G4Beamline PbBi
Development of a Positron source using a PbBi converter and a Solenoid
Task List
1.) new electron and positron files for the case of two 0.25 mm thick SS windows around the PbBi target.
2.) Determine electron energy deposition in SS pipe per cm^2 of pipe surface area for pipes with diameter of 34.8, 47.5, 60.2, 72.9, and 97.4 mm and thickness of 1.65mm along the z-axis.
3.) Insert uniform B-field that can be scaled from 0 to 0.3 and 1 Telsa.
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) I ( A) = 10 MeV 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
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
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According to the above figure, GEANT4 predicts a total of 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
If this energy were uniformly distributed along the 5 mm thick beam pipe having a diameter of 3.48 cm then I would see
if you assume a 1 mA beam of electrons then this becomes
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.
If you use the above factors to weight the histogram, then the figure below shows that GEANT4 predicts a power deposition density of , 1 cm downstream of the target. Back scattered electrons appear to create the hottest spot of about 1cm upstream of the target.
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| 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.
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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
Results Table
| Beam Pipe Diameter (mm) | Hot Spot () | Hot Spot () |
| 34.8 | 0.35 | |
| 47.5 | 0.24 | |
| 60.2 | 0.20 | |
| 72.9 | 0.16 | |
| 97.4 | 0.12 |
| B-field (Tesla) | Hot Spot () | Hot Spot () |
| 0.0 | 0.35 | |
| 0 .1 | 0.29 | |
| 0 .2 | ||
| 0.3 | 0.007 | |
| 0.5 | ||
| 0.7 | ||
| 1.0 | 0.006 |
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
Inner Radiusu=
Outer Radius =
Length =
Current=
Magnetic Field Map in cylindrical coordinates (Z & R) from Niowave