G4Beamline PbBi

Development of a Positron source using a PbBi converter and a Solenoid

Conclusions

1. A 0.3 (0.6) Tesla Solenoid with a diameter to allow a 9.74 (3.94) cm diameter pipe would collect a positron per thousand incident electrons on a 2mm thick PbBi target with 0.125 mm thick SS windows.
2. A 4 Tesla Solenoid will remove beam pipe heating from scattered electrons downstream of the target when using a 3.94 cm diameter beam pipe.

Task List

1.) Report on previous simulation work

2.) Create a positron (10,000 positrons) and electron event file containing t,x,y,z,Px,Py,Pz for positrons exiting the solenoid and an incident Gaussian beam 1cm in diameter and with a sigma of 1cm.

3.) Determine the back ground when using a 3.94 diameter beam pipe and Solenoid fields of 0.3 and 0.6 Tesla for a NaI detector placed at

Beam Pipe Heating

A 10 MeV electron beam with a radius of 0.5 cm was incident on a 2 mm thick PbBi target. The target is positioned at Z = -902 mm.

Element	dimension
Inner beam pipe radius	1.74 cm
Inner beam pipe thickness	0.165 cm
water jacket thickness	0.457 cm
outer beam pipe radius	2.362 cm
outer beam pipe thickness	0.165 cm
Solenoid inner radius	2.527 cm
Solenoid outer radius	4.406 cm

Max available power from beam heating

If you assume a 1mA beam then the beam power incident on the target is

Beam Power = E(MeV) [math] \cdot [/math]I ([math]\mu[/math] A) = 10 MeV [math]\times[/math] 1000 mA = 10 kW

If the beam does not interact with the target and all the beam power is distributed uniformly along a 100 cm long beam pipe with a diameter of 3.38 cm then the power deposited per area would be

[math]10000 \mbox{W} \times \frac{1}{100 \mbox{cm}}\times \frac{1}{ \pi \times 3.48 \mbox {cm} } = 2.3 \frac{\mbox{W}}{\mbox{cm}^2}[/math]

A simulation predicts that about 8 out of 20 electrons will interact with the target and intercept a 34.8 mm diameter beam pipe surrounding the target.

Heating along the Z-axis

GEANT4 predicts that scattered electrons, photons, and positrons (mostly scattered electrons) deposit

Energy deposited (MeV) in a 1 m long 3.48 cm diameter beam pipe surrounding a 2 mm target located at Z=-900 mm.

According to the above figure, GEANT4 predicts a total of [math]3.08\times 10^7[/math] MeV (the integral adds up the energy in each 1cm bin) of energy will be deposited in a 1m long beam pipe surrounding a 2 mm thick PbBi target located at Z=-902 mm when 20 million electrons impinge the target. The peak energy deposition is 0.3 MeV/e[math]^-[/math]

If this energy were uniformly distributed along the 5 mm thick beam pipe having a diameter of 3.48 cm then I would see

[math]3.08 \times 10^{10} \mbox{keV} \times \frac{1}{100 \mbox{cm}}\times \frac{1}{ \pi \times 3.48 \mbox {cm} } \times \frac{1}{2 \times 10^7 \mbox{e}^-}=3.5\frac{\mbox{keV}}{\mbox{cm}^2 \;\;\mbox{e}^-}[/math]

if you assume a 1 mA beam of electrons then this becomes

[math]\left ( \frac{3.5 \; \mbox{W} }{ \mbox{cm}^2 } \right) [/math]

I converted the above histogram to deposited power by 1000 mA, divide by the number of incident electrons, divide by the circumference of the beam pipe, convert the number of electrons to Coulombs, and use a unit conversion from MeV to W-s per MeV.

[math]\left(Counts \frac{\mbox{MeV}}{\mbox{cm}}\right) \times \left( \frac{1}{2 \times 10^{7} \mbox{e}^-} \right ) \times \left( \frac{1}{ \pi \times 3.48 \mbox{cm}} \right ) \times \left( \frac{1. \times 10^{-3}\mbox{ C}}{\mbox{s} }\right )\times \left( \frac{\mbox{e}^- }{1.6 \times 10^{-19}\mbox{ C}}\right ) \left( \frac{1.6 \times 10^{-13}\mbox{W} \cdot \mbox{ s}}{\mbox{MeV} }\right ) \times [/math]

If you use the above factors to weight the histogram, then the figure below shows that GEANT4 predicts a power deposition density of [math]= 4 \frac{W}{cm^2}[/math], 1 cm downstream of the target. Back scattered electrons appear to create the hottest spot of [math]= 15 \frac{W}{cm^2}[/math] about 1cm upstream of the target.

Power Deposition Zoomed in and 902 mm offset applied	Power deposition over the 1 m long beam pipe

The plot below shows the energy deposited in MeV along the pipe. The Z axis is along the beam direction. The distance around the beam pipe is determine by taking the pipe radius (34.8 mm) and multiplying it by the Phi angle around the pipe. The bins are 1cm x 1cm.

A maximum of 450,000 MeV is deposited in a 1 cm[math]^2[/math] bin when 20 Million , 10 MeV electrons are incident on a 2 mm thick PbBi target located at Z=-902 mm.

Below is energy deposited contributions from from photons(AVSzWg), positrons (AVSzWpos), and electrons.

Why is the positron hotspot upstream of the target?

root commands used

TH2D *AVSz=new TH2D("AVSz","AVSz",100,-1000,0,12,-60,60)
BeamPipeE->Draw("35.*atan(PosYmm/PosXmm):PosZmm>>AVSz","DepEmeV"); 
AVSz->Draw("colz");

BeamPipeHeating_4mmthick_PbBi_PositronTarget

Scattered Electron Momentum and Energy lot in Beam Pipe

Unit conversion

The energy deposited by photon, electrons, and positrons is predicted by GEANT4 and recorded in energy units of keV per incident electron on the PbBi target. To convert this deposited energy to a power you need to assume a beam current. Assuming 1 beam current of 1 mA, the conversion is given easily as

[math]\left( \frac{\mbox{keV}}{\mbox{cm}^2 \mbox{e}^-}\right) \times \left( \frac{ \mbox{e}^-}{1.6 \times 10^{-19}\mbox{C}} \right ) \times \left( \frac{1 \times 10^{-3} \mbox{C}}{\mbox{s}} \right ) \times \left( \frac{1.6 \times 10^{-16}\mbox{W} \cdot \mbox{ s}}{\mbox{keV} }\right )[/math]

[math]\left( \frac{\mbox{keV}}{\mbox{cm}^2 \mbox{e}^-}\right) = \left( \frac{\mbox{W} }{\mbox{cm}^2 } \right )[/math]

Results Table

Beam Pipe Diameter (mm)	Hot Spot ([math]MeV/e^-[/math])	Hot Spot ([math]keV/cm^2/e^-[/math])
34.8	0.35
47.5	0.24
60.2	0.20
72.9	0.16
97.4	0.12

Converter target properties

Definition of Lead Bismuth

1cm diameter target 2 mm thick PbBi

0.5 Tesla solenoid

Desire to know

Emmittance (mrad * mm)

dispersion (Delta P/P) (mradian/1000th mm/1000th)

of electrons after the PbBi target.

pole face rotation in vertical plane.

G4BeamLine and MCNPX

Target thickness optimization

PbBi_THickness_GaussBeam

Dmitry's processing of Tony's GEANT simulations showing transverse phase space portrait (left) and longitudinal phase space portrait (right). Phase space portraits show coordinate x or y vs diveregense=px/pz or py/pz (or time vs kinetic energy ). Captions show:

1. geometric (not normalized) emittance for transverse and emittance for longitudinal phase space portraits (ellipse areas divided by "pi")

2. Twiss parameters

3. Ellipse centroid for longitudinal phase portrait

4. sqrt(beta*emittance) and sqrt(gamma*emittance) - half sizes of the projections of the ellipses on the coordinate and divergence axes respectively.

Electrons - RMS

Electrons - 68.2% core

Positrons - RMS

Positrons - 68.2% core

PbBi_THickness_CylinderBeam

Dmitry's processing of Tony's GEANT simulations showing transverse phase space portrait (left) and longitudinal phase space portrait (right). Phase space portraits show coordinate x or y vs diveregense=px/pz or py/pz (or time vs kinetic energy ). Captions show:

1. geometric (not normalized) emittance for transverse and emittance for longitudinal phase space portraits (ellipse areas divided by "pi")

2. Twiss parameters

3. Ellipse centroid for longitudinal phase portrait

4. sqrt(beta*emittance) and sqrt(gamma*emittance) - half sizes of the projections of the ellipses on the coordinate and divergence axes respectively.

Electrons - RMS

Electrons - 68.2% core

Positrons - RMS

Positrons - 68.2% core

PbBi_THickness_PntSource

Electrons and Positrons after 2mm of LBE:

Electrons:

Positrons:

Energy Deposition in Target system (Heat)

MCNPX simulations of energy deposition into different cells are below. There is a slight overestimate (they add up to about 120%). Positrons contribute less than 1% of electrons' contribution. No magnetic filed is assumed.

Solenoid

Uniform ideal Solenoid

Beam Pipe Heating with SOlenoid

The energy deposited by electrons scattered into a 3.48 diameter stainless steel beam pipe (1.65 mm thick) from a PbBi target as a function of a uniform Solenoidal magnetic field.

The histogram is binned in 100 (10 cm) bin widths. The surface area becomes [math]10 cm \times 2 \pi 3.48/2 = 109.33 cm^2[/math]

To convert From Mev/ e- to kW/cm^2 assuming a current of 1mA (10^-3 C/s) you

[math]\left( \frac{\mbox{MeV}}{\mbox{cm}^2 \mbox{e}^-}\right) \times \left( \frac{ \mbox{e}^-}{1.6 \times 10^{-19}\mbox{C}} \right ) \times \left( \frac{1 \times 10^{-3} \mbox{C}}{\mbox{s}} \right ) \times \left( \frac{1.6 \times 10^{-13}\mbox{W} \cdot \mbox{ s}}{\mbox{MeV} }\right )[/math]

[math]\left( \frac{\mbox{keV}}{\mbox{cm}^2 \mbox{e}^-}\right) = \left( \frac{\mbox{W} }{\mbox{cm}^2 } \right )[/math]

B-field (Tesla)	Hot Spot ([math]MeV/e^-[/math])
0.0	0.35
0.3	0.35
1.0	0.35
1.5	0.22
2.0	0.10
4.0	0.002

Energy deposited (MeV) along a 1 m long beam pipe of stainless steel 1.65 mm thick.

With SS windows

Positrons->Draw("sqrt(evt.BeamPosPosX*evt.BeamPosPosX+evt.BeamPosPosY*evt.BeamPosPosY)","evt.BeamPosMomZ>0 && evt.BeamPosPosZ>-500 && sqrt(evt.BeamPosPosX*evt.BeamPosPosX+evt.BeamPosPosY*evt.BeamPosPosY)<97.4/2");

Positron Collection rates with Solenoid

Sample Positron Production Events

When the solenoid is 1.5 Tesla, a 10 MeV electron produces a 6.5 MeV photon that pair produces a 4.4 MeV positron and a 1 MeV electron	Same Event but this time the solenoid is 0.3 Tesla and the positron hits the beam pipe, annihilates and makes two 511 keV photons

Sample Brem event producing no positrons

When the solenoid is set to 1.5 Tesla, a 10 MeV electron produces three photons less than 1 MeV in the target, two of them compton scatter in the beam pipe	The same event but this time the electron produces only 1 photon than ionizes in the target

With SS windows

Positrons->Draw("sqrt(evt.BeamPosPosX*evt.BeamPosPosX+evt.BeamPosPosY*evt.BeamPosPosY)","evt.BeamPosMomZ>0 && evt.BeamPosPosZ>-500 && sqrt(evt.BeamPosPosX*evt.BeamPosPosX+evt.BeamPosPosY*evt.BeamPosPosY)<97.4/2");

B-field (Tesla)		39.4 mm diameter pipe	47.5	60.2	72.9	97.4
0.0	0.35	1,2,4,4,5	2,3,4,4,6	4,4,6,7,9	6,8,9,10,11	16,14,15,16,17
0.1		225,236,250,246,249=241[math] \pm[/math] 10	282,282,293,294,306=291[math] \pm[/math] 10	373,366,370,364,373=369[math] \pm[/math] 4	451,437,440,438,451=443[math] \pm[/math] 7	602,584,563,558,570=575[math] \pm[/math] 18
0.3	0.35	626,619,596,619,611 =614[math] \pm[/math] 11	720,726,706,730,717=720[math] \pm[/math] 9	871,864,840,841,834 =850[math] \pm[/math] 16	987,968,939,943,952 =958[math] \pm[/math] 20	1118,1106,1069,1067,1080=1088[math] \pm[/math] 23
0.6		929,935,949,969,961=949[math] \pm[/math] 17	1022,1031,1046,1059,1052 =1042[math] \pm[/math] 15	1120,1130,1152,1154,1146 =1140[math] \pm[/math] 15	1168,1184,1210,1221,1206 =1198[math] \pm[/math] 21	1212, 1218,1240,1254,1242=1233[math] \pm[/math] 18
1.0	0.35	1117,1085,1083,1061,1085=1086[math] \pm[/math] 20	1188,1154,1140,1111,1134=1145[math] \pm[/math] 28	1225,1190,1178,1149,1172 =1183[math] \pm[/math] 28	1243.1208,1195,1164,1184=1199[math] \pm[/math] 30	1252,1219,1206,1178,1200=1211[math] \pm[/math] 27
1.5	0.22
2.0	0.10	1198,1210,1215,1223,1176=1204[math] \pm[/math] 18	1216,1227,1235,1241,1196 =1223[math] \pm[/math] 18	1237,1243,1252,1257,1214=1241[math] \pm[/math] 17	1249,1252,1262,1266,1225 =1251[math] \pm[/math] 16	1257,1262,1270,1276,1234=1260[math] \pm[/math] 16
4.0	0.002

Positron Rates -vs- Solenoid Field for 2mm thick PbBi target and several Beam pipe diameters

Positron & Electron event files

Event files were generated assuming an ideal solenoid having an inner radius of 2.527 cm surrounding a beam pipe with a radius of 1.74 cm. Electrons impinge a 2mm thick PbBi liquid target that has a surface area of 2.54 cm x 2.54 cm. Stainless steel windows 0.25 mm thick sandwhich the PbBi target at locations Z= -90.325 and Z= -89.875 cm. The target is located at Z =-90.1 cm and the beam begins 20 cm upstream at Z = -110.1 cm. The incident electron beam is a 0.5 cm radius cylinder.

/vis/viewer/zoom 2

/gps/pos/centre 0.0 0.0 -150.

/vis/viewer/panTo -90.1 0 cm

/vis/viewer/reset

Solenoid Map

Inner Radiusu=

Outer Radius =

Length =

Current=

Magnetic Field Map in cylindrical coordinates (Z & R) from Niowave

Beam Line Design

PbBi_BeamLine_Elements

goals for JLab

Positrons#Simulations