1. High resolution RF cavity BPM design for Linear Collider Andrei Lunin 8th DITANET Topical Workshop on Beam Position Monitors

2. Page 2 Jan. 2012, A. Lunin Outline Introduction Operating parameters of the cavity BPM for CLIC project Strategy of the Cavity BPM design Cavity BPM spectrum calculation Monopole mode coupling - mechanical tolerances analysis - multi-bunch regime Dipole modes cross coupling Cold RF measurements Analog Downconverter R&D Conclusions

3. Page 3 Jan. 2012, A. Lunin CLIC CTF Nominal bunch charge [nC]0.6 Bunch length (RMS) [µm]44225 Batch length, bunch spacing [nsec]156, 0.51-150, 0.667 Beam pipe radius [mm]44 BPM time resolution [nsec]<50 BPM spatial resolution<0.1 BPM dynamic range [µm]±100 BPM dipole mode frequency f 110 [GHz] 14.000014.98962 REF monopole mode frequency f 010 [GHz] 10.00008.993774 Cavity BPM for CLIC project The beam position monitor (BPM) have to have both, high spatial and high time resolution ! Waveguides Beam Pipe Cavity WG-Coaxial Transitions Coupling Slot

4. Page 4 Jan. 2012, A. Lunin Cavity BPM for CLIC. Operating Principles The off-axis beam passing the cavity induces two orthogonal dipole TM 110 modes with amplitudes proportional to the off-axis shift. A resonant cavity behaves like a damped oscillator with the EM- field decaying exponentially in time: where τ= 2Q/ω 0 The maximum loaded Q-factor is given by: For t max = 50ns, Qmax ~ 300 Magnetic coupling with waveguide

5. Page 5 Jan. 2012, A. Lunin R4 R11.22 2 0. 5 5.2 2 14 20 5.6 4.84 5 R1.8 R0.2 R3.9975 R11.23 The width of waveguide (14 mm) was chosen such, that its cut-off frequency is located between TM 010 and TM 110 cavity modes. The monopole signal is exponentially decaying along the waveguide, therefore, it is better to minimize the height (2 mm) The length (20 mm) was chosen in order to eliminate a waveguide resonance. Cavity BPM Design. Waveguide Dimentions.

6. Page 6 Jan. 2012, A. Lunin 1.General idea: - low Q-factors - monopole modes decoupling BPM parameters: - Cavity length - Waveguide dimensions - Coupling slot - Coaxial transition 3.Parasitic signals: - monopole modes - quadruple modes 5. Tolerances calculation: -coupling slots -waveguide to cavity - cavity to pipe 2. Cavity spectrum calculations: - Frequency - R/Q, Q - TM11 output voltage 4. Cross coupling: - waveguide tuning - 2 ports vs 4 ports loop Cavity BPM Design

7. Page 7 Jan. 2012, A. Lunin 4.84 5 c_dr R0.4 Cavity BPM Design. Waveguide Matching. The waveguide is matched to the output coaxial by a resonance antenna coupling

8. Page 8 Jan. 2012, A. Lunin Mode TM 11 Mode TM 01 Mode TM 21 Mode TM 02 Cavity BPM Design. Spectrum Calculation.

9. Page 9 Jan. 2012, A. Lunin Mode WG_TM 11 Mode WG_TM 21 Cavity BPM Design. Waveguide Resonances.

10. Page 10 Jan. 2012, A. Lunin HFSS EigenMode Calculation (II) Bunch trajectories (I) Matched Impedance, P coax HFSS Data: W - Stored Energy P coax - Exited RF Power Ez - E-field along bunch path g sym - Symmetry coefficient Scale Factor: Output Power: r e-e- Estimated Sensitivity (q 0 = 1nQ): V/nQ/mm Cavity BPM Design. Output Signal Calculation.

11. Page 11 Jan. 2012, A. Lunin + Slot Rotation Slot Shift HφHφ HzHz ∆α∆α Strong Magnetic Coupling ~∆α x ∆x HφHφ HzHz Slot Tilt Weak Electric Coupling Weak Magnetic Coupling 2. Slot tilt causes the non zero projection of TM 01 azimuth magnetic (H φ ) and longitudinal electric (E z ) filelds components in the cavity to a transverse (H x ) and vertical (E y ) components of TE 10 mode in the waveguide. Because both H x and E y are close to zero near the waveguide wall tilt error causes the weak electric and weak magnetic coupling of monopole mode to waveguide. ∆θ∆θ HφHφ EyEy EyEy HxHx 1. Slot rotation causes the non zero projection of TM 01 azimuth magnetic field component (Hφ) in the cavity to a longitudinal one (Hz) of TE 10 mode in the waveguide. Small slot shift is equivalent to rotation with angle: α x ~ arctan(Δx/Rslot). Therefore both slot rotation and shift cause strong magnetic coupling of monopole mode to waveguide. Cavity BPM Design. Monopole Mode Coupling.

12. Page 12 Jan. 2012, A. Lunin ∆x a) ∆α∆α Slot Rotation Slot Shift ∆θ∆θ Waveguide Tilt If we accept machining tolerances of ~10 μm, the equivalent slot rotation computes 2Δ x /L slot ~ 0.16 degree, which corresponds to ~50 mV output voltage. Therefore, the total TM 010 mode leakage caused by all machining errors on the coupling slot could be roughly estimated to be less than 100 mV for each coaxial output. Cavity BPM Design. Monopole Mode Coupling.

13. Page 13 Jan. 2012, A. Lunin +0.5 degree rotation -0.5 degree rotation 180 degree phase flip Cavity BPM Design. Monopole Mode Phase Flip.

14. Page 14 Jan. 2012, A. Lunin B B – Filter Passband Monopole mode rejection (red) f, [Hz] B, [Hz] Spectral density Cavity BPM Design. Frequency Discrimination.

15. Page 15 Jan. 2012, A. Lunin Single Bunch Signals : TM 11 signal TM 01 signal TM 21 signal Rejection: Multi-bunch regime (2 GHz) TM 01, TM 11, TM 21 Time, [s] Cavity BPM Design. Multi-bunch Regime.

16. Page 16 Jan. 2012, A. Lunin 1 - Stainless steel resonator material 2 – RMS value; normalized to 1 nC charge 3 - Signals are from a single coaxial output at the eigenmode frequency. Multipole modes are normalized to 1 mm off-axis shift 4 – For TM 210 only Cavity BPM Design. Spectrum of Output Signal.

17. Page 17 Jan. 2012, A. Lunin Cavity BPM Design. Predicted BPM resolution. 1 – Stainless steel material was used. 2 – RMS value of the sum signal of two opposite coaxial ports at the 14 GHz operating frequency after all filters applied; signals are normalized to 1 nC charge

18. Page 18 Jan. 2012, A. Lunin Port 1 Port 2 a) b) c) a)Vertical Waveguide coupling with slots b)Vertical Waveguide coupling, no slots c)Horizontal Waveguide coupling, no slots Crosscoupling Cavity BPM Design. Dipole Modes Crosscoupling. The waveguide to coaxial transition brakes coupling symmetry and hence the orthogonality of the dipole modes !

19. Page 19 Jan. 2012, A. Lunin Port 1 Port 2 a) b) c) Vertical Waveguide coupling with slots (case a) has the lesser TM 11 mode cross coupling due to geometry errors. Nevertheless, the case b) was chosen due to manufacturing simplicity. Cavity BPM Design. Dipole Modes Crosscoupling.

20. Page 20 Jan. 2012, A. Lunin Mechanical Tolerances 1,2 Cross Coupling -40 dB Cross Coupling -30 dB Cross Coupling -20 dB Slot Rotation, [deg]< 0.05< 0.2< 0.6 Slot Shift, [μm]< 5< 15< 40 Other, [μm]< 50 Max Dynamic Range, [μm] 1002510 1 - In-phase signals reflection (worse case) is taken into account. 2 – The reflection from LLRF part is assumed less than -20 dB. Cavity BPM Design. Dipole Modes Crosscoupling. The cross coupling between the two polarizations of the TM 110 mode limits a dynamic range of the beam position measurement. The actual effect of cross coupling depends on amplitude and phase of reflected signals from the read-out electronics front-end, e.g. LLRF parts like hybrids or band-pass filters. For our estimation we assumed a worst case scenario, i.e. the reflected signals are in- phase and the SWR of the LLRF components is about -20 dB. Limitations of BPM resolution due to TM 110 modes cross coupling

21. Page 21 Jan. 2012, A. Lunin Cavity BPM Design. Mechanical Drawings.

22. Page 22 Jan. 2012, A. Lunin Cavity BPM Design. Cold Measurements. The first prototype of the BPM was manufactured by CERN and sent to RHUL for low power RF measurements. All parts have been assembled together using special clamps and leveling brackets. For monopole and dipole modes excitation we used a coaxial antenna inserted through the upper end of a beam pipe.

23. Page 23 Jan. 2012, A. Lunin Cavity BPM Design. Cold Measurements. Monopole Mode*, Freq. [GHz], Q load Dipole Mode Freq. [GHz], Q load Experiment11.158 – 11.172, 260-31014.990 – 14.995, 240-250 Simulation 11.195 360 15.000 290 * – Results depend on the antenna penetration

24. Page 24 Jan. 2012, A. Lunin Cavity BPM Design. Cold Measurements. Dipole Modes Crosscoupling, [dB] Experiment-37 max Simulation, nominal 0.5 deg slot rotation -48 max -34 max

25. Page 25 Jan. 2012, A. Lunin Fermilab has several analog downconverter R&D activities: –714 MHz -> 15.1 MHz downconverter for ATF damping ring >90 dB usable dynamic range (for each attenuator/gain setting)! Low noise amplifier (LNA) with switchable gain 28 dB step attenuator Image rejection (SSB) mixer Remote control (CAN-bus) of attenuator & gain, read-back of voltages, LO-level, temperatures, etc. PCB boards for RF and CAN-bus controls –4…10 GHz -> 70 MHz donwconverter for cavity HOM coupler signals Connectorized experimental setup (no PCB yet) Beam studies in February 2012 (DESY FLASH 3.9 GHz HOM studies) –CLIC BPM analog downconverter proposal Based on ATF/HOM concepts, e.g. SSB-mixer, att. & LAN, CAN-bus controls 15 GHz -> 70 MHz IF FD/TD optimized BPF (quasi Tchebycheff) defines waveform On-board PLL-locked (to external RF) local oscillator (LO) Analog Downconverter R&D

26. Page 26 Jan. 2012, A. Lunin HOM BPM Single Channel Downconverter

27. Page 27 Jan. 2012, A. Lunin The CLIC cavity BPM delivers a pulse-like beam signal with high frequency (15 GHz) contents. The delivered signal levels of the dipole mode cavity are ranging from nV to mV. The downconverter is an analog signal conditioning system to adapt the cavity BPM signals to the digitizer, providing two functions: 1.Frequency translation:  using an image rejection or single sideband (SSB) mixer is preferable  the digitizer, operating in the first Nyquist passband  digitizer sampling rate is in the 200...250 MS/s range  The proposed IF frequency is 70 MHz 2. Variable signal gain with minimum distortion :  adaption the large input signal level range to the typical ± 1 volt input level range of the digitizer  lowest noise and highest linearity (wide dynamic range) are key elements for choosing the electronics components  the IF section needs to provide an anti-aliasing low-pass filter at the downconverter output Analog Downconverter R&D

28. Page 28 Jan. 2012, A. Lunin Analog Downmixer (prototype) The downconverter needs to be located physically close to the BPM, in the tunnel, because of high insertion losses of signal cables at 15 GHz. This calls for remote control of attenuator and gain settings, as well as read-back of some parameters, e.g. supply voltages, LO signal level, temperatures, etc. We developed a CAN-bus control system for our donwconverters, at the VME crate level it is managed by a PMC CAN-bus card, located at the crate controller CPU.

29. Page 29 Jan. 2012, A. Lunin  We designed a high resolution cavity BPM for CLIC project.  The BPM can operate in single and multi-bunch regimes with a submicron resolution at acceptable mechanical tolerances.  The first cold RF measurements show a promising results and a good coinciding with numerical simulations. Still there are areas of improvements on the coupling scheme and the BPM mechanical design.  The BPM parts are ready for brazing and further experiments at CTF3 beam facility are planned.  Fermilab continues various R&D activities on a high precision analog signal processing. Cavity BPM Design. Summary.