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are 3-argument functions. In order to avoid discontinuities
due to the n-photon threshold, following variables (in addition to )
are used as the independent variables instead of (, , x):
- q
- Defined by . The n-photon threshold is
given by .
- y
- Defined by .
represents electrons with energy and
those . Since
and are even functions of y, only the part
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 ,
)
- MPH
- Maximum number of laser photons. ()
- MXI
- Number of 's. (,
)
- MQ
- Number of q's. Non-equally-spaced MQ points are
selected in .
- XIMAX
- Maximum .
- ETAMAX
- Maximum . Must satisfy .
Otherwise, no pair creation is possible.
- LENHBW
- Flag to apply a rate enhancement function.
- ENHBWF
- Enhancement function name declared external. Used when
LENHCP1.
- 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
() only and it
must be an even function of y and for all y. (Actually, only the part
is used.)
The probability functions are multiplied
by ENHBWF(y). Note that 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
MYMPHMXIMQ
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. ( HG ).
- 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/m).
- 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 , 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 WGT (actually, ), each of the final pair should be
asigned the weight and the initial photon still be retained
with the weight , where 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
- is larger than XIMAX.
- IRTN=1002
- 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 ,
where k=K, n=NPH, =XI, =ETA,
and x=X=.
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: Algorithm
Up: Breit-Wheeler Process
Previous: Formulas
Toshiaki Tauchi
Thu Dec 3 17:27:26 JST 1998