# Presentation: 773205

## 3 GeV,1.2 MW, Booster for Proton Driver

*G H Rees, RAL*

## Bunch Train Patterns

- .

*Accel. of trains of 80 **μ**±** **bunches *
*                                                                            *
*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 targets**                                             *

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

*μ**±*  *bunch rotation           P  target    *

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

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

*3*

*2*

*2*

*3*

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

*1*

*2*

*3*

*80 **μ**ˉ or** **μ**+** **bunches*

## Schematic Layout of 3 GeV, RCS Booster

- .

*200 MeV H **ˉ beam                      Low field injection dipole*

*RF cavity systems                            **Beam loss collectors*

*Extraction system                                **RF cavity systems** *

*Triplet quads                                                   **Main dipoles*

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

## 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 blocks*
*Collimators            **μ** = 90**°        **μ** =160**°     Momentum collimators*
*                                                                    **Radiation hard magnet*
*          **Triplet quadrupoles               Secondary momentum 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 RCS, Driver and Decay ring 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*

## BNL, FNAL & CERN, 4MW Drivers?

*Parameters needed so that comparisons may be made with:*
*BNL’s scheme of single, 25 GeV bunches (15/50 Hz)*
*FNAL’s, 8 GeV linac-accumulator-compressor scheme*
*CERN’s, 5 GeV SPL-accumulator-compressor scheme*
*The 50 Hz, 3 GeV booster is not well suited to BNL option as:*
*A 3 GeV and a 25 GeV holding ring would be needed*
*The booster rf system would be at very low frequency *
*FNAL/CERN options need compatible rings, 1-turn extractions,*
*non-adiabatic bunch compression & multiple trains in **μ**±** **rings.*
*Linacs need low chopping duty cycles and hence long pulses.*

## 4MW, 50 Hz,10 GeV Proton Driver

*.*

*200 MeV H**ˉ **Linac           Achromatic H**ˉ** Collimation Line*

*                                                                **10 GeV NFFAG*
*     **n = 5, h = 5                                           n = 5, h = 40                             *
*3 GeV RCS booster                                    **Δ**T = 2 (p + m/5) T**p** *
*                                                                   **for m = 1-5*

*2                        5**                              **R**p** = 2 R**b** = 2 x 63.788 m  *

*3                     4*

*1*

*1*

*3                                               4*

*5                                      2*

## 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*

## R & D Requirements 

*Development of FFAG space charge tracking code.*
*Injection tracking with space charge in the booster.*
*Space charge tracking for booster and driver rings.*
*Building an electron model for NFFAG proton driver. *
*Study of NFFAGs as possible muon accelerators.*
*Development of multiple pulse kicker systems.*
*RCS, NFFAG & Decay ring, magnet design & costing.*
*Site lay-out drawings & conventional facilities design*