FFAG Acceleration
David Neuffer
Fermilab
FFAG Workshop ‘03
JNF Scenario
 Use 50 GeV p-bunch to
produce pions
 Capture beam in 20-T  5-T
transport channel
 Short decay line; inject beam
directly into low-energy FFAG
 Capture beam in low-frequency
rf bucket
 Accelerate up chain of FFAGs
to 20GeV
 Inject into 20GeV storage ring
2
JNF- FFAGs lattice design
 Lattices are “scaling” radialsector FFAGs
 Triplet focusing with reversebend D-quads
 Low to high energy orbit width
is ~0.5m




0.3  1.0 GeV,
1  3.0 GeV
3.010 GeV
10 20 GeV FFAGs
 Lattices have been generated
using SAD, DIMAD
3
Parameters for JNF FFAG lattices
4
Acceleration and Decay
 Acceleration must avoid
muon decay
dN 
ds
dE
ds
1
N
L 
 eVrf
mc2
 LeVrf
 E0
 
N 0  E 
N

mc2
 LeVrf

E0


 E0  eVrf s 
 Need ~1MV/m to avoid
decay (2 MV/m gradient
in cavities)
5
JNF Acceleration Parameters
 For acceleration, use superconducting (smaller-radius) FFAGs
 At 1MV/m, ~ 10 turns acceleration / FFAG
 Assume harmonic h = 1 on lowest-energy FFAG; keep frequency
constant
 h = 1  4.75 MHz rf (???)
 Initial beam from decay
 300150MeV/c; 10ns

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Longitudinal Motion in FFAG
 Equations of motion:
E n  E n 1  eVrf cos(n )
 P  k 1 

s
n  n 1  2h  
 1
 P s  



1
 Motion is fairly isochronous (at
low frequencies)
 h = 1 and h = 2 accelerations
are OK
 (~4.75 and 9.5 MHz)
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Scenario requires ~2MV/m rf
 Harmonic=1 (for lowest energy
FFAG) implies 4.75 MHz;
 Harmonic=2 implies 9.5 MHz;
works OK in 1-D simulation
 Experience indicates 26MHz
cavity is more realistic
(Iwashita)
 Use 26 MHz + 3rd harmonic ?
8
~25MHz OK (from 1 to 20 GeV)
 Third harmonic useful;
particularly for 13 GeV
FFAG
 131020 GeV
20 GeV
 Could not get a good fit for 0.3
to 1.0 GeV FFAG
10 GeV
3 GeV
1 GeV
9
Bunch sizes for various rf scenarios
Ez / c
Rf frequency E (MeV)
(±)
z (m)
(±)
(eV-s)
JNF
(~300MeV)
5 MHz ??
150
3.00
4.7
~Study 2
(~125MeV)
200MHz
25
0.25
0.065
250 MeV
200MHz
50
0.25
0.13
125 MeV
100MHz
25
0.5
0.13
250 MeV
100MHz
50
0.5
0.26
125 MeV
50MHz
25
1.0
0.26
250 MeV
50MHz
50
1.0
0.52
Case
10
“Scaling” FFAG longitudinal dynamics
 Longitudinal motion changes:
E n  E n 1  eVrf cos( 2 z n 1 )
( E n  E0 )2
z n  z n 1  A  B
2
E0
 Position change has quadratic
dependence on energy
 Example I: A=-0.15, B=0.45,
E0=12.5 GeV, E0 = 6.5 GeV ,
620 GeV acceleration
 Example II: A=-0.05, B=0.15,
E0=15 GeV, E0 = 5 GeV ,
1020 GeV acceleration
Example I
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“Acceptable” Solutions
 Example I (620;45 cm)
 200 MHz, 6 turns, 2.75GV/turn
 20% 3rd harmonic reduces distortion
 200 MHz, with 3rd harmonic ,
8turns, 2GV/turn +1 GV/turn 3rd
 100MHz, 11 turns, 1.4 GV/turn
 Example II (10 20; 15cm)
 200 MHz, 16 turns, 0.7 GV/turn
 20% third harmonic reduces
distortion (0.75 GV +0.15 3rd)
Example II –16 turns
12
With third harmonic
Example II –16 turns
With 20% third harmonic
13
Summary
 Baseline acceleration scenario for JNF is ~25MHz
 Set by 1 initial bunch scenario (0.31.0 Gev at ~10MHz or less)
 Multiple-bunch scenario should allow higher frequency
 “Guttertron” acceleration works OK at 200MHz
if z(E) < ~15cm
+ third harmonic
14