    Either one of MY,MPH,MXI,MQ is too large.
    IRTN=1100
    The enhancement function less than 1 at some y.

An event is generated by 1ex

     NLBWGN(PG,HG,WL,NL,HL,PD,DT,PMAX,IRR,NPH,PELE,HELE,PPOS,HPOS,
            PROB,WGT,IRTN)

Input variables

    PG
    Array of dimension (0:3). Initial (high energy) photon 4-momentum (eV/c).
    HG
    Photon helicity. (tex2html_wrap_inline11140 HG tex2html_wrap_inline7954).
    WL
    Laser photon energy (eV).
    NL
    Array of dimension 3. Unit vector along the laser direction.
    HL
    Laser helicity (-1 or +1).
    PD
    Laser power density (Watt/mtex2html_wrap_inline7792).
    DT
    Time interval times the velocity of light (meter).
    PMAX
    Maximum probability of pair creation in DT. Same as in NLCPGN.
    IRR
    Random number seed.

Output variables

    NPH
    If tex2html_wrap_inline11152, number of absorbed laser photons. If 0, no pair creation.
    PELE
    Array of dimension (0:3). 4-momentum of final electron.
    HELE
    Helicity of final electron.
    PPOS
    Array of dimension (0:3). 4-momentum of final positron.
    HPOS
    Helicity of final positron.
    PROB
    Calculated event probability. Same as in NLCPGN.
    WGT
    Event weight. Same as in NLCPGN.
    IRTN
    Return code.
The event weight is always 1 if initialized with LENHBW=0. When WGTtex2html_wrap_inline11496 (actually, tex2html_wrap_inline7954), each of the final pair should be asigned the weight tex2html_wrap_inline11500 and the initial photon still be retained with the weight tex2html_wrap_inline11166, where tex2html_wrap_inline11168 is the weight of the initial photon before the event. When WGT=1, the initial photon should be eliminated.

Possible errors

    IRTN=1000
    Initialization nit yet done.
    IRTN=1001
    tex2html_wrap_inline7924 is larger than XIMAX.
    IRTN=1002
    tex2html_wrap_inline7944 is larger than ETAMAX.
    IRTN=100
    The total rate exceeds PMAX.

Real*8 function

N LBWFN(KK,K,NPH,XI,ETA,X)

returns the value of the function tex2html_wrap_inline11512, where k=K, n=NPH, tex2html_wrap_inline7924=XI, tex2html_wrap_inline7944=ETA, and x=X=tex2html_wrap_inline11524. The first argument KK selects either the direct calculation using a Bessel function routine (KK=1) or use interpolation of the stored table (KK=2). In the latter case, initialization must be done in advance and K must be 1 or 3.


next up previous contents index
Next: Algorithm Up: Breit-Wheeler Process Previous: Formulas

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