4th Order Resonance at the PS

R. WASEF, S. Gilardoni, S. Machida

Acknowledgements: A. Huschauer, G. Sterbini

SC meeting, 05/03/15

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Status and Introduction of the PS

• Started operation in 1959• 100m radius• 100 combined function

magnets

• Each magnet consists of 10 blocks: 5 F and 5 D (cell: FDODF)

• Tunes are controlled with:- LEQ at low energy- PFW at high energy

• Injection kinetic energy 1.4GeV.

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Coil system: main circuit and auxiliary coils

Narrow circuit

B

BWide circuit

I8L

Thermographic inspection of PFW

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Coil system contributions

IFWIDN

IFNIDW

I8L

– Hyperbolic pole shape– Only dipolar and quadrupolar field at low field

level

– Iron saturation– Sextupolar and higher order

components at high field level

Main coil

Pole-face windings + and figure-of eight loop

– 5-Current Mode

– Un-balanced N and W circuit current generate octupolar and higher components

– Non-linearities at high field (iron saturation)

– Field probably up to decapole

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The beam tune-spread is trapped between the 4Qy=25 and the integer. If one increases the vertical tune to avoid growth due to the integer, the losses increase

because of the 4th order resonance There are less losses with higher tune-spread because the proton population becomes

smaller on the 4Qy=25 after compression. The choice of the working point is a compromise between losses and emittance blow-up

Core of the beam

Halo particles

Motivation

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4th order measurements in 2012

The 4th order resonance seems to be excited by space charge

Maximum detuning due to space charge:

Beam 1 : (-.22 ; -.4)

Beam 2 : (-.18 ; -.37)

Beam 3 : (-.08 ; -.07)

Beam 4 : (-.01 ; -.01)

Horizontal tune fixed at 6.23Vertical tune: 6.24->6.3->6.24

6.24

6.3

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Hypothesis

• Structure resonance driven by Space Charge.• Structure h=50 (lattice 50xFDODF).• Driven by space charge because doesn’t exist at low brightness (Tune-

diagrams).

• Mitigation:

A full compensation of space `charge potential is not possible

A partial compensation seems extremely challenging because of the difference in magnetic center.

Change of the integer, would avoid the harmonic 50.

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Change of integer tune

• Using the F8L:

low current needed and very small multipolar errors.

Moves the integers in the opposite directions.

• Using the PFW:

Qx , Qy independent

Multipole errors not predicted with matrix

Larger beam size (not a problem for LHC-type beams)

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Advantages of Scheme 2

• Smaller SC maximum tune shift.• The structure resonance (h=10) is in horizontal.• Smaller mismatch at injection Δσ

(considering Δp/p=10-3)

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First Simulations

• The aim of the following study is to verify the hypothesis of structure resonance driven by space charge.

• The simulated beam is different from the measured ones, to have a smaller tune-spread, to overlap only the 4Qy=25.

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Horizontal Vertical

RMS

Emitt

ance

95%

Em

ittan

ceFirst Simulations

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2014 Measurements

• Successful injection at (5,7) integers.• Large closed orbit with new optics (expected)• Emittance increase (~10%)• Verification of tunes (tune measurement [0:0.5]):

- Tune direction at change

- Closed orbit enlargement when approaching the integer

Vertical Orbit Horizontal Orbit

0.1

mm

PU PU

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Optics Measurements: βx

• β measurement using turn by turn bpm data.

• Good agreement between model and measurement.

Emittance could be estimated at the position

of the wirescanner using the model optics

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Optics Measurements: Dx

• Dispersion measurement: varying the MRP (Energy) and measuring the displacement at bpm.

• Good agreement between model and measurement.

Emittance could be estimated at the position

of the wirescanner using the model optics

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Measurements

• 2 sets of measurements:

I. Constant tunes including injection: qx=0.21 and qy=0.29. For simulation: No ramp, therefore a short simulation can be extrapolated for longer measurement.

II. A tune step: qx=0.21 and qy= 0.23 Tune Plateau X 0.23 Easily quantified and visible beginning and end of beam loss

• For both cases, measurements are donefor nominal and scheme 2 optics.

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Tune Step: Nominal Optics (6,6)

• Qx=6.21

• Qy= 6.24X6.24

As expected: The higher is the tune, the larger are the lossesSC meeting, 05/03/15

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Tune Step: Optics (5,7)

• Qx=6.21

• Qy= 6.24X6.24

• The observed loss is for the step at 6.34 (effect of the 3rd order resonance)

The resonance has no significant effect on the beam lossSC meeting, 05/03/15

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Tune Step: Optics (5,7)

Nominal Optics

Optics (5,7)

• At the new optics, there is no significant effect of the 4th order. (Qv=.34 not in this plot)

• The resonance should be structure one because it depends on the integer.

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Significant improvement at the new integers

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BEAM PARAMETERS

• Measured and simulated beam parameters for static tunes.

• ~20% difference in the maximum tune shift due to SC.

Acceptable comparison

TUNES (6,6) (5,7)

INTENSITY 170 170

εx [μm] 2.53 2.7

εy [μm] 2.05 2.15

Δp/p 1.02 10-3 1.02 10-3

bl [ns] 175 175

Qx 6.21 7.21

Qy 6.29 7.29

Ek [GeV] 1.4 1.4

ΔQ (SC) -0.23 / -0.31 -0.22 / -0.24

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Static Tune: Measurements

• Constant tunes qx=0.21, qy=0.29.

• Very small asymptotic loss for the optics (5,7).

(No closed orbit correction)

• Simulated case starting at 300ms.

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• Direct SC method.

• ~ factor 2.2 in beam loss.

Simulation starts with clean beam.

if one neglect the first 50ms, the factor becomes 1.6 .

Closed Orbit not taken in account.

Static Tune: PTC-ORBIT Simulations

Only 60% difference in slope after 50ms, closed orbit has to be taken in account

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Horizontal Vertical

Sim

ulati

ons

@ s

tart

of P

SM

easu

rem

ents

@ S

S64

Static Tune: PTC-ORBIT Simulations

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• Results in an acceptable agreement with measurement (60%).• Closed orbit may improve the agreement.• A test with more particles may improve the agreement.• The starting profile should also include tails one should compare after

development of the tail.

• The hypothesis of structure resonance is confirmed No excitation at new integer.

• The hypothesis of SC driving the resonance is confirmed Simulations tested with no other octupolar errors.

• The change of integer is very promising, tests are ongoing to find a way to move to (7,7) with PFW.

Static Tune: PTC-ORBIT Simulations

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SC meeting, 05/03/15 252Qy=104Qy=20

2Qx=104Qx=20

8Qy=50

3Qy=20

8Qx=503Qx=20

Qx+2Qy=20

2Qx-Qy=10

-Qx+2Qy=10

2Qx+2Qy=25

Qx+3Qy=25

-Qx+3Qy=10

2Qx+Qy=20

3Qx-Qy=103Qx+Qy=25

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Backup Slides

III. 4th order Resonance

Testing the effect of the 4qy by changing the population crossing it (Bunch compression @ C1000)

Tune spread before and after compression

If the working point is close to the resonance, before and after the compression it is mainly the halo crossing the resonance

If the working point is relatively far from the resonance the population crossing the resonance changes after compression

Losses due to the resonance are expected to be different

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III. 4th order Resonance

No effect of the compression (losses due to change of W.P.)

Qy=6.24

Qy=6.3Qy=6.27

Bunch compression @ C1000

Before compression: losses are faster in the case of Qy=6.27After compression: No effect for Qy=6.27 but faster losses for Qy=6.3

Inte

nsi

ty [

E1

0 p

pb]

Time[ms]

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Inte

nsi

ty [

E1

0 p

pb]

III. 4th order Resonance

• Testing if the 4qy=1 is excited by Space Charge:- Bunch compression @ C190- Tune step between C500 and C800

Set tunes Measured tunes

• 4 different settings: I=115 e10 ppb Tune-spread =(.22 ; .4) (for Q21Q23 optics) I=80 e10 ppb Tune-spread =(.18 ; .37) (for Q21Q23 optics) I=35 e10 ppb Tune-spread =(.08 ; .24) (for Q21Q23 optics) I=115 e10 ppb Debunched

Time[ms]

7

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PTC-ORBIT vs. IMPACT PTC-ORBIT with different # of MP

• The main goal of these simulations is not to have an absolute value of emittance growth but to verify the relative behavior with the different settings.

Simulations tend to confirm the hypothesis of the 4 th order being a structure resonance driven by space charge.

First Simulations

SC meeting, 05/03/15