1. Emittance growth AT PS injection
W. Bartmann
LIU beam parameter meeting, 22nd July, 2016

2. Emittance growth at PS injection
22/07/2016
Emittance growth at PS injection
Overview 1
Aim: fully deploy LHC potential of L4 beams at 2 GeV PS injection
So far damper not taken into account
Try to understand if damper HW can handle injection errors in terms of peak oscillation and frequency spectrum – damper bandwidth also important during cycle
Error catalogue – Wolfgang, Vincenzo
Which errors
Injection oscillation amplitude
Frequency of systematic errors
Mitigations
Damper (and what is impacting the damper spec from instability side) – Guido
Specifications of magnets/converters - Wolfgang

3. Emittance growth at PS injection
22/07/2016
Emittance growth at PS injection
Overview 2
What info is missing
PS closed orbit stability
Errors from bumpers
Chromaticity dependence, resistive wall studies (more for HI beams) – Guido, Alex
Study effect of damper theoretically - Wolfgang
Saturation at 2 GeV
Which margin for unknowns like ½ h timescale drifts?
Measurements to be done
Chromaticity studies with single bunch high intensity, go up to transition, with/out damper (Guido)
Brightness curve at PS (Guido)
Amplitude dependent detuning (Wolfgang)
Damping time (Wolfgang)
KFA45 field measurements, ideally with improved instrumentation (Vincenzo)

4. Error sources for delivery precision
22/07/2016
Emittance growth at PS injection
Error sources for delivery precision
Correctable errors
Magnet misalignment
Magnet systematic (different laminations, steel,…) and random errors (different transfer function within a series)
Long term drifts due to temperature, humidity,…
All these errors lead to trajectory variations that can be corrected
Since the transfer function is considered correctable  ΔI/I = ΔB/B
Uncorrectable (dynamic) errors
Random errors: Shot-to-shot stability, in particular in view of ppm operation between 1.4 and 2.0 GeV
Systematic errors: Power converter ripple, kicker waveforms

5. Stability calculation
22/07/2016
Emittance growth at PS injection
Stability calculation
Assign correctable errors and verify correction feasibility
Only limited by BPM readings and correction strategy  checked in Oct-13, OK
Assume machine free of correctable errors and assign separately dynamic errors to identify the main contributors to delivery imprecision
Calculate delivery precision of position and angle at PS injection
Check aperture in the lines (losses, radiation)
Check foreseen margins for CO and betabeat in GFR
Calculate emittance growth from steering error
Calculate unavoidable emittance growth from optics and dispersion mismatch
Sum all error sources into overall emittance growth and potential particle loss for LHC and HI beams R

6. Emittance growth at PS injection
22/07/2016
Emittance growth at PS injection
Error source
Tolerance ΔI/I
x rms (mm)
px rms (μrad)
Rx2/ε0
[1e-3]
y rms (mm)
py rms (μrad)
Ry2/ε0
Random effects
PSB orbit
± 0.15/0.10 mm (h/v)
0.04 4
0.4 2
0.2
BVT10
1e-4
0.08 1
0.3
SMV10
0.13
QNO10
5e-4
0.11
QNO20
0.03
0.06
KFA10
3e-4
0.02
SMV20
0.01
KFA20
BVT20
0.05 3
BT.BHZ10
0.07
All random effects 17
5.1
0.21 6
4.0
Systematic effects
5e-3
0.39 15
0.22 8 5
Sensitivity table

7. Trajectories for all dynamic errors applied
22/07/2016
Emittance growth at PS injection
Trajectories for all dynamic errors applied
Contributions for trajectory variation in aperture OK
Betabeating from uncorrectable quadrupole errors is in the regime of a few percent (20% assumed in the aperture calculation) and therefore negligible compared to the systematic optics differences between the four lines

8. Distribution of trajectories for all dynamic errors applied
22/07/2016
Emittance growth at PS injection
Distribution of trajectories for all dynamic errors applied

9. Present situation (LHC)
22/07/2016
Emittance growth at PS injection
Emittance growth
From steering error at PS injection due to power converter ripple and kicker waveforms
Rx2/ε0 (random errors ) gives and 0.004
Rx2/ε0 (systematic offset) gives 0 and (extraction kicker waveform not included)
From optics mismatch between different lines
Energy error, geometrical mismatch and coupling negligible
All error sources considered independent
Error
Emittance growth [%]
Present situation (LHC)
LHC beam
HI beam
Hor
Vert
Steering error
0.25
1.45
0.05
0.48
Betatron mismatch
4.55
6.81
2.31
0.02
2.0
Dispersion mismatch
4.40
8.77
0.09
5.36
0.03
5.25
Total
6.33
11.20
2.53
5.45
2.00
5.27

10. Distinguish field quality for beam type
22/07/2016
Emittance growth at PS injection
Distinguish field quality for beam type
BT.BHZ10
Field homogeneity of 1e-4 rms  max value of ±2e-4
Possible approach:
use this requirement only for LHC beam size (±19/21 mm instead of ±51.5/51.5 mm)  optimize for emittance
Accept higher field inhomogeneities for HI beams as long as they fit into the acceptance  optimise for losses

11. HI beams - particle loss
22/07/2016
Emittance growth at PS injection
HI beams - particle loss
Assuming ∫ΔB/B for the large GFR
BT.BHZ10: 5e-4 rms (max at ±1e-3)
BT.BVT10/20: 5e-4 rms (max at ±1e-3)
Together with other recombination error sources leads to steering error of 0.4 (hor) and 1.6 mm (vert)  comparable to the assumed orbit tolerance of 1.5 mm in the ring

12. HI beams - particle loss
22/07/2016
Emittance growth at PS injection
HI beams - particle loss
Aperture bottleneck at PS injection when bump is fully on:
33 mm radial aperture
Subtract 2 mm for alignment errors
3 mm for the orbit already included in beam size
Fit 3.3 sigma horizontally of HI beam at 1.4 GeV
New septum will have increased vertical aperture (4.1 sig)
Beam size changes by 0.8% due to optics mismatch after filamentation has taken place
Bump is collapsed within 500 turns

13. Taking longitudinal distribution into account for kickers
22/07/2016
Emittance growth at PS injection
Taking longitudinal distribution into account for kickers
Can distinguish importance of rise/fall/flattop/postpulse
Measured emittance growth is 40% smaller than theoretically expected

14. Emittance growth at PS injection
22/07/2016
Emittance growth at PS injection
Conclusions
Comparison of different sources of emittance growth show:
Difference in optics between the four lines is the main cause of emittance growth, in particular the dispersion mismatch
Emittance growth from steering errors due to power converter ripple is a minor contributor and can in principle be damped
Assuming similar systematic contributions from PSB extraction and PS injection kicker in the horizontal plane as for the recombination kickers gives as maximum expected oscillations to be damped: +/- 1.5 mm in both planes (for LHC beams)
Error from injection bump and PS closed orbit not yet estimated
Different requirements for LHC and HI beams
Relaxed field homogeneity for HI beams leads to increased trajectory variations at PS injection (0.4 mm hor, 1.6 mm vert)
Bottleneck during injection when bump is fully on in horizontal plane
Fit 3.3 sigma at 1.4 GeV
Folding bunch distribution with kicker waveforms allows to get weighted effect of ripple
Measure 40% less than expected