Optimization of Positron Capturing

• Thickness of the Tungsten target: 1.25 mm
• Beam size at Tungsten target: Gaussian, [math]\sigma_{x,y} = 3~mm[/math]

Optimization with ELEGANT Simulation on the Region from Gun Exit to Tungsten Target

Emittance: [math] \epsilon_{x,y} = 13~\mu m[/math] (Not sure yet, need to be calculated)

Average Peak [math] Q = 14~pC [/math]

Beam Energy: [math] 10~MeV [/math]

Energy Spread: [math] \sigma_{\delta}=4.23% [/math]

Alpha Function: [math] \alpha = [/math]

Beta Function: [math] \beta = [/math]

RMS longitudinal Bunch Length: [math] \sigma_{z} = 10.6~ps[/math]

GEANT4 Simulation for 2 mm W-Target

Thickness of the Tungsten target: 2 mm

Electron Beam:

Beam size at Tungsten target: Gaussian, [math]\sigma_{x,y} = 3~mm[/math]

Beam divergence at target: 0

Beam Energy: [math] 10~MeV [/math]

Energy Spread: [math] \sigma_{\delta}=4.23% [/math]

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, [math]\epsilon_{rms}[/math].

Long and short axis of these two ellipse are: a = 3.791; b = 1.189;

X phase space

Y phase space

Transverse Beam Size

X

Y

Transverse Beam Divergence

X

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

Y

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