IR Optics and Nonlinear Beam
Dynamics
Fanglei Lin for MEIC study group at JLab
2nd Mini-workshop on MEIC IR Design, November 2, 2012
Outline
MEIC overview
IR design considerations and features
 Detector-optimized IR optics
 Crab crossing scheme
 Chromaticity compensation concept
 Momentum acceptance and dynamic aperture
Goals and timeline (from 2012 NP proposal)
F. Lin
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MEIC Design Parameters
• Energy
(bridging the gap of 12 GeV CEBAF & HERA/LHeC)
– Full coverage of s from a few 100 to a few 1000 GeV2
– Electrons 3-11 GeV, protons 20-100 GeV, ions 12-40 GeV/u
• Ion species
– Polarized light ions: p, d, 3He, and possibly Li, and polarized heavier ions
– Un-polarized light to heavy ions up to A above 200 (Au, Pb)
• Up to 3 detectors
– Two at medium energy ions: one optimized for full acceptance, another for high luminosity
– Third one for ion energies lower than 20 GeV/u
• Luminosity
– Greater than 1034 cm-2s-1 per interaction point
– Maximum luminosity should optimally be around √s=45 GeV
• Polarization
– At IP: longitudinal for both beams, transverse for ions only
– All polarizations >70% desirable
• Upgradeable to higher energies and luminosity
– 20 GeV electron, 250 GeV proton, and 100 GeV/u ion
F. Lin
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MEIC Layout
Cross sections of tunnels for MEIC
F. Lin
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Stacked Figure-8 Rings
Ion path
Interaction
Regions
Electron
path
Large Ion
Booster
Electron
Collider
• Vertical stacking for identical ring circumferences
• Horizontal crab crossing at IPs due to flat colliding beams
• Ion beams execute vertical excursion to the plane of the electron orbit
for enabling a horizontal crossing, avoiding electron synchrotron
radiation and emittance degradation
F. Lin
Interaction point locations:
 Downstream ends of the
electron straight sections to
reduce synchrotron radiation
background
 Upstream ends of the ion
straight sections to reduce
residual gas scattering
background
Ion
Collider
• Ring circumference: 1340 m
• Maximum ring separation: 4 m
• Figure-8 crossing angle: 60 deg.
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Parameters for Full Acceptance Interaction Point
Proton
Electron
Beam energy
GeV
60
5
Collision frequency
MHz
750
750
Particles per bunch
1010
0.416
2.5
Beam Current
A
0.5
3
Polarization
%
> 70
~ 80
Energy spread
10-4
~3
7.1
RMS bunch length
mm
10
7.5
Horizontal emittance, normalized
µm rad
0.35
54
Vertical emittance, normalized
µm rad
0.07
11
Horizontal β*
cm
10
10
Vertical β*
cm
2
2
Vertical beam-beam tune shift
0.014
0.03
Laslett tune shift
0.06
Very small
7
3
Distance from IP to 1st FF quad
Luminosity per IP, 1033
m
cm-2s-1
F. Lin
5.6
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IR Design Considerations and Features
•
•
•
•
•
•
•
•
•
•
•
Large detector space (7m) for a full-acceptance detector
Detection of forward scattered hadrons down to 0
– Large aperture downstream ion final focusing quadrupoles
– Large machine-element-free drift space after large spectrometer dipole
– Secondary focus after large spectrometer dipole combined with large dispersion for better
momentum resolution
Detection of low-Q2 electrons and electron momentum analysis
Large 50 mrad crab crossing angle for faster beam separation (to reduce parasitic collisions due to
high repetition rate and increase space for magnets) and better detector resolution
IPs close to exit from ion arcs (reduce residual gas scattering background) and far from exit from
electron arcs (reduce synchrotron radiation background)
Use permanent-magnet design for some of the electron final focusing quadrupoles to move them
closer to the IP without reducing detector solid angle coverage
Vertical ion chicane to avoid electron synchrotron radiation and emittance degradation
Compatibility with crab crossing to restore head-on collisions
Small * for high luminosity
Different*x and *y for a more balanced optics design
Large momentum acceptance and dynamic aperture
– Symmetric chromaticity compensation scheme
– Asymmetric detector space (upstream ion final focusing block moved closer to the IP)
F. Lin
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Detector-Optimized Optics
•
•
•
•
Upstream FFB is placed much closer to the IP than that
on the downstream
 Upstream FFB reduces the maximum betatron
functions and the contribution to the chromaticity
 Downstream FFB was designed to have larger
apertures of its quadrupole, plus increasing
distance from the IP, to maximize its acceptance
to the forward-scattered hadrons
Further focusing in the downstream (small beam size)
allows to place the detectors close to the beam center.
Combining with ~1m dispersion at the focal point, it can
detect particles with small momentum offset Δp/p
F. Lin
Similar optics
In addition, two permanent magnetic quadrupoles are
used in the upstream FFB and vey close to the IP to
maximize the ion detector acceptance by reducing the
solid angle blocked by the final focusing quadrupoles.
Changing of their focusing strengths with energy can be
compensated by adjusting the upstream electric
quadruples.
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Crab Crossing Scheme
• Restore effective head-on bunch collisions with 50 mrad crossing angle  Preserve luminosity
• Dispersive crabbing (regular accelerating / bunching cavities in dispersive region) vs.
Deflecting crabbing (novel TEM-type SRF cavity at ODU/JLab, very promising!)
• Compensation scheme for crab crossing
 Global (KEK B-Factory): only one cavity installed in each collider ring
 Local (MEIC):
• Two identical crab cavities, one for crabbing and one for restoration.
• The locations of two crab cavities have phase advance (n+1)π/2 relative to IP to minimize the
required integrated crab kicking voltage
• Confine the beam gymnastics only in the IR.
MEIC crab cavity design
F. Lin
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Crab Crossing Scheme
• Linear Optics
• Two cavities are placed
to ensure phase advance
(n+1) π/2 relative to IP.
• Two cavities are placed
at those locations with
relatively large βx to
reduce the required crab
kicking voltage.
• Tracking Simulations
Incoming
π/2
3π/2
At IP
F. Lin
Outgoing
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Chromaticity Compensation Concept
• Modular approach: IR designed independently to be later integrated into ring
• Dedicated symmetric Chromaticity Compensation Blocks (CCB)
• Each CCB is designed to satisfy the following symmetry conditions
– ux is anti-symmetric with respect to the center of the CCB
– uy is symmetric
– D is symmetric
– n and ns are symmetric
F. Lin
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Compensation of Main 2nd-Order Terms
•
Chromatic terms




0
0
0
0
2 Dnsux2 ds   nu x2 ds, 2 Dnsu y2 ds   nu y2ds
•
are compensated using sextupoles located in CCB’s attaining
2nd-order dispersion term and sextupole beam smear due to betatron beam size

•


 D(Dns  n)ux ds  0,
3
n
u
s
x
 ds  0,
2
n
u
u
ds  0
s
x
y

0
0
0
are automatically compensated.
In a conclusion, CCB scheme actualizes
– local chromaticity compensation including contributions of both the final focusing
quadrupoles and the whole ring
– simultaneous compensation of chromatic and sextupole beam smear at IP restoring
luminosity
F. Lin
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Ion IR Optics
Ion beams
BES
CCB
FFB (up)
FFB (down)
D
1
•
•
•
•
•
DSB
D
2
BES: Beam Extension Section
FFB: Final Focusing Block
D1,D2: Spectrometer Dipoles
DSB: Dispersion Suppression Block
Two sextupole families are inserted
symmetrically in the CCB (the shorter
bar in the above lattice plot) for the
chromaticity compensation
F. Lin
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Complete Ion Collider Ring Layout
•
•
•
CCB dipoles in the upstream of IPs bend particles outside of the ring
Spectrometer dipoles in the downstream of IPs bend particles inside of the ring
Such an arrangement leads to put the neutron detector “ZDC” outside of the ring, leaving
the space inside for electron cooling channels.
CCB
CCB
Spectrometer dipoles
Electron cooling channels
F. Lin
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Emittance Impact For Electron Ring
This particular scheme involves placing dipoles in the regions with extended beam in
order to produce and suppress the dispersion
Higher dispersion magnitude allows chromaticity compensation with lower sextupole
fields
Maximum dispersion magnitude for electron beam is limited by maximum acceptable
emittance increase
Normalized equilibrium horizontal emittance growth due to two horizontal bends in the
current electron ring CCB design
I 5 x
  Cq
I2
N
x
•
I2   (
3
1
 x2

1
 y2
)ds 
8
3  arc
 x Dx'2  2 x Dx Dx'   x Dx2
I 5 x  
ds
3

IR
At the entrance of CCB bend Dx 0 , Dx' 0  0 , so
 s 

xD
  x 

 IR 
s3
2 x Dx' Dx  2 x 2
2
 x ~ a few hundred meters
'2
x
 IR
 xD
2
x

1   x s4
 x  IR2

 x Dx'2

 I 5 x / CCB  
ds  x 3
3
 IR
IR  IR
x  0
x 
1   x2
x
F.Lin
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
L
0
s2

2
IR
ds 
2 x 3
IR
3  IR2
Emittance Impact For Electron Ring (cont.)
•
Emittance increase  N / CCB  1 C   arc  3 3  0.0012  arc E 3 (GeV 3 ) 3 (deg 3 )
x
q x
IR
x
IR
4
 IR2
 IR2
•
Suppose
then,
•
•
 x  400m, arc  43.5m,  IR  200m, E  5GeV, IR  30mrad
 xN / CCB  1.75μm
N
N
Current electron ring design has  arc  36μm and  x / design  54μm
 xN / 2CCB
~ 6.4%
 xN / design
Therefore,
 xN / CCB
~ 3.2%
 xN / design

 xN / 4CCB
~ 12.8%
 xN / design
The emittance impact for electron ring due to the CCB dipoles can be mitigated by
suppressing the horizontal beta function in the dipoles. This will be considered in the
future electron CCB design.
F.Lin
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Old Optics For Chromaticity Compensation
Ion beam
Electron beam
F.Lin
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IR Geometry For Chromaticity Compensation
Geometrical matching of electron and ion IR’s (MAD-X survey)
– Weak bend for electrons to avoid emittance degradation
– Strong bend for ions to generate large dispersion
– Alternating bends in ion interaction region
Ion Ring
Electron Ring
F.Lin
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Ion Ring Parameters
Unit
IP * functions
Proton beam momentum
Optics for Chrom.
Compensation
Detector optimized
optics
cm
10/2
GeV/c
60
Circumference
m
Arc’s net bend
deg
240
Straights’ crossing angle
deg
60
Arc length
m
391.0
Maximum horizontal / vertical  functions
m
Maximum horizontal dispersion Dx
m
Horizontal / vertical betatron tunes x,y
Horizontal / vertical chromaticitiesx,y (2 IPs)
1340.92
2225 / 2450
23.273/ 21. 285
23.223/22.371
-278 / -268
-207/-191
5.12 10-3
Transition energy tr
Maximum horizontal / vertical rms beam size x,y
2300/2450
1.78
Momentum compaction factor 
Horizontal / vertical normalized emittance x,y
1394.47
13.97
µm rad
mm
F.Lin
0.35 / 0.07
3.5 / 1.6
3.6/1.6
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Momentum Acceptance & Dynamic Aperture
• Study of simplified, yet more challenging (due to higher chromaticity) symmetric 7 m Ion IR design
• Compensation of chromaticity with 2 sextupole families only using symmetry
• Non-linear dynamic aperture optimization and studies of error impact under way
Ions
Electrons
5 p/p
5 p/p
p/p = 0.710-3 at 5 GeV/c
p/p = 0.310-3 at 60 GeV/c
Ions
Ions
y /y
x /x
 / 
F. Lin
with Octupole
w/o Octupole
x /x
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Goals and Timeline (1st Year)
For the first year
– First and second quarters
• Continue the chromaticity correction scheme CCB design of the interaction region
• Complete the chromaticity correction studies for momentum acceptance
• Study the nonlinear characteristics of the collider ring and develop correction schemes for
dynamic aperture
• Orbit diagnostics and control (maintenance) in the CCB sections
– Third and fourth quarters
• Evaluate both necessary and attainable precision of orbit control in CCB to exclude error
impact to the dynamic aperture beyond the admissible level
• Develop a concept for beam control at collision points
• Develop a detailed model of the detector field for dynamic aperture studies
• Start evaluation of particle tracking algorithm and codes
F. Lin
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Goals and Timeline (2nd Year)
For the second year
– First and second quarters
• Develop a genetic algorithm based multi-objective-function optimization routine to optimize
momentum acceptance and dynamic aperture
• Continue studies of nonlinear correction schemes for collider rings
• Complete studies of momentum acceptance and dynamic aperture for ideal collider rings
– Third and fourth quarters
•
•
•
•
Complete establishing the multidimensional optimization routines
Investigate magnet fringe field and multipole component effects based on particle tracking
Investigate magnet misalignment effects based on particle tracking
Develop a closed orbit correction system
F. Lin
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Goals and Timeline (3rd Year)
For the third year
– First and second quarters
• Initiate particle tracking simulations including the completed integration of the detector region
into the collider rings’ optics
• Initiate particle tracking simulations including the modified optics models for the developed
spin dynamic scheme
• Initiate particle tracking simulations considering magnet fringe field, realistic errors, and
misalignment
• Re-optimize collider rings for adequate momentum acceptance and dynamic aperture
– Third and fourth quarters
• Finalize the conceptual collider rings design
• Demonstrate in simulations an adequate momentum acceptance and dynamic aperture for
collider rings
• Provide the technical and engineering specifications of the collide rings’ magnets
F. Lin
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