# Presentation: 431883

## Bucked cooling channels

**for the neutrino factory**
- R.C. Fernow
- BNL
- IDS Meeting
- FNAL
- 10 June 2008

## Introduction

-  we know that peak RF gradient falls with B at 805 MHz
-  if similar behavior at 201 MHz → Study 2a channel won’t work
-  consequences for the neutrino factory
- live with lower G (longer, more decays, more $)
- switch to open cavities (more RF power, more $)
- use gas-filled channel (OK unless there is beam breakdown) [D. Neuffer]
- use lattice with magnetically insulated RF [R. Palmer]
- use bucked coil lattice

## Bucked coil lattices

-  fits naturally in lattices with the β┴ minimum under coil
-  occurs in special regions of parameter space
-  several examples are under study for the muon collider

## Example 1: Bob

-  at 75 m got Tr=54% and εTN=0.078 mm
-  has also made _ring_ designs with bucked lattices

- d=55 cm, a=4 cm , Bo=26 T, p=200 MeV/c, β┴=0.9 cm

## Example 1: Bob

- wide stop bands

- rapid variation in β

## Example 2: Yuri

-  d=40 cm, a=3 cm, Bo=17 T, p=100 MeV/c, β┴=0.8 cm

- • at 30 m got Tr=30% and εTN=0.044 mm

## Example 2: Yuri

- alternates polarity

## Example 3: Rick

-  d=75 cm, a=8 cm, Bo=23 T, p=200 MeV/c, β┴=1.0 cm
-  larger emittance: input beam from exit of last guggenheim

- • at 60 m got Tr=39% and εTN=0.11 mm

## Example 3: Rick

- very wide
- stop bands

- taper radii

## Neutrino factory

-  can we make a bucked lattice suitable for neutrino factory?
-  initial emittances are much larger
- 	 εTN=17 vs ~0.4 mm
- 	 εLN=19 vs ~0.4 mm
- • Study 2a lattice parameters are much different
- 	a=35 vs ~4 cm
- 	Bo=2.8 vs ~25 T
- 	β┴=80 vs ~1 cm

## Scaled version of Bob’s lattice

-  Bob’s example had best transmission → can we scale it?
- coil radius: 4 to 35 mm → factor ~9
- transverse emittance: 0.3 to 17 mm → factor ~51
- even factor of 9 leads to a **bizarre** design
- 	d = 495 cm
- 	has long ~1.4 m long gaps with no focusing
- 	radial thickness of coils ~ 2 m
- 	J ~ 2 A/mm2
-  we can’t scale the collider designs
-  must look for new solution

## Reexamine parameter space

-  look for solutions with
- 	*d*=100 cm (slightly longer than 75 cm in Study 2a)
- 	*g*=54 cm (leave same 50 cm space for 201 MHz RF)
-  try to increase *a* to ~30 cm to handle large εT
-  look for solutions in second pass band with p2 = 200 MeV/c

## 2nd passband solutions

| a [cm] | g  [cm] | J
 [A/mm2] | p2 [MeV/c] | Δp [MeV/c] | βm [cm] | Bo [T] | Hoop
MPa |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 8 | 54 | 166 | 201 | 27 | 0.8 | 20.4 | 343 |
| 12 | 54 | 190 | 201 | 32 | 1.1 | 18.6 | 546 |
| 16 | 54 | 223 | 201 | 38 | 1.5 | 16.7 | 806 |
| 8 | 54 | 185 | 250 | 35 | 0.9 | 24.3 | 450 |
| 8 | 40 | 125 | 200 | 33 | 1.2 | 17.7 | 220 |

## Comments

-  fixing p2=200 MeV/c requires Bo~20 T and keeps β~1 cm
- much lower β than needed for NF
-  β scales with *a*
-  J increases as *a* increases
-  hoop stress grows with *a*
- Green’s criterion: hoop stress < 350 MPa
- solution with *a*~30 cm difficult
-  raising p2 leaves β ~same, but increases J
-  decreasing *g* increases β and decreases J → less RF room

## 1st passband solutions

-  examine solutions in 1st (high energy) passband, cf. Study 2a
-  keep *d*=100 cm, *g*=54 cm, pref=200 MeV/c
-  look for solutions with pπ= 100 MeV/c

| a [cm] | J
 [A/mm2] | pπ [MeV/c] | Bbnd [T] | βm [cm] | Bo [T] | Hoop
MPa |
| --- | --- | --- | --- | --- | --- | --- |
| 16 | 55 | 100 | 0.00 | 77 | 3.2 | 44 |
| 24 | 85 | 100 | 0.00 | 76 | 3.0 | 123 |
| 32 | 119 | 100 | 0.00 | 74 | 2.9 | 347 |

## First passband solution with a=32 cm

- flat region is gone!!!

- β similar to Study 2a

## Summary

-  made first look at bucked lattices for a neutrino factory
-  extrapolating 2nd passband results to *a* ~ 30 cm
- hoop stress is enormous (~1500 MPa)
- J is very large (~300 A/mm2)
- Bo is much larger than Study 2a (~9 T)
- β┴ is much smaller than necessary (~3 cm)
- • 1st passband solutions similar to Study 2a were found
- large radius bucking coils don’t give significant flat region
-  it is unlikely that a bucked lattice will be suitable for the NF