Computed Pion Yields from a
Tantalum Rod Target
Comparing MARS15 and
GEANT4 across proton energies
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
1 of 38
Proton Driver Energy and Pulse
Structure Implications
(An overall context)
Stephen Brooks
Scoping Study meeting, September 2005
2 of 38
Proton Source Parameters
I.
II.
III.
IV.
Proton energy
Bunch length
Bunch spacing
Pulse length
= Number of bunches × bunch spacing
V.
Pulse spacing
= 1/(Rep. rate)
Assume 4-5MW fixed mean beam power.
Stephen Brooks
Scoping Study meeting, September 2005
3 of 38
Upstream Correlations
2GeV
Linacs
5GeV
10GeV
20GeV
50GeV
Synchrotrons
FFAGs
RF voltage in bunch compression ring vs.
space charge
Bunching ring RF frequency,
…or separate
bucket filling pattern
extraction
Bunching ring circumference strategy
minus extraction gap
Repetition rate of linac or slowest
synchrotron (possibly doubled up)
Stephen Brooks
Scoping Study meeting, September 2005
4 of 38
Target Issues
Solids
Liquids
Energy deposition
minimal around 8GeV
Similar?
Time scale too short to
have an effect
Sufficient spacing can
split up thermal shocks
…so shock is divided by
the number of bunches
“Pump-probe” effects
due to liquid cavitation
may appear on this
timescale
Low rep. rate means a
larger shock each time
Faster rep. rate needs
a high jet velocity
Stephen Brooks
Scoping Study meeting, September 2005
5 of 38
Downstream Correlations
Capture
Phase rotation
Cooling
Acceleration
Storage ring
Pion momentum range increases with
energy, becomes more difficult to capture
Long bunches increase longitudinal
emittance, phase rotation becomes harder
Avoid ‘traffic jams’ in the longer-duration
rings (or provide sufficient circumference)
If bunches stored behind each other in
storage ring, need enough circumference
Low rep. rate means high peak beam
loading; difficult to charge RF cavities
Stephen Brooks
Scoping Study meeting, September 2005
6 of 38
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
Stephen Brooks
Scoping Study meeting, September 2005
7 of 38
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)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
8 of 38
Benchmark Problem
Protons
1cm
Pions
Solid Tantalum
20cm
• Pions counted at rod surface
• B-field ignored within rod (negligible effect)
• Proton beam assumed parallel
– Circular parabolic distribution, rod radius
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
9 of 38
Possible Proton Energies
Proton Driver
Old SPL energy
[New SPL energy 3.5GeV]
FNAL linac (driver study 2)
[FNAL driver study 1, 16GeV]
[BNL/AGS upgrade, 24GeV]
JPARC initial
JPARC changed their mind?
JPARC final
FNAL injector/NuMI
GeV
2.2
3
4
5
6
8
10
15
20
30
40
50
75
100
120
RAL Studies
5MW ISIS RCS 1
Green-field synch.
5MW ISIS RCS 2
RCS 2 low rep. rate
4MW FFAG
ISR tunnel synch.
PS replacement
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
10 of 38
Total Yield of π+ and π−
100GeV
120GeV
40GeV
50GeV
30GeV
20GeV
15GeV
5GeV
6GeV
75GeV
3GeV
0.1000
2GeV
Pions/(Proton*GeV)
0.1200
4GeV
0.1400
8GeV
10GeV
0.1600
Normalised
to unit
beam power
GEANT 4 Pi+
GEANT 4 PiMARS15 Pi+
MARS15 Pi-
0.0800
These are raw yields (on a tantalum
rod) using MARS15 and GEANT4.
0.0600
0.0400
Better to include the acceptance of
the next part of the front end…
(next)
0.0200
0.0000
1
10
100
1000
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
11 of 38
Yield of π± and K± in MARS
4GeV
30GeV
15GeV
20GeV
75GeV
pi+/(p.GeV)
pi-/(p.GeV)
100GeV
120GeV
0.06
3GeV
0.08
40GeV
50GeV
5GeV
6GeV
0.1
8GeV
10GeV
Finer
sampling
0.12
2.2GeV
Pions or Kaons per Proton.GeV (total emitted)
0.14
pi+/(p.GeV)
pi-/(p.GeV)
K+/(p.GeV)
K-/(p.GeV)
•No surprises in SPL region
•Statistical errors small
•1 kaon Æ 1.06 muons
0.04
0.02
0
1
10
100
1000
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
12 of 38
Angular Distribution: MARS15
pi+ 1st Quartile
pi+ Median
pi+ 3rd Quartile
pi- 1st Quartile
pi- Median
pi- 3rd Quartile
100GeV
120GeV
40GeV
50GeV
15GeV
30GeV
60
20GeV
8GeV
10GeV
5GeV
6GeV
Angle from Axis (°)
80
75GeV
4GeV
100
MARS has a
strange kink in
the graph
between 3GeV
and 5GeV
3GeV
2.2GeV
120
40
20
0
1
10
100
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
1000
13 of 38
MARS15 Uses Two Models
<3GeV
MARS15
CEM2003
3-5 >5GeV
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.
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
14 of 38
Angular Distribution: +GEANT4
GEANT4 has its
own ‘kink’ between
15GeV and 30GeV
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
15 of 38
GEANT4 Hadronic “Use Cases”
<3GeV
3-25GeV
>25GeV
LHEP
GHEISHA inherited from GEANT3
LHEP-BERT
Bertini cascade
LHEP-BIC
Binary cascade
Quark-gluon string
model
QGSP (default)
QGSP-BERT
QGSP-BIC
+ chiral invariance
QGSC
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
16 of 38
Total Yield of π+ and π−: +GEANT4
0.25
0.20
GEANT4 Pi+ LHEP-BIC
GEANT4 Pi- LHEP-BIC
Pion/(Proton*Energy(GeV))
GEANT4 Pi+ QGSP
GEANT4 Pi- QGSP
GEANT4 Pi+ QGSP_BIC
0.15
GEANT4 Pi- QGSP_BIC
GEANT4 Pi+ QGSP_BERT
GEANT4 Pi- QGSP_BERT
GEANT4 Pi+ LHEP
GEANT4 Pi- LHEP
GEANT4 Pi+ LHEP-BERT
0.10
GEANT4 Pi- LHEP-BERT
GEANT4 Pi+ QGSC
GEANT4 Pi- QGSC
MARS15 Pi+
MARS15 Pi-
0.05
0.00
0
1
2
3
4
5
6
7
8
9
10
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
17 of 38
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.
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
18 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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
19 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 Æ muon decays and finite source
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
20 of 38
Fate Plot for Chicane/Linac
(Pion distribution used here is from
a 2.2GeV proton beam)
Magenta
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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
21 of 38
Fate Plot for Phase Rotation
Magenta
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, Kenny Walaron
Scoping Study meeting, September 2005
22 of 38
Probability Grids
• Can bin the plots into 30MeV/c squares
and work out the transmission probability
within each
Chicane/Linac
Phase Rotation
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
23 of 38
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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
24 of 38
0.004
75GeV
40GeV
100GeV
120GeV
0.006
50GeV
0.008
Optimum moves
down because
MARS pi+
higher energies
MARS piproduce pions with
GEANT pi+
uncapturably-high
GEANT pimomenta
Transmission from
GEANT4 is a lot
higher (×2) because
it tends to forwardfocus the pions a lot
more than MARS15
30GeV
0.01
20GeV
0.012
15GeV
4GeV
0.014
3GeV
0.016
2.2GeV
Estimated Capture of mu±/(p.GeV)
0.018
5GeV
6GeV
0.02
8GeV
10GeV
Phase Rotator Transmission
Energy dependency is much flatter now
we are selecting pions by energy range
0.002
0
1
10
100
1000
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
25 of 38
100GeV
120GeV
50GeV
20GeV
30GeV
40GeV
75GeV
0.005
Doubled lines give some
idea of stat. errors
3GeV
0.006
4GeV
0.007
15GeV
5GeV
6GeV
0.008
2.2GeV
Pions per Proton.GeV (est. Phase Rotator)
0.009
8GeV
10GeV
Phase Rotator Transmission
(zooming into MARS15)
pi+/(p.GeV)
pi-/(p.GeV)
pi+/(p.GeV)
0.004
Somewhat odd
behaviour for
pi+ < 3GeV
0.003
0.002
pi-/(p.GeV)
0.001
0
1
10
100
1000
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
26 of 38
100GeV
120GeV
30GeV
20GeV
40GeV
50GeV
75GeV
0.004
15GeV
5GeV
6GeV
4GeV
0.005
3GeV
0.006
2.2GeV
Pions per Proton.GeV (est. Chicane/Linac)
0.007
8GeV
10GeV
Chicane/Linac Transmission
(MARS15)
pi+/(p.GeV)
pi-/(p.GeV)
0.003
This other front-end gave very
similarly-shaped plots, at
different yield magnitudes
0.002
0.001
0
1
10
100
1000
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
27 of 38
Chicane/Linac Transmission
(MARS15)
pi+/(p.GeV_th)
100GeV
120GeV
75GeV
30GeV
20GeV
But normalising to
unit rod heating gives
a sharper peak
40GeV
50GeV
4GeV
0.03
3GeV
0.04
15GeV
8GeV
10GeV
5GeV
6GeV
0.05
2.2GeV
Chicane/Linac Pions per Proton.GeV(heat)
0.06
pi-/(p.GeV_th)
0.02
0.01
0
1
10
100
1000
Proton Energy (GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
28 of 38
100GeV
120GeV
75GeV
40GeV
50GeV
30GeV
20GeV
800000
15GeV
1000000
8GeV
10GeV
4GeV
1200000
5GeV
6GeV
Power Dissipation (Watts, normalised to 5MW
incoming beam)
1400000
3GeV
2.2GeV
Energy (heat) Deposition in Rod
600000
If we become limited by the amount of target
heating, best energy will be pushed towards
this 5-20GeV minimum (calculated with
MARS15)
400000
200000
0
1
10
100
1000
Proton Energy (GeV)
• Scaled for 5MW total beam power; the rest is
kinetic energy of secondaries
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
29 of 38
Variation of Rod Radius
• We will change the incoming beam size
with the rod size and observe the yields
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
30 of 38
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:
⎛ pT
reff = r + ⎜⎜
⎝ eBz
2
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
⎞
⎟⎟
⎠
2
31 of 38
Total Yield with Rod Radius
0.16
Multiple scattering decreases
yield at r = 5mm and below
0.14
30GeV
0.12
Rod heating per unit
volume and hence
shock amplitude
decreases as 1/r2 !
Pion Yield
0.1
0.08
2.2GeV
0.06
Fall-off due to
reabsorption is fairly
shallow with radius
pi+/(p.GeV)
pi-/(p.GeV)
0.04
0.02
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Rod Radius (cm)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
32 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)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
33 of 38
Conclusions – energy choice
• Optimal ranges appear to be:
According to: For π+:
For π−:
MARS15
5-30GeV
5-10GeV
GEANT4
4-10GeV
8-10GeV
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
34 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?
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
35 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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
36 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!
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
37 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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
38 of 38
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
39 of 38
Total Yield of π+ and π−
From a purely target point of view,
‘optimum’ moves to 10-15GeV
pi-/(p.GeV_th)
75GeV
40GeV
50GeV
15GeV
30GeV
pi+/(p.GeV_th)
100GeV
120GeV
0.2
3GeV
0.4
4GeV
0.6
20GeV
5GeV
6GeV
0.8
8GeV
10GeV
1
2.2GeV
Pions per Proton.GeV of rod heating
1.2
0
1
10
100
1000
Proton Energy (GeV)
• Normalised to unit rod heating (p.GeV = 1.6×10-10 J)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
40 of 38
Angular Distribution
2.2GeV
6GeV
2.2 GeV
6 GeV
1400
250
Pions
150
1200
8%
12%
1000
800
piplus
piminus
Pions
Backwards
π+ 18%
π− 33%
200
piplus
piminus
600
100
400
50
200
0
0
0
20
40
60
80
100
120
140
160
180
0
200
20
40
60
80
100
120
140
160
180
200
Off-axis angle (°)
Off-axis angle (°)
15GeV
120GeV
15 GeV
120 GeV
4500
30000
4000
2500
7%
10%
20000
piplus
piminus
2000
1500
Pions
3000
Pions
25000
8%
11%
3500
15000
piplus
piminus
10000
1000
5000
500
0
0
0
20
40
60
80
100
120
140
160
180
200
0
20
40
60
Off-axis angle (°)
80
100
120
140
160
180
200
Off-axis angle (°)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
41 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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
42 of 38
Simple Cuts
• It turns out geometric angle is a badlynormalised measure of beam divergence
• Transverse momentum and the magnetic
field dictate the Larmor radius in the
solenoidal decay channel:
pT
r=
eBz
pT [MeV/c](108 / c) pT
≈
r[cm] =
Bz [ T ]
3 Bz
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
43 of 38
Simple Cuts
• Acceptance of the decay channel in
(pL,pT)-space should look roughly like this:
pT
Larmor radius = ½ aperture limit
pTmax
Pions in this region
transmitted
θmax
Angular limit (eliminate backwards/sideways pions)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
pL
44 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 Æ muon decays and finite source
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
45 of 38
Simple Cuts
• So, does it?
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
46 of 38
Simple Cuts
• So, does it? Roughly.
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
47 of 38
Simple Cuts
• So, does it? Roughly.
• If we choose:
– θmax = 45°
– pTmax = 250 MeV/c
• Now we can re-draw the pion yield graphs
for this subset of the pions
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
48 of 38
Cut Yield of π+ and π−
0.015
0.01
0.005
3GeV
0.02
pi+/(p.GeV)
100GeV
120GeV
75GeV
30GeV
20GeV
4GeV
0.025
40GeV
50GeV
0.03
15GeV
5GeV
6GeV
0.035
8GeV
10GeV
0.04
2.2GeV
Pions per Proton.GeV (within 45°, pt<250MeV/c)
0.045
pi-/(p.GeV)
High energy yield now appears a
factor of 2 over low energy, but
how much of that kink is real?
0
1
10
100
1000
Proton Energy (GeV)
• Normalised to unit beam power (p.GeV)
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
49 of 38
Cut Yield of π+ and π−
0.35
This cut seems to have moved this
optimum down slightly, to 8-10GeV
75GeV
pi-/(p.GeV_th)
100GeV
120GeV
0.05
pi+/(p.GeV_th)
20GeV
15GeV
3GeV
4GeV
0.1
40GeV
50GeV
0.15
30GeV
5GeV
0.2
8GeV
10GeV
6GeV
0.25
2.2GeV
Cut Pions per Proton.GeV(heat)
0.3
0
1
10
100
1000
Proton Energy (GeV)
• Normalised to unit rod heating
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
50 of 38
Chicane/Linac Transmission
pi+/(p.GeV_th)
100GeV
120GeV
75GeV
20GeV
30GeV
40GeV
50GeV
4GeV
0.03
3GeV
0.04
15GeV
8GeV
10GeV
5GeV
6GeV
0.05
2.2GeV
Chicane/Linac Pions per Proton.GeV(heat)
0.06
pi-/(p.GeV_th)
0.02
6-10GeV now looks good enough if we
are limited by target heating
0.01
0
1
10
100
1000
Proton Energy (GeV)
• Normalised to unit rod heating
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
51 of 38
75GeV
100GeV
120GeV
0.03
3GeV
0.04
20GeV
30GeV
40GeV
50GeV
4GeV
0.05
15GeV
5GeV
6GeV
0.06
2GeV
Phase Rotator Pions per Proton.GeV(heat)
0.07
8GeV
10GeV
Phase Rotator Transmission
pi+/(p.GeV_th)
pi-/(p.GeV_th)
0.02
0.01
0
1
10
100
1000
Proton Energy (GeV)
• Normalised to unit rod heating
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
52 of 38
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
53 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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
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
• 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, Kenny Walaron
Scoping Study meeting, September 2005
55 of 38
Yield Decreases with Hole
0.14
1.2
30 GeV
0.12
1
0.1
0.8
2.2 GeV
0.08
pi+/(p.GeV)
0.6
pi-/(p.GeV)
Area fraction
0.06
0.4
0.04
0.2
0.02
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
0
0.009
56 of 38
Yield per Rod Area with Hole
0.14
30 GeV
0.12
0.1
2.2 GeV
0.08
pi+ eff.
pi- eff.
0.06
0.04
This actually decreases at the largest hole size!
0.02
0
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
0.008
0.009
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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 crosssectional shapes, multiple scattering of
protons in the tantalum is noticeable
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 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 εx
Focus radius
25 mm.mrad
10mm
extracted from
5mm
proton machine
2.5mm
2mm
Divergence
Focus length
2.5 mrad
4m
5 mrad
1m
10 mrad
25cm
12.5 mrad
16cm
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
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Cut Yield with Rod Radius
Pion Yield Within 45° of Axis and Transverse Momentum Below 250MeV/c
0.05
0.045
30GeV
0.04
Rod heating per unit
volume and hence
shock amplitude
decreases as 1/r2 !
0.035
Multiple scattering decreases
yield at r = 5mm and below
0.03
0.025
2.2GeV
0.02
Fall-off due to
reabsorption is fairly
shallow with radius
pi+/(p.GeV)
pi-/(p.GeV)
0.015
0.01
0.005
0
0
0.5
1
1.5
2
Rod Radius (cm)
2.5
3
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
3.5
4
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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
Stephen Brooks, Kenny Walaron
Scoping Study meeting, September 2005
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