Difference between revisions of "Optimization of Positron Capturing"
(5 intermediate revisions by the same user not shown) | |||
Line 276: | Line 276: | ||
= GEANT output = | = GEANT output = | ||
+ | |||
+ | Root files and data files at | ||
+ | |||
+ | aztec.iac.isu.edu:/home/setisadi/pos_Tar_Opt/ana/dif_tar_pos | ||
== SteppingVerbose == | == SteppingVerbose == | ||
Line 320: | Line 324: | ||
detector.dat detector_T.root | detector.dat detector_T.root | ||
+ | |||
+ | [[File:hrrl_pos_sim_g4_output_det_xp.png | 300 px]] | ||
+ | [[File:hrrl_pos_sim_g4_output_det_yp.png | 300 px]] | ||
+ | |||
== detector1 == | == detector1 == | ||
Line 326: | Line 334: | ||
detector1.dat detector1_25mm.root | detector1.dat detector1_25mm.root | ||
+ | |||
+ | |||
+ | [[File:hrrl_pos_sim_g4_output_det1_xp.png | 300 px]] | ||
+ | [[File:hrrl_pos_sim_g4_output_det1_yp.png | 300 px]] | ||
== detector8 == | == detector8 == | ||
Line 332: | Line 344: | ||
detector8.dat detector8_200mm.root | detector8.dat detector8_200mm.root | ||
+ | |||
+ | |||
+ | [[File:hrrl_pos_sim_g4_output_det8_xp.png | 300 px]] | ||
+ | [[File:hrrl_pos_sim_g4_output_det8_yp.png | 300 px]] | ||
+ | |||
+ | == Ratio of the positrons on detectors == | ||
+ | |||
+ | NT = 215111 | ||
+ | |||
+ | N1 = 103506 | ||
+ | |||
+ | N8 = 3787 | ||
+ | |||
+ | NT:N1=2.08 | ||
+ | |||
+ | NT:N8=56.8 | ||
+ | |||
+ | N1:N8=27.3 | ||
+ | |||
+ | = Conclusions = | ||
+ | |||
+ | Positrons coming out of W-target: | ||
+ | |||
+ | <math>\epsilon_{x,y} = 14030~mm*mrad</math> | ||
+ | |||
+ | <math>\sigma_x = 3.41 \pm 0.01 ~mm</math> | ||
+ | |||
+ | <math>\sigma_y = 3.43 \pm 0.01 ~mm</math> | ||
+ | |||
+ | <math>\sigma_{x',y'} = 0.732 \pm 0.002 ~rad</math> | ||
+ | |||
+ | |||
+ | <math>\beta_x = \frac{\sigma_x^2}{\epsilon_x} = \frac{0.00341^2}{0.01403} = 0.00082154~m</math> | ||
+ | |||
+ | <math>\beta_y = \frac{\sigma_y^2}{\epsilon_y} = \frac{0.00343^2}{0.01403} = 0.00083121~m</math> | ||
+ | |||
+ | |||
+ | <math>\gamma_x = \frac{1 + \alpha_x^2}{\beta_x} </math> | ||
+ | |||
+ | <math>\gamma_y = \frac{\sigma_{y'}^2}{\epsilon_y} = \frac{0.732^2}{0.01403} = 37.857 </math> | ||
+ | |||
+ | Imaginary <math> \alpha_x </math> function? | ||
+ | |||
+ | <math> \alpha_x = \sqrt{\gamma_x \beta_x-1} = \sqrt{37.857 \times 0.00082154 -1} = \sqrt{0.0311 -1} </math> |
Latest revision as of 09:02, 12 April 2012
- Thickness of the Tungsten target: 1.25 mm
- Beam size at Tungsten target: Gaussian,
Optimization with ELEGANT Simulation on the Region from Gun Exit to Tungsten Target
Emittance:
(Not sure yet, need to be calculated)Average Peak
Beam Energy:
Energy Spread:
Alpha Function:
Beta Function:
RMS longitudinal Bunch Length:
GEANT4 Simulation for 2 mm W-Target
Thickness of the Tungsten target: 2 mm
Electron Beam:
Beam size at Tungsten target: Gaussian,
Beam divergence at target: 0
Beam Energy:
Energy Spread:
A volume called "detector" is placed at the of the W-target to get the information on the only of the outgoing positrons from the W-target. Followings are from "detector".
Phase Spaces of e+ Created
Phase space for positrons coming out W-target. Include 100 % of the particles
X phase space
Y phase space
Phase Spaces ellipse of 39% particles
Total positrons created are 75483, and 39 % of them will be 29438. Core 39% area of the phase space ellipse is RMS emittance,
.Long and short axis of these two ellipse are: a = 3.791 mm; b = 1.189 rad;
Area of this ellipse would be:
X phase space
Y phase space
Transverse Beam Size
X
FCN=1008.69 FROM MIGRAD STATUS=CONVERGED 62 CALLS 63 TOTAL EDM=5.73734e-06 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 8.62885e+02 4.11205e+00 4.92422e-02 -8.37091e-04 2 Mean -1.58596e-04 1.25728e-02 1.95074e-04 -1.22250e-03 3 Sigma 3.41790e+00 1.03579e-02 1.17273e-05 -8.88590e-02
So
Y
FCN=1016.5 FROM MIGRAD STATUS=CONVERGED 62 CALLS 63 TOTAL EDM=4.46233e-06 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 8.58714e+02 4.10556e+00 4.91913e-02 -7.80242e-04 2 Mean 6.57793e-03 1.26416e-02 1.96791e-04 5.52501e-03 3 Sigma 3.43480e+00 1.04943e-02 1.18410e-05 -3.65830e-01
Transverse Beam Divergence
XP
FCN=1205.9 FROM MIGRAD STATUS=CONVERGED 60 CALLS 61 TOTAL EDM=9.41429e-08 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 2.08367e+03 9.54533e+00 1.29688e-01 1.45076e-05 2 Mean 1.65233e-03 2.93970e-03 4.98630e-05 -1.42668e-01 3 Sigma 7.32175e-01 2.40413e-03 1.53830e-05 8.15997e-02
So
So
YP
FCN=1278 FROM MIGRAD STATUS=CONVERGED 60 CALLS 61 TOTAL EDM=2.39023e-07 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 2.08210e+03 9.52221e+00 1.33471e-01 4.78861e-05 2 Mean 3.97056e-03 2.94127e-03 5.13379e-05 1.97481e-01 3 Sigma 7.31984e-01 2.38977e-03 1.57624e-05 2.99074e-01
Energy and Momentum Distributions
En
P
Py vs Px
Conclusion
Positrons coming out of W-target:
Target Placed 20 cm from Quadrupole 4
x
In mm unit
FCN=314.927 FROM MIGRAD STATUS=CONVERGED 67 CALLS 68 TOTAL EDM=7.23115e-08 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 6.26496e+01 1.31186e+00 9.22753e-03 -2.86419e-04 2 Mean -1.55703e+00 2.98157e-01 2.40433e-03 7.26565e-04 3 Sigma 1.34518e+01 2.49312e-01 4.42013e-05 -3.10903e-02
y
In mm unit
FCN=203.003 FROM MIGRAD STATUS=CONVERGED 68 CALLS 69 TOTAL EDM=3.25951e-09 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 6.07799e+01 1.28695e+00 7.08046e-03 1.59797e-05 2 Mean 6.24506e-01 3.19737e-01 2.20644e-03 -2.42181e-04 3 Sigma 1.47606e+01 3.17675e-01 4.40665e-05 5.56943e-03
xp
In rad unit
FCN=265.085 FROM MIGRAD STATUS=CONVERGED 61 CALLS 62 TOTAL EDM=3.01383e-09 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 8.80056e+01 1.73095e+00 1.18113e-02 -2.55131e-05 2 Mean 6.16198e-04 1.10788e-03 8.81846e-06 -5.90190e-03 3 Sigma 6.18004e-02 7.08426e-04 2.61954e-05 -2.34453e-02
yp
In rad unit
FCN=329.265 FROM MIGRAD STATUS=CONVERGED 62 CALLS 63 TOTAL EDM=1.51428e-08 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 9.27538e+01 1.80938e+00 1.39977e-02 -3.41258e-05 2 Mean -1.83324e-03 1.06761e-03 9.45216e-06 1.51733e-01 3 Sigma 6.01380e-02 6.22891e-04 2.62088e-05 -1.60567e-02
En
In MeV unit
FCN=431.695 FROM MIGRAD STATUS=CONVERGED 79 CALLS 80 TOTAL EDM=3.43935e-09 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Constant 9.06730e+01 2.25831e+00 1.58988e-02 -4.86385e-05 2 Mean 2.73284e+00 3.48882e-02 3.44084e-04 2.48074e-04 3 Sigma 1.69962e+00 4.06010e-02 5.82766e-05 -6.72485e-03
Pn
In MeV/c unit
GEANT output
Root files and data files at
aztec.iac.isu.edu:/home/setisadi/pos_Tar_Opt/ana/dif_tar_pos
SteppingVerbose
if( fTrack->GetVolume()->GetName() =="Detector4" && fTrack->GetDefinition()->GetPDGEncoding()==-11 )//e+ { float Px, Py, Pz, Px2, Py2, Pz2; Px = fTrack->GetMomentum().x(); Py = fTrack->GetMomentum().y(); Pz = fTrack->GetMomentum().z(); Px2 = pow(Px, 2); Py2 = pow(Py, 2); Pz2 = pow(Pz, 2);
float xp, yp, P2, En, DelEn;
xp = atan(Px/Pz); yp = atan(Py/Pz);
P2 = Px2 + Py2 + Pz2; En = sqrt ( P2 + 0.511*0.511 ); DelEn = 10 - En;
if(Px2>0 || Py2>0 || Pz2>0 ){ outfile_detector4
<<fTrack->GetKineticEnergy() << " " << fTrack->GetPosition().x()<< " " << fTrack->GetPosition().y()<< " " << fTrack->GetPosition().z()<< " " << fTrack->GetMomentum().x() << " " << fTrack->GetMomentum().y() << " " << fTrack->GetMomentum().z() << " "
<< xp << " " << yp << " " << En << " " << DelEn << " "
<< G4endl;
}
So, the data file contains columns of
KE x y z Px Py Pz xp yp En DelEn
detector
Detector right after the W target.
detector.dat detector_T.root
detector1
Detector 25 mm from W target.
detector1.dat detector1_25mm.root
detector8
Detector 200 mm from W target.
detector8.dat detector8_200mm.root
Ratio of the positrons on detectors
NT = 215111
N1 = 103506
N8 = 3787
NT:N1=2.08
NT:N8=56.8
N1:N8=27.3
Conclusions
Positrons coming out of W-target:
Imaginary
function?