# MIPP beam needs

Rajendran Raja 20-March-2003

I have modified the Hartouni calculations contained in the file
E907_rate_calculations.xls

To include the following changes

1)Primary target length increased from 2" Cu to 20cm Cu

2)Maximum primary intensity of protons changed from 3E11 to 2 E11

3)Acceptance of beam line changed down from 3.2E-6 x p to 0.135E-6x p to
match with Kostin's numbers at 90GeV positives.

4)I have added pion and kaon decays.

One "data point" as per the proposal is 3 million events. For simplicity
and conservativeness, I have assumed that each data point is spread over
an average of 5 positive and 5 negative energies in calculating the
number of primary protons.

With these, the beam requirements are

Table 1 Physics request and proton needs

  ------------ ------------- ----------- -------------------- -----------------
  **Target**   Physics       Data Points Primary proton       Total number

                                         Average              of Primary
                                         Intensity/spill      Protons

                                                              

  **Numi 1**   MINOS         3.3         125000               2.06E+10

  **NUMI 2**   MINOS         3.3         125000               2.06E+10

  **H2**       Scaling       6           9.76E+09             2.93E+15

  **N2**       Atmospheric ν 4           9.76E+09             1.95E+15

  **Be**       pA            2           9.76E+09             9.76E+14

  **Be**       Survey        1           9.76E+09             4.88E+14

  **C**        Survey        1           9.76E+09             4.88E+14

  **Cu**       pA            2           9.76E+09             9.76E+14

  **Cu**       Survey        1           9.76E+09             4.88E+14

  **Pb**       pA            2           9.76E+09             9.76E+14

  **Pb**       Survey        1           9.76E+09             4.88E+14

                                                              

  **Total**                  26.6                             9.76E+15
  ------------ ------------- ----------- -------------------- -----------------

The tables 3,4,5 and 6 of the proposal get modified to

Table 3 Particle rates, prescale factors and event yields for a positive
secondary beam

  --------- --------- ------- -------- ---------- ---------- ---------- --------- --------- --------- --------
  **p       p Hz      K Hz    π Hz     p prescale K prescale π Prescale p events  K events  π events  spills
  GeV/c**                                                                                             

  **5**     15.32     1.41    139.25   1.31       14.20      0.14       766098    70441     1000000   30609

  **15**    161.81    19.07   414.21   0.12       1.05       0.05       1000000   953648    1000000   49227

  **25**    525.63    36.94   652.95   0.04       0.54       0.03       1000000   1000000   1000000   50000

  **30**    815.81    44.87   740.69   0.02       0.45       0.03       1000000   1000000   1000000   50000

  **40**    1666.44   55.65   808.77   0.01       0.36       0.02       1000000   1000000   1000000   50000

  **50**    2928.89   57.55   741.73   0.01       0.35       0.03       1000000   1000000   1000000   50000

  **60**    4598.56   51.25   585.47   0.00       0.39       0.03       1000000   1000000   1000000   50000

  **70**    6522.70   39.53   396.38   0.00       0.51       0.05       1000000   1000000   1000000   50000

  **80**    8297.15   25.90   223.09   0.00       0.77       0.09       1000000   1000000   1000000   50000

  **90**    9172.82   13.60   96.72    0.00       1.47       0.21       1000000   680078    1000000   44668

  **100**   8097.63   4.93    26.83    0.00       4.05       0.75       1000000   246735    1000000   37446

  **110**   4289.40   0.76    2.60     0.00       26.44      7.70       1000000   37827     129841    19461
  --------- --------- ------- -------- ---------- ---------- ---------- --------- --------- --------- --------

Table 4 Particle rates, prescale factors and event yields for a negative
secondary beam

  --------- ------- ------- -------- ------------ ---------- ---------- --------- -------- --------- --------
  **P       pbar Hz K Hz    π Hz     pbar         K prescale π prescale pbar      K events π events  spills
  GeV/c**                            prescale                           events                       

  **5**     10.40   1.00    89.95    1.92         20.08      0.22       519979    49802    1000000   26163

  **15**    22.16   10.57   304.41   0.90         1.89       0.07       1000000   528616   1000000   42144

  **25**    18.88   14.45   346.08   1.06         1.38       0.06       943858    722560   1000000   44440

  **30**    16.03   14.63   338.57   1.25         1.37       0.06       801643    731310   1000000   42216

  **40**    10.16   12.42   299.10   1.97         1.61       0.07       508086    620766   1000000   35481

  **50**    5.31    8.45    238.65   3.77         2.37       0.08       265278    422260   1000000   28126

  **60**    2.21    4.65    168.50   9.05         4.31       0.12       110462    232268   1000000   22379

  **70**    0.70    2.02    102.20   28.63        9.88       0.20       34933     101249   1000000   18936

  **80**    0.15    0.66    50.78    130.46       30.37      0.39       7665      32924    1000000   17343

  **90**    0.02    0.14    18.84    1026.91      143.15     1.06       974       6986     941884    15831

  **100**   0.00    0.01    4.21     21233.38     1420.83    4.75       47        704      210470    3520

  **110**   0.00    0.00    0.28     4461428.36   83385.44   70.84      0         12       14116     235
  --------- ------- ------- -------- ------------ ---------- ---------- --------- -------- --------- --------

Table 5 Primary beam rates, secondary beam rates and event yields for a
positive secondary beam

  --------- ---------- -------- ------ -------- -------- --------- --------- --------- ---------
  **p       Primary    p Hz     K Hz   π Hz     Total Hz p events  K events  π events  total
  GeV/c**   p/spill                                                                    events

  **5**     9.66E+09   7404     1583   116013   125000   1000000   340391    1000000   2340391

  **15**    2.10E+09   16968    4651   74886    96505    1000000   1000000   1000000   3000000

  **25**    1.08E+09   28457    4651   60948    94055    1000000   1000000   1000000   3000000

  **30**    8.92E+08   36365    4651   56926    97942    1000000   1000000   1000000   3000000

  **40**    7.19E+08   59890    4651   50114    114655   1000000   1000000   1000000   3000000

  **50**    5.76E+08   84327    3854   36820    125000   1000000   828519    1000000   2828519

  **60**    4.37E+08   100367   2601   22032    125000   1000000   559231    1000000   2559231

  **70**    3.43E+08   111720   1575   11705    125000   1000000   338524    1000000   2338524

  **80**    2.86E+08   118639   861    5500     125000   1000000   185184    1000000   2185184

  **90**    2.67E+08   122354   422    2224     125000   1000000   90714     645042    1735755

  **100**   3.07E+08   124115   176    709      125000   1000000   37818     205646    1243464

  **110**   5.82E+08   124819   51     130      125000   1000000   11007     37783     1048790
  --------- ---------- -------- ------ -------- -------- --------- --------- --------- ---------

Table 6 Primary beam rates, secondary beam rates and event yields for a
negative secondary beam

  --------- ---------- ------ ------ -------- -------- --------- --------- --------- ---------
  **p       Primary    pbar   K Hz   π Hz     Total Hz pbar      K events  π events  total
  GeV/c**   p/spill    Hz                              events                        events

  **5**     1.49E+10   7747   1726   115527   125000   1000000   431391    1000000   2431391

  **15**    3.78E+09   4192   4651   99287    108130   1000000   1000000   1000000   3000000

  **25**    2.77E+09   2613   4651   82580    89843    1000000   1000000   1000000   3000000

  **30**    2.73E+09   2192   4651   79822    86666    1000000   1000000   1000000   3000000

  **40**    3.94E+09   2000   5683   101496   109179   1000000   1000000   1000000   3000000

  **50**    5.73E+09   1520   5626   117855   125000   858621    1000000   1000000   2858621

  **60**    8.24E+09   910    4449   119641   125000   514056    1000000   1000000   2514056

  **70**    1.38E+10   481    3241   121278   125000   271690    810316    1000000   2082006

  **80**    2.80E+10   215    2145   122640   125000   121342    536302    1000000   1657644

  **90**    7.62E+10   74     1237   123688   125000   41906     309340    1000000   1351246

  **100**   2.00E+11   9      327    72576    72913    5322      81839     1000000   1087161

  **110**   2.00E+11   0      6      4867     4873     25        1394      1000000   1001420
  --------- ---------- ------ ------ -------- -------- --------- --------- --------- ---------

The tables 7 and 8 below show the momenta selected for estimating the
average flux of protons needed per data point.

Table 7 Selected positive secondary momenta and number of primary
protons required

  ----------------- ------------- ----------- -------- -------------- ----------
  **P GeV/c**       Selection=1   Proton      Spills   Primary        events
                                  Intensity            protons        

  **5**             1             9.66E+09    39007    3.77E+14       2340391

  **15**            1             2.10E+09    50000    1.05E+14       3000000

  **25**            1             1.08E+09    50000    5.41E+13       3000000

  **30**            0             0.00E+00    0        0.00E+00       0

  **40**            0             0.00E+00    0        0.00E+00       0

  **50**            1             5.76E+08    47142    2.71E+13       2828519

  **60**            0             0.00E+00    0        0.00E+00       0

  **70**            1             3.43E+08    38975    1.34E+13       2338524

  **80**            0             0.00E+00    0        0.00E+00       0

  **90**            1             2.67E+08    28929    7.72E+12       1735755

  **100**           0             0.00E+00    0        0.00E+00       0

  **110**           0             0.00E+00    0        0.00E+00       0

                                                                      

  **Total**         6             1.40E+10    254053   5.84E+14       1.52E+07

  **Average**                     2.34E+09    50000    1.15E+14       3.00E+06
  ----------------- ------------- ----------- -------- -------------- ----------

Table 8 Selected negative secondary momenta and number of primary
protons required

  ----------- ------------- ------------- -------- --------------- ----------
  **P GeV/c** Selction=1    Proton        Spills   Primary protons Events
                            Intensity                              

  **5**       1             1.49E+10      40523    6.04E+14        2431391

  **15**      1             3.78E+09      50000    1.89E+14        3000000

  **25**      1             2.77E+09      50000    1.38E+14        3000000

  **30**      0             2.73E+09      0        0.00E+00        0

  **40**      0             3.94E+09      0        0.00E+00        0

  **50**      1             5.73E+09      47644    2.73E+14        2858621

  **60**      0             8.24E+09      0        0.00E+00        0

  **70**      1             1.38E+10      34700    4.78E+14        2082006

  **80**      0             2.80E+10      0        0.00E+00        0

  **90**      1             7.62E+10      22521    1.72E+15        1351246

  **100**     0             2.00E+11      0        0.00E+00        0

  **110**     0             2.00E+11      0        0.00E+00        0

  **total**   6             1.17E+11      245388   3.40E+15        1.47E+07

              Average       1.95E+10      50000    6.92E+14        3.00E+06

                                                                   

                                                                   

              Average +/-   9.76E+09      50000    4.03596E+14     3.00E+06
  ----------- ------------- ------------- -------- --------------- ----------