Chamber Resolution

Cosmic runs were used to calculate chamber resolutions. For each cosmic event, I require exactly two hits on each chamber. From one pair of points on one chamber, a straight line was obtained and the intersecting points of this line with the other chamber were calculated. The difference between the registered points and the calculated points was filled into histograms and viewed as chamber resolution in each direction.

chamber 1 in X
chamber 1 in Y
chamber 1 in Z
chamber 2 in X
chamber 2 in Y
chamber 2 in Z

Optimizing Parameters In Mwpc.c

To address the problem of double-peak in X-resolution in chamber 2, we plotted deltaX vs phi. From the graph , one can see phi's were seperated into two groups--one below 180 degrees and one above 180 degrees.
There is a variable in mwpc.c named:
phi_corr_in_2
which will control the offset of phi's obtained. By changing this value, the phi obtained below 180 degree and above 180 will move in oppsite direction along Y(deltaX) and when the value is optimal, each group should center at deltaX=0, which results in the best X-resolution.

Procedures

Since resolutions of one chamber were defined by the other, both offset parameters:
phi_corr_in_2
phi_corr_in_1
affect the resolution. We first fixed one while optimizing the other, then fixed the optimized one and optimizing the other. We knew
phi_corr_in_1 = 0.0
was roughly the best value and that double peaks only showed in chamber 2. so we fixed phi_corr_in_1=0 and did optimization on phi_corr_in_2. SigmaX in chamber 2 vs phi_corr_in_2 were plotted. Then we fixed phi_corr_in_2=-0.362 and tried a few phi_corr_in_1 values around 0.0.

From above, we can safely say that the optimal value of phi_corr_in_2 is between -0.364 and -0.361, the optimal value of phi_corr_in_1 is between -0.1 and 0.1. In this range, the change of resolutions are marginal. Further determination of these two parameters needs a development of systematic methods.

Results

with phi_corr_in_2 = -0.362
phi_corr_in_1 = 0.0
the resolutions of chamber 1 and chamber 2 are presented.

More Parameters For Alignment

Between Wires and Cathod Strips

For each chamber, phi's were obtained from both cathod strips and anode wires. To address the possible misalignment between cathod and anode, we defined one variable for each chamber, namely
phi_corr_wire[0] and phi_corr_wire[1].
By studying the difference between phi obtained from wires and cathod strips for chamber 1 and chamber 2, we found following offsets will compensate for the misalignments

phi_corr_wire[0] = 0 for chamber 1
phi_corr_wire[1] = 0.6130 for chamber 2

After applying above values, the differences of phi's from wires and strips center at zero for both chamber 1 and chamber 2.

Alignment Of Two Chambers In Z Direction

From resolution histograms for chamber 1 and chamber 2, one can see that z are not centered at 0 which means two chambers are not aligned in z direction. We added two parameters and set the values as
z_offset_1 = 0.931 z_offset_2 = -0.931
to achive centered z resolution for chamber 1 and chamber 2.

Resolutions In X and Y

As one would expect, the resolution in x and y should be the same although they are not from above resolution histograms for chamber 1 and chamber 2.
The reason is because the resolution were calculated with cosmic events which were mostly from upword, or along the Y direction. The variation in Y thus is smaller than that in x. To study the dependence of resoluiton on phi, we ploted resolutions in X, Y and phi vs. phi for chamber 1 and resolutions in X, Y and phi vs. phi for chamber 2.

To get enough statistics, eight runs(35998-36005) were used.Changes in mwpc.c and the relevent histograms defined in histo.c were also documented for further use.

Target Position

Under the coordinate system defined by above two wire chambers, the position of the 9-piece target were also determined using cosmic events.

Since chamber 1 and chamber 2 have already alligned as described above, the position of target was determined relative to chamber 1. For each cosmic event which left two hits in chamber 1, we calculate the path length of this track through the target, which was centered at x=x_offset, y=y_offset and z=z_offset.
Combining calculated pathlength in target and signals registered in target, there are four possibilities for each cosmic event:

pathlength is zero, no signal in target.
pathlength is above zero, no signal in target.
pathlength is zero, signal registered in target. These events were counted in N_miss.
pathlenth is above zero, signal registered in target. These events were counted in N_hit.

By varying target offsets, the dependence of ratio on tgt offsets were obtained. The right offsets of the target were determined when N_hit/(N_hit+N_miss) had maximum value.

Results

Three 2-dimention histograms were obtained. Ratio vs. x and y, ratio vs. x and z and ratio vs. y and z .
From histogram of x and z, one can get

x_offset = -0.51 mm 
z_offset = 6.3 mm

From histogram of x and y one can get

x_offset = -0.9 mm
y_offset = -4.3 mm

From histogram of y and z one can get

y_offset = -4.0 mm
z_offset = 6.3 mm

The maximumization of ratio is an iterating process with three parameters involved. The best way is use MINUIT. Currently we would accept the average of these offsets. Besides, since we used cosmic rays which mostly came in Y direction, the offset in y was most difficult to get.

The uncertainties mostly came from the chamber resolution and target efficiency. The statistical error is neglegible.

Notes

Programms used to get above results are stored as tgtprofile_histo.c which contains the statements used in histo.c, and tgt_cal.c which was used to calculate ratio and fill histograms.
Auxiliary programs including Makefile and quad.c, which was used to calculate pathlength, are also available.