Luminosity spectra 
          at TESLA Photon Colliders
             
           (User's guide, version 2, 22.12.2003)
                 
                 V.Telnov
            telnov@inp.nsk.su
            telnov@mail.desy.de               

Files in this directory contain information on collisions at the
photon collider at TESLA: types, energies and polarizations of
colliding particles.  One can use them for simulations as realistic
luminosity distributions.  Read it to your computer and use.

Structure: 

files fort.n contain array A(6,1000000). One can read it in your
fortran code

dimension A(6,1000000)
read (n) ((A(I1,I2),I1=1,6),I2=1,1000000)
close (n)

IMPORTANT NOTE: in files with n>50  each event contain more elements:
                A(10,1000000), all particle polarization are included,
                therefore one should use "10" instead of "6" in above
                commsnds. Below structures of files with dimentions
                6 and 10 is presented.

For files with the number n<50
---------------------------------   
A(1,1) - number of collisions, somewhat smaller than 1 M.
A(2,1) - geometric ee luminosity, in units 10^{34}
A(3,1) - total ee luminosity in units of geom.luminosity 
A(4,1) - total gamma-e luminosity in units of geom.luminosity 
A(5,1) - total gamma-gamma luminosity in units of geom.luminosity 
A(6,1) - now nothing

A(i,j)  for 1<j<=A(1,1)+1

A(1,j) - type of the first particle in the collision 
        (0.-photon,-1.-electr, +1 -positron)
A(2,j) - type of  the second particle
A(3,j) - energy (GeV) of the first particle
A(4,j) - energy (GeV) of the second particle
A(5,j) - helicity of  the first particle (from -1 to +1)
A(6,j) - helicity of  the second particle

for files with the number  n>=50
-----------------------------------
A(1,1) - number of collisions, somewhat smaller than 1 M.
A(2,1) - geometric ee luminosity, in units 10^{34}
A(3,1) - total ee luminosity in units of geom.luminosity 
A(4,1) - total gamma-e luminosity in units of geom.luminosity 
A(5,1) - total gamma-gamma luminosity in units of geom.luminosity 
A(6-10,1) - now nothing

A(i,j)  for 1<j<=A(1,1)+1

A(1,j) - type of the first particle in the collision 
        (0.-photon,-1.-electr, +1 -positron)
A(2,j) - type of  the second particle
A(3,j) - energy (GeV) of the first particle
A(4,j) - energy (GeV) of the second particle
A(5,j) - first particle, 1-st component of polarization 
A(6,j) - first particle, 2-nd component of polarization
A(7,j) - first particle, 3-d component of polarization
A(8,j) - second particle, 1-st component of polarization 
A(9,j) - second particle, 2-nd component of polarization
A(10,j) -second particle, 3-d component of polarization

Components of polarization mean for electrons x,y,z projectrions of
the polarization vector (z - longitudinal polarization), for photons
--these are Stocks parameters: \ksi_2 - circular polarization, \ksi_1
= l_g sin(2\phi), \ksi_3= l_g cos(2\phi, where l_g --the degree of
linear polarization, \phi the angle between the direction of the
maximum linear polarization and axis x. 

-------------------------------------------------------------
Note, that these collisions are produced by simulation of about 20
 bunch collisions and their properties are changed in the time (index
 "j").  For obtaining of correct spectra one should use all events or
 take them randomly from j=2 to j=A(1,1)+1
 ---------------------------------------------------------------

In most of files below the polarizations are taken in such a way that
total helicity of two high energy photons is near 0 (2P_c
\lambda_e=-1).  To get the situation when one of electron beams and
the corresponding laser change their polarization to opposite
simultaneously just change polarization of the "second" particles to
opposite.  All luminosity distributions remain the same but 
L_0 -> L_2 and L_2 -> L_0.


Available data:

case 1-4 corerspond to TDR, only in the case 4 here \rho=5 (8 in TDR).
K_i are conversion coefficients = 1- exp(-t/\lambda_c), where
t/\lambda_c is the thickneed of laser target in units of Compton
collision length.

files    2E_0  P_e P_las  k1   k2  \rho  x  wavelength \xi^2   note  
         GeV                                   \mu m
-------------------------------------------------------------
fort.1   200   0.85 -1  0.74  0.74   2  1.8   1.05     0.15  TESLA

fort.2   500   0.85 -1  0.632  0.632 1  4.6   1.05     0.3   TESLA

fort.3   800   0.85 -1  0.632  0.632 1  7.17  1.05     0.4   TESLA

fort.4   500   0.85 -1  0.632  0.0   5  4.6   1.05     0.3   TESLA

fort.44 3000   0.85 -1  0.632  0.632 1  6.5   4.4      0.3  CLIC(3000)*   

fort.57  500   0.85 -1  0.632  0.632 60 4.6   1.05     0.3  TESLA **
------------------------------------------------------------------
*for CLIC the electron beam parameters at IP are the same as for e+e-
case
** the distance between interaction and conversion points is
increased to obtain mote monochromatic spectrum for measurement of 
\gamma\gamma luminosity. 


In comparision with TDR, in the present simulation nonlinear effects
are simulated more precicely taking into account first order
corrections (effective electron mass and scattering on two laser
photons). In TDR we just changed x to x/(\xii2 +1)), where \xii2 is
proportional to local density of laser photons. So, graphs are differ
somewhat (some smearing of the high energy edge of the spectra). Also
polarization effects in beamstrahlung are included approximatelly.

----------------------------------------------------------------------
Some words about particle helicities given by elements A(5,j),A(6,j)

Longitudinaly polarized electron (and circilarly polarized photons)
have some probability P_f to have spin along direction of motion and
P_b=1-P_f in opposite direction.  Polarization degree P (which is
given in arrays) = P_f - P_b= 2P_f-1. From this we get 

P_f=0.5(1+P)
P_b=0.5(1-P)

   If two particles with polarization P_1 and P_2 are collided, then
the system of two particles can have the tolal helicity 0 and 2.
The probabilities of helicity O and 2 (contribution to L_0 and L_2) are 

L_0= (P_{f,1} * P_{f,2} +P_{b,1}*P_{b,2})*L =0.5*(1+P_1*P_2)*L
L_2= (P_{f,1} * P_{b,2} +P_{b,1}*P_{f,2})*L =0.5*(1-P_1*P_2)*L

where L = L_0 +L_2   is the total luminosity 




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Short description of the simulation code, beam parameters and some figures
are given is the file comments.ps (11 pp)

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