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WORK IN PROGRESSSensitivity of LHC ADT to intra-bunch motion

Gerd Kotzian, Wolfgang Hofle, Daniel Valuch

HSC meeting, 22. January 2014

Sensitivity of LHC ADT

to intra-bunch motion

Transverse Damper in General

- The transverse damper is a feedback system: it measures the bunch-by-bunch oscillations and damps them by fast electrostatic kickers.
- Key elements:
- Beam position monitor(s)
- Signal processing system
- Power amplifiers
- Electrostatic kickers
- Key parameters:
- Feedback loop gain, phase, and total loop delay
- Kick strength
- System bandwidth

D. Valuch, “TRANSVERSE FEEDBACK: HIGH INTENSITY OPERATION, ABORT GAP CLEANING, INJECTION GAP CLEANING AND LESSONS FOR 2012”, in LHC Beam Operations Workshop, Evian 2011.

Sensitivity of LHC ADT

to intra-bunch motion

LHC Transverse Damper (ADT)

Sensitivity of LHC ADT to intra-bunch motion

Analog Front-End

- Apply and test various input combinations and evaluate the output responses.

long. profile

sym

asym

no internal saturation allowed

Analog Processing

Digital Processing

norm. transverse

position

trans. oscillation

pattern

movement of

centre-of-charges

even sym

odd sym

Sensitivity of LHC ADT

to intra-bunch motion

Analog Front-End

GOAL:

- to have 1 position reading per bunch
- bunch-synchronous digitization, sampling frequency fs = 40.08 MHz
- no cross-talk between adjacent bunches (a.k.a. ISI – Inter-Symbol-Interference) at the ADC input
- time-domain response:

Sampling points (40 MHz)

no cross-talk to

adjacent bunches

Sensitivity of LHC ADT

to intra-bunch motion

Analog input signal to the sampling ADC:

Discrete-time sequence of bunch-to-bunch

positions as seen by the damper signal processing

Sensitivity of LHC ADT

to intra-bunch motion

Beam Position Module (BPos) – Current HW

Calculates normalized beam position bunch by bunch, independent of intensity

Sensitivity of LHC ADT to intra-bunch motion

BPMC – Coupler Type Pick-ups

logarithmic scale: dBMax(1V/m), 70 dB range

Frequency Domain

|ZT (w)|

^

ZT (w) = ZT j sin(wT0/2) e -jwt/2

t

^

ZT

…

load or short

Beam

L=150 mm

… assuming

w

f=1/(2t)

T0 = 2 L/c

PU output voltage,

matched in 50 Ω

notches in

freq. response

direct representation

of the bunch profile

Sensitivity of LHC ADT to intra-bunch motion

BPMC – Coupler Type Pick-Ups

… transverse offset

- Peak voltage (beam centered) for ultimate beam @ collision: ~140 V very large
- Position information encoded in the signal amplitude: AM-modulated!
- Strong common signal (Σ), with (ideally) only small contribution by difference signal (Δ)
- Why not sample and digitize & directly? limited dynamic range
- most of the of the ADC input range would be consumed by common signal

Sensitivity of LHC ADT to intra-bunch motion

Coaxial Transmission Lines

max. PU response @ 500 MHz

max. PU output

(σ=0.375 ns)

@ 320 MHz

max. signal outputafter 650m COAX

@ 180 MHz (σ=0.375 ns)

- cable attenuates to levels acceptable to hybrid(signal transmission over 500 – 700m)
- Coaxial transmission line adds dispersion to pulse response:
- Frequency domain: maximum from PU output @ 500 MHz
- after the cable the Frequency maximum lowered to approx. 180 MHz

Sensitivity of LHC ADT to intra-bunch motion

180o – Hybrid: Sum & Delta

Coax line Tunnel-SR4

(500-700m, 7/8” Flexwell)

CONVOLUTION

A

0o

0o

B

0o

180o

MODULATION

CONVOLUTION

- Hybrid calculates from and two signals:
- Assuming ideal Hybrid, i.e. no cross-talk between and .
- Combine to eliminate-dependence of position

For a set of Hybrids (M/A-COM H9) the average cross-talk at 400 MHz was found to be better than -40 dB. For more details see IBIC 2013, WEPC12

Sensitivity of LHC ADT to intra-bunch motion

180o – Hybrid Output: Time and Freq. Domain

CONVOLUTION

MULTIPLICATION

…Fourier transform

and its inverse,

MODULATION

CONVOLUTION

Transverse oscillation causes shift in the spectrum …

Sensitivity of LHC ADT to intra-bunch motion

Band Pass Filter 400 MHz

IN

OUT

- Why Band Pass Filter?
- Look only at 400 MHz component
- Harmonic chosen for simplicity: less complexity in terms of HW
- “Sampled line” type comb filter (9 sections)

D. Valuch and P. Baudrenghien “Beam Phase Measurement and Transverse Position Measurement Module for the LHC”, in LLRF07 Workshop, Knoxville TN, USA, October 2007.

Sensitivity of LHC ADT to intra-bunch motion

Band Pass Filter 400 MHz

“Analogue version of digital FIR filter”

1st replica

2nd replica

3rd replica

9th replica

- where is the response of the directional coupler:
- bipolar pulse (same shape as )

Filter response designed for time-limited impulse response Tresp < 25 ns:

rectangular window shorter than bunch spacing

no mixing between adjacent bunch signals

Sensitivity of LHC ADT to intra-bunch motion

Band Pass Filter response

BP directional coupler response:

Delay-line response:

side lobes due

to rect. window

Band Pass filter response:

phase

zero at DC,

800 MHz, etc.

max. at 400 MHz,

1200 MHz, etc.

Sensitivity of LHC ADT to intra-bunch motion

Band Pass Filter output: Signal

Sensitivity of LHC ADT to intra-bunch motion

Band Pass Filter output: Signal

“Deformations” in wavelet mostly due to asymmetries around 400 MHz, i.e. dispersion of cable

Sensitivity of LHC ADT to intra-bunch motion

I/Q – Demodulator and Baseband Sampling

D. Valuch and P. Baudrenghien “Beam Phase Measurement and Transverse Position Measurement Module for the LHC”, in LLRF07 Workshop, Knoxville TN, USA, October 2007.

Designed in 2006

information encoded in the envelope for the RF signal

“RF” domain

Base-band (DC domain)

Demodulation

Sensitivity of LHC ADT to intra-bunch motion

I/Q – Demodulator: Signal

DEMOD

examine in base-band (around DC)

with:

In-phase component of 400 MHz = real part symmetric; cosine

Quadrature component of 400 MHz = imaginary part anti-symmetric; sine

Sensitivity of LHC ADT to intra-bunch motion

RECAP: on Mixing & Convolution

Sensitivity of LHC ADT to intra-bunch motion

I/Q – Demodulation: Signal

In-phase component (even sym.):

DEMOD

Quadrature component (odd sym.):

where

room to play

Sampling

point

- Flat plateau (= stretched pulse) for sampling with ADC
- Possibility – to some extend – to shift hardware complexity between and

Sensitivity of LHC ADT to intra-bunch motion

I/Q – Demodulation: Signal

long. bunch profile

DEMOD

baseband bunch signal (400 MHz comp.)

Sampling

- Adjacent bunch signals are well separated (some overlap in the tails, but has no influence on the sampled values)

Sensitivity of LHC ADT to intra-bunch motion

I/Q – Demodulation: Signal

MOD

DEMOD

In-phase component:

Shifting the spectrum …

and down by

… up by

Quadrature component:

MOD

DEMOD

with

- Order of multiplication is important!
- Transverse position modulation
- demodulation with

Sensitivity of LHC ADT to intra-bunch motion

Sampling of I/Q in and

Out of a continuous-time signal one value is picked:

The discrete-time representation of the continuous-time signal through periodic sampling is obtained from the relation

Since we have no cross-talk, i.e. it follows for :

masking / sifting property

Sampling

point

Sensitivity of LHC ADT to intra-bunch motion

Beam Position Module (BPos) – Current HW

Normalized bunch position calculation

angle fDS determined during

setting-up, different settings required for

different gains in pre-amplification chain

this factor becomes one

if properly adjusted – will be

assumed in the following

Sensitivity of LHC ADT to intra-bunch motion

NUMERICAL SIMULATIONS

- MATLAB SIMULINK model (reference)
- all blocks included
- simulations are time-consuming

- exploit the analytical approach and verify versus MATLAB SIMULINK

Sensitivity of LHC ADT to intra-bunch motion

25 ns Bunch Spacing (HW “as is”)

25 ns

1e11 ppb, σ=0.375 ns @ INJ

Beam current (blue),

Bunch position modulation, e.g. 1mm / 20 MHz (red)

Pick-up electrode voltages:

VA (blue), VB(red)

sign flip

Hybrid output voltage (after 650 m transmission line)

10x DELTA (blue), SUM (red)

sign flip

Band Pass filtered output (400.8 MHz)

10x DELTA (blue), SUM (red)

Baseband Magnitude ()

10x abs{DELTA} (blue), abs{SUM} (red)

flat top for

sampling

Normalized Position (UNSAMPLED)

in mm (blue)

x10-7

Special e-cloud bunch spacing: ADT compatibility

5-20 ns from SPS

20 MHz “even mode”

5 ns

5 ns

2x 5e10 ppb, σ=0.375 ns @ INJ

Beam current (blue),

Bunch position modulation, e.g. 1mm / 20 MHz (red)

lower peak voltage

electrode voltages:

VA (blue), VB(red)

Hybrid output voltage (after 650 m transmission line)

10x DELTA (blue), SUM (red)

“stepped

onset”

same peak voltage as in the 25 ns case

Band Pass filtered output (400.8 MHz)

10x DELTA (blue), SUM (red)

Baseband Magnitude ()

10x abs{DELTA} (blue), abs{SUM} (red)

reduced

flat top

Normalized Position (UNSAMPLED)

in mm (blue)

x10-7

Special e-cloud bunch spacing: ADT compatibility

5-20 ns from SPS

20 MHz odd mode: no movement of COG

2x 2e11 ppb, 4σ=2.5 ns @ INJ

Beam current (blue),

Bunch position modulation, e.g. 1mm / 20 MHz (red)

up

down

Pick-up electrode voltages:

VA (blue), VB(red)

up

Hybrid output voltage (after 650 m transmission line)

10x DELTA (blue), SUM (red)

leads to cancelation

down

Band Pass filtered output (400.8 MHz)

10x DELTA (blue), SUM (red)

Baseband Magnitude ()

10x abs{DELTA} (blue), abs{SUM} (red)

odd mode invisible

Normalized Position (UNSAMPLED)

in mm (blue)

… sensitive to beam profiles and symmetries

x10-7

Special e-cloud bunch spacing: ADT compatibility

Transverse Excitations (Intra-bunch)

- for a given longitudinal profile
- apply transverse excitation of 1 mm peak oscillation:
- for various frequencies
- in even mode: symmetric case
- in odd mode: anti-symmetric case
- in both even and odd the excitation is aligned with the centre of the long. profile
- record the normalized position as implemented in the BeamPos HW
- plot the movement of the centre of charges
- the longitudinal profile is considered to be symmetric

(asymmetric longitudinal profiles convert modes from symmetric to asymmetric and vice versa)

Sensitivity of LHC ADT to intra-bunch motion

Longitudinal Profile

From measurement:

Numerical input for simulation:

Taken from: “UPDATE ON BEAM INDUCED RF HEATING IN THE LHC”, B. Salvant et.al., IPAC’13, May 12-17, 2012, Shanghai, China:

Fig. 2: Effect of reducing bunch length on measured LHC beam spectrum (in dB) from 1.2 ns (in blue) to 1.04 ns (in red). The first notch of the distribution is observed to shift from 1.5 GHz to 1.7 GHz. The peaks beyond 2.7 GHz are believed to be due to the acquisition system bandwidth.

Sensitivity of LHC ADT to intra-bunch motion

Simulation Results: Symmetric Excitation

- Analytical and numerical results are in agreement.
- Damper sensitivity on symmetric intra-bunch motion is a function of the longitudinal beam spectra
- For the anti-symmetric excitation no movement of the centre of charges, hence
- for the anti-symmetric case no oscillation amplitude is detected by the current normalization algorithm odd modes not visible to the damper
- Alternate beam position processing scheme for odd modes…

movement of

centre-of-charges

normalized position as implemented

in the BeamPos HW

NB: although higher even modes visible the damper is acting only in baseband up to 20 MHz – for damping of higher frequencies wideband transverse feedback

Sensitivity of LHC ADT to intra-bunch motion

Simulation Results: Anti-Symmetric Excitation

alternate processing scheme to detect and indicate anti-sym. oscillations:

- indication of odd-mode oscillations!
- Question: since asym. oscillations are detectable by HW, could a narrow-band high freq. damper @ 400 MHz counteract this?

Sensitivity of LHC ADT to intra-bunch motion

Summary and Conclusions

- Signals from even-symmetric intra-bunch movement > 20 MHz seen by damper corrective measure applied in baseband (up to 20 MHz)
- Signal from anti-symmetric (odd-symmetric) intra-bunch movement can be made accessible with only minor firmware update diagnostics indicator
- Information on excitation frequency lost only indication on the presence of instability (transverse)
- Damper sensitivity is a function of the longitudinal bunch spectrum (and the oscillation frequency)
- Notches in the beam spectra will render the damper blind for certain frequencies
- [notches in bunch spectrum ≠ blind frequencies]
- mode conversion: even – odd, requires precise adjustment of I/Q coordinate rotation, done during setting up: align Coordinate systems of - and -pairs
- even/odd signals visible for asymmetric bunch profiles:
- practical implementation:

even

odd

Sensitivity of LHC ADT to intra-bunch motion

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