Average number of Interactions / crossing

Luminosity/crossing is calculated as Lum/turn/N(bunch).
Average number of interactions/crossing is sigma * Lum/crossing.

Luminosity (/cm^2/s)
2.00E+32

ring radius (m)
1000
circumference (m)          T (sec)       lum/turn (cm^2)
6283.18531              2.0944E-05      4.1888E+27

minbias cross-section = 47 mb
      
   N(bunch)             lum/crossing    int/crossing
                          (cm^2)
       6                6.9813E+26      32.8121899
      36                1.1636E+26      5.46869832
      99                4.2311E+25      1.98861757

Probability of N interactions / crossing

Probablitiy of a certain number of interactions is determined by a Poisson distribution, with < N > as given above.


        Probability of N(interactions)/crossing

 N(int)          36 bunch        99 bunch
   0            0.00421672      0.13688453
   1            0.02305996      0.27221098
   2            0.06305397      0.27066177
   3            0.11494105      0.17941425
   4            0.15714448      0.08919658
   5            0.17187515      0.03547558
   6            0.15665555      0.01175789
   7            0.122386        0.00334028
   8            0.08366151      0.00083032

1 or more       0.99578328      0.86311547
2 or more       0.97272333      0.5909045
4 or more       0.79472831      0.14082848
8 or more       0.18666714      0.00105815

You can also see interactions/crossing for L = 8E31 (Run "IIa" conditions)

C. Klopfenstein, UC-Davis