*********************************************************************** Effective Target Length for the CLAS g1a Run R. A. Schumacher, C.M.U. July-7-1999 *CLAS-NOTE 99-010* *********************************************************************** Abstract: The hemispherical endcaps of the liquid hydrogen target used during the CLAS g1a and g6a runs in May through August 1998 effectively reduced the target length from the maximum length. The actual maximum length was also found to be larger than the nominal length. For the g1a running at 2.5 GeV, it is concluded that the best value for the target thickness is 183.2 +- 0.2 (random) +- 1.0 (systematic) mm. Thus, the correction to the length amounts to a 1.8% increase from the original nominal length. The systematic uncertainty on this number is about +- 0.6%, as estimated using several different models for the beam profile at the target location, and considering possible misalignments of the target and beam. Discussion: The Real Photon target for CLAS was designed and built by the Saclay group, and is described in a memo dated February 12, 1998 by Steve Christo, Laurent Farhi, and Claude Marchand. "Target #1" was the one actually used, and it was 180mm in nominal length and 59.68mm in nominal diameter. It was made of .170mm thick mylar. No measurement uncertainty was given, so I will assume it is equal to the thickness of the material, i.e. +- 0.2mm. The target cell had hemispherical endcaps on both ends. The actual length of the target used during the 1998 runs was measured by Dave Kashy on 6-3-99 (private communication), and again on 6-11-99 by Jim Dahlberg, as recorded in a "Jefferson Lab Alignment Group Data Transmittal" to Steve Christo. The actual maximum length was 186.1 +- .2 mm, where the error estimate comes from comparing the results of the two reported independent measurements. The photon beam produced at the radiator traversed about 15m of vacuum before striking the target, and another 15m of vacuum before hitting the Pair Counter which was used to determine the beam profile at the dump. A standard estimate for the beam width at the target position is to assume a Gaussian profile with a sigma given via the bremsstrahlung cone angle computed as 1/gamma, where gamma is the relativistic gamma of the electron beam, i.e. m/E. Here m is the electron mass and E is the beam energy. A better estimate of the ideal beam profile is obtained using the actual angular distribution of bremsstrahlung radiation in some fairly realistic approximation. This can be found in Landau and Lifshitz's "The Classical Theory of Fields", equation 73.13. Finally, it seems, as shown below, that the measured profile is wider than either of the analytic estimates, which may be reasonable considering the electron beam emittance and electron multiple scattering in the radiator (I have not verified this numerically). A calculation was done to convolve the beam profile at the target location with the hemispherical endcaps of the target itself in order to estimate the effective target length. For four beam energies, the estimate using a Gaussian beam profile looks as follows: Target offset by 0 mm Gaussian Beam Profile CLAS g1 Effective Target Length Electron Beam Beam Sigma Effective Target Beam Fraction Energy Width Length Missing Target (GeV) (mm) (mm) (no collimation) ---------------------------------------------------------------------- 1.80 4.26 184.9 0.0000 2.50 3.07 185.5 0.0000 3.20 2.40 185.7 0.0000 4.00 1.92 185.9 0.0000 As can be seen, the effective target length is reduced from 186.1mm by about 0.6mm to 185.5mm for the 2.5 GeV beam used during g1a. The last column above gives the fraction of the beam which misses the target; that fraction is always zero for the beam energies considered. We can compare this table to the calculation using the more accurate beam profile given by the Landau & Lifshitz formula: Target offset by 0 mm Landau-Lifshitz Beam Profile CLAS g1 Effective Target Length Electron Beam Beam Sigma Effective Target Beam Fraction Energy Width Length Missing Target (GeV) (mm) (mm) (no collimation) ---------------------------------------------------------------------- 1.80 4.26 185.5 0.0000 2.50 3.07 185.8 0.0000 3.20 2.40 185.9 0.0000 4.00 1.92 186.0 0.0000 The difference is that at 2.5 GeV this more accurate result differs by 0.3mm from the Gaussian approximation, such that in the g1a case of 2.5 GeV beam the target is effectively 185.8mm long. Next, I looked through the paper log book for recorded Pair Counter scans, which measured the width of the photon beam in the downstream alcove. I found NO such scans during the May running period, and 5 during the July period. I found the following scans, and the widths were measured with a ruler off the graphs: U (FWHM) V (FWHM) 7-14-98 1.25" 1.20" 1.50" 1.25" 7-20-98 1.33" 1.25" 7-16-98 1.25" 1.20" 7-22-98 1.25" 1.15" The "inches" units refer to the FWHM of the beam, as given by the scale on the graphs in the log book. Taking the statistical average of the U and V measurements, and then taking the weighted mean of the averages I found the estimate of the beam width at the Pair Counter to be (1.22 +- 0.04)inches = (31+-1)mm FWHM ==> (13.2 +- 0.4)mm sigma. Given that the physics target is 1/2 the distance from the radiator as the Pair Counter, the sigma width of the beam at the target is (6.6 +- 0.2)mm. There is thus a 3% uncertainty on the width of the beam at the target position by this method. The value of 6.6mm is large compared to the 3.07mm estimate given above, suggesting that other effects may be present which widen the beam spot. These can include finite beam emittance and multiple scattering of the electrons in the radiator. Another possibility is that the finite resolution of the Pair Counter results in a too-wide effective beam width measurement. We discount this latter possibility at present. Given this empirical width estimate we find: Target offset by 0 mm Empirical Beam Profile CLAS g1 Effective Target Length Electron Beam Beam Sigma Effective Target Beam Fraction Energy Width Length Missing Target (GeV) (mm) (mm) (no collimation) ---------------------------------------------------------------------- 2.50 6.60 183.2 0.0000 This last effective target length of 183.2mm is probably the most realistic value to use. Taking the uncertainty in sigma into account leads to a final estimate of the effective target length of (183.2 +- 0.2)mm. The fractional uncertainty on the target length is very small in this estimate: only 0.1%. Relative to the norminal 180mm length, this effective length represents a 1.8% increase reduction in the target length, and therefore will reduce all cross sections by this amount. We must also consider possible misalignments of the target and the beam. During the e1 run period I recall start-up difficulties traced to beam-target misalignments on the order of several millimeters. For e1 this was a big problem since the entrance window on the target cell only allowed for about one millimeter of deviation before a massive flange was hit. For g1 it was not possible to get a direct measure of beam-target misalignment. However, given the history of the target setup in e1, we must be prepared to admit that in g1 we may have had misalignments of similar magnitude to e1. A calculation was done to estimate the size of possible systematic error of this sort on the effective target length. A conservative estimate might be to suppose a possible misalignment of the target relative to the beam of 5 millimeters. This results in the following: Target offset by 5 mm Empirical Beam Profile CLAS g1 Effective Target Length Electron Beam Beam Sigma Effective Target Energy Width Length (GeV) (mm) (mm) --------------------------------------------- 2.50 6.60 182.2 The effective target length is reduced by 1.0 mm. An extremely conservative systematic error estimate would be to say that the effective target length is somewhere between 182.2mm and 184.2mm, such that the systematic error on the length amounts to +- 1.0mm. In conclusion, for running CLAS at 2.5 GeV with the Saclay liquid hydrogen target #1, the effective target length is (183.2 +- 0.2 +-1.0)mm, where the first uncertainty is the "random" measurement error estimate, and the second number is the estimate of the systematic error. ________________________________________________________________________