Bunch length modulation in storage rings
C. Biscari
LNF – INFN - Frascati
Workshop on “Frontiers of short bunches in storage rings” – Frascati – 7-8 Nov 2005
Bunch length manipulation routinely done
in linear systems: linacs, fels, ctf3,….
T
R56
li
D( s)
  
ds
i 0  (s)
By using dispersion in dipoles and
correlation in the longitudinal phase plane
introduced by rf acceleration
Bunch length (mm)
measurements (2004)
CTF3 stretcher - compressor
3.5
3
2.5
sl calibr
sl model calib
sl - sim meas
sl - sim env
sl model calib F
K
L
2
1.5
1
0.5
0
-0.1
RRR
===
-=0.4
0.3
0.1
R
00.1
0.5
56
5656
R
=
0.2
56
56
0
0.1
0.2
R
_56
(m)
0.3
0.4
0.5
In storage rings
Even if particles follow different paths according to the different
energy, their oscillations around the synchronous one are usually
within the natural bunch dimensions
Large dispersion in dipoles
and
large rf cavity voltage derivative
can force the oscillations to grow and
lead to correlation in longitudinal phase plane
Longitudinal plane oscillations in a ring with one rf cavity*
 l 
Described by the vector  p 


 p 


One-turn matrix
Rf cavity lens
Sections
with dipoles
M ( s )  M ( s  srf )M rf M ( srf  s )
 1
M rf  
 U
0

1
U
2 Vrf
E / e rf
 1 R1 ( s ) 
M ( srf  s )  

1 
0
 1 R2 ( s ) 
M ( srf  s )  

0
1


Drift functions:
R1  s  
srf
D  s '
  s ' ds ' and R2  s    c L  R1  s 
 
s
Momentum compaction
1 D
C   ds
L 
*A. Piwinski, “Synchrotron Oscillations in High-Energy Synchrotrons,” NIM 72, pp. 79-81 (1969).
One turn longitudinal matrix – one cavity in the ring
1  UR2
M s  
 U
C L  UR1 R2 
 L
  cos  I  sin  
1  UR1

  L
L 

 L 
Longitudinal Twiss functions
cos   1 
L  s 
C L
2
U
1
 C L  R1 (s) R2 (s)U 
sin 
U
L 
sin 
Phase advance
determined by cL and rf
Bunch length can be
modulated
Energy spread constant
along the ring and defined
by rf and phase advance
Longitudinal emittance and energy spread*
Energy spread defined
by eigen values of
matrix M, considering
radiation damping and
energy emission
E 
L
5

  CL
2
L||
 E 
2
L  s 
  s
3
ds
Emittance diverges for  = 0, 180° (Qs = 0, 0.5)
1  E 
1
L  

 L  E 
sin 
2
E/E
 L L
l
 L  s    L L  s 
*A.W. Chao, “Evaluation of Beam Distribution Parameters in an Electron Storage Ring”,
Journal of Applied Physics 50: 595-598, 1979
 L  L s 
The idea of squeezing the bunch longitudinally in a limited
part of the ring came to Frascati when working in
Superfactories studies
(A. Hofmann had proposed a similar experiment in LEP)
Short bunches at IP
+ high currents per bunch
Low energy: microwave instability dominates the
longitudinal bunch dimensions
Strong rf focusing
Strong rf focusing – monotonic R1 *
R1  s  
srf
D  s '
  s ' ds '
 
s
High rf voltage + high momentum compaction:
High synchrotron tune
Ellipse rotates always in the same direction
Longitudinal phase space
From RF to IP
IP
From IP to RF
RF input
Energy
spread
RF center
*A. Gallo, P. Raimondi,
M.Zobov ,“The Strong RF
Focusing: a Possible Approach to
Get Short Bunches at the IP”,
e-Print Archive:physics/0404020.
Proceedings of the 31th ICFA BD
workshop, SLAC 2003
RF output
Bunch length
Evolution of Strong rf focusing – non monotonic R1*
High rf voltage + high derivative of R1 (s):
Low synchrotron tune
Ellipse rotates on both directions
dR1/ds < 0
dR1/ds > 0
Energy
spread
Bunch length
* C. Biscari - Bunch length modulation in highly dispersive storage rings", PRST–AB, Vol. 8, 091001 (2005)
Reference ring – DAFNE like
R1  s  
srf
D  s '
  s ' ds '
 
s
C = 100 m
E = 0.51 GeV
frf = 1.3 GHz
Vmax = 10 MV
cL
rf cavity
Monotonic R1(s)
Non Monotonic R1(s)
Phase advance and minimum beta
cos   1 
C L
2
U
Longitudinal phase advance as
a function of V for different c
 L min
C L

1  cos  
2sin 
Minimum L as a function of cL
for different V
Behavior of L(s) along the ring
c = 0.001
c = 0.01
c = 0.02
c = 0.03
Monotonic R1(s)
Opposite the cavity
- - - V = 3MV
V = 7.5 MV
 L
0 
s
Non Monotonic R1(s)
Near the cavity
R1  smin  
C L
2
Two minima appear in L(s) if the cavity position
is not in the point where R’1(s) changes sign
The energy spread and the emittance increase with the modulation in L

E  L

C
L


2
L||
 E 
2
1  
L   E 
L  E 
5
L  s 
  s
3
ds
2
 L  s    L L  s 
Bunch length in the reference ring for two values of V
Proposal for an experiment on DAFNE:
A. Gallo’s talk tomorrow
Needed:
• Flexible lattice to tune drift function R1
O.K. with limits due to dynamic and physical apertures
• Powerful RF system (high U)
Extra cavity – 1.3 GHz, 10 MV
D. Alesini et al: "Proposal of a Bunch Length Modulation Experiment in DAFNE", LNF-05/4(IR), 22/02/2005
C. Biscari et al , “Proposal of an Experiment on Bunch Length Modulation in DAFNE”, PAC2005, Knoxville, USA - 2005
6x6 single particle dynamics in SRFF regime
s L
R  s    Ri
Ri : ith element of the ring, including rf cavity
s
L p 1
C 
/ 
L
p
L

l
1 nD i D( s )
ds   
ds

L i 1 0  ( s )
D
R56 (s)  C L  D(s) = D’(s) = 0 and the rf cavity effect is neglected
R56 (s) is modified by the rf cavity and changes along the ring
In a transfer line:
T
R56
li
  
i 0
D( s)
ds
 (s)
Transverse and longitudinal plane are coupled:
 x  H

 
x
'

 H
 y  


 y'  
 l   R

  51
  E / E   R61
H
R15
H
R25
V V
V V
R52
R55
R62
R65
R16   x 


R26   x ' 
 y 


y
'


R56    l 
 


R66    E / E o
 L  s    L  L  s   R51 ( s ) x ( s)   R52 ( s) ' x ( s)  
2
2
2
2
2







 L  L  s   R ( s )  x  x  s    D( s ) p   R52 ( s )  x x  s    D '( s) p  




2
51
Bunch lengthening through emittance and dispersion also outside dipoles
How much does this effect weight on the bunch longitudinal dimensions?
Usually negligible
Can appear in isochronous rings*
with SRFF the effect can be very large due to
• Large dispersion, usually associated with large emittance
• Large energy spread
• Strong rf cavity
In the points where D = D’= 0 => R51 = R52 = 0
The lengthening does not appear at the IP.
*Y. Shoji: Bunch lengthening by a betatron motion in quasi-isochronous storage rings,
PRST–AB, Vol. 8, 094001 (2005)
Terms R51, R52, R55, R56, along the ring with MADX*
DAFNE now  =0.02
[email protected], V=8 MV,  =0.004, R non monotonic
c
c
15
1
15
R51
R52
R55
R56
10
R51
R52
R55
R56
10
5
5
0
0
-5
-5
-10
-10
-15
-15
0
20
60
40
80
100
s(m)
DAFNE Now
Frf = 368 MHZ - V = 0.3 MV
*Matrix calculations by C. Milardi
0
20
40
60
80
100
s(m)
DAFNE for SRFF – non monotonic
Frf = 1.3 GHZ - V = 8 MV
Bunch length with transverse contribution ??
SRFF conditions
Usual conditions
[email protected], V=8 MV, a =0.004, R non monotonic
DAFNE now -  = 0.02, V = 300 kV, frf =368MHz
c
c
30
1
30
sigl(mm)
siglt(mm)
sigl(mm)
siglt(mm)
25
20
20
sigl(mm)
25
15
15
10
10
5
5
0
0
20
40
60
80
100
0
0
20
s(m)
40
60
s(m)
 L  s    L  L  s   R51 (s) x (s)  R52 (s) 'x (s)
2
2
80
100
D = D’ = 0
D = - 4 m D’ = 0
D = -1 m D’ > 0
2 particles: 1 x, 1 p
Horizontal phase plane
Structure C – 4 MV @1.3GHz
D = 2m D’ = 0
 x   x  x   D p 
D = -2 m D’ >> 0
2
D = D’ = 0
R51 = R52 = 0
IP1 (long bunch)
? 500 turns-
2 particles: 1 x, 1 p
Longitudinal phase plane
At rf on short
At Long dipole
at SLM
IP2 (short bunch)
R51 = R52 = 0
R51 = R52 = 0
IP1 (long bunch)
2000 turns
2 particles: 1 x, 1 p
Longitudinal phase plane
At rf on short
At Long dipole
at SLM
IP2 (short bunch)
R51 = R52 = 0
DAFNE with SRFF
Bunch lengthening*
 /p
rf acc (%)
p
0.002
I th 
accrf(%)
0.0015
15
0.001
10
R  Z L / n eff
I (mA)
th
100
0.0005
2 c  E / e   p / p   L
2
20
accrf(%)
sigmap
sigmap
 Z L / n eff
 1
5
0
0
0
2
4
6
8
Monotonic -  = 0.073
10
c
10
V(MV)
 >(mA)
L
10
1
Non monotonic -  = 0.004
Non monotonic -  = 0.004
8
c
c
6
0.1
0
4
2
4
6
8
10
V(MV)
2
Monotonic -  = 0.073
c
0
0
2
4
6
V(MV)
8
10
*L. Falbo, D. Alesini
Simulation with distributed impedance
along the ring in progress
Possible applications of SRFF
Colliders and Light sources
Colliders: DAFNE can be used to test the principle
Exploiting the regime needs a specially dedicated lattice
and optimization of impedance distribution
Light sources:
Excluding those with field index dipole
(large dispersion in dipoles can lead to negative partition numbers)
BESSY II – data by G. Wuestefeld
Exercise
High momentum compaction
  1.4 e-03  rad
c = 7.2 e-04
  1.7e-02  rad
c = 3.8 e-02
Increasing c increases emittance in low emittance lattices
BESSY II - High momentum compaction
14
 (mm)
E = 0.9 GeV
frf = 500 MHz
V = 1.5
V = 27.9
V = 32.8
V = 36.1
L
12
V (MV)
Qs
p/p
(10-4)
1.5
0.064
3.69
27.9
0.333
11.9
32.8
0.389
16.5
36.1
0.444
26.9
10
8
6
4
2
0
0
50
100
150
s (m)
200
250
PEP-II like - High dispersion - high  = 0.011
35
c

8
D (m)
(mm)
L
V = 1 MV
V = 4 MV
V = 8 MV
V = 12 MV
V = 15 MV
30
25
6
20
4
15
2
10
5
0
-2
0
0
500
1000
1500
2000
2500
0
500
1
2000
2500
E = 3 GeV, frf = 1.5 GHz
-5
c
2
8
D (m)
1500
s(m)
s (m)
PEP-II like - Non monotonic R - small  = few 10
1000

L
(mm)
V = 4 MV
V = 16 MV
V = 37 MV
V = 65 MV
6
1.5
4
1
2
0
-2
0.5
0
500
1000
1500
2000
s (m)
lattice calculations by M. Biagini
2500
0
0
500
1000
1500
s(m)
2000
2500
PEP II like storage ring
Bunch current threshold (mA)
Boussard criteria with average bunch length
10
low ac - Ith(mA)
High ac - Ith(mA)
1
low ac - sigmap
low ac - accrf(%)
high ac - sigmap
high ac - accrf(%)
pep II like - energy spread and acceptance
0.01
10
p
rf acceptance (%)
0.001
1
0.1
0.01
0.001
0.0001
0
5
10
15
20
25
30
35
40
0.0001
0
5
V(MV)
10
15
20
25
30
V(MV)
----
Dashed lines – low c - non monotonic R1
Full lines – high c
35
0.1
40
Two cavities in the ring
cos   1 
L  s  
L 
C L
2
1
2
U1  U 2   C L  R3  R3U1U 2
1 
 C L   R2  s   R3  R1  s U1   R1  s   R3  R2  s U 2  R1  s  R2  s  R3U1U 2 

sin 
1
U1  U 2  R3U1U 2 
sin 
example
Synchrotron tune and energy spread
depend on the drift distance between the
two cavities
Conclusions
Bunch length modulation can be obtained in storage rings
in different regimes with high or low synchrotron tune
In any case it is associated to increase of natural energy spread
Qs
High
Low
Dynamic aperture
Rf acceptance
Microwave Instab threshold
Needed voltage
Talks on different aspects of the same subject by
P. Piminov - Dynamic Aperture of the Strong RF Focusing Storage Ring
S. Nikitin - Simulation of Touschek Effect for DAFNE with Strong RF Focusing
F.Marcellini - Design of a Multi-Cell, HOM Damped SC for the SRFF Experiment at DAFNE
A Gallo - The DAFNE Strong RF Focusing Experiment