Nonlinear Dynamic Study of FCC-ee
Pavel Piminov,
Budker Institute of Nuclear Physics,
Novosibirsk, Russia
Acceleraticum is home-made code
• Linear optics (Twiss, Lebedev-Bogacz parametrization)
• Radiation parameters calculation for Twiss
• Symplectic 6D tracking
• Computation of different nonlinear parameters
(dynamic aperture, nonlinear chromaticity, tuneamplitude dependence, etc)
• Optimization (linear optics, nonlinear optics from
tracking)
• Shatilov’s LIFETRAC uses Acceleraticum tracking
module for simulation of the beam-beam with the
nonlinear lattice
Main elements
•
•
•
•
Drift
Quadrupole with hard-edge nonlinear fringe
Bending magnet with gradient and high order multipoles
n-order multipole lens
Solenoid with gradient and high order multipoles
RF-Cavity
Coordinate system transformation
Gaussian Beam-Beam interaction with an arbitrary crossing
angle
• Kinematic term in all elements
• Errors & Misaligments
•
•
•
•
Code comparison
• Comparison of Lattice Codes by
D.Einfeld, 2nd Nonlinear Beam Dynamic
Workshop, Diamond, 2009
• Checking by myself with MAD-8, MADX, SAD
• Used for VEPP-4M, VEPP-2000 (round beams),
ALBA, DAФNE, Super-ct-Factory (Novosibirsk),
SuperB, SuperKEKB, ultra low emittance ring
projects, etc
• Good agreement with SAD for SuperKEKB with
realistic interaction region
SuperKEKB with realistic IR
IR length of 8 m is sliced by 1 cm solenoids with
dipole and gradient (rotated and shift) and
nonlinear kicks (up to 21st multipole order) including
quadrupole fringe field and kinematic term
Local orbit in IR HER SuperKEKB
COORDINATE SYSTEM TRANSFORMATION
VERTICAL
HORIZONTAL
IP
FCC-ee Dynamic Aperture Procedure
1. Arcs w/o IR dynamic aperture & energy
acceptance optimization
2. Local compensation of nonlinear distortion
of the Interaction Region
3. Study of Crab Sexts Influence
4. Advance Optimization of the whole Ring
with Interation Region
5. Solenoids, Realistic field, Damping,
Errors, etc…
Dynamic Aperture @ IP
E = 175 GeV, Ex=1.3 nm·rad, 0.2% coupling
z, sz
200
180
IR + Arc Sexts
IR Sexts
160
140
Dynamic
120 Aperture is limited by the Arc’s Sexts!
FODO Horizontal Phase Advance is 0.25
80 cells with resonance condition 4 Qx = 1
135
100
Arc Sexts
60
40
20
0
-100
-50
0
50
100
x, sx
3 Qx
9
4 Qx
10
5 Qx
Ax, Az, cm
FODO DA vs Phase Advance
8
7
6
5
4
3
2
1
0
0.1
0.2
0.3
0.4
Qx
Ax, sx
FODO DA vs Phase Advance
140
120
100
80
60
40
20
0
0.1
0.2
0.3
0.4
Qx
FODO Energy Acceptance
D E/E
0.25
0.2
0.15
0.1
0.05
0
0.1
0.2
0.3
0.4
Qx
Ex, nm rad
FODO Emittance vs Phase Advance
10
E = 175 GeV
9
8
7
6
5
4
3
2
1
0
0.2
0.4
Qx
Qx=0.25, Ex=0.96 nm·rad
4
z, cm
z, cm
Qx=0.22, Ex=1.35 nm·rad
3.5
4
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
-5
0
5
0
x, cm
Ex = 0.96 nm·rad
-5
0
z, cm
Qx=0.28, Ex=0.72 nm·rad
ΔE/E = -3%
4
3.5
ΔE/E = 0
3
2.5
ΔE/E = +3%
2
1.5
1
0.5
0
-5
0
5
x, cm
5
x, cm
Qx=0.25, Ex=0.96 nm·rad
Qx=0.22, Ex=1.35 nm·rad
z, sz
z, sz
4000
4000
3500
3500
3000
3000
2500
2500
2000
2000
1500
1500
1000
1000
500
500
0
-100
0
100
0
x, sx
Ex = 0.96 nm·rad
-100
0
100
Qx=0.28, Ex=0.72 nm·rad
ΔE/E = -3%
z, sz
4000
3500
ΔE/E = 0
3000
2500
ΔE/E = +3%
2000
1500
1000
500
0
-100
0
100
x, sx
x, sx
Plans
• Choose Optimal Phase Advance in FODO
• Check Dynamic Aperture & Energy
Acceptance of the whole Ring w/o
Interaction Region
• Choose several Sextupole families in
Arcs?
• …