1. LATLAT Beam Test Workshop May 17th 2006 1 GLAST Program Beam Test Workshop The c alibration strategy of the magnetic spectrometer A.Brezbrez@pi.infn.it

2. LATLAT Beam Test Workshop May 17th 2006 2 Definition of the spectrometer geometry  out  in Si1 Si2 Si3 Si4 BL x z P = 0.3 BL/[sin(  out )- sin(  in )] tan  out )=(X4-X3)/a1) tan(  in ) =(X2-X1)/a a a dd Simmetric spectrometer In this work I try to choose the best BL, d and a parameters and to extimate the influence of the errors of the parameters: 1.a 2.d 3.Xo1,Xo2,Xo3,Xo4 4.The parallelism of the strips to the vertical direction 5.The real value of the magnet bending power BL The multiple scattering has been evaluated with the parametric formulas  MS =  /p = [0.0136×(x/Xo) ½ ×(1+0.0038ln(x/Xo))] /p(GeV )  X MS =  MS ×L/  3

3. LATLAT Beam Test Workshop May 17th 2006 3 d, a The parametric Monte Carlo is in rough agreement with the analytical calculation by Bruel and with the experimental distributions obtained by the Agile group  p/p=  /0.3BL(1+cos  out ) which is contant in P We have to plce the SI odoscopes as close as possible to the magnet The pulse resolution is quite flat for a>0.5m. A lower a value is more easy (we have not much space) and define a large acceptance angle

4. LATLAT Beam Test Workshop May 17th 2006 4 Si spatial resolution and SI parallelism The foreseen Si rms is 241/  12=70  m If a Si detector is rotated by an angle , the true coordinate is X true =X meas +  ×Y meas The example shows the effetcs of a tilt of the last Si detector (beam height 10mm) 10mrad correspond to a non parallelism of about 1mm

5. LATLAT Beam Test Workshop May 17th 2006 5 BL, a, d, Si offsets errors The errors in the knowledge of these parameters generate systematic errors on P What is the precision we need to know these parameters? Two simple formulas Suppose that we have an unknown offset of the Si detectors, so that what we measure is X meas =X+X off We drive the beam on the odoscopes with two pulses P 1 and P 2 X off4 -X off3 =X meas4 -X meas3 -0.3aBL/[p 2 -(0.3BL) 2 ] ½ 0.3aBL/[p 1 2 -(0.3BL) 2 ] ½ - 0.3aBL/[p 2 2 -(0.3BL) 2 ] ½ = (X 4 (P 1 )-X 4 (P 2 ))/(a+d) These two formulas allow to define BL and the relative shift of chamber 4 and 3 (chamber 1 and 2 are suppoesd aligned to the beam)

6. LATLAT Beam Test Workshop May 17th 2006 6 Exercise Suppose X off3 =10mm, X off4 =12mm much more than what we should do We suppose to take 2 runs at 2.0GeV/c and 1.7 GeV/c From the previous formula we obtain: X off4 -X off3 =2.34mm with a 0.34mm error BL=.907Tm These numbers can be refined if the real shape of the spatial distribution is taken into account. If we take into account the Bremmstrahlung we extimate X off4 -X off3 =2.013mm with a 0.013mm error BL=.895Tm Theor. peak 0.1362 Theor. peak 0.2044

7. LATLAT Beam Test Workshop May 17th 2006 7 Xint if  out,  in « 1 Z int X int The incoming and ougoing trajectories of the electron should cross in Zint. The difference between the two tracks calculated in Zint is a sensible parameter which indicates the systematics errors. In the prevoius example Xint=10.139mm that indicates that the second arm coordinates are shifted. After 2 iteration the final parameters are X off3 =10.014mm (it was 10mm) X off4 =12.027mm (it was 12mm)

8. LATLAT Beam Test Workshop May 17th 2006 8 a, d In the previous formula we have assumed a perfect knowledge of a and d a=.5m The relative distance between Si3 and Si4 on the optical bench can be well defined and measured with an error <1mm From the approximate relation (X4-X3)/a=0.3BL/p we have:  p/p=  a/a<1/500 The distance of the Si odoscope from the magnet axis could be more difficult to measure. In this case, with a=0.5m, d=1m,  BL/BL=  p/p=0.6% per cm of error on d.

9. LATLAT Beam Test Workshop May 17th 2006 9 conclusions In the Agile test, the beam pulse was changed in steps (0.3GeV/c) to build an expeimental relation between the beam pulse and the measured angles. The spectral analisys of the beam is crucial because the main source of indetermination of the energy of the tagged gamma is the pulse dispersion of the bem itself: E  = E beam (  2%) – E tagged el (  1%) The simple caluclations shown in this talk demonstrate that even with 2 pulse values only, it is possible to determine the parameters of the magnetic spectrometer with a dp/p ~ 1% (which adds to the 2% dp/p of the incoming beam) without relevant systematic errors.