# Presentation: 773206

## 3 GeV, 1.2 MW, RCS Booster and 10 GeV, 4.0 MW, NFFAG Proton Driver

*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*

## Proton Driver Parameter Changes for ISS

*  **Pulse repetition frequency         F = 15 to 50 Hz*
*  **4 MW, proton driver energy       T = (8 or 26) to 10 GeV*
*  **No. of  p  bunches & **μ**±** trains    n = 1 to (3 or 5)*
*      **Reasons for the changes:  **     *
*  **For adiabatic proton bunch compression to ~ 2 ns rms *
*  **For lower peak & average beam currents in **μ**±** rings*
*  **To allow partial beam loading compensation for the **μ**±** *

## Bunch Train Patterns

- .

*                                                                            *
*NFFAG ejection delays:*
*(p + m/n) T**d**  for m = 1 to n (=3,5)*
*Pulse < 40 **μ**s for liquid target                                                                      *
*Pulse > 60 **μ**s for solid target**                                             *

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

*P  target**    *

*1 **                                                                                **1 *

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

*3*

*2*

*2*

*3*

*                         *
*NFFAG    2R**b **, T**p*
*T**p**= T**d **/2*

*1*

*2*

*3*

*80 **μ**ˉ or** **μ**+** **bunches*

*μ**±*  *bunch rotation*

*Acceler. of trains of 80 **μ**±** bunches *

*RCS           ( R**b **)*

## Schematic Layout of 3 GeV, RCS Booster

* **200 MeV H ˉ                           H **ˉ, H**° beam*

*cavities                                     collectors*

*extraction                                             cavities *

*R = 63.788 m*
*n = h = 3 or 5*

*triplet** *
*triplet*

*dipoles*
*8° dipole*
*dipoles*

## Booster Betatron and Dispersion Functions

## Parameters for 50 Hz, 0.2 to 3 GeV Booster 

*Number of superperiods             4*
*Number of cells/superperiod      4(straights) + 3(bends)*
*Lengths of the cells                    4(14.0995) + 3(14.6) m*
*Free length of long straights    16 x 10.6 m*
*Mean ring radius                      63.788 m*
*Betatron tunes (Q**v**, Q**h**)              6.38, 6.30*
*Transition gamma                      6.57*
*Main dipole fields                       0.185 to 1.0996 T*
*Secondary dipole fields             0.0551 to 0.327 T*
*Triplet length/quad gradient      3.5 m/1.0 to 5.9 T m**-1*

## Beam Loss Collection System

*.*

*Primary H,V          Secondary Collectors               Local shielding *
*Collimators            **μ** = 90**°        **μ** =160**°       Momentum collimators*
*                                                                     **Radiation hard magnet*
*                    **Triplet                                       Secondary ****p collector*

*Main dipoles*

## Choice of Lattice

*ESS-type, 3-bend achromat, triplet lattice chosen*
*Lattice is designed around the H**ˉ** injection system*
*Dispersion at foil to simplify the injection painting*
*Avoids need of injection septum unit and chicane*
*Separated injection; all units between two triplets*
*Four superperiods, with >100 m for RF systems*
*Locations for momentum and betatron collimation*
*Common gradient for all the triplet quadrupoles*
*Five quad lengths but same lamination stamping*
*Bending with 20.5**° main & 8° secondary dipoles*

## Schematic Plan of Hˉ Injection

*.*

*Optimum field for n = 4 & 5, H**°** **Stark state lifetimes.*
*                     **0.0551 T, Injection Dipole*

*H**ˉ*
*H**°*
*H**+*

*Stripping Foil                     Septum input*

*H**ˉ*
*H**+*

*8**°*

*5.4446 m*

*   **V1         V2       Vertical steering/painting magnets      V3          V4*
*  **Horizontal painting via field changes, momentum ramping & rf steering*
*  **Separated system with all injection components between two triplets.*
*  **H**ˉ **injection spot at foil is centred on an off-momentum closed orbit.   *

*Foil*

## Electron Collection after Hˉ Stripping

*.*

*200 MeV, 80 kW, H**ˉ beam      5 mm*
*170 injected turns, 28.5 (20 av.) mA*

*H**°*
*H**°*

* **Protons*
* **Protons*

*                               *
*                                    **Cooled copper graphite block*
*Foil support                    109 keV, 90 W, e**ˉ beam*
*Stripping Foil**                         **ρ** = 21.2 mm, B = 0.055 T *

*Foil lattice parameters : **β**v **= 7.0 m, **β**h** = 7.8 m, D**h** = 5.3 m, D**h **/√ **β**h** = 1.93 m**1⁄2** *
*H**ˉ parameters at stripping foil ; **β**v** = 2.0 m, **β**h** = 2.0 m, D**h** = 0.0 m, D**h**'** = 0.0*

## Anti-correlated, Hˉ Injection Painting

- .

*Foil*

- o *H**ˉ     *o*     *

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

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

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

***Y***

***O*****                                                    *****X***

-                         *Vertical acceptance*
*                          **H**ˉ injected beam*
*                       **Initial closed orbits*
*                       **Final closed orbits*
*               **Collapsed closed orbits*
*                                                       *
*     **Δ**p/p spread in X closed orbits*
* **Small v, big h amplitudes at start*
* **Small h, big v amplitudes at end.*

-  1⁄2 ***painted ******ε******(v)***

*                    **1⁄2** ****painted ******ε******(h)***
*Collimator acceptance****      ***
*Horizontal acceptance*

*For correlated transverse painting ****:**** interchange** X closed orbits*

## Why Anti-correlated Painting?

*Assume an elliptical beam distribution of cross-section (a, b).*
*The transverse space charge tune depressions/spreads are :*
*                                        ** *
*          **δ**Q**v **= 1.5 [1 - S/ **∫**(**β**v **ds / b(a+b))] **δ**Q**v **(uniform) *
*           **4S =  **∫[**β**v **/b(a+b)**2**] [(y**2 **(a + 2b)/ 2b**2 **) + (** **x**2**/** **a)] ds*
*Protons with (x = 0, y = 0) have **δ**Q**v **= 1.5 **δ**Q**v **(uniform distrib.)*
*Protons with (x = 0, y = b) have **δ**Q**v **~ 1.3 **δ**Q**v **(uniform distrib.)*
*Protons with (x = a, y = 0) or (x = a/2, y= b/2) have ~ 1.3 factor.*
*δ**Q shift is thus less for anti-correlated than correlated painting.*
*The distribution may change under the effect of space charge.*

## Emittances and Space Charge Tune Shifts 

*Design for a Laslett tune shift (uniform distribution) of **δ**Q**v **= 0.2.*
*An anti-correlated, elliptical, beam distribution has a **δ**Q**v **= 0.26.*
*For 5 10**13 **protons at 200 MeV, with a bunching factor of 0.47,*
*the estimated, normalised, rms beam emittances required are:*
*ε**σ** n  **=   24 (**π**) mm mrad*
*ε**max** = 175 (**π**) mm mrad*
*The maximum, vertical beam amplitudes (D quads) are 66 mm.*
*Maximum, horizontal beam amplitudes (in F quads) are 52 mm.*
*Maximum, X motions at high dispersion regions are < 80 mm. *
*Max. ring/collimator acceptances are 400/200 (**π**) mm mrad.   *

## Fast Extraction at 3 GeV

- .

*     **Fast kicker magnets  Triplet                    Septum unit     Triplet*
*  **Horizontal deflections for the** **kicker and septum magnets *
*  **Rise / fall times for 5 (3) pulse, kicker magnets = 260 ns*
*  **Required are 4 push-pull kickers with 8 pulser systems*
*  **Low transverse impedance for (10 **Ω**) delay line kickers*
*  **Extraction delays, **Δ**T, from the booster and NFFAG rings*
*   **R & D necessary for the RCS and the Driver pulsers** *

*K1  K2   K3   K4  F D F     10.6 m straight section     F D F*

## RF Parameters for 3 GeV Booster 

*Number of protons per cycle            5 10**13          **(1.2 MW)*
*RF cavity straight sections               106 m*
*Frequency range for h = n = 5          2.117 to 3.632 MHz*
*Bunch area for h = n = 5                   0.66 eV sec*
*Voltage at 3 GeV for **η**sc** < 0.4          417 kV*
*Voltage at 5 ms for **φ**s** = 48**°**             900 kV*
*Frequency range for h = n = 3         1.270 to 2.179 MHz*
*Bunch area for h = n = 3                  1.1 eV sec*
*Voltage at 3 GeV for **η**sc** < 0.4          247 kV*
*Voltage at 5 ms for **φ**s** = 52**°**             848 kV*

## Schematic Layout of Booster and Driver 

*3 GeV RCS booster** *

*200 MeV Hˉ linac *

*10 GeV*
*NFFAG** *

* **66 cells*

*Hˉ collimators*

*H°, Hˉ*

## Homing Routines in Non-linear, NFFAG Program

*A linear lattice code is modified for estimates to be made*
*    **of the non-linear fields in a group of FFAG magnets. *
*Bending radii are found from average field gradients*
*    **between adjacent orbits & derived dispersion values, D. *
*D is a weighted, averaged, normalized dispersion of a *
*    **new orbit relative to an old, and the latter to the former.*
*A first, homing routine obtains specified betatron tunes. *
*    **A second routine is for exact closure of reference orbits*
*A final, limited-range, orbit-closure routine homes for **** -t. *
*    **Accurate estimates are made for reference orbit lengths.*
*Full analysis needs processing the lattice output data &*
*    **ray tracing in 6-D simulation programs such as Zgoubi.*

## Non-linear Fields and Reference Orbits

*Low ampl. Twiss parameters are set for a max. energy cell. *
*Successive, adjacent, lower energy reference orbits are then*
*     **found, assuming linear, local changes of the field gradients.*
*Estimates are repeated, varying the field gradients for the required tunes, until self-consistent values are obtained for**:         *
*     **the bending angle for each magnet of the cell*
*     **the magnet bending radii throughout the cell*
*     **the beam entry & exit angle for each magnet*
*     **the orbit lengths for all the cell elements, and*
*     **the local values of the magnet field gradients*

## The Non-linear, Non-scaling NFFAG

*Cells have the arrangement:      O-bd-BF-BD-BF-bd-O*
*The bending directions are :            -    +    +    +    -*
*Number of magnet types is:                        3*
*Number of cells in lattice is:                      66*
*The length of each cell is:                       12.14 m*
*The tunes, Q**h** and Q**v** ,are:           20.308 and 15.231*
*Non-isochronous FFAG:                 **ξ**v** **≈ **0 and **ξ**h** **≈** 0*
*Gamma-t is imaginary at 3 GeV, and **≈** 21 at 10 GeV *
*Full analysis needs processing non-linear lattice data & *
*    **ray tracing in 6-D simulation programs such as Zgoubi*

## Lattice Cell for the NFFAG Ring

*          **bd(-)      BF(+)             BD(+)           BF(+)        bd(-)*
* **2.2    0.62      1.29               1.92 (m)       1.29           0.62    2.2                          **            **           *
*        –**1.65°    3.5523°          1.65°            3.5523°   **–**1.65°*
*                *
*  **Lengths and angles for the 10.0 GeV closed orbit*

## 10 GeV Betatron & Dispersion Functions

## Gamma-t  vs.   for the Driver and E-model

*              **Proton Driver                             Electron Model  *
*       **** **=E/Eo       gamma-t                   **** =E/Eo       gamma-t  *
*                      *
*   **11.658         21.8563                   11.658         19.9545       *
*   **10.805         23.1154                   10.980         22.4864       *
*   **10.379         23.9225                   10.393         24.2936       *
*     **9.953         24.8996                     9.806         28.9955       *
*     **9.100         27.6544                     9.219         51.1918     *
*     **8.673         29.7066                     8.632         34.7566 i *
*     **8.247         32.5945                     8.045         19.6996 i *
*     **7.608         40.0939                     7.458         14.2350 i *
*     **6.968         64.0158                     6.871         11.8527 i    *
*     **4.197         18.9302 i (imag.)          –                  – *

## Loss Levels for NFFAG Proton Driver

*Beam power for the 50 Hz Proton Driver  =  4 MW*
*Total loss through the extraction region < 1 part in10**4 *
*Average loss outside coll./ extr. region  < 1 part in10**4*
*Total loss in primary & sec. collimators  = 1 part in10**3*
*Remotely operated positions for primary collimators.*
*Quick release water fittings and component flanges.*
*Local shielding for collimators to reduce air activation.*

## Vertical Collimation in the NFFAG

- .

*3 GeV proton beam   10  GeV proton beam*
*Coupling may limit horizontal beam growth *

*X*

*Loss collectors         Y*

## Loss Collection for the NFFAG

*Vertical loss collection is easier than in an RCS*
*Δ**P loss collection requires beam in gap kickers*
*Horizontal beam collimation prior to the injection*
*Horizontal loss collection only before the ejection*
*   *
*Minimize the halo growth during the acceleration*
*Minimise non-linear excitations as shown later.*

## NFFAG Loss Collection Region

*                **20**°**                                                    160**°*
*     **Primary collimators (upstream end of 4.4 m straight)*
*Direct beam loss localised in the collection region*
*Beam 2.5 **σ**, Collimator 2.7 **σ** and Acceptance 4 **σ*

*Secondary collectors*

*p beam*

*Cell 1*

*Cell 2*

*Cell 3*

## NFFAG Non-linear Excitations

*    **Cells     Q**h**         Q**v **      3rd Order        Higher Order*
*      **4       0.25**       0.25        zero        n**Q**h**=nQ**v** & **4th order *
*      **5       0.20**       0.20        zero        n**Q**h**=nQ**v** & 5th order*
*      **6       0.166**     0.166      zero        n**Q**h**=nQ**v** & 6th order *
*      **9       0.222**     0.222      zero        n**Q**h**=nQ**v** & 9th order *
*     **13      4/13       3/13        zero  to  13th except 3**Q**h**=4Q**v*
*        **Use (13 x 5 ) + 1 = 66 such cells for the NFFAG*
*        **Variation of the betatron tunes with amplitude?*
**       *******-t  imaginary at low energy and ~ 20 at 10 GeV *

## Bunch Compression at 10 GeV

*For 5 proton bunches:*
*Longitudinal areas of bunches   = 0.66 eV sec*
*Frequency range for a h of 40    = 14.53-14.91 MHz*
*Bunch extent for 1.18 MV/ turn   = 2.1 ns rms*
*Adding of h = 200, 3.77 MV/turn = 1.1 ns rms*
*For 3 proton bunches:*
*Longitudinal areas of bunches   = 1.10 eV sec*
*Frequency range for a h of 24    = 8.718-8.944 MHz*
*Bunch extent for 0.89 MV/ turn   = 3.3 ns rms*
*Adding of h = 120, 2.26 MV/turn = 1.9 ns rms*
*Booster and Driver tracking studies are needed*

## 50 Hz,10 GeV, RCS Alternative

*Same circumference as for the outer orbit of the NFFAG*
*Same box-car stacking scheme for the ****±** **decay rings*
*Same number of proton bunches per cycle (3 or 5)*
*Same rf voltage for bunch compression (same gamma-t)*
*Increased rf voltage for the proton acceleration (50% ?)*
*3 superperiods of (15 arc cells and 6 straight sections)*
*5 groups of 3 cells in the arcs for good sextupole placings*
*2 quadrupole types of different lengths but same gradient*
*2 dipole magnet types, both with a peak field of 1.0574 T*

## 10 GeV NFFAG versus RCS

*Pros:*
*Allows acceleration over more of the 50 Hz cycle *
*No need for a biased ac magnet power supply*
*No need for an ac design for the ring magnets *
*No need for a ceramic chamber with rf shields*
*Gives more flexibility for the holding of bunches*
*    **Cons:*
*Requires a larger (~ 0.33 m) radial aperture*
*Needs an electron model to confirm viability*

## R & D Requirements 

*Development of an FFAG space charge tracking code.*
*Tracking with space charge of booster and driver rings.*
*Building an electron model for NFFAG proton driver. *
*Magnet design & costing for RCS, NFFAG & e-model.*
*.*
*Development of multiple pulse, fast kicker systems.*
*Site lay-out drawings & conventional facilities design*
*NFFAG study (with beam loading) for **μ**±* *acceleration*