# Presentation: 519864

## A 3 Pass, Dog-bone Cooling Channel

*G H Rees, ASTeC, RAL*

## Introduction

*Studies for the ISS:*
*1. Proton booster and driver rings for 50 Hz, 4 MW and 10 GeV.*
*2. Pairs of triangle and bow-tie, 20 (50 GeV) ****±* *decay rings.*
*Studies after the ISS: *
*1. A 3 - 5.45 MeV electron model for the 10 GeV, proton NFFAG.*
*2. An alternative proton driver using a 50 Hz, 10 GeV, RCS ring.*
*3. A three pass, ****±** cooling, dog-bone re-circulator. *

## Schematic of Dog-bone Re-circulator

-     *Muon Cooling Channel*

*K1 off/on                  K2 on/off*

* **S*

*Solenoids, S*

***±*

*Solenoids, S*

***±*

*S*

## Mode Of Operation

*Solenoids match the ****±** beams between the input *
*    **and output transport lines and the cooling channel *
*Additional solenoid matching  is needed between*
*    **the cooling channel and the re-circulator end loops** *
*The kickers contribute to the beam matching and are integral parts of the first (last) lattice cell of the rings*
*Initially, kicker K1 is off, and it is switched on after a bunch train is in the cooling channel, but before it returns to K1 *
*Kicker K2 is kept on until it is turned off for beam extraction*
*    **Ring operation is close to but below its transition energy  *

## Potential Advantages

*Compatibility with the trains of 80 **μ**+** and 80 **μ**ˉ bunches *
*Common, dispersion free, input and output ****±** beam lines*
*Lower power kickers for field rise and fall times > 300 ns*
*Single transits of  the end loops for three channel passes*
*Enhanced cooling due to the three (or 5) channel transits*
*Cooling ahead of entry into the down and upstream loops*
*Improved **μ** to **ν** divergence angle ratio in the decay rings *

## End Loop Lattice Requirements 

*Entry and exit ring closure after completion of a 180° bend *
*Mirror symmetry about the input or the output ****±** beam lines*
*Zero dispersion at entry must transform to zero (D,D′) at exit *
*Equal β**h**, β**v** values at entry must match to same β at exit*
*Equal α**h**, α**v** at entry must change sign, but not value, at exit*
*Lattice functions must not vary too much around the rings *
*Optimisation for the design of the K1 and K2 kickers *

## Re-circulator End Loop

*Bend sequence:*
*Kicker    **–** 9**°*
*BN       – 42**°*
*BP       + 51**°*
*BR       – 45**°*
*BD       + 45**°*
*BD       + 45**°*
*BD       + 45**°*
*Mirror symmetry*
*for return bends*

*Kicker*

*BN   BP       BR  BD       BD    BD*

*BN   BP       BR  BD       BD    BD*

## End Loop Geometry

- ..................................................................................

*   **C 4               *

*BD      2.2254 m       BD        BD*

*C 6      1.4185 m*

*2.5581 m*

*2.0 m*

*2.1604 m*

*C 7      1.4185 m*

*BD (45**°, **n<1) are** asymmetric in the* *** = 60**°,* *cells C4, C5, C6.*

*1.4185 m*

*0.8069 m*

*0.8069 m*

*BN            BP                     BR*

*C 5*

## End Loop Matching

*Kicker requirements set** inputs at **β** = 4.0 m and **α** = 0.82 *
*BD (and BR) require an n = 0.5886 to obtain **** = 60**° cells*
*Need **α**v** = **α**h** = D′**h** = 0 at 3-BD **π** section and half way point *
*Variables are n and **θ**bend** of BN, BP, and straights next to BP *
*Ring closure and approximate matching sets the **θ**bend **values *
*This leaves four parameters to find a three parameter match*
*Ring closure is restored via asymmetry of BD cell positions*
*Input-output matching obtained but not cell to cell matching *

## Lattice Parameters

*Zero dispersion on entry becomes negative after kicker but positive after BR magnet & then continues to increase until half way around the ring, where D = 3.4216** **m and **D′ = 0.*
*Functions change in a mirror symmetric way on return to the kicker. Due to **π phase shift for 3 adjacent BD cells, the point **between **(– **** –) and (**** **** ****) sections also has** D′ (and α) zero*
*Beta functions are matched from input to output but not from cell to cell, due to asymmetric BD cells and other effects. The kicker deflection is over a region of reducing** β**h** (4.0 to 2.3 m) *
*The β**v** variation over the kicker is similar **(4.0 to 2.4 m), and the maximum value of **β**v** around the ring reaches 4.102 m, while t**he maximum value for β**h** in the ring is 4.757 m. *

## Loop Betatron and Dispersion Functions 

## Magnet Parameters

*Magnet    Length (m)    Angle          B**o **(T)               n*
*  **K1,2          1.800           **– **9**°         0.**07947         0.00000*
*   **BN           0.672         + 42**°         0.99334         0.65624*
*   **BP           0.816         **– **51**°         0.99334         0.59333*
*   **BR           0.720        **– **45**°         0.99334          0.58863*
*   **BD           0.720        + 45**°         0.99334          0.58863*

## Isochronous Position

*For an isochronous point ahead of the end loop, its **gamma-t *
*    **must be < the muon gamma of 2.7705462 (at 273 MeV/c) *
*The isochronous path length for the gamma-t of 2.621948 is *
*    **(2.7705462 / 2.621948)**2** x 39.125404 m (ring path length) *
*Thus, the isochronous position ahead of the end loop is at a distance of 2.321435 m from the input end of the kicker *
*The path length from and back to the point is 43.68592 m*
*    **while 63 (**βλ**/2) for** the 201.25 MHz cavities is 43.76085 m *

## Kicker Magnets

*Max. normalised input emittances at K1: 45,000 (π) mm mr *
*    **Max. normalised input emittances at K2: 30,000 (π) mm mr *
*The beam size is reduced for the first K1 pass (when it is off) and this requires an extra pulsing system for the focusing *
*K1,2 have 9° kick**,** 435 mm gap, 794.7 G field, 300 ns fall time and 51.9 kV /section for push-pull drives & subdivision in two   *
*Each of eight pulse systems need 428.3 J of energy per pulse, while earlier coolers needed 10,000 J, and typical kickers. 20J *
*Kicker R and D remains an important issue, because of the  required high level of  the pulse currents at 27.509 kA* * *

## Future Work

*Chromatic correction for the end loops (B = B**o **(r/r**o**)**ˉ **n  **?)*
*Inclusion of cooling channel in re-circulator (C Rogers)*
*Input and output matching for re-circulator (C Rogers)*
*Muon tracking studies for the three channel transits*
*Determine losses, emittance and momentum acceptance*
*Study the possibility of adding an end loop to MICE*