Bunch length modulation in storage rings

1
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
2
Bunch length manipulation routinely done in
linear systems linacs, fels, ctf3,.
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
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
4
Longitudinal plane oscillations in a ring with
one rf cavity
One-turn matrix
Described by the vector
Rf cavity lens
Sections with dipoles
Drift functions
Momentum compaction
A. Piwinski, Synchrotron Oscillations in
High-Energy Synchrotrons, NIM 72, pp. 79-81
(1969).
5
One turn longitudinal matrix one cavity in the
ring
Longitudinal Twiss functions
Phase advance determined by acL and rf Bunch
length can be modulated Energy spread constant
along the ring and defined by rf and phase advance
6
Longitudinal emittance and energy spread

• Energy spread defined by eigen values of matrix
  M, considering radiation damping and energy
  emission

Emittance diverges for m 0, 180 (Qs 0, 0.5)
A.W. Chao, Evaluation of Beam Distribution
Parameters in an Electron Storage Ring, Journal
of Applied Physics 50 595-598, 1979
7

• 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

8
Longitudinal phase space
Strong rf focusing monotonic R1
High rf voltage high momentum compaction High
synchrotron tune Ellipse rotates always in the
same direction
From RF to IP
From IP to RF
IP
RF input RF center RF output
Energy spread
A. Gallo, P. Raimondi, M.Zobov ,The Strong RF
Focusing a Possible Approach to Get Short
Bunches at the IP, e-Print Archivephysics/04040
20. Proceedings of the 31th ICFA BD workshop,
SLAC 2003
Bunch length
9
Evolution of Strong rf focusing non monotonic
R1

• High rf voltage high derivative of R1 (s)
• Low synchrotron tune
• Ellipse rotates on both directions

Energy spread
Bunch length
C. Biscari - Bunch length modulation in highly
dispersive storage rings", PRSTAB, Vol. 8,
091001 (2005)
10
C 100 m E 0.51 GeV frf 1.3 GHz Vmax 10 MV
Reference ring DAFNE like
acL
rf cavity
Monotonic R1(s)
Non Monotonic R1(s)
11
Phase advance and minimum beta
Longitudinal phase advance as a function of V
for different ac
Minimum bL as a function of acL for different V
12
Behavior of bL(s) along the ring
ac 0.001 ac 0.01 ac 0.02 ac 0.03
Monotonic R1(s) Opposite the cavity
Non Monotonic R1(s) Near the cavity
- - - V 3MV V 7.5 MV
13
Two minima appear in bL(s) if the cavity position
is not in the point where R1(s) changes sign
14
The energy spread and the emittance increase with
the modulation in sL
Bunch length in the reference ring for two values
of V
15
Proposal for an experiment on DAFNE A. Gallos
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
16
6x6 single particle dynamics in SRFF regime
Ri ith element of the ring, including rf cavity
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
17
Transverse and longitudinal plane are coupled
Bunch lengthening through emittance and
dispersion also outside dipoles
18
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 gt R51 R52 0
• The lengthening does not appear at the IP.

Y. Shoji Bunch lengthening by a betatron motion
in quasi-isochronous storage rings, PRSTAB,
Vol. 8, 094001 (2005)
19
Terms R51, R52, R55, R56, along the ring with
MADX
DAFNE Now Frf 368 MHZ - V 0.3 MV
DAFNE for SRFF non monotonic Frf 1.3 GHZ - V
8 MV
Matrix calculations by C. Milardi
20
Bunch length with transverse contribution ??
SRFF conditions
Usual conditions
21
D -1 m D gt 0
D D 0
D - 4 m D 0
2 particles 1 sx, 1 sp
Horizontal phase plane
Structure C 4 MV _at_1.3GHz
D D 0
D 2m D 0
D -2 m D gtgt 0
22
R51 R52 0
IP1 (long bunch) ? 500 turns-
At Long dipole
Longitudinal phase plane
2 particles 1 sx, 1 sp
At rf on short at SLM IP2 (short
bunch)
R51 R52 0
23
R51 R52 0
IP1 (long bunch) 2000 turns
At Long dipole
Longitudinal phase plane
2 particles 1 sx, 1 sp
At rf on short at SLM IP2 (short
bunch)
R51 R52 0
24
Bunch lengthening
DAFNE with SRFF
L. Falbo, D. Alesini Simulation with distributed
impedance along the ring in progress
25
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)
26
BESSY II data by G. Wuestefeld
Exercise
High momentum compaction
e 1.4 e-03 m rad ac 7.2 e-04
e 1.7e-02 m rad ac 3.8 e-02
Increasing ac increases emittance in low
emittance lattices
27
BESSY II - High momentum compaction
E 0.9 GeV frf 500 MHz
V (MV) Qs sp/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
28
E 3 GeV, frf 1.5 GHz
lattice calculations by M. Biagini
29
PEP II like storage ring
- - - - Dashed lines low ac - non monotonic
R1 Full lines high ac
30
Two cavities in the ring
example
Synchrotron tune and energy spread depend on the
drift distance between the two cavities
31
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