Upload
others
View
0
Download
0
Embed Size (px)
Citation preview
Improvements on the working point control and resonance compensation scheme in the PS
S. Gilardoni, A. Huschauer, M. Juchno, D. Schoerling, R. Wasef April 23rd, 2013
Special thanks to all people involved in the continuous improvement of the PS machine for many discussions
Daniel Schoerling TE-MSC-MNC 2
Overview
I. Motivation of the magnet study II. Introduction to PS main magnets III. Working point control IV. Resonance compensation V. Conclusion
Daniel Schoerling TE-MSC-MNC 3
I. Motivation of magnet study
• Higher brightness beams are required for the LHC to achieve its high luminosity objective Consolidating and upgrading PSB, PS, SPS and using the newly built LINAC4 PS’ injection energy will be increased from 1.4 to 2 GeV to reduce space charged
induced tune shift Upgrade program for hardware in the PS machine: correctors, skew
quadrupoles, radio-protection shielding, injection kickers, etc.
• Transverse beam stability requires careful optimization of the working point New working point control with a 5 current matrix using PFW and F8 to be
developed • Laslett tune shift will be large (possibly beyond 0.3) and particles likely cross integer
and/or 1/3 stop bands • Resonance compensation scheme required
See H. Damerau et al., TUXA02, IPAC’12, New Orleans
Daniel Schoerling TE-MSC-MNC 4
II. PS main magnets
B1 1.2 T
B2 5.2 T/m
B3 2.8 T/m2
B4 36.4 T/m3
Taylor decomposition of field (26 GeV/c)
N
S
S N
SN
S
N
S
NN
S
+ + + … =
• 5+1 independent currents allow for many different settings of multipoles
• Due to symmetry constraints no skew components allowed in perfect PS main magnets
3x2y - y3 = ± r3 2xy= ± r2 y= ± r
Dipole: B1 Quadrupole: B2 Sextupole: B3
y
x z
Main coils
Figure-of-eight
W + N PFW
Courtesy : Thomas Zickler
Daniel Schoerling TE-MSC-MNC 5
II. PS main magnets
-Pole profile is optimized to obtain a dipolar and quadrupolar component
-Pole face windings: narrow and wide circuit available (cross section 9 x 3 mm2) for multipole creation and correction -Figure-of-eight loop for tune adjustment available
Daniel Schoerling TE-MSC-MNC 6
II. PS main magnets
• Open and closed block of the main magnet units + different current modes
• 5+1 independent currents available to control the field components and therewith the beam properties (underactuated system):
• Momentum p • Tune Qx, Qy • Linear chromaticity ξx, ξy • Non-linear chromaticity Qx’’, Qy’’
Closed Open
Closed Closed
Closed Closed
Open Open
Open Open
Daniel Schoerling TE-MSC-MNC 7
II. PS main magnets
• Fits from simulation exist for multipoles up to octupole
• Influence of currents on field components varies strongly with position
-0.05 -0.03 -0.01 X [m]
0.01 0.03 0.05
-1.2
-0.8
-0.4
0 x 10 -4
∆B
[T/A
]
Figure-of-eight
W-PFW
N-PFW W+N-PFW
Dipole, Focusing
Quadrupole, Focusing
0
1
2
3 x 10 -3
X [m] -0.05 -0.03 -0.01 0.01 0.03 0.05 -0.05 -0.03 -0.01
X [m] 0.01 0.03 0.05
∆G
[Tm
-1/A
]
-0.02
0
0.02
0.04
-0.05 -0.03 -0.01 X [m]
0.01 0.03 0.05
Sextupole, Focusing
ΔS [T
m-2
/A]
x 10-3
-1
-0.5
0.5
1.5
1
Octupole, Focusing
∆O
[Tm
-3/A
]
x 10-3
Daniel Schoerling TE-MSC-MNC 8
III. Working point control
Working point control
• Calculate 5-current mode matrix to be able to set machine tunes, linear and second order chromaticity
• Small validity of the measured matrix, because independent current offsets in the windings lead to losses in the machine
• A precise magnetic model is required to predict a 5-current mode matrix which predicts the machine tunes, linear and second order chromaticity
Daniel Schoerling TE-MSC-MNC 9
III. Working point control
• Fits of the magnetic field excited from each electrical circuit up to the octupolar component were produced by using Opera software
• Variants of the PS magnet representation in the ring lattice:
• Prediction of tune & chromaticity variation is calibrated to the reference working point, i.e., below 1% tuning of 2 x gradient length and 2 x sextupolar integral to match with measured tune/chromaticity of the reference working point
Defocusing Half-unit (SBEND)
Focusing Half-unit (SBEND)
Drift space
(DRIFT)
Drift space
(DRIFT)
Defocusing higher order (B4,…) components (MULTIPOLE)
Focusing higher order (B4,…) components (MULTIPOLE)
Defocusing Half-unit (SBEND)
Focusing Half-unit (SBEND)
Drift space
(DRIFT)
Drift space
(DRIFT)
Defocusing higher order (B4,…) components
(PTC MULTIPOLE)
Focusing higher order (B4,…) components
(PTC MULTIPOLE)
Pure MAD-X (8 elements) MAD-X+PTC (4 elements)
Daniel Schoerling TE-MSC-MNC 10
III. Working point control
6.04
6.06
6.08
6.1
6.12
6.14
6.16
6.18
6.2
6.22
6.24
6.26
-0.013 -0.008 -0.003 0.002 0.007 0.012 0.017
Tune
∆p/p
Horizontal Measurement
Vertical Measurement
Horizontal Simulation
Vertical Simulation
Reference working point
Multipoles up to decapoles are included in the simulation and ∆p/p = ± 0.05
Conclusion: Excellent prediction
Para-meter
Mea-sured
Simu-lated
Measured -
Simulated
Tune
Qx 6.10 6.11 -0.01
Qy 6.20 6.20 0.00 Linear chromaticity
ξx 0.72 0.68 0.04
ξy -1.03 -0.98 -0.05 Second order chromaticity
Qx’’ 2105 1832 273
Qy’’ -874 -1000 126 • Model is tuned relative to measured tune and linear chromaticity
Daniel Schoerling TE-MSC-MNC 11
III. Working point control
Target working point • Qx’’ = 0, all other parameters
unchanged: 5CM matrix with Qy’’ as free parameter used
Achieved working point (difference to targeted WP)
Conclusion: Model is able to predict tune, linear chromaticity, and second order chromaticity for reasonably small momentum offset ∆p/p
6.05
6.1
6.15
6.2
6.25
6.3
6.35
-0.013 -0.008 -0.003 0.002 0.007 0.012 0.017
Tune
∆p/p
Horizontal Measurement
Vertical measurement
Horizontal simulation
Vertical simulation]
Measured
Simulated
Measured -
Simulated
Tune
∆Qx 0.00 0.01 -0.01
∆Qy 0.01 0.01 0.00 Linear chromaticity
∆ξx -0.05 -0.02 -0.03
∆ξy 0.22 0.29 -0.07 Second order chromaticity
∆Qx’’ 3418 2868 550
∆Qy’’ -663 -1140 477
More results, see presentation PS-LIU Meeting 42, Indico #209746
Daniel Schoerling TE-MSC-MNC 12
VI. Resonance compensation
• Increase the available space in the tune diagram, i.e., resonance compensation caused by magnet alignment errors and magnet manufacturing errors
• Reduce the tune-spread of the beam (large dispersion optics, flat bunches, etc.)
Overcome space charge limitations
Daniel Schoerling TE-MSC-MNC 13
IV. Resonance compensation
• Magnetic & alignment (σ = 200 µm) errors are essential for space charge studies because at low energy (bare machine) they are the main cause of resonance excitation, and cause therefore losses and emittance growth
• PS is implemented in MAD with ideal lattice
• In MAD the main magnets are divided in 4 half units 2D & 2F 400 elements
F F D D
• Magnetic errors (Systematic & Gaussian distribution µ, σ) can be implemented for each element in the lattice up to the normal & skew octupolar component.
• For each half unit one set of multipolar field errors is created, i.e., 400 numbers per multipolar field error have to be generated
Half unit Half unit Half unit Half unit
Daniel Schoerling TE-MSC-MNC 14
IV. Resonance compenasation • The simulation and measurement [1] of
the deformation of the magnet are similar • The magnetic field is used to derive the
normal and skew components of the magnetic fields in Taylor series
• The effect on the optics of the machine were calculated with MAD-X and PTC
• The effect of the deformation is especially visible for 26 GeV/c, because F ∝ B2
• The mechanical deformations cannot explain the resonances at low energy
[1] M. Buzio, M. Tortrat, Deformation of the PS reference magnet U101 during operation: geometrical survey and impact on B-train magnetic field measurements, April 2010
Qx Qy ξx ξy 14 GeV/c, normal components (negligible difference between
magnetic and structural) 6.2058 6.3032 0.2023 0.6837
14 GeV/c, normal & skew com. 6.2058 6.3032 0.2022 0.6839 26 GeV/c, no deformation, only normal components 6.2686 6.2219 0.0381 0.4770
26 GeV/c, with deformation, only normal components 6.2647 6.2179 0.1196 0.3961 26 GeV/c, with deformation, normal & skew components 6.2647 6.2179 0.1646 0.3506
UY
Daniel Schoerling TE-MSC-MNC 15
IV. Resonance compensation
• 2D calculation including Gaussian distribution of the position of the coils and the shape of the iron with up to 22 DOFs per magnet (OPERA)
• 1000 models per magnet type and current level have to be calculated (<1 d with advanced and additional licenses, before 10 d)
• Performed for momentum of 2.14 GeV/c, 2.78 GeV/c, 14 GeV/c, 26 GeV/c
Coils can be displaced, no rotation: Main coils (2 x 4 DOFs), σ = 3 mm F8 (2 x 4 DOFs), σ = 1 mm PFW (2 x 2 DOFs), σ = 0.7 mm Iron is displaced in y-direction, σ = 0.02/3 mm
2.14 GeV/c
Reference radius r = 10 mm
Daniel Schoerling TE-MSC-MNC 16
IV. Resonance compensation
• In the 80’s several compensation schemes using normal and skew sextupoles in the PS (sections 2, 52, 14, 64) were applied: Y. Baconnier, Tune shifts and stop bands at injection in the CERN proton synchrotron, CERN/PS 87-89 (PSR), 1987
• The air-cooled sextupole magnets have been installed in the winter shutdown in sections 2, 52, 14, 72 (instead of 64)
• A compensation scheme for each of the resonances 2Qx+Qy=19 and 3Qy=19 was implemented, using the new locations and the magnetic field error distribution
• Compensating both resonances requires larger skew sextupole fields, which cannot be generated with the currently installed magnet-power supply installation
601
602
Daniel Schoerling TE-MSC-MNC 17
IV. Resonance compensation
Scan Direction
Scan Direction
Compensated resonance 2q
x +qy =1
Daniel Schoerling TE-MSC-MNC 18
IV. Resonance compensation
Scan Direction
Scan Direction
Compensated resonance 3q
y =1
Daniel Schoerling TE-MSC-MNC 19
IV. Resonance compensation
• The magnetic error estimation has to be optimized since the amplitude of the non-linearities to create the phase space deformation is not enough to create the observed losses
• Advanced 3D magnetic model available, which is optimized and running to repeat the statistical study performed with Opera 2D in 3D
• Alignment between blocks will be treated within this model • Study on the effect of permeability variations within the electrical steel
1 2 3 4 5 6 7 8 9 10
Daniel Schoerling TE-MSC-MNC 20
V. Conclusion
• For the first time: it was shown that the resonances are caused by magnetic field errors the field errors were predicted an outstanding resonances compensation scheme could be implemented the working point for 5 current mode could be predicted based on the magnetic
model of the PS machine
• In the future: we will explore the use of stronger skew sextupoles to compensate both
mentioned resonances the available advanced 3D magnetic model will allow to repeat the statistical
study performed with Opera 2D in 3D in order to further correct the phase space deformation
in LS1 spare and removed magnets will be mechanically measured