4 th Order Resonance at the PS R. WASEF, S. Gilardoni, S. Machida Acknowledgements: A. Huschauer, G. Sterbini SC meeting, 05/03/15

Status and Introduction of the PS Started operation in m 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. 3 SC meeting, 05/03/15

4 Coil system: main circuit and auxiliary coils Narrow circuit B B Wide circuit I 8L Thermographic inspection of PFW

5 Coil system contributions I FW I DN I FN I DW I 8L – 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

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 4 th 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 SC meeting, 05/03/15 6

4 th order measurements in 2012  The 4 th 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 6.23 Vertical tune: 6.24->6.3-> SC meeting, 05/03/15 7

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. SC meeting, 05/03/15 8

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) SC meeting, 05/03/15 9

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 ) SC meeting, 05/03/15 10

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= SC meeting, 05/03/15

12 Horizontal Vertical RMS Emittance 95% Emittance First Simulations

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 13 SC meeting, 05/03/15

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 14 SC meeting, 05/03/15

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 15 SC meeting, 05/03/15

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 done for nominal and scheme 2 optics. 16 SC meeting, 05/03/15

Tune Step: Nominal Optics (6,6) Qx=6.21 Qy= 6.24  X  6.24  As expected: The higher is the tune, the larger are the losses 17 SC meeting, 05/03/15

Tune Step: Optics (5,7) Qx=6.21 Qy= 6.24  X  6.24 The observed loss is for the step at 6.34 (effect of the 3 rd order resonance)  The resonance has no significant effect on the beam loss 18 SC meeting, 05/03/15

Tune Step: Optics (5,7) Nominal Optics Optics (5,7) At the new optics, there is no significant effect of the 4 th order. (Qv=.34 not in this plot) The resonance should be structure one because it depends on the integer. 19 SC meeting, 05/03/15  Significant improvement at the new integers

BEAM PARAMETERS Measured and simulated beam parameters for static tunes. ~20% difference in the maximum tune shift due to SC.  Acceptable comparison 20 SC meeting, 05/03/15

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. 21 SC meeting, 05/03/15

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 22 SC meeting, 05/03/15

Horizontal Vertical start of PS SS64 Static Tune: PTC-ORBIT Simulations 23

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 24 SC meeting, 05/03/15

2Qy=10 4Qy=20 2Qx=10 4Qx=20 8Qy=50 3Qy=20 8Qx=50 3Qx=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 SC meeting, 05/03/1525

Backup Slides SC meeting, 05/03/1526

III. 4 th order Resonance Testing the effect of the 4qy by changing the population crossing it (Bunch 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 5

III. 4 th order Resonance  No effect of the compression (losses due to change of W.P.) Qy=6.24 Qy=6.3 Qy=6.27 Bunch C1000 Before compression: losses are faster in the case of Qy=6.27 After compression: No effect for Qy=6.27 but faster losses for Qy=6.3 Intensity [E10 ppb] Time[ms] 6 Intensity [E10 ppb]

III. 4 th order Resonance Testing if the 4qy=1 is excited by Space Charge: - Bunch 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

PTC-ORBIT vs. IMPACTPTC-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 30 SC meeting, 05/03/15