Computed Pion Yields from a Tantalum Rod Target

Stephen Brooks, Kenny WalaronScoping Study meeting, September 2005

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Computed Pion Yields from a Tantalum Rod Target

Comparing MARS15 and GEANT4 across proton energies

Stephen BrooksScoping Study meeting, September

2005

2 of 38

Proton Driver Energy and Pulse Structure

Implications(An overall context)


2005

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Proton Source ParametersI. Proton energyII. Bunch lengthIII. Bunch spacingIV. Pulse length

= Number of bunches × bunch spacingV. Pulse spacing

= 1/(Rep. rate)Assume 4-5MW fixed mean beam power.


2005

4 of 38

Upstream Correlations

RF voltage in bunch compression ring vs. space chargeBunching ring RF frequency, bucket filling pattern

…or separate extraction strategy

Bunching ring circumference minus extraction gapRepetition rate of linac or slowest synchrotron (possibly doubled up)

Linacs SynchrotronsFFAGs

2GeV 5GeV 10GeV 20GeV 50GeV


2005

5 of 38

Target IssuesSimilar?

“Pump-probe” effects due to liquid cavitation may appear on this timescaleFaster rep. rate needs a high jet velocity

Energy deposition minimal around 8GeVTime scale too short to have an effectSufficient spacing can split up thermal shocks…so shock is divided by the number of bunchesLow rep. rate means a larger shock each time

Solids Liquids


2005

6 of 38

Downstream CorrelationsPion momentum range increases with energy, becomes more difficult to captureLong bunches increase longitudinal emittance, phase rotation becomes harderAvoid ‘traffic jams’ in the longer-duration rings (or provide sufficient circumference)If bunches stored behind each other in storage ring, need enough circumferenceLow rep. rate means high peak beam loading; difficult to charge RF cavities

Capture Acceleration Storage ringPhase rotation Cooling


2005

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Scoping Study and Beyond…

• There are a lot of interactions going on– Can we really do this in our heads?– Perhaps they should be tabulated somewhere

• There are a lot of parameters– How do we run all possibilities… automation?

• There are a lot of constraints– Can we handle this systematically?

• Defining “engineerable ranges” would be useful


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Contents

• Benchmark problem• Physics models and energy ranges

– Effects on raw pion yield and angular spread• Probability map “cuts” from tracking

– Used to estimate muon yields for two different front-ends, using both codes, at all energies

• Target energy deposition• Variation of rod radius (note on tilt, length)


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Benchmark Problem

• Pions counted at rod surface• B-field ignored within rod (negligible effect)• Proton beam assumed parallel

– Circular parabolic distribution, rod radius

20cm

1cmSolid Tantalum

Protons

Pions


10 of 38

Possible Proton EnergiesProton Driver GeV RAL StudiesOld SPL energy 2.2

3 5MW ISIS RCS 1

[New SPL energy 3.5GeV] 45 Green-field synch.

6 5MW ISIS RCS 2

FNAL linac (driver study 2) 8 RCS 2 low rep. rate

10 4MW FFAG

[FNAL driver study 1, 16GeV] 15 ISR tunnel synch.

[BNL/AGS upgrade, 24GeV] 20JPARC initial 30 PS replacement

JPARC changed their mind? 40JPARC final 50

75100

FNAL injector/NuMI 120


11 of 38

8GeV

10G

eV

15G

eV

20G

eV

4GeV

3GeV

2GeV

5GeV 6G

eV

30G

eV

40G

eV50

GeV

75G

eV

100G

eV12

0GeV

0.0000

0.0200

0.0400

0.0600

0.0800

0.1000

0.1200

0.1400

0.1600

1 10 100 1000

Proton Energy (GeV)

Pion

s/(P

roto

n*G

eV)

GEANT 4 Pi+GEANT 4 Pi-MARS15 Pi+MARS15 Pi-

Total Yield of + and −

Normalisedto unit

beam power

These are raw yields (on a tantalum rod) using MARS15 and GEANT4.

Better to include the acceptance of the next part of the front end… (next)


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Yield of ± and K± in MARS2.

2GeV

3GeV

4GeV

20G

eV

30G

eV

40G

eV50

GeV

75G

eV

100G

eV12

0GeV

15G

eV

10G

eV8G

eV

6GeV

5GeV

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 10 100 1000

Proton Energy (GeV)

Pion

s or

Kao

ns p

er P

roto

n.G

eV (t

otal

em

itted

)

pi+/(p.GeV)

pi-/(p.GeV)

pi+/(p.GeV)pi-/(p.GeV)

K+/(p.GeV)

K-/(p.GeV)•No surprises in SPL region•Statistical errors small•1 kaon 1.06 muons

Finer sampling


13 of 38

Angular Distribution: MARS15

2.2G

eV

3GeV

4GeV

5GeV

6GeV

8GeV

10G

eV

15G

eV

20G

eV

30G

eV

40G

eV50

GeV

75G

eV

100G

eV12

0GeV

0

20

40

60

80

100

120

1 10 100 1000

Proton Energy (GeV)

Ang

le fr

om A

xis

(°)

pi+ 1st Quartilepi+ Medianpi+ 3rd Quartilepi- 1st Quartilepi- Medianpi- 3rd Quartile

MARS has a strange kink in the graph between 3GeV and 5GeV


14 of 38

MARS15 Uses Two Models<3GeV 3-5 >5GeV

MARS15 CEM2003 Inclusive• The “Cascade-Exciton Model” CEM2003 for

E<5GeV• “Inclusive” hadron production for E>3GeV

Nikolai Mokhov says: A mix-and-match algorithm is used between 3 and 5 GeV to provide a continuity between the two domains. The high-energy model is used at 5 GeV and above. Certainly, characteristics of interactions are somewhat different in the two models at the same energy.


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Angular Distribution: +GEANT4

GEANT4 has its own ‘kink’ between 15GeV and 30GeV


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GEANT4 Hadronic “Use Cases”

<3GeV 3-25GeV >25GeVLHEP GHEISHA inherited from GEANT3LHEP-BERT Bertini cascade

LHEP-BIC Binary cascade

QGSP (default) Quark-gluon string model

QGSP-BERT

QGSP-BIC

QGSC + chiral invariance


17 of 38

Total Yield of + and −: +GEANT4

0.00

0.05

0.10

0.15

0.20

0.25

0 1 2 3 4 5 6 7 8 9 10

Proton Energy (GeV)

Pion

/(Pro

ton*

Ener

gy(G

eV))

GEANT4 Pi+ LHEP-BICGEANT4 Pi- LHEP-BICGEANT4 Pi+ QGSPGEANT4 Pi- QGSPGEANT4 Pi+ QGSP_BICGEANT4 Pi- QGSP_BICGEANT4 Pi+ QGSP_BERTGEANT4 Pi- QGSP_BERTGEANT4 Pi+ LHEPGEANT4 Pi- LHEPGEANT4 Pi+ LHEP-BERTGEANT4 Pi- LHEP-BERTGEANT4 Pi+ QGSCGEANT4 Pi- QGSCMARS15 Pi+MARS15 Pi-


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Raw Pion Yield Summary

• It appears that an 8-30GeV proton beam: – Produces roughly twice the pion yield…– …and in a more focussed angular cone

...than the lowest energies.• Unless you believe the BIC model!• Also: the useful yield is crucially

dependent on the capture system.


19 of 38

Tracking through Two Designs

• Both start with a solenoidal channel• Possible non-cooling front end:

– Uses a magnetic chicane for bunching, followed by a muon linac to 400±100MeV

• RF phase-rotation system:– Line with cavities reduces energy spread to

180±23MeV for injecting into a cooling system


20 of 38

Fate Plots

• Pions from one of the MARS datasets were tracked through the two front-ends and plotted by (pL,pT)– Coloured according to how they are lost…– …or white if they make it through

• This is not entirely deterministic due to pion muon decays and finite source


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Fate Plot for Chicane/LinacMagenta Went backwards

Red Hit rod again

Orange Hit inside first solenoid

Yellow/Green Lost in decay channel

Cyan Lost in chicane

Blue Lost in linac

Grey Wrong energy

White Transmitted OK

(Pion distribution used here is from a 2.2GeV proton beam)


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Fate Plot for Phase RotationMagenta Went backwards

Red Hit rod again

Orange Hit inside first solenoid

Yellow/Green Lost in decay channel

Blue Lost in phase rotator

Grey Wrong energy

White Transmitted OK


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Probability Grids

• Can bin the plots into 30MeV/c squares and work out the transmission probability within each

Chicane/Linac Phase Rotation


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Probability Grids

• Can bin the plots into 30MeV/c squares and work out the transmission probability within each

• These can be used to estimate the transmission quickly for each MARS or GEANT output dataset for each front-end


25 of 38

Phase Rotator Transmission

2.2G

eV 3GeV

4GeV 5G

eV6G

eV 8GeV

10G

eV

15G

eV

20G

eV

30G

eV

40G

eV50

GeV

75G

eV

100G

eV12

0GeV

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

1 10 100 1000

Proton Energy (GeV)

Estim

ated

Cap

ture

of m

u±/(p

.GeV

)

MARS pi+

MARS pi-

GEANT pi+

GEANT pi-

Transmission from GEANT4 is a lot higher (×2) because it tends to forward-focus the pions a lot more than MARS15

Energy dependency is much flatter now we are selecting pions by energy range

Optimum moves down because higher energies produce pions with uncapturably-high momenta


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Phase Rotator Transmission (zooming into MARS15)

120G

eV10

0GeV

75G

eV50G

eV40

GeV30

GeV

20G

eV

15G

eV

10G

eV

4GeV

2.2G

eV

3GeV

5GeV

6GeV

8GeV

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

1 10 100 1000

Proton Energy (GeV)

Pion

s pe

r Pro

ton.

GeV

(est

. Pha

se R

otat

or)

pi+/(p.GeV)

pi-/(p.GeV)

pi+/(p.GeV)

pi-/(p.GeV)

Doubled lines give some idea of stat. errors

Somewhat oddbehaviour forpi+ < 3GeV


27 of 38

Chicane/Linac Transmission (MARS15)

3

GeV

4

GeV

8

GeV

4

0GeV

5

0GeV

7

5GeV

1

00G

eV

120

GeV

3

0GeV

6G

eV

2

.2G

eV 1

5GeV

1

0GeV

5

GeV

2

0GeV

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

1 10 100 1000

Proton Energy (GeV)

Pion

s pe

r Pro

ton.

GeV

(est

. Chi

cane

/Lin

ac)

pi+/(p.GeV)

pi-/(p.GeV)

This other front-end gave very similarly-shaped plots, at different yield magnitudes


28 of 38

Chicane/Linac Transmission (MARS15)

2.2

GeV

3G

eV

4G

eV

5

GeV

6G

eV

8G

eV

15G

eV

20G

eV

30G

eV

40G

eV

5

0GeV

75G

eV

100

GeV

120

GeV

10G

eV

0

0.01

0.02

0.03

0.04

0.05

0.06

1 10 100 1000

Proton Energy (GeV)

Chic

ane/

Lina

c Pi

ons

per P

roto

n.G

eV(h

eat)

pi+/(p.GeV_th)

pi-/(p.GeV_th)

But normalising to unit rod heating gives a sharper peak


29 of 38

Energy (heat) Deposition in Rod

• Scaled for 5MW total beam power; the rest is kinetic energy of secondaries

2.2G

eV

3GeV

4GeV

5GeV

6GeV

8GeV

10G

eV

15G

eV

20G

eV 30G

eV

40G

eV50

GeV

75G

eV

100G

eV12

0GeV

0

200000

400000

600000

800000

1000000

1200000

1400000

1 10 100 1000

Proton Energy (GeV)

Pow

er D

issi

patio

n (W

atts

, nor

mal

ised

to 5

MW

in

com

ing

beam

)

If we become limited by the amount of target heating, best energy will be pushed towards this 5-20GeV minimum (calculated with MARS15)


30 of 38

Variation of Rod Radius

• We will change the incoming beam size with the rod size and observe the yields


31 of 38



• For larger rods, the increase in transverse emittance may be a problem downstream

• Effective beam-size adds in quadrature to the Larmor radius:

22

z

Teff eB

prr


32 of 38

Total Yield with Rod Radius

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 0.5 1 1.5 2 2.5 3 3.5 4

Rod Radius (cm)

Pion

Yie

ld


30GeV

2.2GeV

Rod heating per unit volume and hence shock amplitude decreases as 1/r2 !

Multiple scattering decreases yield at r = 5mm and below

Fall-off due to reabsorption is fairly shallow with radius


33 of 38

Note on Rod Tilt

• All tracking optimisations so far have set the rod tilt to zero

• The only time a non-zero tilt appeared to give better yields was when measuring immediately after the first solenoid

• Theory: tilting the rod gains a few pions at the expense of an increased horizontal emittance (equivalent to a larger rod)


34 of 38

Conclusions – energy choice• Optimal ranges appear to be:

According to: For +: For −:

MARS15 5-30GeV 5-10GeV

GEANT4 4-10GeV 8-10GeV


35 of 38

Conclusions – codes, data

• GEANT4 ‘focusses’ pions in the forward direction a lot more than MARS15– Hence double the yields in the front-ends

• Binary cascade model needs to be reconciled with everything else

• Other models say generally the same thing, but variance is large– HARP data will cover 3-15GeV, but when?


36 of 38

Conclusions – other parameters

• A larger rod radius is a shallow tradeoff in pion yield but would make solid targets much easier

• Tilting the rod could be a red herring– Especially if reabsorption is not as bad as we

think• So making the rod coaxial and longer is

possible


37 of 38

Future Work

• Different rod materials (C, Ni, Hg) for scoping study integration– Length varied with interaction length

• Replace probability grids by real tracking– Also probes longitudinal phase-space effects,

e.g. from rod length• Extend energies to below 2.2GeV to

investigate MARS ‘kink’, if physical!


38 of 38

References

• S.J. Brooks, Talk given at NuFact’05: Comparing Pion Production in MARS15 and GEANT4; http://stephenbrooks.org/ral/report/

• K.A. Walaron, UKNF Note 30: Simulations of Pion Production in a Tantalum Rod Target using GEANT4 with comparison to MARS; http://hepunx.rl.ac.uk/uknf/wp3/uknfnote_30.pdf

Now updated

http://stephenbrooks.org/ral/report/

http://hepunx.rl.ac.uk/uknf/wp3/uknfnote_30.pdf


39 of 38


40 of 38

Total Yield of + and −

2.2G

eV

3GeV 4G

eV5G

eV6G

eV 8GeV

10G

eV

15G

eV

20G

eV

30G

eV

40G

eV50

GeV

75G

eV

100G

eV12

0GeV

0

0.2

0.4

0.6

0.8

1

1.2

1 10 100 1000

Proton Energy (GeV)

Pion

s pe

r Pro

ton.

GeV

of r

od h

eatin

g

pi+/(p.GeV_th)pi-/(p.GeV_th)

• Normalised to unit rod heating (p.GeV = 1.6×10-10 J)

From a purely target point of view, ‘optimum’ moves to 10-15GeV


41 of 38

Angular Distribution2.2 GeV

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200

Off-axis angle (°)

Pion

s pipluspiminus

6 GeV

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200

Off-axis angle (°)

Pion

s pipluspiminus

15 GeV

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 20 40 60 80 100 120 140 160 180 200

Off-axis angle (°)

Pion

s pipluspiminus

120 GeV

0

5000

10000

15000

20000

25000

30000

0 20 40 60 80 100 120 140 160 180 200

Off-axis angle (°)

Pion

s pipluspiminus

2.2GeV 6GeV

15GeV 120GeV

Backwards+ 18%− 33%

8%12%

8%11%

7%10%


42 of 38

Possible Remedies• Ideally, we would want HARP data to fill in

this “gap” between the two models• K. Walaron at RAL is also working on

benchmarking these calculations against a GEANT4-based simulation

• Activating LAQGSM is another option• We shall treat the results as ‘roughly

correct’ for now, though the kink may not be as sharp as MARS shows


43 of 38

Simple Cuts

• It turns out geometric angle is a badly-normalised measure of beam divergence

• Transverse momentum and the magnetic field dictate the Larmor radius in the solenoidal decay channel:

z

T

eBpr

z

T

z

T

Bp

Bcpr

3]T[)/10](MeV/c[]cm[

8


44 of 38

Simple Cuts

• Acceptance of the decay channel in (pL,pT)-space should look roughly like this:

pL

pTLarmor radius = ½ aperture limit

Angular limit (eliminate backwards/sideways pions)

Pions in this region transmitted

max

pTmax


45 of 38

Simple Cuts

• So, does it?• Pions from one of the MARS datasets

were tracked through an example decay channel and plotted by (pL,pT)– Coloured green if they got the end– Red otherwise

• This is not entirely deterministic due to pion muon decays and finite source


46 of 38

Simple Cuts

• So, does it?


47 of 38

Simple Cuts

• So, does it? Roughly.


48 of 38

Simple Cuts

• So, does it? Roughly.• If we choose:

– max = 45°– pT

max = 250 MeV/c

• Now we can re-draw the pion yield graphs for this subset of the pions


49 of 38

Cut Yield of + and −

• Normalised to unit beam power (p.GeV)

3GeV

4GeV

5GeV

8GeV

10G

eV

20G

eV

40G

eV

50

GeV

75G

eV

100G

eV

12

0GeV

15G

eV

2.2G

eV

6GeV

30G

eV

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

1 10 100 1000

Proton Energy (GeV)

Pion

s pe

r Pro

ton.

GeV

(with

in 4

5°, p

t<25

0MeV

/c)

pi+/(p.GeV)

pi-/(p.GeV)

High energy yield now appears a factor of 2 over low energy, but how much of that kink is real?


50 of 38

2.2G

eV

3GeV

4G

eV

5G

eV

6GeV

8GeV

10G

eV

15G

eV

20G

eV

30G

eV

40G

eV

50

GeV

75G

eV

100G

eV

12

0GeV

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1 10 100 1000

Proton Energy (GeV)

Cut P

ions

per

Pro

ton.

GeV

(hea

t)

pi+/(p.GeV_th)

pi-/(p.GeV_th)

Cut Yield of + and −

• Normalised to unit rod heating

This cut seems to have moved this optimum down slightly, to 8-10GeV


51 of 38

Chicane/Linac Transmission

2.2

GeV

3G

eV

4G

eV

5

GeV

6G

eV

8G

eV

15G

eV

20G

eV

30G

eV

40G

eV

5

0GeV

75G

eV

100

GeV

120

GeV

10G

eV

0

0.01

0.02

0.03

0.04

0.05

0.06

1 10 100 1000

Proton Energy (GeV)

Chic

ane/

Lina

c Pi

ons

per P

roto

n.G

eV(h

eat)

pi+/(p.GeV_th)

pi-/(p.GeV_th)


6-10GeV now looks good enough if we are limited by target heating


52 of 38

Phase Rotator Transmission


2G

eV

3G

eV

4G

eV

5GeV

6G

eV

8G

eV

15

GeV

20

GeV

30

GeV

40

GeV

50

GeV

75

GeV

10

0GeV

12

0GeV

10

GeV

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1 10 100 1000

Proton Energy (GeV)

Phas

e Ro

tato

r Pio

ns p

er P

roto

n.G

eV(h

eat)

pi+/(p.GeV_th)

pi-/(p.GeV_th)


53 of 38


54 of 38

Rod with a Hole

• Idea: hole still leaves 1-(rh/r)2 of the rod available for pion production but could decrease the path length for reabsorption

Rod cross-section r

rh


55 of 38

Rod with a Hole

• Idea: hole still leaves 1-(rh/r)2 of the rod available for pion production but could decrease the path length for reabsorption

• Used a uniform beam instead of the parabolic distribution, so the per-area efficiency could be calculated easily

• r = 1cm• rh = 2mm, 4mm, 6mm, 8mm


56 of 38

Yield Decreases with Hole

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.0090

0.2

0.4

0.6

0.8

1

1.2

pi+/(p.GeV)

pi-/(p.GeV)

Area fraction

30 GeV

2.2 GeV


57 of 38

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009

pi+ eff.

pi- eff.

Yield per Rod Area with Hole

30 GeV

2.2 GeV

This actually decreases at the largest hole size!


58 of 38

Rod with a Hole Summary

• Clearly boring a hole is not helping, but:• The relatively flat area-efficiencies suggest

reabsorption is not a major factor– So what if we increase rod radius?

• The efficiency decrease for a hollow rod suggests that for thin (<2mm) target cross-sectional shapes, multiple scattering of protons in the tantalum is noticeable


59 of 38



• This is not physical for the smallest rods as a beta focus could not be maintainedEmittance x Focus radius Divergence Focus length

25 mm.mrad extracted from proton machine

10mm 2.5 mrad 4m

5mm 5 mrad 1m

2.5mm 10 mrad 25cm

2mm 12.5 mrad 16cm


60 of 38

Cut Yield with Rod Radius

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 0.5 1 1.5 2 2.5 3 3.5 4

Rod Radius (cm)

Pion

Yie

ld W

ithin

45°

of A

xis

and

Tran

sver

se M

omen

tum

Bel

ow 2

50M

eV/c


30GeV

2.2GeV

Rod heating per unit volume and hence shock amplitude decreases as 1/r2 !

Multiple scattering decreases yield at r = 5mm and below Fall-off due to

reabsorption is fairly shallow with radius


61 of 38

Future Work

• Resimulating with the LAQGSM added• Benchmarking of MARS15 results against

a GEANT4-based system (K. Walaron)• Tracking optimisation of front-ends based

on higher proton energies (sensitivity?)• Investigating scenarios with longer rods

– J. Back (Warwick) also available to look at radioprotection issues and adding B-fields using MARS

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Computed Pion Yields from a Tantalum Rod Target

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