Transverse Emittance Preserving Arc Compressor

ERL'15, Stony Brook Univ., NY [email protected]

Transverse Emittance Preserving Arc

Compressor: Sensitivity to Beam Optics,

Charge and Energy

S. Di Mitri

Elettra Sincrotrone Trieste

2

FERMI

Where I come from...

is a nonprofit shareholder company of national interest,

established in Trieste, Italy in 1987 to construct and

manage synchrotron light sources as international

facilities.

ERL'15, Stony Brook Univ., NY [email protected] 4

OutlineOutlineOutlineOutline

� Prologue

• Motivations and Challenges

• Arc Compressors in Literature

� Optics Balance in a Transfer Line (C=1)

• 1-D CSR model & Experimental Proof

� Periodic Arc Compressor (C=45)

• Optics Considerations

• Analysis and Simulations: Emittance vs. Bunch Charge,

Energy and Optics

� Conclusions & Outlook


Motivations & ChallengesMotivations & ChallengesMotivations & ChallengesMotivations & Challenges� Why magnetic bunch length compression?

� What are the challenges of σσσσz-compression?

� Why an arc compressor?

• FELs:

Pout ∝∝∝∝ I

• Linear Colliders: ∆ε∆ε∆ε∆εx,y(w⊥) ∝∝∝∝ I-1

FEL

Recirculation AND

CompressionTURNAROUND

• ERLs: BC1

ARC COMPRESSOR

FEL

• Single-Pass:

• CSR:

∆ε∆ε∆ε∆εx ∝∝∝∝ (σσσσz,CSR)-8/3

x

z

x

z


Arc Compressors in (Recent) LiteratureArc Compressors in (Recent) LiteratureArc Compressors in (Recent) LiteratureArc Compressors in (Recent) Literature

� Past ERLs design studies: BNL (2001), KEK (2007), ANL (2008), JLAB (2011),

Cornell (2013).

� Our proposal:

E >0.6 GeV

Q = 50–150 pC

C <30 (77pC,3.0GeV)

∆ε∆ε∆ε∆εnx ∼∼∼∼ 0.1 µµµµm

� Minimize the CSR-dispersion function. [R. Hajima, 528 (2004) 335].

� CSR primarily suppressed with a low charge.

E >0.5 GeV

Q = 100-500 pC

C = 45 (500pC,2.4GeV)

∆ε∆ε∆ε∆εnx ∼∼∼∼ 0.1 µµµµm

� Optics balance to cancel successive CSR kicks… [Di Mitri, Cornacchia, Spampinati, PRL 110 014801 (2013)].

� …extended to a varying bunch length. [Di Mitri, Cornacchia, EPL 109 (2015) 62002].

� Background: D.Douglas, JLAB-TN-98-012 (1998);

Y.Jiao et al., PRTSAB 17, 060701 (2014).


CSR PictureCSR PictureCSR PictureCSR Picturedipole

�head

tail Radiation catches up

with electrons ahead

� Consider 1-D steady-state CSR emission, and

linear optics.

� Transient CSR effects and nonlinear dynamics

will be included in the simulations.

��, �� = . � �� · ��

��

�

��/�

�� /�

RELATIVE ENERGY SPREAD of GAUSSIAN bunch, per DIPOLE:

Initial reference (dispersive) trajectory, xη

Initial betatron oscillation, xβ

Photon emission/absorption,∆x = ∆xβ+ ∆xη = 0

New betatron amplitude, ∆xβ,phot = –ηδphot

New dispersive trajectory, xη,phot = xη + ηδphot

Bunch head

gains energy Bunch tail

is not affected

head tail

Bunch core

loses energy

For a SINGLE PARTICLE: For a BUNCH:x

z

Note: distortion is both in x and x’


Projected Projected Projected Projected Emittance Emittance Emittance Emittance Growth, Growth, Growth, Growth, σσσσzzzz = const.= const.= const.= const.� Multiple and identical CSR kicks (this applies to an isochronous transfer line):

A. Use the Courant-Snyder formalism forthe particle coordinates, linear transportmatrices, x1=Mx0, and J(0)=0.

B. When traversing a dipole, add the CSRinduced η-terms. This leads to anincrease of the particle’s C-S invariant:

C. Repeat until the end of the line. All kicksare identical in module, and we can writeJf=Jf(J1). After averaging we find:

x

x

xw

β

β=

+= ββ

β

αββ xxw

x

xxxx ''

πµ =∆ 2,1

#1

( )', ηη ++

#3

( )', ηη −+

πµ =∆ 3,2

#5( )', ηη −−

πµ =∆ 4,3

( )', ηη +−

#7πµ =∆ 2,1 πµ =∆ 3,2

πµ =∆ 4,3

� Final CSR induced C-S invariant is zero (cancellation).

( ) 2

1

22'

11

'

111

2

11

2'

11

'

111

2

111

2

2

CSRCSR H

xxxxJ

δδηβηηαηγ

βαγ

≡++=

=++=

( ) ( )xxxCSRxxfx XJ µαβσεεε δ ,,2

,10,

2

0,

2

, +=

0

ERL'15, Stony Brook Univ., NY

Experimental Proof at FERMIExperimental Proof at FERMIExperimental Proof at FERMIExperimental Proof at FERMI

Dipole Quadrupole

for scan

Horiz. energy

dispersion, ηηηηxOne quadrupole’s strength is scanned to vary the phase advance between the DBAs.

Quadrupoles

Quadrupoles ensure π-phase advance between dipoles and proper values of βx, αx to cancel the CSR-emittance.

βx

βy

[email protected] 9

Results:

• Minimum εn,x for nominal optics (π-phase advance and optimum Twiss parameters).

• Larger εn,x for shorter beam.

500pC, 0.4 ps rms 0.2 ps rms

PRL 109, 014801 (2013)

Phys. Reports 539, 1 (2014)

DBA

DBA

εεεεx measure-

ment


Periodic Arc CompressorPeriodic Arc CompressorPeriodic Arc CompressorPeriodic Arc Compressor� Hx has to be small at the dipoles ⇒ θ and βx small

� R56 has to large enough to cumulate a C>30 ⇒ θ not too small

� Suitable βx, αx, µx along the line for CSR cancellation ⇒ many quadrupoles

� We want to linearize the longitudinal phase during compression ⇒ sextupoles

� Possibly simple, robust and compact lattice

• 6 DBA cells (Elettra-like lattice, ECG).• 180o, 125 m long at 2.4 GeV• R56 = +35 mm per cell

Due to symmetry and short bends, ∆µx ≈ π.

DBA cell


Optimum Optics in a Single DBA:Optimum Optics in a Single DBA:Optimum Optics in a Single DBA:Optimum Optics in a Single DBA:

( ) ( )

( ),22

22

2

3/1

1

3/1

3

1

3/4

2

22

3/1

1

3/1'

3

2

3/4

1

3/4

3

+=

−−−−=

−+−−=

θρθρδ

θρβ

αθρθρ

θρθρ

θθθθ

θθθθ

kk

SCkSkSkx

SCkSCkx

For a single DBA, at the exit of the 2nd dipole we have:( ) ( )

iii

izi

kCk

k

SC

3/4

11

3/4

,e )Q/(e0.2459r

2sin,2cos

++ =

=

==

γσ

θθ θθ

( ) ( ) ( )[ ] ( )( )

−+

+−+−

++

≅ 31

6231

6

11

2

3/43/4

2

23/42

2

23/4

2

2

23/4

2

223/1

13

CCl

CCl

Ck

J bb ααβ

βθρ

0

0

2

2

2

3

2

3

≡

≡

α

β

β

α

d

dJ

d

dJ

Look for the optimum Twiss parameters at the dipoles:

( )

( ) ( )( )1

31

6

3

1

6

3/4

23/42

2

23/4

,2

3/4

3/4

2

,2

+

−+−

=

−

+

−=

C

CCl

C

C

l

b

opt

b

opt

αβ

βα

( ) ,6

1,2

,2

b

opt

optl

Cβ

α −==

103 =⇔= CJ

where

as already in [Y. Jiao et al. PRTSAB 17, 060701 (2014)].

CSR kick scales with σz


∏=

−−

=

+=

j

i

loc

i

tot

j

ii

loc

i

CC

RhCC

1

5611

,1

1

1. The local Ci depends on the upstream E-chirp, which varies along the arc: izi

idz

dE

Eh

,

0,

0

1

σ

σδ≈

=

6,...,1, =ji

2. The optimum βx,dip depends on Ci, thereby it varies along the arc.

Optimum βx,dip, Ciloc and Ji, for αx,dip=0: Ji vs. βx,dip, for αx,dip=0:

Most of the CSR dynamics is the very last cell(Ctot=45)

ββββx too small

ββββx,i optimum

ββββx larger

Optimum Optics Optimum Optics Optimum Optics Optimum Optics alongalongalongalong the Arc Compressor:the Arc Compressor:the Arc Compressor:the Arc Compressor:


Final Emittance vs. Charge and OpticsFinal Emittance vs. Charge and OpticsFinal Emittance vs. Charge and OpticsFinal Emittance vs. Charge and OpticsE = 2.4 GeV Ctot = 45

σσσσz,0 = 3 mm εεεεnx,0 = 0.8 µµµµm

h0 = -4.7 m-1

Each step corresponds to a different ββββx,dip.

∆ε∆ε∆ε∆εx,CSR = ββββx,dip is the same for all the dipoles (periodic solution).

Chromatic aberrations ( ) are NOT corrected at each step.

minimum growth

minimum growth


Final Emittance vs. Charge and EnergyFinal Emittance vs. Charge and EnergyFinal Emittance vs. Charge and EnergyFinal Emittance vs. Charge and Energy

11,

2

1,

2

, −−− += iixixix Jεεε

0,

1

1

1

10,

2

0,

2

, x

j

i

j

ixxfx JJ εεεε <<⇔+≈ ∑∑ −−

Ansatz: the emittance sums in quadrature after each DBA: • Theory: Ji as above.

• Steady: 1-D CSR in Elegant.

• Total: Steady + Edges + Drifts.

If,0.5=1.5 kA

If,0.3=1.0 kA

If,0.1=0.4 kA

This is:

sqrt[(εεεεnx,f)2 – (εεεεnx,0)

2],and εnx,0 = 0.8 µm.

We may achieve

∆εnx ≤ 0.1 µm for, e.g.:

• 100pC, E > 0.5 GeV

• 300pC, E > 1.0 GeV

• 500pC, E > 2.0 GeV


Full Particle Tracking (Elegant)Full Particle Tracking (Elegant)Full Particle Tracking (Elegant)Full Particle Tracking (Elegant)� Particle tracking now including:

• 3rd order transport matrices, ISR and CSR transient effects,

• CSR-induced microbunching from a quiet start and 5 M-particles

• Enlarged uncorrelated energy spread, as from a laser heater (30 keV rms)

� Two sets of beam parameters at 2.4 GeV, C=45:

• Q = 100 / 500 pC

• If = 1.3 / 2.2 kA

• σσσσδδδδ,0 = 0.1 / 0.4 %

• εεεεnx,0 = 0.2 / 0.8 µµµµm rad

100pC 500pC

Slice emittances and peak current

EPL 109, 62002 (2015)

∆ε∆ε∆ε∆εx,SLICE ≤≤≤≤ 0.05 µµµµm

∆ε∆ε∆ε∆εx,SLICE ≤≤≤≤ 0.05 µµµµm


Nonlinear DynamicsNonlinear DynamicsNonlinear DynamicsNonlinear Dynamics� Nonlinearities in the longitudinal phase space evolve during compression due to:

• Incoming RF curvature,

• T566 of the DBA cells,

• Nonlinear CSR-induced energy chirp.

� 24 sextupole magnets linearize the compression. Strengths and positions

optimized for minimizing chromatic aberrations (these are responsible for the

emittance modulation along the line, see below).

100pC 500pC

ISR

3rd ORDER

CSR

EPL 109 (2015) 62002

∆ε∆ε∆ε∆εx,PROJ. ≤≤≤≤ 0.13 µµµµm

∆ε∆ε∆ε∆εx,PROJ. ≤≤≤≤ 0.15 µµµµm


Microbunching InstabilityMicrobunching InstabilityMicrobunching InstabilityMicrobunching Instability

100pC 500pC

� The effect of CSR-induced microbunching (MB) is damped by the initial beam

heating. The strength of MB dynamics sounds over-estimated because:

• E/I-modulations tend to smear as the # of particles increases from 0.1 to 5 M;

• filtering suppresses λf ≤ 1 µm, while MB appears at λf > 10 µm;

• transverse emittance smearing effect not included.

� Accurate MB analysis is pending. See, e.g., C.-S. Tsai’s talk (today, this session)

EPL 109 (2015) 62002


Conclusions & OutlookConclusions & OutlookConclusions & OutlookConclusions & Outlook

� The extension of CSR-driven liner optics balance to the case of

varying bunch length leads to a simple formula for a periodic system.

� The final emittance estimate is in reasonable agreement with 1-D

tracking results (see also C.Hall’s talk, this session).

� For a DBA-based 180o arc compressor, we expect a “gain”∼∼∼∼ 10 in

“Q × C / E”, w.r.t. the existing literature.

� Working plan:

• more accurate microbunching instability analysis;

• massive numerical optimization of the emittance vs. linear and

nonlinear dynamics;

• scaling to a (low energy) compact ERL, and to a (high energy)

single-pass beamline.

� A proof-of-principle experiment may be possible at the FERMI Main

e-Beam Dump line (two big dipoles and quads available at 1.5 GeV).


AcknowledgementsAcknowledgementsAcknowledgementsAcknowledgements

A special thank to my good friends, collaborators, and often co-authors,

M. Cornacchia and S. Spampinati:

M.CORNACCHIA S.SPAMPINATI

Acknowledgements to Y. Jiao, X. Cui, M. Venturini, D. Douglas, R. Li

and C.-S. Tsai for interesting and productive discussions.

Thanks to the FERMI Team for making the machine available for physics

studies, and to the FERMI Management for supporting this activity.

Thank You for Your attention

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Transverse Emittance Preserving Arc Compressor