Bunch length modulation in storage ringsBunch length modulation in storage rings C. Biscari C. Biscari

LNF – INFN - FrascatiLNF – INFN - Frascati

Workshop on “Frontiers of short bunches in storage rings” – Frascati – 7-8 Nov 2005

0

0.5

1

1.5

2

2.5

3

3.5

-0.1 0 0.1 0.2 0.3 0.4 0.5

sl calibrsl model calibsl - sim meas sl - sim envsl model calib FKL

R_56

(m)

CTF3 stretcher - compressor Bunch length (mm) measurements (2004)

R56 = - 0.1R56 = 0R56 = 0.1R56 = 0.2R56 = 0.3R56 = 0.4R56 = 0.5

Bunch length manipulation routinely done in linear systems: linacs, fels, ctf3,….

560

( )( )

ilT

i

D sR dss

By using dispersion in dipoles and correlation in the longitudinal phase planeintroduced by rf acceleration

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 dipolesand

large rf cavity voltage derivative

can force the oscillations to grow and lead to correlation in longitudinal phase plane

1C

D dsL

Longitudinal plane oscillations in a ring with one rf cavity*

1

2

( ) ( ) ( )

1 0 21 /

1 ( )( )

0 1

1 ( )( )

0 1

rf rf rf

rfrf

rf

rf

rf

s s s s s

VU

U E e

R ss s

R ss s

M M M M

M

M

M

1 2 1

'' and

'

rfs

cs

D sR s ds R s L R s

s

Drift functions:

lpp

*A. Piwinski, “Synchrotron Oscillations in High-Energy Synchrotrons,” NIM 72, pp. 79-81 (1969).

Described by the vector

Rf cavity lens

One-turn matrix

Momentum compaction

Sectionswith dipoles

One turn longitudinal matrix – one cavity in the ring

2 1 2

1

1cos sin

1C L L

L L

UR L UR Rs

U UR

M I

1 2

cos 12

1 ( ) ( )sin

sin

C

L C

L

LU

s L R s R s U

U

Longitudinal Twiss functions

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

2 5

3||2

LE LL

sC ds

E L s

Emittance diverges for = 0, 180° (Qs = 0, 0.5)

21 1sin

EL

L E

L L Ls s

E/E

l

LL

sLL

*A.W. Chao, “Evaluation of Beam Distribution Parameters in an Electron Storage Ring”, Journal of Applied Physics 50: 595-598, 1979

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

Longitudinal phase space

RF input

RF center

RF output

IP

Bunch length

Energyspread

High rf voltage + high momentum compaction:High synchrotron tune

Ellipse rotates always in the same direction

From RF to IP

Strong rf focusing – monotonic R1 * 1

''

'

rfs

s

D sR s ds

s

*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

From IP to RF

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

Bunch length

Energyspread

* C. Biscari - Bunch length modulation in highly dispersive storage rings", PRST–AB, Vol. 8, 091001 (2005)

Reference ring – DANE like

1

''

'

rfs

s

D sR s ds

s

rf cavity

Monotonic R1(s) Non Monotonic R1(s)

cL

C = 100 mE = 0.51 GeVfrf = 1.3 GHzVmax = 10 MV

min 1 cos2sinC

LL

Longitudinal phase advance asa function of V for different c

Minimum L as a function of cLfor different V

Phase advance and minimum beta

cos 12CLU

1 min02CL L

R ss

Behavior of L(s) along the ring

Monotonic R1(s)Opposite the cavity

Non Monotonic R1(s)Near the cavity

c = 0.001c = 0.01c = 0.02c = 0.03

- - - V = 3MV V = 7.5 MV

Two minima appear in L(s) if the cavity position is not in the point where R’1(s) changes sign

2 5

3||2

LE LL

sC ds

E L s

21 EL

L E

L L Ls s

The energy spread and the emittance increase with the modulation in L

Bunch length in the reference ring for two values of V

Proposal for an experiment on DAFNE: A. Gallo’s talk tomorrow

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

Needed:

•Flexible lattice to tune drift function R1O.K. with limits due to dynamic and physical apertures

•Powerful RF system (high U)Extra cavity – 1.3 GHz, 10 MV

6x6 single particle dynamics in SRFF regime

s L

i

ss

R R Ri : ith element of the ring, including rf cavity

1 0

1 1 ( )( )

/iD ln

Ci

L p D D sds dsL p L L s

56 ( ) CR s L D(s) = D’(s) = 0 and the rf cavity effect is neglected

560

( )( )

ilT

i

D sR dss

In a transfer line:

R56 (s) is modified by the rf cavity and changes along the ring

2 251 52

2 22 251 52

( ) ( ) ( ) ' ( )

( ) ( ) ( ) '( )

L L L x x

L L x x p x x p

s s R s s R s s

s R s s D s R s s D s

15 16

25 26

51 52 55 56

61 62 65 66

' '

' '

/ /o

H H R Rx xH H R Rx x

V Vy yV Vy y

R R R Rl lR R R RE E E E

Bunch lengthening through emittance and dispersion also outside dipoles

Transverse and longitudinal plane are coupled:

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)

*Matrix calculations by C. Milardi

Terms R51, R52, R55, R56, along the ring with MADX*

DAFNE NowFrf = 368 MHZ - V = 0.3 MV

DAFNE for SRFF – non monotonicFrf = 1.3 GHZ - V = 8 MV

Bunch length with transverse contribution ??

2 251 52( ) ( ) ( ) ' ( )L L L x xs s R s s R s s

Usual conditions SRFF conditions

2 particles: 1 x, 1 pHorizontal phase plane

Structure C – 4 MV @1.3GHz 2

x x x pD

D = D’ = 0

D = D’ = 0D = 2m D’ = 0

D = - 4 m D’ = 0 D = -1 m D’ > 0

D = -2 m D’ >> 0

IP1 (long bunch) ? 500 turns- At Long dipole

At rf on short at SLM IP2 (short bunch)

Longitudinal phase plane

R51 = R52 = 0

R51 = R52 = 0

2 particles: 1 x, 1 p

IP1 (long bunch) 2000 turns At Long dipole

At rf on short at SLM IP2 (short bunch)

R51 = R52 = 0

R51 = R52 = 0

Longitudinal phase plane 2 particles: 1 x, 1 p

Bunch lengthening*

0.1

1

10

100

0 2 4 6 8 10

Ith ( mA)

V(MV)

Non monotonic - c = 0.004

Monotonic - c = 0.073

*L. Falbo, D. AlesiniSimulation with distributed impedance along the ring in progress

22 / /

/c p L

thL eff

E e pI

R Z n

/ 1L effZ n

DAFNE with SRFF

Possible applications of SRFF

Colliders and Light sources

Colliders: DANE can be used to test the principleExploiting 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)

1.4 e-03 radc = 7.2 e-04

1.7e-02 radc = 3.8 e-02

BESSY II – data by G. Wuestefeld

High momentum compaction

Increasing c increases emittance in low emittance lattices

Exercise

0

2

4

6

8

10

12

14

0 50 100 150 200 250

V = 1.5 V = 27.9V = 32.8V = 36.1

L (mm)

s (m)

BESSY II - High momentum compaction

V (MV) Qsp/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

E = 0.9 GeVfrf = 500 MHz

-2

0

2

4

6

8

0 500 1000 1500 2000 2500s (m)

D (m)

PEP-II like - High dispersion - high c = 0.011

-2

0

2

4

6

8

0 500 1000 1500 2000 2500s (m)

D (m)

PEP-II like - Non monotonic R1 - small

c = few 10-5

0

5

10

15

20

25

30

35

0 500 1000 1500 2000 2500

V = 1 MVV = 4 MVV = 8 MVV = 12 MVV = 15 MV

L ( mm)

s(m)

0

0.5

1

1.5

2

0 500 1000 1500 2000 2500

V = 4 MVV = 16 MVV = 37 MVV = 65 MV

s(m)

L ( mm)

lattice calculations by M. Biagini

E = 3 GeV, frf = 1.5 GHz

0.0001

0.001

0.01

0.1

1

10

0 5 10 15 20 25 30 35 40

pep II like - energy spread and acceptance

low ac - sigmaphigh ac - sigmap

low ac - accrf(%)high ac - accrf(%)

p

V(MV)

rf acceptance (%)

- - - - Dashed lines – low c - non monotonic R1

Full lines – high c

0.0001

0.001

0.01

0.1

1

10

0 5 10 15 20 25 30 35 40

low ac - Ith(mA)

High ac - Ith(mA)

Bunch current threshold (mA) Boussard criteria with average bunch length

V(MV)

PEP II like storage ring

1 2 3 3 1 2

2 3 1 1 1 3 2 2 1 2 3 1 2

1 2 3 1 2

1cos 12 2

1sin

1sin

CC

L C

L

LU U L R R U U

s L R s R R s U R s R R s U R s R s R U U

U U R U U

Two cavities in the ring

example

Synchrotron tune and energy spreaddepend on the drift distance between the two cavities

Conclusions

Talks on different aspects of the same subject byP. Piminov - Dynamic Aperture of the Strong RF Focusing Storage RingS. 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

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 LowDynamic apertureRf acceptanceMicrowave Instab thresholdNeeded voltage