Muons, Inc.
March 2, 2011 TJR G4beamline Validation 1

A major concern of the MAP review committee was the apparent lack of validation of the simulation tools we are using.
This talk is based on the document written in response: http://www.muonsinc.com/g4beamline/G4beamlineValidati on.pdf
•Basic Properties of G4beamline Simulations
– Object placement, tracking, regression tests
•Physics Processes from Geant4
– Multiple scattering, energy loss, hadronic interactions
•Physics Processes Implemented in G4beamline
– Fixes to Geant4 processes, collective computations, space charge (in vacuum)
•Beamline Elements
– solenoid, genericbend, genericquad, multipole
•Summary
March 2, 2011 TJR G4beamline Validation 2

• Object Placement:
– An object that kills all tracks with x<5 is accurate to 2 nanometers in tracking – this is far more accurate than real surfaces can be placed.
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• Tracking:
– A proton traveling 10 7 meters in vacuum with no fields, is in the correct place at the correct time, to the accuracy of a float. That is 10 8 steps of 100 mm each.
– 25 MeV electrons traveling perpendicular to a uniform 0.01 T magnetic field
(circumference = 52 meters) have the correct period and radius to 6 significant digits. The accuracy with which they return to their starting point depends on the step size:
Typical
15 nm
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• Regression Tests
– Most of these numerically verify an instance of the command they test.
test01: simple geometry and tracking test (1 sec) test02: BLFieldMap test (1 sec) test03: tracking through quads and bend (1 sec) test04: tracking mu+ through Aluminum (5 sec) test05: multiple successive transforms (1 sec) test06: HistoScope test07: tracking through a group of 2 solenoids (7 sec) test08: FOR009.DAT output (2 sec) test09: ntuple, particlefilter test (2 sec) test10: timentuple (1 sec) test11: trace test (1 sec) test12: multipole test (1 sec) test13: tracing through FieldMaps and bend (1 sec) test14: Eloss and multiple scattering in LH2 (15 sec) test15: fieldexpr test (8 sec) test16: particlefilter require argument (1 sec) test17: various kill arguments (7 sec) test18: various object arguments on the place command test19: geometrical args on place command (1 sec) test20: beamlossntuple (7 sec) test21: field of rotated solenoid and solenoid cache file test22: argument expressions (1 sec) test23: place OFFSET with 2 solenoids (7 sec) test24: virtualdetector NTuple name test (1 sec) test25: particlefilter nWait and referenceWait test (1 sec) test26: ntuple with for009.dat (2 sec) test27: randomseed command (4 sec) test28: printf (1 sec) test29: 3 nested tune-s (2 sec) test30: tune By of genericbend (2 sec) test31: tune maxGradient of 4 pillbox-es (2 sec) test32: tune reference momentum (2 sec) test33: profile command (15 sec) test34: element naming (1 sec) test35: tune By of idealsectorbend (2 sec) test36: the if and the define commands (1 sec) test37: zntuple (2 sec) test38: Root input and output (6 sec) test39: zntuple + beam rotation (2 sec) test40: MICEPhysicsList (1 sec)
Test41 LISAPhysicsList test42: rotated trace (1 sec) test43: various coordinates arguments (2 sec) test44: steppingVerbose (1 sec)
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• Regression Tests
– Most of these numerically verify an instance of the command they test.
test45: psuedo random number generator seeds test46: do loops and complex (multi-line) if-s (1 sec) test47: tune By of six idealsectorbends (2 sec) test48: reference coordinates (2 sec) test49: multiple beam commands eventide-s (1 sec) test50: require arguments on NTuple commands (1 sec) test51: newparticlentuple (2 sec) test52: tune fieldexpr (2 sec) test53: tune fieldmap (2 sec) test54: Zcl (2 sec) test55: compile and run BLMinimize (1 sec) test56: extrusion (2 sec) test57: eventcuts file (1 sec) test58: NIST material database, output command (1 sec) test59: multiple beam-s and corner-s (3 sec) test60: tracker (4 sec) test61: linac (3 sec) test62: 120 GeV/c beam (10 sec) test63: zntuple tracked both directions (2 sec) test64: torus (2 sec) test65: pillbox B field (2 sec) test66: tracker (4 sec) test67: various comma-separated list arguments (3 sec) test68: polycone (1 sec) test69: genericbend as a parent (3 sec) test70: tracked preservation (1 sec) test71: basic collective tracking (1 sec) test72: compiling user code with g4blmake (20 sec) test73: totalenergy (2 sec) test74: pillbox fixed timeOffset (2 sec) test75: pillbox kill=1 (2 sec) test76: ntuple command (1 sec) test77: unary minus in expressions (5 sec) test78: setdecay command (1 sec) test79: reference noEloss and no field (2 sec) test80: particlesource command (1 sec) test81: veto argument to ntuple command (2 sec) test82: fieldntuple (2 sec) test83: multiple reference particles, noEfield and noEloss test84: extended NTuple formats (2 sec) test85: synchrotron radiation (2 sec) test86: multiple NTuple-s to single ASCII file (1 sec) test87: spacecharge (12 sec) test88: helicalharmonic (2 sec)
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• All Geant4 physics lists are available in G4beamline
• In almost every case they are unchanged, so the Geant4 validation applies (modified processes in next section).
• This talk will discuss:
– Multiple scattering
– Energy loss
– Straggling
– X-rays from μ − capture
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• Geant4 has several different implementations for electromagnetic processes.
• The current default for muons is G4WentzelVIModel.
• There are also models for low energy particles (< ~1 MeV):
– Penelope
– Livermore
• Plots comparing to the MuScat experiment are below (172 MeV/c μ + ).
• While the simulation certainly reproduces the general distributions, treated as a 0parameter fit to the data the χ 2 values are not very good:
8 March 2, 2011 TJR G4beamline Validation

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March 2, 2011 TJR http://pdg.lbl.gov/2010/reviews/rpp2010-rev-passage-particles-matter.pdf
The discrepancy for
>100 GeV/c is said to be due to μ pair production, which was not included in the G4beamline simulations here.
This will be studied.
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• Energy deposition of protons in Xenon gaseous detector; data are from NIM 217 (1983) 277.
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• 49.10 MeV protons after a 2.675 g/cm 2 Al absorber.
The peak energy loss differs by about 1 MeV, out of 40
MeV in energy loss, a difference of 2.5%.
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μ −
March 2, 2011 TJR G4beamline Validation
(Their detector loses efficiency below 2 keV.)
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• Modifications to Geant4 processes:
– Rare charged-pion decays:
• π + ➞
μ + ν
μ
(1.230E-4)
• π −
➞
μ − ν
μ
(1.230E-4)
• (Modes < 1e-6 were not added.)
– Fix for tracks that turn around in E field.
• Geant4 tracks in space, which is singular for zero velocity.
• Approximation is stable and accurate to a fraction of a micron.
• Applies only to charged tracks anti-parallel to qE within a few degrees.
– Fix for missing neutrons in μ − capture.
• Collective computations
• Space charge
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• Geant4 is inherently a single-particle toolkit
• G4beamline implements a general infrastructure for performing collective computations
– Replaces the RunManager, EventManager, TrackManager, and
SteppingManager
– Tracks a vector of tracks from the beam command(s), in “parallel”
• Used for space charge computations
• Extensible to other collective computations
• Comparison to standard tracking, scattering in Fe:
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• The computation solves Poisson’s equation in the beam frame
– Boosts particles to the beam frame, puts them into a grid (up to ~ 128x128x128)
– Green’s Function convolution via FFTs
– Boosts E beamframe to E lab and B
– Tracking as usual via Geant4.
lab
• Uses macro-particles to simulate larger bunches.
• Can handle up to about a million macro-particles.
• Requires a bunched beam, with a reference particle for each bunch.
• Comparison to known sources:
– A 1 Coulomb charge at 1 meter has E=8.987551787E9 V/m.
A macro-particle with 1 Coulomb has E=8987.54 MV/m.
– A current of 1,000 Amps, at 0.1 meter, has B=0.002 T.
101 macro-particles with charge +0.001 Coulomb, spaced 1 cm, moving at 10,000 meter/sec, has B=0.001971 T.
• There is also a Lienard-Wiechert computation
– Computationally infeasible for more than ~500 macro-particles
– Beam need not be bunched; reference not needed
– Rigorously correct (without radiation term), and useful to verify the other computation.
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• Comparison to a computation in Reiser’s textbook for uniform charge density.
• The 3 lines are for different initial conditions.
March 2, 2011 TJR
Scaled Z position (propagation axis)
G4beamline Validation
Only 500 macro-particles
100,000 macro-particles
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• At the center of a pair of Helmholtz coils,
B z
= 32 π N I / (5 3/2 R 10)
The coil separation is of course equal to the radius R. For N=1, I=10,000 A,
R=50 cm, this formula gives 179.84 gauss. G4beamline gives 0.017984
Tesla.
• Comparison to the analytic formula for the on-axis field
(radius=200 mm, length=2,000 mm, thickness=1 mm).
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• The CERN Courier (Jan. 2010) showed a chaotic B field from two current loops at 90 degrees; this plot of a single field line is qualitatively similar.
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• This plot of field lines shows the form of the fringe field – in particular, it is valid only inside the extended aperture.
(The field lines are drawn in 3-D, so their density in projections such as this is not an accurate representation of the field magnitude.)
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• This plot of field lines shows the form of the fringe field – in particular, it is valid only inside the extended aperture.
(The field lines are drawn in 3-D, so their density in projections such as these is not an accurate representation of the field magnitude.)
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• Comparison of genericquad to a Tosca field map of a quadrupole triplet in MICE.
March 2, 2011 TJR G4beamline Validation
Plot credit:
Marco Apollonio
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(The field lines are drawn in 3-D, so their density in projections such as these is not an accurate representation of the field magnitude.)
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• Many tests of G4beamline have been performed, which display its accuracy in many situations and processes.
• As it is based on Geant4, G4beamline shares the deficiencies of
Geant4.
– Primarily related to hadronic production in thick targets.
– Not so inaccurate that it is unusable.
– Benefits from the ongoing effort to improve Geant4.
• In many cases, the realism of a simulation will be determined by the difficulties involved in accurately describing the physical components, not by inaccuracies in the program.
• There are a few known deficiencies that require further study.
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