# Presentation: 669721

## Neutrino Factory, ±  Decay Rings

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

## 20 GeV Isosceles Triangle Rings (2)

*20 GeV Isosceles Triangle Rings (2)*

*Neutrinos*

*Neutrinos*

***±** ** injections*

*Collimation, rf and tune change*

*End bend*

*Apex **α*

## 50 GeV Isosceles Triangle Rings (2)

*Solenoid focusing*

*16/11 cell arc, Q=3.2/2.2*

*ξ**  correction in 5-cell sets*

*10 cell arc, Q=2** *

*10 cell arc, Q=2*

* **Production  straights may  be extended*

## Triangle Ring Design Changes

*Change from equilateral to an isosceles triangle ring.*
*Design for MW intensities:  **βγ**A = 30 (1.5)**2 ** (**π** mm r)*
*Use box-car stacking for trains of 80 **μ**+** & **μˉ** bunches.*
*Introduce a beam loss collection system for muons.*
*Use combined not separated function magnets in arcs.*
*Use solenoid focusing in the two production straights.*
*Use bend units at the ends of the production straights.*
*Use matching section bends to suppress dispersion*
*(these influence the production straight orientations).*
*Modify the lattice when upgrading from 20 to 50 GeV.*
*Change some magnets and re-align ring for 50 GeV.*

## Decay Ring Triangle Apex Angles

*        **Numbers of arc cells determine triangle apex angles.*
*        **Five cell groups are used for the chromaticity control.*
* **Arc cells  Apex angles  Circ.  Prod. st.  RF harmonic  Efficiency *
*                         **(**o**)          (m)         (m)             (h)               (%)*
*10+10+10     ~60.**0    1573.05    364.0      2**5** x3 x11      2 x 23.1*
*10+10+11     ~52.8    1573.05    378.0      2**5 **x3 x11      2 x 24.0*
*10+10+12     ~45.0    1525.38    388.0      2**10                        **2 x 25.4*
*11+11+15     ~34.5    1525.38**    412.2      **2**10**                2 x 27.0*
*10+10+16     ~22.4** **   1573.05    465.5      **2**5 **x3 x11**      2 x 29.6*
*Note:  Detectors at 7500 & 3500 km need apex angles of ~ 50**°.*

## Proton and Muon, n =5, 50 Hz Bunch Trains

*                                        **                                               **O**                                            *
*Proton booster (n=5, h=6)**                                  **O        O**                                                                     *
*                                                                              **O   O**                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        *
*                                                            **                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             *
*                                                                                                   **O*
*Proton driver (n=5, h=36)**                                                     **O**                                                                                                                                                                                                                                                             *
*                                                                             **O   O   O       **                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             *
*Proton bunches at target                O          O          O          O    **T**    O*
*Pion bunches after target               ****O          O          O          O          O***
*Muon, 400 ns bunch trains**                                                           *
*                                                                                                                          *
*(n-1)T< 60 **μ**s (liquid target)**                                                                      **T*
*T > 60 **μ**s (for solid targets)**                                             **μˉ*
*20 GeV **μ**+ **& **μˉ** accelerator                                 **μ**+ *
*20/50 GeV **μ**+ **decay ring                      600                    600                     600                                                                                                                                  *
*C>1500 m circumference              **400 ns bunch trains & > 600(+) ns gaps*
*20/50 GeV **μˉ** decay ring                            600                     600                                                                                         *

* *

## Ring Harmonic Numbers

*       **Rings             Beta       Circ (m)       **h**    **RF (MHz)**   N**b **/Ring*
***50 GeV μ Decay        0.9999977      1573.0691      ******1056******        ******201.250******   ******         5x80***
***20 GeV μ Decay        0.9999861      1573.0509      ******1056******        ******201.250****** ******           5x80***
***8-20 GeV μ******± ******Acc        0.9999861      1135.0991        ******762 ******       ******201.250****** ******         10x80***
***3.2-8 GeV μ******±****** Acc       0.9999150                                             ******201.250****** ******         10x80***
***1-3.2 GeV μ******±****** Acc       0.9994890  ******                                       ******201.250******          10x80***
***3-10 GeV P Driver     0.9963143        801.44744       ******36******     13.079-13.417            5               ***
***                                                                                  ******216******           80.500                  5***
***                                                                                  ******540 ******       ******201.250******    ******             5***
***0.18-3 GeV Booster  0.9712057        400.72372         ******6******     2.4422-4.3595            5***
***                                                             ***

## Box-car Transfer of μ+ & μˉ to Decay Rings

*The 20 GeV decay rings, 8-20 GeV **μ**±** **acc & P driver, of periods T**d** , T**a** , T**p **, *
*all have 201.25 MHz as a harmonic. **The integers p (= 1,2,3 ,4), n and m ** *
*are chosen so the proton bunch delays** **are a good approximation to:** *
*                                        *
*                               **(n ± p/5) T**d**   **≈**  **(m ± 1/12) T**p*
*T**d** , T**a** , T**p** =  5.2472044, 3.7863345, 2.6832296 μs,   **(T**d** /T**p**) =  1.9555554*
*Target      **m      n        p**        **(m ± 1/12)       (n ± p/5)** **(T**d** /T**p**)**    **|Difference|*
*Solid       23     12      -1      23 + 0.083333      23.075553          **0.007780**                     *
* *
*Liquid       5       3      -2        5 + 0.083333        5.084444           **0.001111*
*                     *
*For solid target:**     **(m + 1/12) T**p ** =  n T**d**  -**  **207** **T**b    **(RF period T**b **)*
* *
*For liquid target**:    **(m + 1/12) T**p ** =  n T**d**  -  423** **T**b *

## N=5, Muon Bunch Pattern in Decay Rings

- .

*148(136)*
*solid/liquid*

*80 **μ**+*

*80 **μ**+*

*80 **μ**+*

*80 **μ**+*

*80 **μ**+*

*127(!30)*

*127(130)*

*127(130)*

*127(130)*

*2 of 5  interleaved 80 **μ**ˉ** *
*bunch** **trains of 2nd ring** *

*80 full and 127 (or 130) empty RF buckets*

*> 100ns intervals*

## Other Triangle Ring Options

*A wider range of apex angles may be obtained *
*      **by adding half cells in one or more of the arcs.*
*2.   Production straights may have different lengths,*
*      **but **ξ** gain of longer is < loss in **ξ**  of  the latter.*
*3.   **For specified detector distances, the smallest *
*      **apex angle is for a triangle in a vertical plane.*
*4.   Smaller circumference rings may be considered*
*      **with n reduced from 5 to 4, 3 or 2 ** **bunch trains.*

## Efficiencies for Smaller Decay Rings 

*Circumference (m)  Prod St (m)   Efficiency  Racetrack*
*                     **1573.05             2 x 378.0        48.0%           38%*
*        **1258.44             2 x 268.0        42.6%           35%       *
*                **943.83             2 x 156.9        33.2%           30%*
*              ** **629.22   **           **2 x   14.8**            **4.7%**             **20%*
*Each reduction in circumference lowers the efficiency*
*and, for the last case, a racetrack is the more efficient.*
*There is concern for the > 400 m depths of triangle *
*and racetrack rings, at the circumference of 1573 m.*
*         *

## Vertical Plane Triangle Ring

*.*

***ν***

*α**θ*

***ν***

*      **sin **α**  = **** ****L**1 **/2R** **                           **sin **θ**  =  L**2 **/2R*
*L**1**, L**2** detector distances            R the equatorial radius*
*     **L1                   L2                      Apex angle (**α** **+ **θ**)*
*3500 km          7500 km                       ~ 52.0**°*
*2500 km          7500 km                       ~ 47.5**°*

*Apex*

***ν***

## Site Examples

*NuFact  Detector 1        Detector 2     Apex **α**   Vert. tilt  *
*BNL      Carlsbad         Arlit **(7369 km)**    48.4**°       0.9°*
*            **(2883 km)*
*RAL     Carlsbad    Baksan (3375 km)    60.2**°     33.9°  *
*            **(7513 km)   Cyprus (3251 km)    51.7**°**     10.7**°*
*                                  **Crete (2751 km)    48.6**°       1.0°**                       *

## 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).*
*The ring acceptances are:  **βγ**A = 30 (1.5)**2 ** (**π** mm r).*
* *

##  Arc Cell Design

*      **CERN 10,10,10 FODO design:*
*Lengths = 9.703, 0.7 m, **** = **π**/2, **β**max** = 16.6 m, D**max **= 1.4 m.*
*      **New 10,10,16 BFOBDO, FFAG design:   *
*Lengths = 7.80, 1.4 m, **** = 2**π**/5, **β**max** = 12.1 m, D**max **= 1.2 m.*
*(**space for cryostat ends, valves, correctors, diagnostics, vacuum & cooling)  *

## Production Straight Focusing

*A figure of merit for lattice focusing is:   1 / (**γβ**max **)*
*                           *
*For a thin lens FODO: **γβ**max **= 2/(1 - sin **μ**/2)    > 2*
*For an OSO lattice of weak solenoids:   **γβ**max** ≈  I*
*So, the OSO cell has a 50% lower value for **β**max**.*
*For 52.8**°, use** 8, 4.75 m units in 378.0 m straights: *
*At 20 GeV,  **β**max **≈ 99 m for solenoids with 4.3 T. *
*At 50 GeV, **β**max **≈ 163 m for solenoids with 6.4 T.*

## 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      0.098          0.119*
*Number of solenoids                       8                 8*
*Solenoid fields (T)                           4.272          6.369*
*Length of solenoids (m)                  4.75            4.75*
*Half  of inter space (m)                 16.8            16.8*
*β** value at beam waist (m)          ~94.3        ~160.3*
*β** (max) in solenoid (m)              ~99.1        ~163.1*

## Effect of Production Region 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*
*modified matching is needed for the 50 GeV upgrade**. *

## 20 GeV Lattice Functions outside Production Straights

## Production to Collimation Straight Matching

## Storage Ring Parameters

*Efficiencies for 22.4**° apex **Δ**:**                2 x 29.6 %*
*Efficiencies for 52.8**° apex **Δ**:**                2 x 24.0 %*
*Production straights of above:       465.5, 378.0 m*
*Decay rings’ circumference:                   1573.1 m*
*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:                     117.0 m*
*Max **β** in the ring at 50 GeV:                     184.0 m*
*Q**h **and** **Q**v** values at 20 GeV:         13.367, 13.184 *
*Q**h **and Q**v** values at 50 GeV:         13.187, 12.817*

## First Tracking of 22.4°, 1170.8 m, 20 GeV Ring  

*On-momentum muons:*
*Horizontal **ε**n **= 60 (**π**) mm rad only, Q**h **= 10.79 -10.80*
*Vertical **ε**n **= 60 (**π**) mm rad only, Q**v** = 11.147 - 11.155*
*Hor. & **vert. **ε**n **= 30 (**π**) mm rad, Q**h **,Q**v**= 10.81, 11.166*
*Effect of the solenoid ( **+-+-+-+- **) coupling is small.*
*Off-momentum muons:*
*Δ**p/p = 0.5%, **hor. & **vert. **ε**n **= 60 (**π**) mm rad; stable.*
*Δ**p/p = 1.0%, **h. & **v. **ε**n **= 45 (**π**) mm rad; just unstable. *
*Q**v **decreases to 11.0, in agreement with **ξ**v** estimates.*

## Injection of n Trains of 80 ± Bunches 

- .

*Solenoid 1*

*Solenoid 2*

*Solenoid 3*

*Injection septum*

*Train of 80, ****** or** ****** **bunches*

*Fast kicker          magnets, K*

*Long neutrino production straight section*

*Superconduc-ting solenoids*

*K stored energy/power is large due to the big acceptance &  *
*the ~ 600 ns rise & fall times for the 1573.1 m circumference *
*ring, which has n (= 5) injected bunch trains per 50 Hz cycle.*
*Induction kickers may be needed for the upgrade to 50 GeV.*

## Injection System Parameters

*Inject at upstream end of long straight nearest surface.*
***k** **≈** **√**β**k **(**√A + √**ε** + t**s **/√**β**s**) / (**β**k** sin **Δμ** + **1⁄2 **NL cos **Δμ**)      *
*NL I (number, length, current)  =  2 (B**ρ**) ****k** **√(A **β**v **)** **/ **μ**o*
*NT V (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**=67.064 T m, T= 435 ns:*
*Use 8, shorted, 3m, 10 **Ω** delay line, push pull K with*
*16, 50 kV PFN; 16, 5 kA pulsers and 16, 10 **Ω** feeders.*
*NL = 24 m, ****k** = 6.47 mr, ** I = 5000 A, NT V = 0.16 V s*

## Longitudinal Motion and RF

*RF needed to keep 100 ns gaps if n=5, but not if n<5.              *
*Injected bunch trains are tilted in longitudinal phase *
*space & rotate in RF cavity & wall impedance fields. *
*Injected bunches are allowed to expand in phase until*
*             **Δφ** = **± **π**/2** rad, for **Δ**p/p = **± 0.01 *
*Required are 30 MV, 201 MHz containing fields/ ring.*
*The required net RF containing field scales as (**Δ**p/p)**2*
*and the dynamic aperture also improves at lower **Δ**p/p. *

## RF System for Rings

*Inductive wall fields are defocusing as **γ** > **γ**t** .                             *
*Fields become small after the bunches expand. *
*Reactive beam loading comp.; cavities on tune.*
*Loading alters after each injected bunch train.*
*Reflected power dissipated in circulator loads.*
*The peak power for n = 5 is ~ 5.4 MW per ring.*
*So, for 2x1 MW input couplers: 3 cavities/ring.    *

## Design Summary

*An outline design has been made for 2, isosceles*
*triangle, 20 (potentially 50) GeV, ****±** storage **rings.*
*For a single detector, 2 racetrack rings are preferred.*
*For 2 detectors, 2 vertical triangle rings have higher **ξ**.*
*C = 1573.1 m, L = 378 m, **ξ** = 2 x 24.0%, 52.8**° apex **Δ**. *
*C = 1258.4 m, L = 268 m, **ξ** = 2 x 21.3%, 52.8**° apex **Δ**.*
*The MW rings have large **βγ**A, at 30 (1.5)**2 ** (**π** mm r).** *
*Production straight solenoids give lower beam sizes.*
*μ** **to** **ν** **angle ratios are 0.10 & 0.12, at 20 & 50 GeV. *
*F Meot is tracking to find dynamic aperture with errors.*
*Injection difficult  for uncooled (45 **π** mm r) ****±** **beams. *