Computed Pion Yields from a Tantalum Rod Target

Stephen Brooks, Kenny WalaronNuFact’05 ENG Meeting, August 2005

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Computed Pion Yields from a Tantalum Rod Target

Comparing MARS15 and GEANT4 across proton energies


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Contents

• Benchmark problem

• Physics models and energy ranges– MARS15 model– GEANT4 “use cases”– 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


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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


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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

40JPARC final 50

75100

FNAL injector/NuMI 120


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8G

eV

10

Ge

V

15

Ge

V

20

Ge

V

4G

eV

3G

eV

2G

eV

5G

eV

6G

eV 3

0G

eV

40

Ge

V

50

Ge

V

75

Ge

V

10

0G

eV

12

0G

eV

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)

Pio

ns/

(Pro

ton

*GeV

)

GEANT 4 Pi+

GEANT 4 Pi-

MARS15 Pi+

MARS15 Pi-

Total Yield of + and −

Normalisedto unit

beam power

NB: Logarithmic scale!


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Yield of ± and K± in MARS

2.2

Ge

V

3G

eV

4G

eV

20

Ge

V

30

Ge

V

40

Ge

V5

0G

eV

75

Ge

V

10

0G

eV

12

0G

eV

15

Ge

V

10

Ge

V

8G

eV

6G

eV

5G

eV

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 10 100 1000

Proton Energy (GeV)

Pio

ns

or

Ka

on

s p

er

Pro

ton

.Ge

V (

tota

l e

mit

ted

)

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

New


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Angular Distribution: MARS15

2.2

Ge

V

3G

eV

4G

eV

5G

eV

6G

eV

8G

eV

10

Ge

V

15

Ge

V

20

Ge

V

30

Ge

V

40

Ge

V5

0G

eV

75

Ge

V

10

0G

eV

12

0G

eV

0

20

40

60

80

100

120

1 10 100 1000

Proton Energy (GeV)

An

gle

fro

m A

xis

(°)

pi+ 1st Quartile

pi+ Median

pi+ 3rd Quartile

pi- 1st Quartile

pi- Median

pi- 3rd Quartile

What causes the strange kink in the graph between 3GeV and 5GeV?


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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. Your results look quite reasonable, although there is still something to improve in the LANL's low-energy model, especially for pion production. The work is in progress on that. A LAQGSM option coming soon, will give you an alternative possibility to study this intermediate energy region in a different somewhat more consistent way.


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Angular Distribution: +GEANT4

GEANT4 appears to have its own ‘kink’ between 15GeV and 30GeV


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GEANT4 Hadronic “Use Cases”

<3GeV 3-25GeV >25GeV

LHEP GHEISHA inherited from GEANT3

LHEP-BERT Bertini cascade

LHEP-BIC Binary cascade

QGSP (default) Quark-gluon string model

QGSP-BERT

QGSP-BIC

QGSC + chiral invariance


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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)

Pio

n/(

Pro

ton

*En

erg

y(G

eV))

GEANT4 Pi+ LHEP-BIC

GEANT4 Pi- LHEP-BIC

GEANT4 Pi+ QGSP

GEANT4 Pi- QGSP

GEANT4 Pi+ QGSP_BIC

GEANT4 Pi- QGSP_BIC

GEANT4 Pi+ QGSP_BERT

GEANT4 Pi- QGSP_BERT

GEANT4 Pi+ LHEP

GEANT4 Pi- LHEP

GEANT4 Pi+ LHEP-BERT

GEANT4 Pi- LHEP-BERT

GEANT4 Pi+ QGSC

GEANT4 Pi- QGSC

MARS15 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.


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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


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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


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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)

Pio

ns p

er P

roto

n.G

eV (e

st. C

hica

ne/L

inac

)

pi+/(p.GeV)

pi-/(p.GeV)

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


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Phase Rotator Transmission (MARS15)

3GeV

4GeV

8GeV

40G

eV

50

GeV

75G

eV

100G

eV

12

0GeV

30G

eV

6GeV

2.2G

eV

15G

eV

10G

eV

5GeV

20G

eV

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)

Pio

ns p

er P

roto

n.G

eV (e

st. P

hase

Rot

ator

)

pi+/(p.GeV)

pi-/(p.GeV)


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Chicane/Linac Transmission (GEANT4)


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Phase Rotator Transmission (GEANT4)


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Conclusions (energy choice)• While 30GeV may be excellent in terms of

raw pion yields, the pions produced at higher energies are increasingly lost due to their large energy spread

• Optimal ranges appear to be:

According to: For +: For −:

MARS15 5-30GeV 5-10GeV

GEANT4 4-10GeV 8-10GeV


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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– Need HARP data in the range of interest!


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References

• S.J. Brooks, Talk on Target Pion Production Studies at Muon Week, CERN, March 2005; 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


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Energy Deposition in Rod (heat)

• 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)

Po

wer

Dis

sip

atio

n (

Wat

ts,

no

rmal

ised

to

5M

W

inco

min

g b

eam

)


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Total Yield of + and −

2.2G

eV

3GeV 4G

eV

5GeV

6GeV 8G

eV

10G

eV

15G

eV

20G

eV

30G

eV

40G

eV

50G

eV

75G

eV

100G

eV12

0GeV

0

0.2

0.4

0.6

0.8

1

1.2

1 10 100 1000

Proton Energy (GeV)

Pio

ns

per

Pro

ton

.GeV

of

rod

hea

tin

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


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Angular Distribution2.2 GeV

0

50

100

150

200

250

0 20 40 60 80 100 120 140 160 180 200

Off-axis angle (°)

Pio

ns piplus

piminus

6 GeV

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200

Off-axis angle (°)

Pio

ns piplus

piminus

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 (°)

Pio

ns piplus

piminus

120 GeV

0

5000

10000

15000

20000

25000

30000

0 20 40 60 80 100 120 140 160 180 200

Off-axis angle (°)

Pio

ns piplus

piminus

2.2GeV 6GeV

15GeV 120GeV

Backwards+ 18%− 33%

8%12%

8%11%

7%10%


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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


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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

eB

pr

z

T

z

T

B

p

B

cpr

3]T[

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

8


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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


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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


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Simple Cuts

• So, does it?


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Simple Cuts

• So, does it? Roughly.


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Simple Cuts

• So, does it? Roughly.

• If we choose:– max = 45°

– pTmax = 250 MeV/c

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


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Cut Yield of + and −

• Normalised to unit beam power (p.GeV)

3GeV

4G

eV

5G

eV

8GeV

10G

eV

20G

eV

40G

eV

50G

eV

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)

Pio

ns

per

Pro

ton

.GeV

(w

ith

in 4

5°,

pt<

250M

eV/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?


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2.2

Ge

V

3G

eV

4G

eV

5

Ge

V

6G

eV

8G

eV

1

0G

eV

15

Ge

V

20

Ge

V

30

Ge

V

40

Ge

V

50

Ge

V

75

Ge

V

10

0G

eV

1

20

Ge

V

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1 10 100 1000

Proton Energy (GeV)

Cu

t P

ion

s p

er P

roto

n.G

eV(h

eat)

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


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Chicane/Linac Transmission

2

.2G

eV

3

Ge

V

4

Ge

V

5G

eV

6

Ge

V

8

Ge

V

1

5G

eV

2

0G

eV

3

0G

eV

4

0G

eV

5

0G

eV

7

5G

eV

1

00

Ge

V

12

0G

eV

1

0G

eV

0

0.01

0.02

0.03

0.04

0.05

0.06

1 10 100 1000

Proton Energy (GeV)

Ch

ican

e/L

inac

Pio

ns

per

Pro

ton

.GeV

(hea

t)

pi+/(p.GeV_th)

pi-/(p.GeV_th)


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


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Phase Rotator Transmission


2G

eV

3G

eV

4G

eV

5G

eV

6G

eV

8G

eV

15

Ge

V

20

Ge

V

30

Ge

V

40

Ge

V

5

0G

eV

75

Ge

V

10

0G

eV

12

0G

eV

10

Ge

V

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

1 10 100 1000

Proton Energy (GeV)

Ph

ase

Ro

tato

r P

ion

s p

er P

roto

n.G

eV(h

eat)

pi+/(p.GeV_th)

pi-/(p.GeV_th)


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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


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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


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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 0.009

0

0.2

0.4

0.6

0.8

1

1.2

pi+/(p.GeV)

pi-/(p.GeV)

Area fraction

30 GeV

2.2 GeV


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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!


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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


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Variation of Rod Radius

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


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• This is not physical for the smallest rods as a beta focus could not be maintained

Emittance 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


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

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

2

2

z

Teff eB

prr


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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)

Pio

n Y

ield

pi+/(p.GeV)

pi-/(p.GeV)

30GeV

2.2GeV


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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)

Pio

n Y

ield

Wit

hin

45

° o

f A

xis

an

d T

ran

sv

ers

e M

om

en

tum

Be

low

25

0M

eV

/c

pi+/(p.GeV)

pi-/(p.GeV)

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


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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)


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Note on Rod Length

• Doubling the rod length would:– Double the heat to dissipate– Also double the pions emitted per proton– Increase the longitudinal emittance

• The pions already have a timespread of RMS 1ns coming from the proton bunch

• The extra length of rod would add to this the length divided by c


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Conclusion

• Current results indicate 6-10GeV is an optimal proton driver energy for current front-ends– If we can accept larger energy spreads, can go to a

higher energy and get more pions

• 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


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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

Computed Pion Yields from a Tantalum Rod Target

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