Last week Chris suggested that I double check the calculation of the
effect of the bugfix in bgrid2.blast. So here are the results for three
test tracks. I plotted the magnetic field along the trajectory of each
track, and estimated the change in momentum and track angle between the
old and new fieldmap.
The formulas derive from the cyclotron frequency: p = q B r,
p=momentum, q=charge, B=field, r=radius, and e kG cm = 3e-4 GeV/c.
delta theta = q/p int delta B ds,
integrated over the pathlength from the vertex to middle chamber
delta p / p = < delta B > / < B >,
averaged over the pathlength between the three wire chambers
In each case, the first plot shows the difference between the two
fields, with the BLAST geometry and a track. The second plot shows the
old fieldmap (biot-savart) in red, with the corrected field in blue, and
the six superlayers are also shown.
The anomaly in the left sector at 33-38 deg was due to holes in the real
fieldmap that need filled in still.
The macro is checked in to: exp/analysis/macros/est_offset.C
In conclusion, the previous analysis was correct. The effect on theta
is tiny, because of the already large radius of curvature. The effect
on p is on the order of 1%, because most of the change in field occurs
before the wire chambers. Finally, the new fieldmap needs some work
before it is ready for recrunch. I am still working on the effect of
possible geometry mistakes.
--Chris
root [0] draw_track(25,0,0)
theta diff: 0.0549277 deg
mom diff: 0.0143555 = 1.83228 %
offset diff: 0.0146209 = 1.86614 %
root [1] draw_track(30,0,0)
theta diff: 0.00435438 deg
mom diff: 0.00713515 = 0.941341 %
offset diff: 0.00715843 = 0.944413 %
root [2] draw_track(35,0,0)
theta diff: 0.0180963 deg
mom diff: 0.00313036 = 0.428631 %
offset diff: 0.00323338 = 0.442737 %
root [3] draw_track(40,0,0)
theta diff: 0.0608038 deg
mom diff: 0.00149394 = 0.21302 %
offset diff: 0.00185164 = 0.264024 %
root [4] draw_track(45,0,0)
theta diff: 0.107963 deg
mom diff: 0.00210959 = 0.31406 %
offset diff: 0.00275054 = 0.409479 %
root [5] draw_track(50,0,0)
theta diff: 0.148258 deg
mom diff: 0.0035138 = 0.547202 %
offset diff: 0.00438492 = 0.682861 %
root [6] draw_track(55,0,0)
theta diff: 0.178339 deg
mom diff: 0.0048431 = 0.789948 %
offset diff: 0.00586423 = 0.956502 %
root [7] draw_track(60,0,0)
theta diff: 0.199514 deg
mom diff: 0.00570756 = 0.975718 %
offset diff: 0.00680669 = 1.16362 %
root [8] draw_track(66,0,0)
theta diff: 0.215976 deg
mom diff: 0.00596811 = 1.0796 %
offset diff: 0.00708862 = 1.28229 %
root [9] draw_track(70,0,0)
theta diff: 0.223257 deg
mom diff: 0.00574788 = 1.07942 %
offset diff: 0.00685321 = 1.28699 %
root [10] draw_track(75,0,0)
theta diff: 0.22946 deg
mom diff: 0.00517125 = 1.017 %
offset diff: 0.00623585 = 1.22637 %
root [11] draw_track(80,0,0)
theta diff: 0.232542 deg
mom diff: 0.0043115 = 0.887065 %
offset diff: 0.00531641 = 1.09382 %
root [12] draw_track(35,180,0)
theta diff: -0.59869 deg
mom diff: -0.0632454 = -8.66002 %
offset diff: -0.0666436 = -9.12532 %
This archive was generated by hypermail 2.1.2 : Mon Feb 24 2014 - 14:07:32 EST