Large Booster and Collider Ring
Vasiliy Morozov
MEIC Ion Complex Design Mini-Workshop, January 27, 2011
MEIC Layout
Prebooster
0.2 GeV/c  3-5 GeV/c
protons
Big booster
3-5 GeV/c  up to 20 GeV/c
protons
3 Figure-8 rings
stacked vertically
Big Booster
• Acceleration of protons from 3-5 GeV/c to up to 20 GeV/c for
injection into ion collider ring
• Big booster implementation options
– Separate warm ring in collider rings’ tunnel (current baseline)
– Using the electron ring
– Separate cold ring in the prebooster’s tunnel
• Big booster design considerations
– Avoid transition energy crossing
– Space charge  higher injection energy for larger ring
– Matching RF systems  debunch low-frequency beam and then
rebunch it at higher frequency?
Figure-8 Collider Rings
• Geometrical matching of electron and ion rings
– Spin rotators in the electron ring
– Siberian snakes in the proton ring arcs
Ion Ring
IP
Potential IP
IP
Siberian snake
Siberian snake
Electron Ring
RF
Spin rotators
IP
IP
Potential IP
Spin rotators
RF
Modular Design Concept
• Design separately and incorporate/match into the ring
–
–
–
–
–
–
Vertical chicanes for stacking the ion ring arcs on top of the electron ring
Injection section
Electron cooling section
Siberian snakes
Interaction region with horizontal crossing
Section for local chromaticity compensation
Full-Acceptance Detector
Proton
Electron
Beam energy
GeV
60
5
Collision frequency
GHz
1.5
1.5
Particles per bunch
1010
0.416
1.25
Beam Current
A
1
3
Polarization
%
> 70
~ 80
Energy spread
10-4
~3
7.1
RMS bunch length
cm
1
0.75
Horizontal emittance, normalized
µm rad
0.35
53.5
Vertical emittance, normalized
µm rad
0.07
10.7
Horizontal β*
cm
10
10
Vertical β*
cm
2
2
Vertical beam-beam tune shift
0.007
0.03
Laslett tune shift
0.07
Very small
7
3.5
Distance from IP to 1st FF quad
Luminosity per IP, 1033
m
cm-2s-1
5.6
IR Design Challenges
• Low * is essential to MEIC’s high-luminosity concept
• Large size of extended beam f * = F2
– Chromatic tune spread  limited momentum aperture
– Chromatic beam smear at IP F ~ Fp/p >> *  limited luminosity

– Sextupole compensation of chromatic effects  limited dynamic
aperture  compensation of non-linear field effects
– High sensitivity to position and field errors
Compensation of 2nd-Order Terms
• Consider parallel beam after extension, u describes the dominant (cos-like)
parallel component of the trajectory while  is associated with the small
remaining angular spread (sin-like trajectory), then, neglecting the angular
divergence, one can approximate x1  axu x , y1  a y u y to obtain

1
x     u x [(2 Dns  n)qaxu x  D ( Dns  n)q 2  ns (a x2u x2  a y2u y2 )]ds
u x 0

2

1
y     u y [(2 Dns  n)qa y u y  2ns axu x a y u y ]ds
u y 0

2
• In order to have x2  0, y2  0 the following conditions must be satisfied




0
0
0
0
2  Dns u x2 ds   nu x2 ds, 2 Dns u y2 ds   nu y2 ds,

 D( Dn
s
0

 n)u x ds  0,

 n u ds  0,  n u u ds  0
3
s x
0
s x
0
2
y
Symmetry Concept
• Modular approach: IR designed independently to be later integrated into ring
• Dedicated Chromaticity Compensation Blocks symmetric around IP
• 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
Compensation of Main 2nd-Order Terms
• 2nd-oder 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.
• Chromatic terms




2 Dn u ds   nu ds, 2 Dnsu ds   nu y2ds
2
s x
0
2
x
0
2
y
0
0
are compensated using sextupoles located in CCB’s attaining
– local chromaticity compensation including contributions of both the
final focusing quadrupoles and the whole ring
– simultaneous (due to symmetry around IP) compensation of chromatic
and sextupole beam smear at IP restoring luminosity
Ion Collider Ring Geometry with IR (I)
• CCB’s on the opposite sides of IP bend the same way
IP
IP
Ion Collider Ring Geometry with IR (II)
• CCB’s on the opposite sides of IP bend in the opposite directions
– Simpler matching with electron IR’s, which have smaller bending
IP
IP
IP
IP
Ion Collider Ring Geometry with IR (III)
IP
IP
IP
50
IP
Basic Ring Parameters
Proton beam momentum
GeV/c
60
Circumference
m
1353.75
Arc’s net bend
deg
230
Straights’ crossing angle
deg
50
Arc length
m
381
Arc average radius
m
95
Straight section length
m
295.9
Lattice basic cell
Arc FODO cell length
Nominal phase advance per cell x / y
Total number of arc FODO cells
Dispersion suppression
FODO
m
9
deg
60 / 60
56
Adjusting quad strengths
Magnet Parameters
Proton beam momentum
GeV/c
Number of arc dipoles
60
144
Dipole length
m
3
Bending radius
m
53.8
Bending angle
deg
3.2
T
3.7
Bending field at 60 GeV/c
Number of quads
Quad length
364
m
0.5
Quad strength in arc FODO cells
T/m
92
Maximum quadrupole strength
T/m
180
Maximum sextupole strength
T/m2
519
Arc FODO Cell
• /3 betatron phase advance in both planes
• Magnet parameters for 60 GeV/c protons:
– Dipoles:
•
•
•
•
length = 3 m
bending radius = 53.8 m
bending angle = 3.2
bending field = 3.7 T
– Quads:
• length = 0.5 m
• strength = 92 T/m
Dispersion Suppressor
• 3 arc quads are used to suppress dispersion while keeping
-functions from growing
• Maximum quad strength at 60 GeV/c = 122 T/m
Short Straight for Siberian Snake
•
•
•
•
Symmetric quad arrangement
Initial  values from the dispersion suppressor
Quads varied to obtain x,y = 0 in the middle at limited max
Maximum quad strength at 60 GeV/c = 117 T/m
Arc End with Dispersion Suppression
• Dispersion suppressed by varying quads with limitations on max and Dmax
• Maximum quad strength at 60 GeV/c = 147 T/m
To straight section
Complete Arc
• Length = 381 m, net bend = 230, average radius = 95 m
Final Focusing Doublet
• Distance from the IP to the first quad = 7 m
• Maximum quad strength at 60 GeV/c = 175 T/m
 x  10 cm
 y  2 cm
Chromaticity Compensation Block
• Satisfies the required symmetries for the orbital motion and dispersion
• Maximum quad strength at 60 GeV/c = 78 T/m
Matching of CCB to Arc
• Maximum quad strength at 60 GeV/c = 180 T/m
Matching of CCB to Straight
• Maximum quad strength at 60 GeV/c = 180 T/m
Interaction Region
• Total length = 143 m
Complete Collider Ring
• Total length = 1353.75 m
Summary of Optics Parameters
Proton beam momentum
GeV/c
60
Circumference
m
1353.75
Arc’s net bend
deg
230
Straights’ crossing angle
deg
50
Arc length
m
381
Straight section length
m
295.9
Maximum horizontal / vertical  functions
m
1952 / 2450
Maximum horizontal dispersion Dx
m
1.7
Horizontal / vertical betatron tunes x,y
24.(34) / 20. (59)
-590 / -812
Horizontal / vertical chromaticitiesx,y
Momentum compaction factor 
5.5 10-3
Transition energy tr
Horizontal / vertical normalized emittance x,y
At 20 GeV/c injection:
Maximum horizontal / vertical rms beam size x,y
At 60 GeV/c:
Maximum horizontal / vertical rms beam size x,y
13.4
µm rad
0.35 / 0.07
mm
19 / 21
mm
3.3 / 1.6
Chromatic Tune Dependence
• No compensation
Chromaticity Compensation
• Two pairs of sextupoles placed symmetrically in each CCB
• Maximum sextupole strength at 60 GeV/c = 519 T/m2
Chromatic Tune Dependence
Before compensation
After compensation