Improvements on the working point control and resonance ... · Improvements on the working point control and resonance compensation scheme in the PS S. Gilardoni, A. Huschauer, M

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


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


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


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


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


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


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



• 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)



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



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


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


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


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



• 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



• 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



Scan Direction

Scan Direction

Compensated resonance 2q

x +qy =1



Scan Direction

Scan Direction

Compensated resonance 3q

y =1



• 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


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

Documents

Improvements on the working point control and resonance ... · Improvements on the working point control and resonance compensation scheme in the PS S. Gilardoni, A. Huschauer, M