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starting some CRL simulations for ID11...
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@jonwright
jonwright committed Jul 30, 2018
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from __future__ import print_function, division
import pylab as pl, numpy as np


# classical electron radius
re = 2.83e-15 # m
# densities
rho_be = 1.845 # g/cm3
rho_si = 2.32 # g/cm3
rho_al = 2.6941 # g/cm3
# atomic weights
aw_be = 9.01218 # g/mol
aw_si = 28.08550 # g/mol
aw_al = 26.9815 # g/mol

avogadro = 6.0221409e23
# number densities (m3)
na_si = 1e6 * rho_si / aw_si * avogadro
na_be = 1e6 * rho_be / aw_be * avogadro
na_al = 1e6 * rho_al / aw_al * avogadro

# electron densities
ne_si = 14 * na_si
ne_be = 5 * na_be
ne_al = 13 * na_al

#print("na_si=",na_si)

# Form factors f' , f" from
# https://physics.nist.gov/cgi-bin/ffast/ffast.pl?Z=13&Formula=&gtype=4&range=S&lower=5&upper=140&density=&frames=no
Esi,f1si,f2si = np.array( [ [float(v) for v in line.split()[:3] ] for line in
"""5.295467E+00 1.43830E+01 7.0743E-01 2.0016E+02 1.2613E+00 2.0142E+02 1.859E+02 2.341E-01
5.660855E+00 1.43657E+01 6.2644E-01 1.6580E+02 1.1967E+00 1.6700E+02 1.541E+02 2.190E-01
6.051453E+00 1.43470E+01 5.5475E-01 1.3735E+02 1.1336E+00 1.3848E+02 1.276E+02 2.049E-01
6.469004E+00 1.43275E+01 4.9128E-01 1.1379E+02 1.0722E+00 1.1486E+02 1.058E+02 1.917E-01
6.915365E+00 1.43080E+01 4.3509E-01 9.4267E+01 1.0128E+00 9.5280E+01 8.763E+01 1.793E-01
7.392525E+00 1.42890E+01 3.8534E-01 7.8099E+01 9.5551E-01 7.9055E+01 7.261E+01 1.677E-01
7.902609E+00 1.42709E+01 3.4129E-01 6.4707E+01 9.0049E-01 6.5607E+01 6.016E+01 1.569E-01
8.447890E+00 1.42537E+01 3.0059E-01 5.3312E+01 8.4782E-01 5.4160E+01 4.955E+01 1.468E-01
9.030794E+00 1.42373E+01 2.6409E-01 4.3815E+01 7.9760E-01 4.4613E+01 4.070E+01 1.373E-01
9.653919E+00 1.42193E+01 2.3060E-01 3.5789E+01 7.4986E-01 3.6539E+01 3.325E+01 1.284E-01
1.032004E+01 1.42018E+01 2.0136E-01 2.9233E+01 7.0464E-01 2.9938E+01 2.716E+01 1.201E-01
1.103212E+01 1.41850E+01 1.7583E-01 2.3879E+01 6.6193E-01 2.4541E+01 2.219E+01 1.124E-01
1.179334E+01 1.41691E+01 1.5354E-01 1.9507E+01 6.2172E-01 2.0129E+01 1.813E+01 1.051E-01
1.260708E+01 1.41542E+01 1.3408E-01 1.5935E+01 5.8398E-01 1.6519E+01 1.481E+01 9.834E-02
1.347697E+01 1.41404E+01 1.1709E-01 1.3017E+01 5.4864E-01 1.3566E+01 1.210E+01 9.200E-02
1.440688E+01 1.41275E+01 1.0225E-01 1.0634E+01 5.1565E-01 1.1150E+01 9.884E+00 8.606E-02
1.540095E+01 1.41156E+01 8.9301E-02 8.6877E+00 4.8493E-01 9.1726E+00 8.074E+00 8.050E-02
1.646362E+01 1.41047E+01 7.7990E-02 7.0976E+00 4.5640E-01 7.5540E+00 6.596E+00 7.531E-02
1.759961E+01 1.40947E+01 6.8113E-02 5.7986E+00 4.2996E-01 6.2286E+00 5.389E+00 7.045E-02
1.881398E+01 1.40856E+01 5.9487E-02 4.7374E+00 4.0551E-01 5.1429E+00 4.402E+00 6.590E-02
2.011215E+01 1.40772E+01 5.1955E-02 3.8705E+00 3.8295E-01 4.2534E+00 3.596E+00 6.165E-02
2.149988E+01 1.40696E+01 4.5377E-02 3.1623E+00 3.6217E-01 3.5245E+00 2.938E+00 5.767E-02
2.298338E+01 1.40628E+01 3.9633E-02 2.5837E+00 3.4306E-01 2.9268E+00 2.400E+00 5.395E-02
2.456923E+01 1.40566E+01 3.4616E-02 2.1110E+00 3.2552E-01 2.4365E+00 1.961E+00 5.046E-02
2.626450E+01 1.40511E+01 3.0235E-02 1.7248E+00 3.0943E-01 2.0342E+00 1.602E+00 4.721E-02
2.807676E+01 1.40462E+01 2.6276E-02 1.4022E+00 2.9470E-01 1.6969E+00 1.302E+00 4.416E-02
3.001405E+01 1.40415E+01 2.2797E-02 1.1380E+00 2.8122E-01 1.4192E+00 1.057E+00 4.131E-02
3.208502E+01 1.40372E+01 1.9779E-02 9.2365E-01 2.6889E-01 1.1925E+00 8.581E-01 3.864E-02
3.429889E+01 1.40333E+01 1.7161E-02 7.4966E-01 2.5761E-01 1.0073E+00 6.965E-01 3.615E-02
3.666551E+01 1.40298E+01 1.4890E-02 6.0846E-01 2.4729E-01 8.5575E-01 5.654E-01 3.381E-02
3.919543E+01 1.40267E+01 1.2919E-02 4.9385E-01 2.3785E-01 7.3170E-01 4.590E-01 3.163E-02
4.189992E+01 1.40239E+01 1.1160E-02 3.9906E-01 2.2920E-01 6.2826E-01 3.708E-01 2.959E-02
4.479101E+01 1.40213E+01 9.6400E-03 3.2246E-01 2.2126E-01 5.4372E-01 2.995E-01 2.768E-02
4.788159E+01 1.40191E+01 8.3272E-03 2.6057E-01 2.1397E-01 4.7454E-01 2.420E-01 2.589E-02
5.118542E+01 1.40170E+01 7.1932E-03 2.1056E-01 2.0725E-01 4.1781E-01 1.955E-01 2.422E-02
5.471721E+01 1.40151E+01 6.2137E-03 1.7015E-01 2.0104E-01 3.7119E-01 1.579E-01 2.266E-02
5.849270E+01 1.40135E+01 5.3676E-03 1.3749E-01 1.9529E-01 3.3278E-01 1.276E-01 2.120E-02
6.252870E+01 1.40120E+01 4.6367E-03 1.1110E-01 1.8993E-01 3.0103E-01 1.031E-01 1.983E-02
6.684318E+01 1.40107E+01 4.0054E-03 8.9782E-02 1.8493E-01 2.7471E-01 8.327E-02 1.855E-02
7.145536E+01 1.40095E+01 3.4605E-03 7.2561E-02 1.8024E-01 2.5280E-01 6.727E-02 1.735E-02
7.638578E+01 1.40084E+01 2.9899E-03 5.8646E-02 1.7582E-01 2.3447E-01 5.435E-02 1.623E-02
8.165640E+01 1.40075E+01 2.5832E-03 4.7399E-02 1.7163E-01 2.1903E-01 4.391E-02 1.518E-02
8.729069E+01 1.40066E+01 2.2319E-03 3.8309E-02 1.6764E-01 2.0595E-01 3.547E-02 1.420E-02
9.331374E+01 1.40059E+01 1.9284E-03 3.0963E-02 1.6382E-01 1.9478E-01 2.866E-02 1.329E-02
9.975239E+01 1.40052E+01 1.6662E-03 2.5026E-02 1.6015E-01 1.8518E-01 2.315E-02 1.243E-02
1.066353E+02 1.40046E+01 1.4396E-03 2.0227E-02 1.5661E-01 1.7684E-01 1.870E-02 1.163E-02
1.139931E+02 1.40041E+01 1.2438E-03 1.6349E-02 1.5317E-01 1.6952E-01 1.511E-02 1.088E-02
1.218587E+02 1.40036E+01 1.0747E-03 1.3214E-02 1.4983E-01 1.6304E-01 1.221E-02 1.017E-02
1.302669E+02 1.40032E+01 9.2859E-04 1.0680E-02 1.4655E-01 1.5723E-01 9.861E-03 9.518E-03
1.392553E+02 1.40029E+01 8.0234E-04 8.6327E-03 1.4335E-01 1.5198E-01 7.967E-03 8.903E-03""".split("\n")]).T

Ebe,f1be,f2be = np.array( [ [float(v) for v in line.split()[:3] ] for line in
"""5.295467E+00 4.00923E+00 3.4651E-03 3.0554E+00 3.0111E-01 3.3565E+00 2.961E+00 2.341E-01
5.660855E+00 4.00820E+00 2.9861E-03 2.4630E+00 2.9098E-01 2.7540E+00 2.387E+00 2.190E-01
6.051453E+00 4.00729E+00 2.5732E-03 1.9855E+00 2.8130E-01 2.2668E+00 1.924E+00 2.049E-01
6.469004E+00 4.00647E+00 2.2175E-03 1.6006E+00 2.7209E-01 1.8727E+00 1.551E+00 1.917E-01
6.915365E+00 4.00574E+00 1.9109E-03 1.2903E+00 2.6336E-01 1.5537E+00 1.250E+00 1.793E-01
7.392525E+00 4.00510E+00 1.6467E-03 1.0401E+00 2.5511E-01 1.2952E+00 1.008E+00 1.677E-01
7.902609E+00 4.00452E+00 1.4191E-03 8.3845E-01 2.4735E-01 1.0858E+00 8.126E-01 1.569E-01
8.447890E+00 4.00401E+00 1.2229E-03 6.7590E-01 2.4006E-01 9.1596E-01 6.550E-01 1.468E-01
9.030794E+00 4.00356E+00 1.0525E-03 5.4417E-01 2.3323E-01 7.7740E-01 5.274E-01 1.373E-01
9.653919E+00 4.00316E+00 9.0177E-04 4.3616E-01 2.2687E-01 6.6303E-01 4.226E-01 1.284E-01
1.032004E+01 4.00280E+00 7.7264E-04 3.4958E-01 2.2094E-01 5.7052E-01 3.387E-01 1.201E-01
1.103212E+01 4.00248E+00 6.6200E-04 2.8019E-01 2.1543E-01 4.9562E-01 2.714E-01 1.124E-01
1.179334E+01 4.00219E+00 5.6721E-04 2.2457E-01 2.1032E-01 4.3489E-01 2.175E-01 1.051E-01
1.260708E+01 4.00194E+00 4.8599E-04 1.8000E-01 2.0559E-01 3.8559E-01 1.743E-01 9.834E-02
1.347697E+01 4.00171E+00 4.1640E-04 1.4427E-01 2.0122E-01 3.4549E-01 1.397E-01 9.200E-02
1.440688E+01 4.00151E+00 3.5677E-04 1.1563E-01 1.9717E-01 3.1280E-01 1.120E-01 8.606E-02
1.540095E+01 4.00134E+00 3.0569E-04 9.2679E-02 1.9343E-01 2.8611E-01 8.973E-02 8.050E-02
1.646362E+01 4.00118E+00 2.6192E-04 7.4282E-02 1.8997E-01 2.6425E-01 7.191E-02 7.531E-02
1.759961E+01 4.00104E+00 2.2441E-04 5.9538E-02 1.8677E-01 2.4631E-01 5.763E-02 7.045E-02
1.881398E+01 4.00092E+00 1.9228E-04 4.7720E-02 1.8379E-01 2.3151E-01 4.619E-02 6.590E-02
2.011215E+01 4.00081E+00 1.6475E-04 3.8248E-02 1.8102E-01 2.1927E-01 3.701E-02 6.165E-02
2.149988E+01 4.00072E+00 1.4116E-04 3.0656E-02 1.7844E-01 2.0910E-01 2.966E-02 5.767E-02
2.298338E+01 4.00063E+00 1.2094E-04 2.4571E-02 1.7602E-01 2.0059E-01 2.377E-02 5.395E-02
2.456923E+01 4.00056E+00 1.0363E-04 1.9694E-02 1.7373E-01 1.9342E-01 1.905E-02 5.046E-02
2.626450E+01 4.00049E+00 8.8788E-05 1.5785E-02 1.7157E-01 1.8736E-01 1.527E-02 4.721E-02
2.807676E+01 4.00043E+00 7.5940E-05 1.2629E-02 1.6951E-01 1.8214E-01 1.221E-02 4.416E-02
3.001405E+01 4.00038E+00 6.4915E-05 1.0099E-02 1.6752E-01 1.7762E-01 9.764E-03 4.131E-02
3.208502E+01 4.00034E+00 5.5490E-05 8.0753E-03 1.6561E-01 1.7369E-01 7.806E-03 3.864E-02
3.429889E+01 4.00030E+00 4.7433E-05 6.4573E-03 1.6374E-01 1.7020E-01 6.240E-03 3.615E-02
3.666551E+01 4.00026E+00 4.0546E-05 5.1635E-03 1.6192E-01 1.6708E-01 4.989E-03 3.381E-02
3.919543E+01 4.00023E+00 3.4660E-05 4.1289E-03 1.6011E-01 1.6424E-01 3.988E-03 3.163E-02
4.189992E+01 4.00020E+00 2.9628E-05 3.3017E-03 1.5833E-01 1.6163E-01 3.188E-03 2.959E-02
4.479101E+01 4.00018E+00 2.5326E-05 2.6401E-03 1.5654E-01 1.5918E-01 2.549E-03 2.768E-02
4.788159E+01 4.00016E+00 2.1649E-05 2.1112E-03 1.5475E-01 1.5686E-01 2.038E-03 2.589E-02
5.118542E+01 4.00014E+00 1.8512E-05 1.6887E-03 1.5295E-01 1.5464E-01 1.629E-03 2.422E-02
5.471721E+01 4.00012E+00 1.5845E-05 1.3522E-03 1.5113E-01 1.5248E-01 1.304E-03 2.266E-02
5.849270E+01 4.00011E+00 1.3563E-05 1.0827E-03 1.4928E-01 1.5036E-01 1.044E-03 2.120E-02
6.252870E+01 4.00009E+00 1.1610E-05 8.6693E-04 1.4741E-01 1.4828E-01 8.360E-04 1.983E-02
6.684318E+01 4.00008E+00 9.9374E-06 6.9417E-04 1.4550E-01 1.4619E-01 6.692E-04 1.855E-02
7.145536E+01 4.00007E+00 8.5061E-06 5.5584E-04 1.4357E-01 1.4413E-01 5.358E-04 1.735E-02
7.638578E+01 4.00006E+00 7.2810E-06 4.4507E-04 1.4159E-01 1.4204E-01 4.289E-04 1.623E-02
8.165640E+01 4.00006E+00 6.2323E-06 3.5638E-04 1.3958E-01 1.3994E-01 3.434E-04 1.518E-02
8.729069E+01 4.00005E+00 5.3347E-06 2.8536E-04 1.3753E-01 1.3782E-01 2.749E-04 1.420E-02
9.331374E+01 4.00004E+00 4.5664E-06 2.2849E-04 1.3544E-01 1.3567E-01 2.201E-04 1.329E-02
9.975239E+01 4.00004E+00 3.9087E-06 1.8296E-04 1.3332E-01 1.3350E-01 1.762E-04 1.243E-02
1.066353E+02 4.00003E+00 3.3457E-06 1.4650E-04 1.3116E-01 1.3131E-01 1.410E-04 1.163E-02
1.139931E+02 4.00003E+00 2.8639E-06 1.1731E-04 1.2896E-01 1.2908E-01 1.129E-04 1.088E-02
1.218587E+02 4.00003E+00 2.4514E-06 9.3931E-05 1.2674E-01 1.2683E-01 9.038E-05 1.017E-02
1.302669E+02 4.00002E+00 2.0984E-06 7.5214E-05 1.2448E-01 1.2456E-01 7.235E-05 9.518E-03
1.392553E+02 4.00002E+00 1.7962E-06 6.0226E-05 1.2220E-01 1.2226E-01 5.792E-05 8.903E-03""".split("\n")]).T


Eal,f1al,f2al = np.array( [ [float(v) for v in line.split()[:3] ] for line in
"""5.295467E+00 1.33392E+01 5.3446E-01 1.5741E+02 1.1376E+00 1.5855E+02 1.470E+02 2.341E-01
5.660855E+00 1.33198E+01 4.7341E-01 1.3043E+02 1.0796E+00 1.3151E+02 1.218E+02 2.190E-01
6.051453E+00 1.33004E+01 4.1935E-01 1.0808E+02 1.0229E+00 1.0910E+02 1.010E+02 2.049E-01
6.469004E+00 1.32816E+01 3.7148E-01 8.9558E+01 9.6791E-01 9.0526E+01 8.370E+01 1.917E-01
6.915365E+00 1.32637E+01 3.2822E-01 7.4022E+01 9.1472E-01 7.4937E+01 6.919E+01 1.793E-01
7.392525E+00 1.32456E+01 2.8857E-01 6.0881E+01 8.6348E-01 6.1744E+01 5.688E+01 1.677E-01
7.902609E+00 1.32277E+01 2.5373E-01 5.0073E+01 8.1431E-01 5.0887E+01 4.677E+01 1.569E-01
8.447890E+00 1.32105E+01 2.2309E-01 4.1186E+01 7.6728E-01 4.1953E+01 3.845E+01 1.468E-01
9.030794E+00 1.31945E+01 1.9580E-01 3.3814E+01 7.2247E-01 3.4536E+01 3.156E+01 1.373E-01
9.653919E+00 1.31795E+01 1.7070E-01 2.7577E+01 6.7991E-01 2.8257E+01 2.574E+01 1.284E-01
1.032004E+01 1.31646E+01 1.4882E-01 2.2491E+01 6.3961E-01 2.3131E+01 2.099E+01 1.201E-01
1.103212E+01 1.31503E+01 1.2975E-01 1.8343E+01 6.0158E-01 1.8945E+01 1.712E+01 1.124E-01
1.179334E+01 1.31369E+01 1.1313E-01 1.4961E+01 5.6579E-01 1.5527E+01 1.397E+01 1.051E-01
1.260708E+01 1.31243E+01 9.8639E-02 1.2202E+01 5.3222E-01 1.2734E+01 1.139E+01 9.834E-02
1.347697E+01 1.31128E+01 8.6005E-02 9.9528E+00 5.0080E-01 1.0454E+01 9.290E+00 9.200E-02
1.440688E+01 1.31021E+01 7.4990E-02 8.1180E+00 4.7149E-01 8.5895E+00 7.577E+00 8.606E-02
1.540095E+01 1.30923E+01 6.5387E-02 6.6216E+00 4.4420E-01 7.0658E+00 6.180E+00 8.050E-02
1.646362E+01 1.30833E+01 5.7015E-02 5.4010E+00 4.1887E-01 5.8199E+00 5.041E+00 7.531E-02
1.759961E+01 1.30752E+01 4.9716E-02 4.4056E+00 3.9539E-01 4.8010E+00 4.111E+00 7.045E-02
1.881398E+01 1.30677E+01 4.3351E-02 3.5936E+00 3.7369E-01 3.9673E+00 3.353E+00 6.590E-02
2.011215E+01 1.30610E+01 3.7802E-02 2.9314E+00 3.5368E-01 3.2851E+00 2.735E+00 6.165E-02
2.149988E+01 1.30548E+01 3.2964E-02 2.3912E+00 3.3524E-01 2.7264E+00 2.231E+00 5.767E-02
2.298338E+01 1.30493E+01 2.8745E-02 1.9506E+00 3.1829E-01 2.2689E+00 1.819E+00 5.395E-02
2.456923E+01 1.30443E+01 2.5066E-02 1.5912E+00 3.0273E-01 1.8939E+00 1.484E+00 5.046E-02
2.626450E+01 1.30397E+01 2.1859E-02 1.2980E+00 2.8846E-01 1.5865E+00 1.210E+00 4.721E-02
2.807676E+01 1.30358E+01 1.8978E-02 1.0542E+00 2.7539E-01 1.3296E+00 9.830E-01 4.416E-02
3.001405E+01 1.30321E+01 1.6453E-02 8.5493E-01 2.6343E-01 1.1184E+00 7.973E-01 4.131E-02
3.208502E+01 1.30288E+01 1.4264E-02 6.9335E-01 2.5248E-01 9.4583E-01 6.466E-01 3.864E-02
3.429889E+01 1.30258E+01 1.2344E-02 5.6128E-01 2.4246E-01 8.0374E-01 5.234E-01 3.615E-02
3.666551E+01 1.30231E+01 1.0660E-02 4.5343E-01 2.3329E-01 6.8672E-01 4.227E-01 3.381E-02
3.919543E+01 1.30206E+01 9.2057E-03 3.6630E-01 2.2489E-01 5.9119E-01 3.414E-01 3.163E-02
4.189992E+01 1.30184E+01 7.9499E-03 2.9591E-01 2.1718E-01 5.1309E-01 2.757E-01 2.959E-02
4.479101E+01 1.30164E+01 6.8656E-03 2.3905E-01 2.1010E-01 4.4915E-01 2.227E-01 2.768E-02
4.788159E+01 1.30146E+01 5.9291E-03 1.9312E-01 2.0359E-01 3.9671E-01 1.798E-01 2.589E-02
5.118542E+01 1.30130E+01 5.1204E-03 1.5602E-01 1.9757E-01 3.5359E-01 1.452E-01 2.422E-02
5.471721E+01 1.30116E+01 4.4218E-03 1.2603E-01 1.9200E-01 3.1803E-01 1.173E-01 2.266E-02
5.849270E+01 1.30103E+01 3.8180E-03 1.0180E-01 1.8683E-01 2.8863E-01 9.474E-02 2.120E-02
6.252870E+01 1.30091E+01 3.2967E-03 8.2227E-02 1.8200E-01 2.6423E-01 7.652E-02 1.983E-02
6.684318E+01 1.30081E+01 2.8466E-03 6.6417E-02 1.7747E-01 2.4389E-01 6.180E-02 1.855E-02
7.145536E+01 1.30072E+01 2.4579E-03 5.3647E-02 1.7321E-01 2.2686E-01 4.991E-02 1.735E-02
7.638578E+01 1.30064E+01 2.1224E-03 4.3333E-02 1.6918E-01 2.1251E-01 4.031E-02 1.623E-02
8.165640E+01 1.30057E+01 1.8326E-03 3.5002E-02 1.6534E-01 2.0034E-01 3.256E-02 1.518E-02
8.729069E+01 1.30050E+01 1.5824E-03 2.8272E-02 1.6168E-01 1.8995E-01 2.629E-02 1.420E-02
9.331374E+01 1.30045E+01 1.3664E-03 2.2837E-02 1.5816E-01 1.8100E-01 2.124E-02 1.329E-02
9.975239E+01 1.30040E+01 1.1798E-03 1.8447E-02 1.5476E-01 1.7321E-01 1.715E-02 1.243E-02
1.066353E+02 1.30035E+01 1.0188E-03 1.4900E-02 1.5146E-01 1.6636E-01 1.385E-02 1.163E-02
1.139931E+02 1.30031E+01 8.7971E-04 1.2036E-02 1.4824E-01 1.6028E-01 1.119E-02 1.088E-02
1.218587E+02 1.30027E+01 7.5962E-04 9.7220E-03 1.4510E-01 1.5482E-01 9.035E-03 1.017E-02
1.302669E+02 1.30024E+01 6.5593E-04 7.8530E-03 1.4202E-01 1.4987E-01 7.297E-03 9.518E-03
1.392553E+02 1.30022E+01 5.6639E-04 6.3434E-03 1.3898E-01 1.4532E-01 5.893E-03 8.903E-03""".split("\n")]).T

# f = R / ( 2 . N . delta)
# 1/f = 1/s1 + 1/s2

X_IVT = 31.5
X_PINHOLE = 49.1
X_IAT = 91.5
X_NSCOPE = 96.0
# 1 2 3 4 5 6 7 8 9 10
N_SI = [ 12,28,52,80,116,160,208,264,324,392 ]
N_BE = [1,2,4,8,16,32]
N_AL = [32, 64]
R_SI = 12.5e-6
R_BE = 0.2e-3
R_AL = 0.2e-3

# Linear attenuation coefficient mu
# mu = 4 pi beta / lambda


wsi = 12.39842e-10 / Esi
wal = 12.39842e-10 / Eal
wbe = 12.39842e-10 / Ebe
delta_si = na_si * re * wsi * wsi * f1si / 2 / np.pi
beta_si = na_si * re * wsi * wsi * f2si / 2 / np.pi
mu_si = na_si * re * wsi * f2si * 2
delta_al = na_al * re * wal * wal * f1al / 2 / np.pi
beta_al = na_al * re * wal * wal * f2al / 2 / np.pi
mu_al = na_al * re * wal * f2al * 2
delta_be = na_be * re * wbe * wbe * f1be / 2 / np.pi
beta_be = na_be * re * wbe * wbe * f2be / 2 / np.pi
mu_be = na_be * re * wbe * f2be * 2

delta_si2 = re * wsi * wsi * ne_si / 2 / np.pi


if 1:
pl.plot( Esi, delta_si, "+-")
pl.plot( Esi, delta_si2, "+-")
pl.show()
pl.plot( Esi, beta_si, "+-")
pl.plot( Eal, delta_al, "+-")
pl.plot( Eal, beta_al, "+-")
pl.plot( Ebe, delta_be, "+-")
pl.plot( Ebe, beta_be, "+-")
pl.show()


# approximately : delta = r0 . w^2 . ne / 2 / pi ne - electron density. We can try this!
# n = 1 - delta + i.beta
# n = c / v ... ratio of speeds.

# Focussing condition is that f*f + dx*dx = pathlength, where dx is off axis distance
# ... this is where the parabola comes from

# parabolic lenses:
# thickness(x) = a*x*x
# circles, center at R:
# x^2 + (y-R)^2 = R^2
# x^2 + y^2 + R^2 - 2*Ry = R^2
# x^2 + y^2 = 2*Ry
# ... x>>y : x^2 = 2Ry
# so Y = x^2/(2R)
x = np.linspace( -.5e-3, .5e-3, 100)
x = np.linspace( -25e-6, 25e-6, 100)
#pl.plot( 1e6*x, 1e6*x*x/(2*R_SI), "-" )
E = 40
mu_si_40 = np.interp( E, Esi, mu_si )
for nsi in N_SI:
total_thickness = nsi * 2 * x*x/(2*R_SI)
transmitted = np.exp( -mu_si_40 * total_thickness )
pl.plot( x, transmitted, "-")

pl.show()

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