# Presentation: 448924

## Neutrino Factory, ±  Decay Rings

*C Johnstone, FNAL, F Meot, CEA, & G H Rees, RAL** *

## Vertical Plane Layout for 2 Isosceles Triangle Rings

***ν***

***ν***

- -----------------------

*apex*

*ground level*

*α*

*θ*

***ν***

*    **sin **α**  =  L**1** /2R**                             **sin **θ**  =  L**2** /2R*
*L**1**, L**2** detector distances            R the equatorial radius*

## Triangle Ring Production Efficiencies

*Best for **ν**-production efficiency are vertically aligned, adjacent,*
*triangular rings of minimum apex angle, with two detectors in *
*opposite directions, in gnomonic projection. Some inclination*
*to a vertical plane is expected for most pairs of detector sites:   *
*For an RAL Neutrino Factory with two, 1608.8 km circumference*
*decay rings, and neutrino detectors at Carlsbad (7513 km) and:    *
*2**nd** detector site    Vertical tilt   Apex angle  Production Efficiency*
*Baksan (3375 km)      30.6**°**           60.2**°              2 x 23.9 %*
*Cyprus  (3251 km)       9.7**°           51.7**°              2 x 25.0 %*
*Crete    (2751 km)   **     0.9**°**  **         48.6**°              2 x 25.4 %*

## Schematic Plan of Triangle Ring

*10 cell arc, Q=2 *

*10 cell arc, Q=2*                           *Production straight*

*Production straight solenoids*

*11 cell arc, Q=2.2*

*Collimation, rf *
*& tune change*

*ν*

*ν*

*Injection*

*End bend*

## Triangle Apex Angles

*  **The number of arc cells sets the apex angle of triangle*
*  **Smallest apex angle is for a triangle in a vertical plane *
*  **Detectors at 7500 & 3500 km need ~ 50**° apex angles.*
*  **Groups of five cells are used for control of chromaticity *
*Arc cells    Apex angles**   **Circumf.   Prod. straight    Efficiency  *
*             *
*10+10+10      ~60.**0**°**       1608.8 m       383.7 m       2 x 23.9 %*
*10+10+11        52.8**°**       1608.8 m       398.5 m       2 x 24.8 %*
*10+10+12      ~45.4**°**       1608.8 m       415.3 m       2 x 25.8 %*
*10+10+16      ~22.4**°** **      1608.8 m       482.0 m       **2 x 30.0 %*

## Features of Isosceles Triangle Rings

*Designed for MW intensities:  **β**γ**A = 30 (1.5)**2**  (**π** mm r)*
*Uses a beam loss collection system for the muons*
*Uses combined not separated function magnets in arcs*
*Uses solenoid focusing in the two production straights*
*Uses bend units at the ends of the production straights*
*Uses box-car stacking for trains of 80 **μ**+** & **μˉ** bunches*
*Uses matching section bends to suppress dispersion*
*    **(these influence the production straight orientations).*
*Lattice is modified when upgrading from 20 to 50 GeV*
*    **(Some magnets changed & ring re-aligned for 50 GeV).*

## Production Straight Focusing

*A figure of merit for lattice focusing is: 1 / (**γ**β**max** )**                **                                                                                    **For a FODO thin lens: **γ**β**max** = 2/(1 - sin **μ**/2) > 2*
*For an OSO lattice of weak solenoids: **γ**β**max** ≈  I*
*   **So, **β**max **(OSO) may be one half of **β**max **(FODO)** *
*Eight, 4.8 m solenoids in 398.4 m straight sections: *
*   **At 20/50 GeV, **β**max**≈99/163 m for 4.3/6.4 T solenoids *

## Production Straight End Bends

*Neutrinos, from ****± **beyond the bends, miss detectors.*
*    **Bends introduce dispersion, however, into the lattice.*
*Matching of dispersion to arcs requires further bends,*
*    **which are different for the 20 and the 50 GeV lattices.*
*Small changes in the arc bend angles are required to*
*    **preserve the orientation of the 2 production straights.*
*Dispersion in the third straight is also affected and so*
*    **modified matching is needed for the 50 GeV upgrade. *

## Neutrino Production Straights

*                                                       **20 GeV      50 GeV*
*Muon norm rms emitt (**π** mm r)       4.80            4.80*
*μ** to **ν** divergence angle ratio, R      0.10            0.12*
*Number of solenoids                       8                 8*
*Solenoid fields (T)                           4.27            6.37*
*Length of solenoids (m)                  4.75            4.75*
*Half  of inter space (m)                 21.1            21.1*
*β** value at beam waist (m)          ~94.3        ~160.3*
*β** (max) in solenoid (m)              ~99.1        ~163.1*

## Arc Cell Design

*Old CERN 10,10,10 FODO design:*
*  **Lengths = 9.703, 0.7 m, **** = 90**°**, **β**max** = 16.6 m, D**max** = 1.4 m.*
*               **New 10,10,11 (BF)O(BD)O design:**   *
*       *
*  **Lengths = 8.200, 1.2 m, **** = 72**°**, **β**max** = 12.7 m, D**max** = 1.4 m.*
*(**space for cryostat ends, valves, correctors, diagnostics, vacuum & cooling)**  *

## Triangle ring lattice functions outside production straight.

## Bunch Train Injection

*       **1*

*2*

*(h=3, n=3)                          (h=24, n=3) (h=5, n=5)                          (h=40, n=5) *

*2*

*3*

*   **μ**±** bunch rotation            P Target*

*1           RCS (R**b **)                        NFFAG (2 R**b **)**     **1**  *

*3*

*1*

*2*

*3*

*Decay rings, T**d *
*   **h = 2**3**3**3**5*

*Accel. of trains of 80 **μ**±** bunches** *
*NFFAG ejection delays:                 (p + m/n) T**d  **; m = 1 to n (= 3,5)*
*Pulse < 40 **μ**s for liquid target**                                                                      *
*Pulse > 60 **μ**s for solid targets**                                             *

*  **Period  T**p** = T**d **/2*

*80 **μ**ˉ** or **μ**+** **bunches** *

## Injection of n Trains of 80 ± Bunches 

*           **Production straight of superconducting solenoids*
*Solenoid 1                       Solenoid 2                          Solenoid 3   *
*            *
*Septum injected bunch trains         Fast kickers *
*                                                                                 *
*R & D is needed for the high stored energy & power, pulsed *
*kickers, with n (5 or 3) injected bunch trains per 50 Hz cycle.*
*Rise & fall times are ~650 ns for the large acceptance rings. *

## Injection Parameters

***k** ≈ **√ **β**k** (√A + √**ε** + t**s** /√**β**s**) / (**β**k** sin **Δμ** +**1⁄2 **NL cos **Δμ**)**      *
*NLI (number, length, current) =  2 (B**ρ**) ****k** √(A **β**v** ) / **μ**o*
*NTV (number, rtime, voltage) =  2 (B**ρ**) ****k** √(A **β**k** )*
*At 20 GeV, for A, **ε** = 354.7, 157.7 mm mr, t**s** = 15 mm *
*β**s**≈**β**k**≈**β**v**≈ 95.0 m, **Δμ**≈25**°, **B**ρ**=67.06 T m, T= 460 ns:*
*Use 8, shorted, 3m, 10 **Ω** delay line, push pull K with *
*14 x [50 kV PFN, 5 kA pulsers & 10 **Ω** feeders] /ring.*
*NL = 24 m, ****k** = 6.47 mr,  I = 5000 A, NTV ~ 0.18 V s*

## Muon Beam Loss Collection

*Due to the e**±** **losses after ****±** decays, the warm bores*
*    **of S/C arc magnets have to be cooled, & clad with Pb.*
*    **(The cladding absorbs > 80% of the e**±** beam power.)*
*Direct ****±** wall loss also leads to magnet heating, and *
*    **to minimise this, ****±** loss collection is proposed, with*
*    **primary and secondary collimators in 4 FODO cells *
*    **at the centre of the short straight section of the ring,*
*Primary collimators are set for :   **βγ**A = 30 (**π** mm r).*
*    **and ring acceptances are:  **βγ**A = 30 (1.5)**2**  (**π** mm r).*

## RF System to Contain Bunch Structure

*An RF system is needed only if n = 5 & **Δ**p/p > **± 2.5 %**  *
*    **Injected bunches may expand in phase until **Δφ** = **±**90**°** *
*The inductive wall fields are defocusing as **γ** is > **γ**-**t ** *
*    **The required net RF containing field scales as (**Δ**p/p)**2*
*30 MV, 201 MHz containing fields/ring for **Δ**p/p =** ±1%** *
*    **3 cavities, 2x1 MW input couplers for ~ 5.4 MW per ring*
*Cavities on tune; loading alters with each injected train *
*    **Reflected power is dissipated in the circulator loads*
*The dynamic aperture improves for lower **Δ**p/p beams*

## Survival (ε=60 (π) mm r, Δ=±4%)    Horizontal phase space                Vertical phase space Tracking of μ± with sextupoles in the triangle ring arcs.      Tracking the linear machine shows very weak coupling       and well-behaved transverse motions for Δp/p = ± 4%.        The effect of  machine errors is next to be determined.

## Parameters for 52.8° Apex Angle Triangle Rings 

*Circumference of decay rings:            1608.8 m*
*Length of production straights:             398.5 m*
*Production straight efficiency:          2 x 24.8 %*
*μ** to **ν** angle ratio at 20 GeV:                    0.098*
*μ** to **ν** angle ratio at 50 GeV:                    0.119*
*Max **β** in the ring at 20 GeV:                120.0 m*
*Max **β** in the ring at 50 GeV:                184.0 m*
*Q**h** and Q**v** values at 20 GeV:      13.37, 13.18*
*Q**h** and Q**v **values at 50 GeV:      13.19, 12.82*

## Design Summary

*An outline design has been made for 2, isosceles*
*    **triangle, 20 (potentially 50) GeV, ****±** storage rings*
*The MW rings have large **β**γ**A, at 30 (1.5)**2**  (**π** mm r).*
*    **C = 1609 m, L = 398 m, **ξ** = 2 x 24.8%, 52.8**° apex **Δ**. *
*Production straight solenoids give lower beam sizes.*
*    **μ** to **ν** **angle ratios are 0.10 & 0.12, at 20 & 50 GeV. *
*Injection difficult  for uncooled (45 **π** mm r) ****±** beams. *
*    **F Meot is tracking to find dynamic aperture with errors.*

## Vertical Bow-Tie Decay Rings

*        **Advantages:*
*    **a reduced vertical tunnel depth of ~ 300 m *
*        **(~ 435 m for triangular and racetrack rings);*
*    **a higher **ν** **production efficiency of 53.4%*
*        **(49.6%  for triangular rings and 38.2% for racetracks);*
*    **a greater choice of the opening angle around 50**°.*
*        **Disadvantages*
*    **a larger number of main bend cells are required (40)*
*       **(31 for comparable isosceles triangle, shaped rings)*
*     *
*        **Polarisation retained?*

## Vertical Bow-Tie Decay Rings

*.*

*                             **430 m production straights    10 cell arcs*
*Tuning*
*quads**                             **ν**     ** ν*
*                           **52.8**°                                 *
*                                                                     **Beam loss*
*                                                                    **collimators*

*10 cell arcs*

*10 cell arcs **             **Depth ~ 300 m**           *
*                              **Efficiency 2 x 26.7%*
*                          **Circumference 1608.8 m           10 cell arcs*

## Relative Costs

*The three ring designs have the arcs, the matching sections *
*and the production straights all interchangeable (in principle).*
*Thus the cost issues reduce to the following:*
*The additional bend cells & fewer quads for the bow-tie rings.*
*The reduced depth of the tunnel for the bow-tie rings.*
*The additional tunnel (smaller cross section) for the racetracks*
*The additional services and beam lines for the racetracks.*

## Ring Comparisons

*1.  If suitable detector sites can be found, the*
*     **triangle or bow-tie shapes are favoured.*
*2.  If suitable detector sites are not available,*
*     **racetracks in separate tunnels are needed.*
*3.  If designs 1 and 2 are both proposed, the*
*     **former has the following advantages:*
*     **the need for only one tunnel and a*
*     **larger neutrino production efficiency*
*     **(which is > the gain of adding **μ**ˉ** beams).*