pion yields from a tantalum rod target using mars15
DESCRIPTION
m. Pion Yields from a Tantalum Rod Target using MARS15. Comparisons across proton driver energies and other parameters. Contents. Problem and parameters Variation of proton energy Total pion yield Simple cuts Probability map “cuts” from tracking Investigation of the hole - PowerPoint PPT PresentationTRANSCRIPT
Stephen Brooks / RAL / March 2005
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Pion Yields from a Tantalum Rod Target using MARS15
Comparisons across proton driver energies and other parameters
Stephen Brooks / RAL / March 2005
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Contents
• Problem and parameters
• Variation of proton energy– Total pion yield– Simple cuts– Probability map “cuts” from tracking
• Investigation of the hole
• Variation of rod radius
• Notes on effect of rod length and tilt angle
Stephen Brooks / RAL / March 2005
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Basic Setup
• Pions counted at rod surface
• B-field ignored within rod (for now)
• Proton beam assumed parallel– Circular parabolic distribution, rod radius
• Rod is not tilted
20cm
1cmSolid Tantalum
Protons
Pions
Stephen Brooks / RAL / March 2005
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Possible Proton EnergiesProton Driver GeVSPL 2.2
34
RAL green-field study 5RAL/ISIS 5MW 6RAL/ISIS 1MW, FNAL linac 8
10RAL/ISR 15
20RAL/PS, JPARC initial 30
40JPARC final 50
75100
FNAL injector/NuMI 120
Stephen Brooks / RAL / March 2005
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Total Yield of + and −
2.2G
eV
3GeV
4GeV
5GeV 6G
eV 8GeV
10G
eV 15G
eV
20G
eV
30G
eV
40G
eV
50G
eV
75G
eV
100G
eV12
0GeV
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
1 10 100 1000
Proton Energy (GeV)
Pio
ns
per
Pro
ton
.GeV
(to
tal
emit
ted
)
pi+/(p.GeV)
pi-/(p.GeV)
• Normalised to unit beam power (p.GeV)
NB: Logarithmic scale!
66% more + at 30GeV than 2.2GeV
57% more − at 30GeV than 2.2GeV
Stephen Brooks / RAL / March 2005
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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
)
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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%
Stephen Brooks / RAL / March 2005
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Angular Distribution
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?
Stephen Brooks / RAL / March 2005
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Some Artifacts?
• MARS15 uses two hadron production models:– 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.
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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Summary 1
• So far, it appears that a 10-30GeV proton beam:– Produces ~60% more pions per p.GeV– …in a more focussed angular distribution– …with ~40% less rod heating
…than the low-energy option
• BUT: the useful yield is crucially dependent on the capture system
With certain provisos on the accuracy of MARS’s pion model over the transition region
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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Simple Cuts
• So, does it?
Stephen Brooks / RAL / March 2005
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Simple Cuts
• So, does it? Roughly.
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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?
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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Tracking through Two Designs
• Possible non-cooling front end– Uses bunch compression chicane after decay
channel– Then an 88MHz muon linac to 400±100MeV
• RF phase-rotation system– Continues the linear solenoid channel– 31.4MHz cavities reduce the energy spread– Goal is 180±23MeV for cooling ring injection
Stephen Brooks / RAL / March 2005
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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)
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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Probability Grids
• Can bin the plots into 30MeV/c squares and work out the transmission probability within each
• These can then be used to estimate the transmission quickly from MARS output datasets at various proton energies
Stephen Brooks / RAL / March 2005
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Chicane/Linac Transmission
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
1 10 100 1000
Proton Energy (GeV)
Pio
ns
per
Pro
ton
.GeV
(es
t. C
hic
ane/
Lin
ac)
pi+/(p.GeV)
pi-/(p.GeV)
Energy dependency is much flatter now we are selecting pions by energy range
• Normalised to unit beam power (p.GeV)
Stephen Brooks / RAL / March 2005
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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)
• Normalised to unit rod heating
6-10GeV now looks good enough if we are limited by target heating
Stephen Brooks / RAL / March 2005
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Phase Rotator Transmission
• Normalised to unit beam power (p.GeV)
3G
eV
4G
eV
8G
eV
40
GeV
50
GeV
75
GeV
10
0GeV
12
0GeV
30
GeV
6G
eV
2.
2GeV
15
GeV
10
GeV
5G
eV
20
GeV
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
per
Pro
ton
.GeV
(es
t. P
has
e R
ota
tor)
pi+/(p.GeV)
pi-/(p.GeV)
Stephen Brooks / RAL / March 2005
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Phase Rotator Transmission
• Normalised to unit rod heating
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)
Stephen Brooks / RAL / March 2005
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Summary 2
• While 30GeV may be excellent in terms of raw pion yields, the pions produced are increasingly lost due to:– Large transverse momenta (above 10-20GeV)– A high energy spread, outside the acceptance
of bunching systems (above 6-10GeV)
• This work suggests the optimal energy is around 6-10GeV, providing a 50% yield improvement over 2.2GeV With certain provisos on the
accuracy of MARS’s pion model over the transition region
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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!
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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Variation of Rod Radius
• We will change the incoming beam size with the rod size and observe the yields
Stephen Brooks / RAL / March 2005
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Variation of Rod Radius
• We will change the incoming beam size with the rod size and observe the yields
• 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
Stephen Brooks / RAL / March 2005
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Variation of Rod Radius
• We will change the incoming beam size with the rod size and observe the yields
• 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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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)
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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
Stephen Brooks / RAL / March 2005
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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