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.