High resolution RF cavity BPM design for Linear Collider
Andrei Lunin
8th DITANET Topical Workshop on Beam Position Monitors
Page 2Jan. 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
Page 3Jan. 2012, A. Lunin
CLIC CTF
Nominal bunch charge [nC] 0.6 0.6
Bunch length (RMS) [µm] 44 225
Batch length, bunch spacing [nsec] 156, 0.5 1-150, 0.667
Beam pipe radius [mm] 4 4
BPM time resolution [nsec] <50 <50
BPM spatial resolution <0.1 <0.1
BPM dynamic range [µm] ±100 ±100
BPM dipole mode frequency f110 [GHz]
14.0000 14.98962
REF monopole mode frequency f010 [GHz]
10.0000 8.993774
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-CoaxialTransitions
CouplingSlot
Page 4Jan. 2012, A. Lunin
Length, [mm]
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Qualit
y F
act
or
0
100
200
300
400
500
600
700
Q-external Q-internal (steel)Q-total (steel)
Cavity BPM for CLIC. Operating Principles
The off-axis beam passing the cavity induces two orthogonal dipole TM110 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:
)cos()( 0/
0 teVtV t
where τ= 2Q/ω0 The maximum loaded Q-factor is given by:
)1000ln(20max
max
tQ For tmax = 50ns, Qmax ~ 300
Magnetic coupling with waveguide
Page 5Jan. 2012, A. Lunin
R4
R11.222
0.5
5.2
214
20
5.6
4.84
5
R1.8R0.2
R3.9975
R11.23
The width of waveguide (14 mm) was chosen such, that its cut-off frequency is located between TM010 and TM110 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.
Page 6Jan. 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 loop
Cavity BPM Design
Page 7Jan. 2012, A. Lunin
4.84
5
c_drR0.4
Cavity BPM Design. Waveguide Matching.
The waveguide is matched to the output coaxial by a resonance antenna coupling
Page 8Jan. 2012, A. Lunin
Mode TM11 Mode TM01
Mode TM21
Mode TM02
Cavity BPM Design. Spectrum Calculation.
Page 9Jan. 2012, A. Lunin
Mode WG_TM11Mode WG_TM21
Cavity BPM Design. Waveguide Resonances.
Page 10Jan. 2012, A. Lunin
HFSS EigenMode Calculation
(II) Bunch trajectories (I) Matched Impedance, Pcoax
HFSS Data:
W - Stored EnergyPcoax - Exited RF PowerEz - E-field along bunch pathgsym - Symmetry coefficient
00 0*
*2*
L j t
scaleHFSS sym
Ez e dzq qk
q g W
Scale Factor:
Output Power:
211 )(*)()( scalecoaxTM krPrP
r
e- Estimated Sensitivity (q0 = 1nQ):
r
OhmrPS TM ][50*)(11 V/nQ/mm
Cavity BPM Design. Output Signal Calculation.
Page 11Jan. 2012, A. Lunin
+
Slot Rotation Slot Shift
Hφ
Hz∆α
Strong Magnetic Coupling
~∆αx ∆x
Hφ
Hz
Slot Tilt
Weak Electric Coupling Weak Magnetic Coupling
2. Slot tilt causes the non zero projection of TM01 azimuth magnetic (Hφ) and longitudinal electric (Ez) filelds components in the cavity to a transverse (Hx) and vertical (Ey) components of TE10 mode in the waveguide. Because both Hx and Ey are close to zero near the waveguide wall tilt error causes the weak electric and weak magnetic coupling of monopole mode to waveguide.
∆θ
Hφ
Ey
Ey
Hx
1. Slot rotation causes the non zero projection of TM01 azimuth magnetic field component (Hφ) in the cavity to a longitudinal one (Hz) of TE10 mode in the waveguide. Small slot shift is equivalent to rotation with angle: αx ~ arctan(Δx/Rslot). Therefore both slot rotation and shift cause strong magnetic coupling of monopole mode to waveguide.
Cavity BPM Design. Monopole Mode Coupling.
Page 12Jan. 2012, A. Lunin
Slot shift, [mm]
0.0 0.2 0.4 0.6 0.8 1.0 1.2
TM
01
volta
ge
, [V
]
0
1
2
3
4
∆x
a)
Slot rotation, [deg]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
TM
01 vo
lta
ge
, [V
]
0.0
0.1
0.2
0.3
0.4
0.5
0.6
∆α
Slot Rotation Slot Shift
Tilt [deg]
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
TM
01
volta
ge
, [V
]
0.00
0.02
0.04
0.06
0.08
0.10
∆θ
Waveguide Tilt
If we accept machining tolerances of ~10 μm, the equivalent slot rotation computes 2Δx/Lslot ~ 0.16 degree, which corresponds to ~50 mV output voltage. Therefore, the total TM010 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.
Page 13Jan. 2012, A. Lunin
+0.5 degree rotation -0.5 degree rotation
180 degree phase flip
Cavity BPM Design. Monopole Mode Phase Flip.
Page 14Jan. 2012, A. Lunin
1 107
1 108
1 109
0
0.02
0.04
0.06
0.08
0.10.1
0
FR01 B( )
FR11 B( )
1 1091 10
7 B
1 109
1.1 109
1.2 109
1.3 109
1.4 109
1.5 109
1.6 109
0
2 107
4 107
6 107
6 107
0
V01 f( )
V11 f( )
1.6 1091 10
9 f
B
B – Filter Passband
I01 B( )
11B
2
11B
2
V01
d I11 B( )
11B
2
11B
2
V11
d
I00 B( )
01B
2
01B
2
V01
d I10 B( )
01B
2
01B
2
V11
d
Monopole mode rejection (red)
FR01 B( )I01 B( )
I11 B( ) FR11 B( )
I10 B( )
I00 B( )
01f01
2Q01 11
f11
2Q11
V01 f( )01
2f2
012
f f01( )2 01
2f f01( )
2
V11 f( )11
2f2
112
f f11( )2 11
2f f11( )
2
f, [Hz]
B, [Hz]
Spectral density
Cavity BPM Design. Frequency Discrimination.
Page 15Jan. 2012, A. Lunin
0 5 109 1 10
8 1.5 108 2 10
8 2.5 108 3 10
8 3.5 108 4 10
8 4.5 108 5 10
81
0.5
0
0.5
11
1
VN01 t 0( )
VN11 t 0( )
VN21 t 0( )
50 1090 t
0 5 109 1 10
8 1.5 108 2 10
8 2.5 108 3 10
8 3.5 108 4 10
8 4.5 108 5 10
80
2
4
6
8
10
1212
0
VS11 t( )
50 1090 t
0 5 109 1 10
8 1.5 108 2 10
8 2.5 108 3 10
8 3.5 108 4 10
8 4.5 108 5 10
80
0.5
1
1.5
22
0
VS01 t( )
50 1090 t
0 5 109 1 10
8 1.5 108 2 10
8 2.5 108 3 10
8 3.5 108 4 10
8 4.5 108 5 10
80
0.5
1
1.5
22
0
VS21 t( )
50 1090 t
Single Bunch Signals :
TM11 signal
TM01 signal
TM21 signal
I11t1
t2
tVS11 t( )
d
I01t1
t2
tVS01 t( )
d
Rejection: 010.08
11
I
I
I21t1
t2
tVS21 t( )
d
Rejection: 01
0.0721
I
I
Multi-bunch regime (2 GHz)
TM01, TM11, TM21
Time, [s]
Cavity BPM Design. Multi-bunch Regime.
Page 16Jan. 2012, A. Lunin
Mode Type Freq. [GHz]
Qtot1, (Ql) R/Q
[Ω], [Ω/mm2], [Ω/mm4]
Output Voltage2,3
[V], [V/mm], [V/mm2]
Frequency Filter Rejection
Phase Filter Rejection4
Multi-bunch Regime Rejection
TM010 10.385 380, (>109) 45 <0.001 0.005 - 0.1TM110 13.999 250, (540) 3 17 - - -
TM210 18.465 80, (100) 0.05 5 0.025 0.1 0.1
TM020 24.300 680, (>109) 12 <0.001 0.001 - 0.05
WG1TM11 12.285 6 - 3 - - -
TM21 12.285 6 - 0.3 - - -
WG2TM11 15.878 4 - 5 - - -
TM21 15.880 4 - 1.2 - - -
WG3 TM21 21.610 7 - - - - -
1 - Stainless steel resonator material2 – RMS value; normalized to 1 nC charge3 - Signals are from a single coaxial output at the eigenmode frequency. Multipole modes are normalized to 1 mm
off-axis shift4 – For TM210 only
Cavity BPM Design. Spectrum of Output Signal.
Page 17Jan. 2012, A. Lunin
Cavity BPM Design. Predicted BPM resolution.
Mode Type
Freq. [GHz]
Qtot1 Beam
shift [µm]
Output voltage2
[mV]
BPM Resolution
[nm]SB MB
TM010 10.385 380 0 <1 40 4TM110 13.999 250 0.1 2.4 - -
TM210 18.465 80 100 <0.18 8 1
TM210 18.465 80 500 <4 200 20
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
Page 18Jan. 2012, A. Lunin
Port 1
Port 2
a)
b)
c)
a) Vertical Waveguide coupling with slotsb) Vertical Waveguide coupling, no slotsc) Horizontal Waveguide coupling, no slots
Freq., [GHz]
13.5 13.6 13.7 13.8 13.9 14.0 14.1 14.2 14.3 14.4 14.5
S1
2, [d
B]
-47
-46
-45
-44
-43
-42
A) CouplingB) CouplingC) Coupling
Cro
ssco
uplin
g
Cavity BPM Design. Dipole Modes Crosscoupling.
The waveguide to coaxial transition brakes coupling symmetry and hence the orthogonality of the dipole modes !
Page 19Jan. 2012, A. Lunin
Port 1
Port 2
a)
b)
c)
Pipe Shift, [mm]
0.00 0.02 0.04 0.06 0.08 0.10
S12
, [dB
]
-45
-40
-35
-30
-25
-20
A) B) C) Vertical Waveguide coupling with
slots (case a) has the lesser TM11
mode cross coupling due to geometry errors. Nevertheless, the case b) was chosen due to manufacturing simplicity.
WG Shift, [mm]
0.00 0.02 0.04 0.06 0.08 0.10
S12
, [dB
]
-45
-40
-35
-30
-25
-20
A) B) C)
WG Rotation, [Deg]
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
S12
, [dB
]
-45
-40
-35
-30
-25
-20
A) B) C)
Cavity BPM Design. Dipole Modes Crosscoupling.
Page 20Jan. 2012, A. Lunin
Mechanical
Tolerances1,2
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 < 50 < 50
Max Dynamic
Range, [μm]
100 25 10
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 TM110 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 TM110 modes cross coupling
Page 21Jan. 2012, A. Lunin
Cavity BPM Design. Mechanical Drawings.
Page 22Jan. 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.
Page 23Jan. 2012, A. Lunin
Cavity BPM Design. Cold Measurements.
Monopole Mode*, Freq. [GHz], Qload
Dipole ModeFreq. [GHz], Qload
Experiment 11.158 – 11.172, 260-310 14.990 – 14.995, 240-250
Simulation 11.195 360 15.000 290* – Results depend on the antenna penetration
Page 24Jan. 2012, A. Lunin
Cavity BPM Design. Cold Measurements.
Dipole Modes Crosscoupling, [dB]
Experiment -37 max
Simulation, nominal0.5 deg slot rotation
-48 max-34 max
Page 25Jan. 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
Page 26Jan. 2012, A. Lunin
HOM BPM Single Channel Downconverter
Page 27Jan. 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
Page 28Jan. 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.
Page 29Jan. 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.