1. HBP impedance calculations
O. Kononenko, D. Macina, B. Salvant, A.Sbrizzi*
*speaker

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Introduction
Every device close enough to the beam produces wakefields (impedance in frequency domain) which perturb beam
Longitudinal wakefields lead to local heating of the devices and perturbations of the synchrotron oscillations
Transversal wakefields lead to perturbations of the betatron oscillations
In order to have sufficiently stable beams and not to destroy devices, the impedance must be minimized.
The limit for forward detectors is set to 1% of the full LHC impedance
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3. Wakefield from sharp edges
Clear improvement with tapers (Benoit at the last AFP week)

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HBP Design
The initial HBP design (90° windows) has been modified with tapers.
The angle of the taper must be optimized to minimize the interference with the beam (small angle) and the physics (larger angle -> less background).
Initial design
New design with tapers
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5. Simple Design with 1 Taper only
PEC
Simple Design with 1 Taper only
The angle of the taper varies between 11º and 51º.
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6. Simple Design with 2 tapers
2 Tapers, 7º and 11º
PEC
Simple Design with 2 tapers
The angle of the 1st taper is fixed at 7º.
The angle of the 2nd taper varies between 11º and 51º.
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7. Simple Design with 2 tapers
PEC
Tube length = 11 m
Taper angle 11º
2 Tapers, 7º and 51º
PEC
Simple Design with 2 tapers
The angle of the 1st taper is fixed at 7º.
The angle of the 2nd taper varies between 11º and 51º.
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8. Calculation of Impedance
The impedance is calculated with two different tools
CST particle studio (Fourier Transform of wakefields)
HFSS (directly results in frequency domain)
CST and HFSS are commercial software, one need a license to run them.
CERN has few licenses (not enough, more are coming)
Being commercial, to some extents they are used as black boxes.
Material on
Notation confusion:
Impedance is usually indicated with Z and is a complex number (Re and Im).
Impedance is usually separated in longitudinal and transverse component.
The longitudinal component is the one along the beam (Z component).
The transversal component is perpendicular to the beam and is indicated with X or Y depending on the symmetry of the device.
For the HBP the transversal component is X.
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Impedance (Re)
The real part of the impedance is responsible for the power loss.
Longitudinal term (ReZ) is dominating.
Transversal term (ReX) is smaller and usually it is neglected.
Power loss is evaluated by convoluting the full ReZ frequency spectrum (excitation modes) with the LHC power spectrum.
Copper is needed to fully dump the oscillations and correctly estimate the amplitude of the excitation modes.
For this kind of calculations, HFSS is preferred to CST.
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Impedance (Im)
The imaginary part of the impedance is related to the beam instabilities.
It is obtained from the low frequency spectrum only (< 0.1 GHz)
Longitudinal term (ImZ)
ImZ/(f/frev) is compared to the full LHC value (90 mOhm)
Transversal term (ImX)
To evaluate the transversal impedance one has to displace the beam.
Minimal position scan: 2 displacements around the central position (1 and 2 mm).
The scan step must be at least the size of the mesh cells (200 microns).
The slope (ImX/distance) is compared with full LHC value (25 MOhm/m).
Numerical noise might be an issue because the transverse term is obtained as a variation of the longitudinal term with the distance (ImX = dImZ/dx).
Reduced by replacing Copper with PEC and by increasing the bunch length (350 mm) so that the maximum simulated frequency falls below the first excitation mode (0.5 GHz).
For this calculation we use CST.
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11. CST results: Zlong and Ztrans
ImZ
51°
ImX
41°
2 Tapers
1 mm
31°
2 Tapers
1 mm
21°
11°
Frequency [GHz]
Frequency [GHz]
ImZ is linear with the frequency at low frequencies and does not depend much on the displacement (as expected).
Zlong = ImZ/(f/frev) is calculated at f = 0.1 GHz and compared to the fill LHC (90 mOhm)
ImX is constant at sufficiently small frequencies (< 0.1 GHz).
Numerical noise is visible in ImX (ROOT fit to obtain the constant term)
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12. Ztrans vs Beam Distance
Good linearity in all configurations.
The slope is compared to the full LHC value (25 MOhm/m)
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13. Zlong and Ztrans vs Taper Angle
2 Tapers design:
Already at 11º, longitudinal impedance approaches the limit 0f 0.5% (of full LHC)
Not yet clear why transversal impedance is larger compared to 1 Taper
2 Tapers design, going from 1 to 2 mm:
Smaller longitudinal impedance (10%)
Smaller transversal impedance (20%)
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14. HFSS results: Power Loss
ReZ
LHC power spectrum before LS1
Total Power Loss [W] at 0.5 mm
Initial
1 Taper
2 Tapers
90º
11º
31º
51º
463 9 30
723
Weak dependence on the distance (10-15% going from 0.5 to 3 mm)
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15. Surface Power Loss Density
Initial Design (90°)
GHz
Power Loss 211 W
2 Tapers Design (11°)
GHz
Power Loss 8.9 W
1 Taper Design (11°)
GHz
Power Loss 3.3 W
Top view, log scale: gives and idea of where losses are localized (for cooling).
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Conclusions
Results are quite advanced but they are not final and should be fully validated with the impedance team to get a final recommendation.
I believe it will be difficult to move from 11 degrees (without ferrite).
Keep in mid that bellows and beta dependence are not yet taken into account here
Thanks a lot to the Impedance group for their help.
I will report the outcome of this week to impedance meeting in june.
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