# Presentation: 662806

## Computed Pion Yields from a Tantalum Rod Target

- Comparing MARS15 and GEANT4 across proton energies

## Proton Driver Energy and Pulse Structure Implications

- (An overall context)

## Proton Source Parameters

- Proton energy
- Bunch length
- Bunch spacing
- Pulse length
- = Number of bunches × bunch spacing
- Pulse spacing
- = 1/(Rep. rate)
- Assume 4-5MW fixed mean beam power.

## Upstream Correlations

|  |  |
| --- | --- |
| RF voltage in bunch compression ring vs. space charge |  |
| Bunching ring RF frequency, bucket filling pattern | ...or separate extraction strategy |
| Bunching ring circumference minus extraction gap |  |
| Repetition rate of linac or slowest synchrotron (possibly doubled up) |  |

- Linacs

- Synchrotrons

- FFAGs

- 2GeV

- 5GeV

- 10GeV

- 20GeV

- 50GeV

## Target Issues

| Similar? |
| --- |
|  |
| “Pump-probe” effects due to liquid cavitation may appear on this timescale |
| Faster rep. rate needs a high jet velocity |

| Energy deposition minimal around 8GeV |
| --- |
| Time scale too short to have an effect |
| Sufficient spacing can split up thermal shocks |
| ...so shock is divided by the number of bunches |
| Low rep. rate means a larger shock each time |

- Solids

- Liquids

## Downstream Correlations

| 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 |

- Capture

- Acceleration

- Storage ring

- Phase rotation

- Cooling

## 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

## 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)

## Benchmark Problem

- Pions counted at rod surface
**B**-field ignored within rod (negligible effect)
- Proton beam assumed parallel
- Circular parabolic distribution, rod radius

- 20cm

- 1cm

- Solid Tantalum

- Protons

- Pions

## Possible Proton Energies

| Proton Driver | GeV | RAL Studies |
| --- | --- | --- |
| Old SPL energy | 2.2 |  |
|  | 3 | 5MW ISIS RCS 1 |
| [New SPL energy 3.5GeV] | 4 |  |
|  | 5 | 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] | 20 |  |
| JPARC initial | 30 | PS replacement |
| JPARC changed their mind? | 40 |  |
| JPARC final | 50 |  |
|  | 75 |  |
|  | 100 |  |
| FNAL injector/NuMI | 120 |  |

## Total Yield of + and −

- Total Yield of + and −

- Normalised
- to 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)

## Yield of ± and K± in MARS

- No surprises in SPL region
- Statistical errors small
- 1 kaon  1.06 muons

**Finer **
**sampling**

## Angular Distribution: MARS15

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

## 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.

## Angular Distribution: +GEANT4

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

## 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 |

## Total Yield of + and −: +GEANT4

## 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.

## 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

## 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

## Fate Plot for Chicane/Linac

| 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 |

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

## 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 |

## Probability Grids

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

- Chicane/Linac

- Phase Rotation

## 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

## Phase Rotator Transmission

- 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

## Phase Rotator Transmission (zooming into MARS15)

- Doubled lines give some idea of stat. errors

- Somewhat odd
- behaviour for
- pi+ < 3GeV

## Chicane/Linac Transmission (MARS15)

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

## Chicane/Linac Transmission (MARS15)

- But normalising to unit rod heating gives a sharper peak

## Energy (heat) Deposition in Rod

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

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

## Variation of Rod Radius

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

## 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:

## Total Yield with Rod Radius

- 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

## 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)

## Conclusions – energy choice

- Optimal ranges appear to be:

| According to: | For +: | For −: |
| --- | --- | --- |
| MARS15 | 5-30GeV | 5-10GeV |
| GEANT4 | 4-10GeV | 8-10GeV |

## 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?

## 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

## 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!

## References

- S.J. Brooks, Talk given at NuFact’05: *Comparing Pion Production in MARS15 and GEANT4*; _[http://stephenbrooks.org/ral/report/](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](http://hepunx.rl.ac.uk/uknf/wp3/uknfnote_30.pdf)_

- Now updated

## Slide 39

## Total Yield of + and −

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

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

## Angular Distribution

- 2.2GeV

- 6GeV

- 15GeV

- 120GeV

- Backwards
- + 18%
- − 33%

- 8%
- 12%

- 8%
- 11%

- 7%
- 10%

## 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

## 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:

## Simple Cuts

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

- pL

- pT

- Larmor radius = 1⁄2 aperture limit

- Angular limit (eliminate backwards/sideways pions)

- Pions in this region transmitted

- max

- pTmax

## 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

## Simple Cuts

- So, does it?

## Simple Cuts

- So, does it?  Roughly.

## 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

## Cut Yield of + and −

- Normalised to unit beam power (p.GeV)

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

## Cut Yield of + and −

- Cut Yield of + and −

- Normalised to unit rod heating

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

## Chicane/Linac Transmission

- Normalised to unit rod heating

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

## Phase Rotator Transmission

- Normalised to unit rod heating

## Slide 53

## 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

## 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

## Yield Decreases with Hole

- 30 GeV

- 2.2 GeV

## Yield per Rod Area with Hole

- 30 GeV

- 2.2 GeV

- This actually decreases at the largest hole size!

## 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

## 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 |

## Cut Yield with Rod Radius

- 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

## 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