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
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Proton Driver Energy and Pulse Structure
Implications(An overall context)
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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.
Stephen BrooksScoping Study meeting, September
2005
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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
Stephen BrooksScoping Study meeting, September
2005
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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
Stephen BrooksScoping Study meeting, September
2005
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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
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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
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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
JPARC changed their mind? 40JPARC final 50
75100
FNAL injector/NuMI 120
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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)
Stephen Brooks, Kenny WalaronScoping Study meeting, September 2005
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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
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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
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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.
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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
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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)
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.
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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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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
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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)
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
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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
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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)
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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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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:
22
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)
Pion
Yie
ld
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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Conclusions – energy choice• 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– HARP data will cover 3-15GeV, but when?
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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
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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!
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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
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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
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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 (°)
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%
Stephen Brooks, Kenny WalaronScoping Study meeting, September 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, Kenny WalaronScoping Study meeting, September 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
eBpr
z
T
z
T
Bp
Bcpr
3]T[)/10](MeV/c[]cm[
8
Stephen Brooks, Kenny WalaronScoping Study meeting, September 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, Kenny WalaronScoping Study meeting, September 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
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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°– pT
max = 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
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?
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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
Stephen Brooks, Kenny WalaronScoping Study meeting, September 2005
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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)
• Normalised to unit rod heating
6-10GeV now looks good enough if we are limited by target heating
Stephen Brooks, Kenny WalaronScoping Study meeting, September 2005
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Phase Rotator Transmission
• Normalised to unit rod heating
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)
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Stephen Brooks, Kenny WalaronScoping Study meeting, September 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
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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 0.0090
0.2
0.4
0.6
0.8
1
1.2
pi+/(p.GeV)
pi-/(p.GeV)
Area fraction
30 GeV
2.2 GeV
Stephen Brooks, Kenny WalaronScoping Study meeting, September 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!
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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
• 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
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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)
Pion
Yie
ld W
ithin
45°
of A
xis
and
Tran
sver
se M
omen
tum
Bel
ow 2
50M
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, Kenny WalaronScoping Study meeting, September 2005
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