transverse emittance preserving arc compressor
TRANSCRIPT
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
ERL'15, Stony Brook Univ., NY [email protected] 5
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
ERL'15, Stony Brook Univ., NY [email protected] 6
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).
ERL'15, Stony Brook Univ., NY [email protected] 7
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’
ERL'15, Stony Brook Univ., NY [email protected] 8
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
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
ERL'15, Stony Brook Univ., NY [email protected] 10
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
ERL'15, Stony Brook Univ., NY [email protected] 11
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
ERL'15, Stony Brook Univ., NY [email protected] 12
∏=
−−
=
+=
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:
ERL'15, Stony Brook Univ., NY [email protected] 13
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
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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
ERL'15, Stony Brook Univ., NY [email protected] 15
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
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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
ERL'15, Stony Brook Univ., NY [email protected] 17
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
ERL'15, Stony Brook Univ., NY [email protected] 18
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).
ERL'15, Stony Brook Univ., NY [email protected] 19
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