# Presentation: 691770

## Neutrino Factory Target Yield Considerations

- _[Click to view with less target stuff](slide27.xml)_

## Intermediate Z Element Needed

- Previously, results for Ta, Hg and C
- C behaviour was very different from others
- C is in P2, the others are in P6

- C

- Ta

- Hg

## Compare: HARP Elements

- P3: Al
- P4: Cu
- P5: Sn

- Hg

- Be

- C

- Al

- Cu

- Sn

- Ta

- Pb

- Want to compare with data
- Sensible target element
- High melting point, density

## Period 2 Elements

- Carbon clearly wins
- Boron and beryllium not so bad
- HARP has Be and C
- None of these densities are very high: require long targets

## Period 3 Elements

- Silicon looks best
- Everything else has a useless melting point
- HARP has aluminium
- Densities no higher than before
- I think P3 is a non-starter

## Period 4 Elements

- Transition metal melting points and densities are better
- HARP’s Cu has high density and moderate melting point
- Also about half-way (logarithmically) between C and Ta/Hg

## Period 5 Elements

- Melting points and densities continue to increase
- HARP’s tin is not good for our target!
- Plenty of workable choices in transition block, if needed

## Period 6 Elements

- Transition metals here have the highest values in the table
- Hence the choice of Ta in the first place
- Hg is obviously a special case

## Period 7 Elements

- Thorium  uranium are OK for very-high-Z if needed
- Most of the rest are radioactive

## Intermediate Z Element Needed

- Hg

- Be

- C

- Al

- Cu

- Sn

- Ta

- Pb

- Previously, results for Ta, Hg and C
- C behaviour was very different from others
- Copper was chosen to represent P4

- Cu

## Scaling of Cylinder Length

- Proportional to hadronic interaction length

| Element | Interaction length (cm) | Equivalent to 20cm Ta |
| --- | --- | --- |
| Ta | 11.18 | 20cm |
| Hg | 13.95 | 25cm |
| C | 36.92 | 66cm |
| Cu | 15.16 | 27cm |
| W | 9.54 | 17cm |

- Data from _[http://](http://www.slac.stanford.edu/comp/physics/matprop.html)__[www.slac.stanford.edu/comp/physics/matprop.html](http://www.slac.stanford.edu/comp/physics/matprop.html)_

- Harold Kirk found ~60cm is optimal

## Summary Statistics (±/p.GeV)

- “Total Pion Yield” = all pions (of one sign) emitted from the *rod surface*
- “Captured Yield” = these weighted by survival probability in (pL,pT) space
- Survival end of (UK) phase rotation into energy band 180±23MeV of cooling ring
- No accounting for finite rod size (e.g. long)
- No accounting for reabsorption effects (later)

## Decay modes of K+ from PDG

- For E>3GeV, kaons add to the production
- “A kaon is equivalent to ~1.06 pions”

| Mode | Fraction | (error) |  and  | Expected |
| --- | --- | --- | --- | --- |
| + | 63.39% | 0.18% | 1 | 0.6339 |
| 0e+e | 4.93% | 0.07% | 0 | 0 |
| 0+ | 3.30% | 0.06% | 1 | 0.033 |
| +0 | 21.03% | 0.13% | 1 | 0.2103 |
| +00 | 1.76% | 0.02% | 1 | 0.01757 |
| ++− | 5.59% | 0.05% | 3 | 0.1677 |
|  | Mean eventual muons: |  |  | 1.06247 |

## Results: Total Pion Yield

- Copper behaviour is somewhere between the high- and low-Z elements, as expected

## Results: Captured Yield

- Copper beats everything at 10GeV!
- Hg and Ta almost indistinguishable

- Carbon low energy behaviour is interesting, so let’s extend the scale...

## Results: Captured Yield

## Observations 

- The carbon peak at 1GeV is huge, but can you build a proton driver at that energy?
- Low energy behaviour is increasingly asymmetrical in sign for low Z
- Proton charge manifests excess of +
- Carbon at 5GeV still apparently beats everything else
- But ignoring the increased cylinder length, reabsorption and longitudinal emittance

## Comparison with FS2, ICOOL

- Harold Kirk’s results for carbon

- ...are a similar shape to my results, with a scaling due to using more efficient RF capture

## Figure of Merit: ++− or +×−?

- For the muon collider they should multiply
- For the neutrino factory, it depends on the physics goals
- Experiments that test matter-antimatter asymmetry would require both signs
- Detectors may be more sensitive to one sign than the other, giving an asymmetric function
- I will graph both + and × cases for interest

## Captured Yield Sum

- Optima at 5GeV for low and intermediate Z; flatter ones at 8GeV for high Z.
- Hg winning very slightly over Ta.

## Captured Yield Product

- This is topologically the same apart from that the 5GeV carbon peak is now nearly as high as the 1GeV one.

## Pion Reabsorption (future work)

- It might be worth re-running MARS with a 20T field in the solenoid bore and collecting the pions at the endplane, to include this effect
- Could be significant in long, low-Z targets
- A rough model for manual tracking can also be obtained by extracting an “absorption length” for pions in material

## Absorption Length Estimate

- MARS15 was run for pions entering a block of tantalum, surviving particles logged at various Z-planes and an exponential decay fit to the data

| Energy | + length | − length |
| --- | --- | --- |
| 100MeV | 82mm | 65mm |
| 300MeV | 107mm | 106mm |
| 1GeV | 139mm | 159mm |

## Feasibility of “1ns” Bunches

- No way

- Adiabatically

- With difficulty

## Higher Energies than 10GeV

- Going from 10GeV to 30GeV
- Loses 10-12% yield with a high-Z target
- Assuming fixed power (unrealistic?)
- Re-optimising the front end for another energy tends to give small gains of order 3%
- Going from 10GeV to 50GeV
- Loses 25-30% yield
- This cannot be ignored so easily

## Summary Statistics (±/p.GeV)

- “Total Pion Yield” = all pions (of one sign) emitted from the *rod surface*
- “Captured Yield” = these weighted by survival probability in (pL,pT) space
- Survival end of (UK) phase rotation into energy band 180±23MeV of cooling ring
- No accounting for finite rod size (e.g. long)
- No accounting for reabsorption effects (later)

## Results: Total Pion Yield

- Copper behaviour is somewhere between the high- and low-Z elements, as expected

## Results: Captured Yield

- Copper beats everything at 10GeV!
- Hg and Ta almost indistinguishable

- Carbon low energy behaviour is interesting, so let’s extend the scale...

## Results: Captured Yield

## Observations 

- The carbon peak at 1GeV is huge, but can you build a proton driver at that energy?
- Low energy behaviour is increasingly asymmetrical in sign for low Z
- Proton charge manifests excess of +
- Carbon at 5GeV still apparently beats everything else
- But ignoring the increased cylinder length, reabsorption and longitudinal emittance

## Figure of Merit: ++− or +×−?

- For the muon collider they should multiply
- For the neutrino factory, it depends on the physics goals
- Experiments that test matter-antimatter asymmetry would require both signs
- Detectors may be more sensitive to one sign than the other, giving an asymmetric function
- I will graph both + and × cases for interest

## Captured Yield Sum

- Optima at 5GeV for low and intermediate Z; flatter ones at 8GeV for high Z.
- Hg winning very slightly over Ta.

## Captured Yield Product

- This is topologically the same apart from that the 5GeV carbon peak is now nearly as high as the 1GeV one.

## Feasibility of “1ns” Bunches

- No way

- Adiabatically

- With difficulty

## Higher Energies than 10GeV

- Going from 10GeV to 30GeV
- Loses 10-12% yield with a high-Z target
- Assuming fixed power (unrealistic?)
- Re-optimising the front end for another energy tends to give small gains of order 3%
- Going from 10GeV to 50GeV
- Loses 25-30% yield
- This cannot be ignored so easily