IBIC 2012 - Learning From Beams
John D. Fox
Stanford Linear Accelerator CenterWork supported by the DOE under contract # DE-AC02-76SF00515 and the DOE LHC
Accelerator Research Program LARP

October 2012

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 2012

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Outline
1 Common Control Room Measurements
2 Signals in the Time and Frequency domains
3

4

5
6
7
8
9

Fourier Transforms
Linear Time Invariant Systems
Impulse Response, Convolution
A QuizSignals from Bunched Beams
Signatures of Betatron Motion
Signatures of Synchrotron Motion
Signals from multiple bunches
Common Pickups and Beam Transducers
Oscilloscopes, Spectrum Analyzers and Network Analyzers
Signals from Beams
A little knowledge is a dangerous thing
choosing a medium power RF amplifier
Summary
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 2012

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Common Control Room Measurements

Common Control Room Measurements• Particle Currents• Total• Current distribution ( bunch by bunch currents)• Orbits• Tunes• Betatron• Synchrotron• Bunch Profile• Transverse• Longitudinal• Bunch Motion, Signatures of Instabilities

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 2012

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Signals in the Time and Frequency domains

Fourier Transforms

Time and Frequency Domains
Fourier transforms
A function f(x) may be Fourier transformed into a function F(s),Z ∞F (s) =
f (x)e−i2πxs dx

(1)

−∞

and likewise a function F(s) can be transformed into a function f(x)f (x) =Z ∞F (s)ei2πxs ds

(2)

−∞

The Laplace transform is related to the Fourier Transform but involves
an integral from 0 to infinity

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 2012

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Signals in the Time and Frequency domains

Fourier Transforms

Time and Frequency Domains
Discrete Fourier Transform
For systems involving discrete samples of data, such as from sampling
circuits or from samples taken from circulating bunches, thediscrete-time Fourier transform is similar
N−1

F (ν) =1 X
f (τ )e−i2π(ν/N)τ
N

(3)

τ =0

f (τ ) =N−1
X

F (ν)ei2π(ν/N)τ

(4)

ν=0

There is a related transform, the Z transform, which is the discrete-time
equivalent of the Laplace transformJohn D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 20125 / 61

Signals in the Time and Frequency domains

Fourier Transforms

Time and Frequency Domains
Convolution of two functions
The convolution of two functions f(x) and g(x) is defined as f (x) ? g(x)f (x) ? g(x) =Z ∞f (u)g(x − u)du

(5)

−∞

In pictorial form

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 2012

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Signals in the Time and Frequency domains

Fourier Transforms

Common Transform Pairs ( from Bracewell)

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

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Linear Time Invariant Systems

Linear Time Invariant Systems

If a system converts an input u(t) into an output y (t)y (t) = L [u(t)](6)

the system is linear if for two constants a1 and a2
L [a1 u1 + a2 u2 ] = a1 L [u1 (t)] + a2 L [u2 (t)] .

(7)

The response of two inputs is the superposition of the individual
outputs. If an input is only a single frequency ω, the output can only
contain that single frequency ω.

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 20128 / 61

Linear Time Invariant Systems

Linear Time Invariant Systems

A system is time invariant if for a time delay δ the output has shift
invariance, or thatJohn D. Fox (SLAC)L [u(t)] = y (t)(8)

L [u(t − δ)] = y (t − δ)

(9)

IBIC 2012 - Learning From Beams

October 2012

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Linear Time Invariant Systems

Impulse Response, Convolution

Impulse response of LTI system

The impulse response I(t) of a system is found by exciting the systemwith a δ-function in the time domain.
b(t)

I(t)
LTI
5-20008545A1for a general input u(t) the output is a convolutiony (t) = u(t) ? I(t)John D. Fox (SLAC)IBIC 2012 - Learning From Beams(10)

October 201210 / 61

Linear Time Invariant Systems

Impulse Response, Convolution

Frequency Response of LTI system
Frequency response H(s) is the transfer function in the frequency
domain. Measured by network analyzer via magnitude and phase vs.
frequency.
A(s)

H(s)
LTI

5-20008545A2For a general input in the frequency domain I(s) the output O(s) is the
product
O(s) = H(s)I(s)John D. Fox (SLAC)IBIC 2012 - Learning From Beams(11)
October 201211 / 61

Linear Time Invariant Systems

Impulse Response, Convolution

Frequency Response and Time Response relationship

The time response is also the inverse transform of the product of theFourier transform of the input u(t) and the frequency response H(s)y (t) = u(t) ∗ I(t)(12)

y (t) = IFT [FT (u(t))H(s)](13)

For an LTI system, we can measure in either domain, and compute theresponse via appropriate convolutions, transforms or inverse
transforms

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201212 / 61

Linear Time Invariant Systems

Impulse Response, Convolution

The sampling function X

n=∞X

X(x) =

δ (x − n)n=−∞

The X is its own Fourier Transformn=∞
X
X(S) =
δ (S − n)n=−∞

For a sampling rate τX(S) = 1/τn=∞Xδ (S − n/τ )n=−∞John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201213 / 61

Linear Time Invariant Systems

Impulse Response, Convolution

The sampling function X multiplied by a waveform

X(x) =n=∞X

δ (x − n)n=−∞John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201214 / 61

Linear Time Invariant Systems

Impulse Response, Convolution

The sampling function X convolved with a spectrum (replicating property)

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201215 / 61

Linear Time Invariant Systems

A QuizA Quiz on LTI Systems

Consider this simple circuit - a voltage divider
R
Vout

Vin
R

5-20008545A16

Is this an LTI system? Is it ALWAYS an LTI system?

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201216 / 61

Linear Time Invariant Systems

A QuizA Quiz on LTI Systems

Consider this simple circuit - a high-pass filter
C

Vin

Vout
R

5-20008545A17

Here the output is frequency dependent. Is this an LTI system?

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201217 / 61

Linear Time Invariant Systems

A QuizA Quiz on LTI Systems

Consider this simple circuit - a diode clipper ( a limiter)
R
Vout

Vin

5-20008545A18

Is this an LTI system? When? What output frequencies are present for
an input at ω?. Two signals ω1 and ω2 ? Does it have an Impulse
Response I(t) ?

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201218 / 61Signals from Bunched Beams

Signals from Beams
Charged particles in a conducting vacuum chamber - Lorentz
contracted longitudinal E-field
1/a

e–

e–

B=0

e–

B<1

+

+

+

B

1

+

<

+

+

+

+
5-20008545A11

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201219 / 61Signals from Bunched Beams

Signals from a single bunch• pick-up signal, time domain a series of impulses• shape related to the bunch structure and the pick-up response.

f (t) =∞X

δ(t − kT0 ),

(14)

k =−∞

T0 is the revolution period of the ring.
• frequency domain -line spectrum, with spacing ∆ω0 = 1/2πT0F (ω) =

Z ∞f (t) exp(−iωt)dt

(15)

−∞

F (ω) = ω0∞X

δ(ω − mω0 )

(16)

m=−∞
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201220 / 61Signals from Bunched Beams

Signals from a single bunch - Frequency Domain• Envelope related to F.T. of bunch distribution (and the pick-up

response).
• typical electron storage ring, the spectrum extends to 20 GHz andA(t)beyondt

6toJohn D. Fox (SLAC)IBIC 2012 - Learning From Beams

5-20008545A3October 201221 / 61Signals from Bunched Beams

Bunch Length Measurement© 1993 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material
for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers
or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

• Measure the spectrum of the bunch signal at two harmonics• Requires bandwidth consistent with harmonics
Main Ring Bunch Length Monitor

K. Meisner and G. Jackson
Ferm Ii National Accelerator Laboratoryl, Box 500, Batavia, IL 60510
Abstract

1st harmonic heterodyne
receiverRing
channelIn the Main
accelerator, TO is nearly constant and the

1st Mixer
53Mhz -)
Hardware to measure the Main Ring
beam bunch
length
BPF
10.7MHz IF +-was installed in January of 1991. The system measures
bunch length by comparing relative strengths of 53Mhz and
159Mhz components of signal fromThe
53Mhz a beam detector.
RF Mixer
output signal is proportional toFRF
bunch
length, 42.3MHzis scaled
in
IN
Amp.
I
nanosec., and has become a very- useful diagnostic tool.
Hardware design and operational performance are presented.
Introduction

95% interval of the beam distribution,
M:BLM53 referred to as the full
455Khz
2nd Mixer
bunch length 4ot,
is the quantity of interest.
*
Detector
455Khz IF
1 amplitude
A quarter wavelength Vcoaxial
stripline detector locatedin the Main Ring at E48 has resonances at (2n+l) Frf.
Signals from the upstream and downstream ends of the
stripline are combined to allow detecting the beam current
from both proton and antiproton beams. Detector output
signals at the 53Mhz fundamental RF frequency and at the
159Mhz third harmonic give good sensitivity for detection ofbunch lengths in the 1-l 2 nsec range of the Main Ring beam.
These two frequencies are chosen for processing by BLMON
electronics, which uses EQN 1 with X=3.

The principle of operation for the Main Ring bunch
RF Mixer
length monitor (BLMON), motivation for it’s design,
choice148.3MHzAmp.
of detector, and circuit components are given
in detail
BLMON Electronics DescriDtion
elsewhere2,3, and will be presented here only briefly.
JI
M:BLM
Electronics developed initially for BLMON early in 1990
Figure 1 is a block diagramof I59the hardware. The beam
2nd Mixer
159Mhz+ exhibited
I st Mixer).
455Khzproduced unexpected noise on the output
andusefulRF inputthrough a 7-bit digitally programmed
IF signal passes
10.7MHz IF +455KhzBPF
Detector
V3 amplitudeoperation over a small range- of beam
intensity.
The
attenuator with 127db range in Idb steps. For test purposes,
emphasis of this paper is on a basic description of thethe attenuatorcan be controlled locally.
For normal
3rd harmonic heterodyne
receiver channel
electronics, improvements made to the original design andoperation, the attenuator is controlled remotely by systemtest procedures, and resulting pertormance.4
parameters
named
M:BUNAnn,
where
“r-m”
designates
one ofFigure 1: Bunch Length Monitor Block Diagram
the seven Main Ring accelerator cycle type Tclk reset events.
Measurement Principle
Each of the cycle types can have unique beam type (proton orbunch intensity, and fill Octoberfactor. Early
John D. Fox (SLAC)IBIC 2012 - Learning antiproton),
From Beams
2012 in the22 / 61

Rela

The left-hand factor of H(!) depends both on frequency
to the " of the original gaussian pulse. A maximum error
fromBeams The first one has been mounted on a motorised translationand on the delay; it does not Signals
depend on". Bunched
The right-hand
11 reflects% has beenfound halfout, offorthea range" from 12 tostageofandbackwards
beam ofradiation.
0.2 H(!) is the spectrum of a single gaussian pulse;
factor of
70 ps.
it is independent on the delay. Therefore, by varying the The second mirror, placed at a fixed location, reflects
delay d, 0thesecondpeak ofthe spectrum
moves
along
the 30 forwards the radiation from the first mirror. As a result,
5
10
15
20
25
0
FIRST
MEASUREMENTS
two parallel 4
beams
are createdand summed up by thespectrum of the single gaussian
pulse.
Frequency (GHz)
It has been computed a maximum of sensitivity for d = photodiode. The delay between the two pulses is
proportional
tothe
distance
betweenthe mirrors and canFigure:1
Theoretical
spectrum
of
the
sum
of
two
4.1
Measurement
set-up0.4428*"; in that situation the second maximum of thein steps much smaller than a pico-second
delayedis gaussian
pulsesenvelope
43.27% of
H(0).( ! =12 ps) with a delay of 50 ps. be variedAs
alreadymentioned,
theopticaldelay line has been(#t=13.3 fs for a 2 µm stepping motor).
implemented by means of two square mirrors (see Fig. 3).
Simulation
set-upfactor
overview•3.2 delay
The left-handof H(!)
depends
on frequency
beam
opticalsignalby τbothcombinewith itself
radiationtranslation
The first one has been mounted incident
on a motorised
onthe
thestored
delay; beam
it doesgenerates
not dependon ".train
The whoseright-handmirror of τ )Since
a pulse• andCombined
spectralenvelope
shows
bunch
length(function
stagesecond
andreflects
backwards half of the beam radiation.
factor of reflectsH(!) is thethe spectrumof a single gaussian
pulse;
periodicity
machine circumference
and itsThe
secondmirror,placedata
fixed
location, reflects
it is independent
ondelay.
Therefore,by varying
A the
NEW
FREQUENCY-DOMAIN
BUNCH
LENGTHfillingmode, simulations
havebeen carriedout to the METHOD
forwards FOR
the radiationfromthe first mirror. As a result,delay thed, thesecond peakof thespectrumalong
evaluate
perfomanceof themethodwhen moves
appliedMEASUREMENT
to a thetwo parallel beams are created and summed up by theof the single
notspectrum
purely gaussian
pulse. gaussian pulse.
photodiode. The delay between the two pulses is
M. Ferianis,
M. Pros, Sincrotrone
Trieste,has been
computeda maximumof sensitivity
forItalyd = and A. Boscolo, Università di Trieste-DEEI, Italy
At Itfirst,
a modelof theMB (80%filling) time
proportional to the distance between the mirrors and can
0.4428*";in thatsituation
the secondof thestructure,normally
used
at ELETTRA,
has maximum
been createdbe varied in steps much smaller than a pico-second
is 43.27%
of H(0).
Abstract
2.2 Method general features
andenvelope
its spectrum
computed(see fig.2) by means of an(#t=13.3 fs for a 2 µm stepping motor).
This new method thoroughly exploits the information
FFT algorithm [12].
A
new method
for bunch length measurement has been
3.2 Simulation
set-upoverviewburied in the short light pulse without using dedicatedFFT of the beam model and teorical curve (envelope)

Bunch Length Measurement via spectrum of
superposition of two short pulses

developed at ELETTRA. It is based on a spectral

Normalized amplitude1

incident radiation

instruments, like the Streak Camera; it has been

observationof thesynchrotronaradiationThe
second mirror
Since the stored
beam
generates
pulse lighttrainpulses.
whose
single pulse spectrum is shaped by means of an optical developed under the assumption of gaussian light pulses.
This new technique is based on the Frequency-Domain
periodicity
reflects
circumference
and its
processthe
whichmachine
gives the method
an increased sensitivity
mirrorto an optically0.8
analysis of a fast photodiodefirst
response
to the usual
spectralobservations.
filling mode, compared
simulations
have
been
carried out to processed version of the beam produced
light pulse. This
Some simulations have been carried out to check theevaluatetheperfomanceofthemethodwhen
appliedtoatechnique,which
makes use of standard laboratory
separatedrays
method in non-ideal conditions. The results of the first
0.6
instrumentation, like the Spectrum Analyser (SA), offers
not purely gaussian
pulse.are also presented.
measurements
Figure:3
Schematicofthedoublemirrors
assembly.
an enhanced resolution if compared to usual
spectralAt first, a model of the MB (80% filling) time observations (see next paragraph).
0.4
a
SA
for
the
acquisition,
thismethoddoes
not the active
structure, normally used 1at INTRODUCTION
ELETTRA, has been created A Using
grin lens is used to focus both rays on
ELETTRA is a third generation synchrotron light provide a Single Shot measurement of the bunch length.
andits spectrum
computed (see fig.2) by means of anof feature
the photodiode0.2
source in operation in Trieste since 1993. In theareaThis
is not of big(25<D<400
concern whenµm).
dealingThe
withsignal fromFFT algorithm ELETTRA[12].
storage ring electrons with energies from 1the stablebeams andis
triggers.
At theELETTRA,
this operating
photo-diodesent toSpectrum
Analyser with noto model2 GeVroutinely
accumulated, both in Multiamplifierconditioninhas
been recently checked out in SB mode [7].
FFT ofGeV
the beam
and areteoricalcurve (envelope)
between.
0 1

Bunch
Bunch (SB)Moreover, the input extended dynamic range of the SA
10 (MB) and
15 in Single20
25 mode. 30
The length of the electron bunches in Storage Rings is[8] could eliminate the need for an amplifier: this is also aFirstadvantage
results: astime-domain
observation
Frequency(GHz) to measure, both for machine4.2 majoran importantparameter
any element between
the source andfirst mirror
Comparison
betweenpulseUsers.
and InMB
Physicists
and for theoretical
Synchrotron Lightfact, thethe acquisition point deteriorates the measurement quality.
bunch length
vs. current curve is necessary when the Some preliminary observations have been carried out
periodic structure pulses
spectra.
2.3 TheopticalGHz
signalrays
processing
broadband impedance of the vacuum chamber is evaluatedwith
a separated
1.5
bandwidth photodiode [10]. The
0.6[1]. Similarly, when Users are doing fast time dependentcorrectness
The opticalsignalprocessingusedin this methodofmethodandpractical
feasibility
have
Figure: 3theSchematicof itsthedoublemirrors
assembly.
Then, distorsions
which canbe foundin bunchreal beams,
experiments,
they needto know thelength in order createsadelayedreplicaof the original pulse. It ischecked with this component.
to haveindication
the time
resolution of theirbeen
0.4 introduced
obtained by means of multiple reflections between parallel
have been
intoanthe
model,of likepulse-to-pulse
experiment [2].
mirrors.
similar
opticalhas beenusedraysat
A Agrinlens
is arrangement
used to focus
bothon the active
amplitude
variations, longitudinal IBIC
oscillations,John D.andFox"(SLAC)2012 - Learning
FrombyBeams
October 201223 / 61
CERN,
E. Rossa, to perform “Real Time Slice0

ormalized amplitude

Figure 0.8:25Signals from Bunched Beams

Signals from a multiple bunches - Uneven fills
Identical, uniformly spaced bunches - ring looks as if it is 1/M smaller.
Non-uniform spacing, or current variations, the time domain signal ismultiplied by a modulating function g(t)f (t) = g(t)

∞ M−1
X
X

δ(t − kT0 − nT0 /M)(17)

k =−∞ n=0

H(ω) = G(ω) ? F (ω)(18)

rectangular gap ( or current variation) is multiplication with amodulating function, transform of the rectangular modulating function
will be of sin(x)/x form. A sin(x)/x envelope will be convolved with theuniform line spectra, replicates information across many revolution
harmonics
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201224 / 61Signals from Bunched Beams

Signatures of Betatron Motion

Signals from an Oscillating bunch - betatron motion• Betatron Motion - amplitude modulation• Position sensitive pickup

f (t) = Aβ cos(ωβ t)∞X

δ(t − kT0 ),

(19)

k =−∞

frequency domain - a convolution of the cosine modulating function
with bunch spectrum∞
Aβ ω0 Xf (ω) =
(δ(ω − mω0 + ωβ ) + δ(ω − mω0 ωβ )).
2 m=−∞

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 2012(20)

25 / 61Signals from Bunched Beams

Signatures of Betatron Motion

Signals from an Oscillating bunch - Betatron motion
A

6t=t`

00

(m-1)to m to (m+1)to00 t
5-20008545A4

Every revolution harmonic has betatron sidebands at ∆ωβ away fromthe revolution harmonics
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201226 / 61Signals from Bunched Beams

Signatures of Synchrotron Motion

Signals from an Oscillating bunch - Synchrotron
motion• Bunch oscillates about synchronous phasef (t) =∞X

δ(t + τ sin(ωs t + φ) − kT0 )

(21)

k =−∞

phase modulation of magnitude τ at the synchrotron frequency ωs .

F (ω) = ω0

∞
X
l=−∞

eilϕ Jl (ωτ )∞X

δ(ω − lωs − mω0 )

(22)

m=−∞

For small oscillation amplitudes we can just consider the lowest orderterms of the Bessel functions (the l=-1,0,1 terms)
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201227 / 61Signals from Bunched Beams

Signatures of Synchrotron Motion

Signals from an Oscillating bunch - Synchrotron
motion6t=ts

0 0 (m-1)t

o

m to

(m+1)to00 t
5-20008545A5Single bunch synchrotron motion is revealed in synchrotron sidebands,
each spaced l∆ωs away from the revolution harmonics. l = −1, 0, 1
sidebands shown, for small amplitudes the higher terms fall off in
amplitude. Amplitudes of l=0 and l=+1/-1 sidebands show themagnitude of the phase oscillation.
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201228 / 61Signals from Bunched Beams

Signatures of Synchrotron Motion

Signals from a multiple bunches- signatures of motion
Consider M coupled oscillators ( bunches coupled via impedances)• M Oscillators - M normal modes
qi-2

qi-1

qi

qi+1

qi+2

5-20008545A14

The phase between bunches is specified for each eigenmode m as

Φi = Φ0 − 2π

im
M

(23)

where the index i runs i = 0, 1...M − 1
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201229 / 61Signals from Bunched Beams

Signals from multiple bunches

Signals from a multiple bunches- signatures of motion

The lowest and highest frequency modes are 0, π between oscillators
q

q

q

q
0 Mode

q

<q

q

<q
/ Mode5-20008545A15

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201230 / 61Signals from Bunched Beams

Signals from multiple bunches

Multiple bunch Betatron Motion Signature

Multi-bunch betatron motion, uniform fill M identical bunches, betatron
amplitude modulationf (t) =∞ M−1
X
X

cos(ωβ t + ϕn )δ(t − (kT0 + nT0 /M))(24)

k =−∞ n=0

Frequency domain sideband information for each mode exist as an
upper sideband, and a lower sideband. Across M revolution harmonics
are found the spectral information for the M normal modes. The
spectrum repeats this information every M revolution harmonics.

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201231 / 61Signals from Bunched Beams

Signals from multiple bunches

Multiple bunch Betatron Motion Signature
Multi-bunch betatron motion, uniform fill M identical bunches, betatron
amplitude modulation

6t`

6t`

004 0 1 2 3 4 0
M x Frev

00 t
5-20008545A6

Multi-bunch betatron spectrum, for the M=5 case. Motion of mode 2 isseen as a lower sideband around the second revolution harmonic, andan upper sideband of the M-2 revolution harmonic.
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201232 / 61Signals from Bunched Beams

Signals from multiple bunches

Multiple Bunch Synchrotron Motion Signature
Multi-bunch Synchrotron motion, uniform fill M identical bunches,
phase modulation

6ts

0

6ts

1

6ts

2

3

4

M x Frev05-20008545A8

Simplified spectrum for multi-bunch synchrotron motion, showing only
the first-order lines. The case M=5 is shown, with motion at mode 0
and mode 1
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201233 / 61

Common Pickups and Beam Transducers

Signals From Beams - Gap Monitor
The most direct sensor for beam image charge• measures charge in beam, longitudinal structure• insensitive to position• RC sets time constant, bandwidths of 5 GHz achievable

Physical implementation - spread lots of R’s around circumferenceJohn D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201234 / 61

Common Pickups and Beam Transducers

Signals From Beams - Ring Electrode
Another sensor for beam image charge• High-pass filter response• measures charge in beam, longitudinal structure• insensitive to position• RC sets time constant, bandwidths of GHz achievable

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201235 / 61

Common Pickups and Beam Transducers

Signals From Beams - Position Monitors
Sensors for position in duct - capacitive coupling• High-pass filter response• RC sets time constant, bandwidths of GHz achievable

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201236 / 61

Common Pickups and Beam Transducers

Signals From Beams - Position Monitors
Sensors for position encoded in relative amplitudes of electrodesignals• Fields found via conformal mapping
Field Lines and Equipotentials

y (cm)

2

0

-2
-4

John D. Fox (SLAC)-20x (cm)

2

IBIC 2012 - Learning From Beams

45-20008545A12October 201237 / 61

Common Pickups and Beam Transducers

Signals From Beams - Position Monitors
Computing position - normalizing for charge• can be processed via Delta-Sigma circuits• Sum signal encodes current• can use independent channels, calculate difference/sum
numerically

A

C

B

D

John D. Fox (SLAC)A (180◦ )D (∆)

B (0◦ )C (Σ)

A (180◦ )D (∆)

B (0◦ )

C (Σ)

C−A
A+C

D−B
B+D

A

B

D

C

A (180◦ )D (∆)

A+D−B−C∆X

B (0◦ )C (Σ)

D+C −A−B∆Y

A (180◦ )D (∆)

B+D−A−CB (0◦ )C (Σ)

IBIC 2012 - Learning From Beams

A+B+C +DΣOctober 201238 / 61

Common Pickups and Beam Transducers

Signals From Beams - Stripline Monitors
Similar to a directional coupler• Can be terminated, open or short circuited strips• Signals taken on upstream port
• Signal is two impulses separated by 2L/c
• Frequency domain - response maxima at l = (2n + 1) λ4• Frequency domain - response minima at nλ/2
• Can be used as a kicker to drive the beam - feed power
downstream
vout

Beam

John D. Fox (SLAC)v

out
IBIC 2012 - Learning
From Beams

5-20008545A13

October 201239 / 61

Oscilloscopes, Spectrum Analyzers and Network Analyzers

Common Control Room Instrumentation
Most control rooms contain a mix of commercial, general purpose
instruments and lab-designed, specialized instruments• Real-Time Oscilloscopes• Digital or analog• Data taken in single continuous triggered sweep• Bandwidth to 2 - 8 GHz Common (gets expensive)• Resolution ( dynamic range) 40 - 50 DB

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201240 / 61

Oscilloscopes, Spectrum Analyzers and Network Analyzers

Common Control Room Instrumentation
Higher bandwidths can be achieved by taking several passes throughthe data• Equivalent-Time ( sampling) Oscilloscopes• Digital or analog• Data taken over multiple triggered sweeps• Bandwidth to 50 + GHz Common (gets expensive)• Requires repetitive waveform• STABLE trigger ( what is risetime on logic signal?)• Resolution of sampler, averaging improves SNR• Related to boxcar integrator

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201241 / 61

Oscilloscopes, Spectrum Analyzers and Network Analyzers

Common Control Room Instrumentation
Spectrum Analyzer and Frequency domain• Tuned radio Receiver• analog heterodyned receiver with multiple IF stages• Dynamic Range up to 120dB or more
• Bandwidth to 50 + GHz Common (gets expensive)• Requires periodic waveform• Can be set zero span, triggered sweep• Intrinsic relationship between resolution bandwidth, sweep time

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201242 / 61

Oscilloscopes, Spectrum Analyzers and Network Analyzers

Common Control Room Instrumentation

Spectrum Analyzer and Frequency domain• FFT ( Fast Fourier Transform) spectrum analyzers• Time domain sampling data acquisition• Bandwidth to 10’s MHz Common (gets expensive)• FFT Band can be heterodyned from higher band
• Numeric computation of DFT• Intrinsic relationship between resolution, sampling rate, length ofsequence bandwidth• Make pretty waterfall displays

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201243 / 61

Oscilloscopes, Spectrum Analyzers and Network Analyzers

Common Control Room Instrumentation
Network Analyzer - tool of frequency domain measurement• Swept excitation, swept complex receiver• Measures ratio of incident and reflected, incident and transmitted• S parameter ( Scattering Matrix) representation

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201244 / 61Signals from Beams

Signals From Beams - Tune measurement
Tunes can be seen in position monitor signals• self-excited (often in colliders)• excited by kicker• measure BPM response, look at betatron sideband

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201245 / 61Signals from Beams

Signals From Beams - Excited Tune measurement

the PLL technique is useful in a tune feedback system
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201246 / 61Signals from Beams

4-13kA DC Current Transducers Enabling Accurate In-Situ Calibration for a New Particle Accelerator Project- LHC

BOUWKNEGT Koos

Signals From Beams - the DC current transformer
2. Basic Principle of a DCCT
N3

N2

NI

Fig. 1: Schematic Diagram of a DCCTThe DCCT is a feedback technique that drives a reference current tonull out the beam current in a non-linear magnetic transformer
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201247 / 61

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N;!J\G!%#M! 2012
October48 / 61

A little knowledge is a dangerous thing

choosing a medium power RF amplifier

Impedance-Controlled LLRF architecture ( LHC
Example)FFT klystron output (LR42 Ibeam=1900mA)
0

ï20

Klystron
Klystron
Polar Loop

+

Y

+

Digital RF
Feedback
Analog RF
FeedbackRF
cav.

Driver

Y
+
Y

+

ï

ï60

ï80

Setpoint+1ïTurn(comb)
Feedback

ï40

ï100

Beam
ï120
ï1000

ï500

0
freq (kHz)

500

1000

A feedback technique where the beam-induced signals are cancelled
through the direct and comb loops, so that the effective impedance
seen by the beam in reduced. Dynamic range of signals within the loop
is 90 dB or more.
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201249 / 61

A little knowledge is a dangerous thing

choosing a medium power RF amplifier

What does Linearity have to do with this?
Klystron
Klystron
Polar Loop

+

Y

+

Digital RF
Feedback
Analog RF
FeedbackRF
cav.

Driver

Y
+
Y

+

ï

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Feedback

Beam

The third-order intercept ( IP3) is a common amplifier specification forcommunications purposes. Two equal amplitude signals at frequencies
ω1 and ω2 are applied, the nonlinear product terms 2ω1 ± ω2 andω1 ± 2ω2 are measured vs input power. Data is available - is this auseful test for a LLRF amp in the block diagram?
What is the IP3 for an LTI amplifier?
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201250 / 61

A little knowledge is a dangerous thing

choosing a medium power RF amplifier

A little knowledge is a dangerous thing

Measuring small-signal transfer function in the presence of alarge-signal carrierJohn D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 2012

51 / 61

A little knowledge is a dangerous thing

choosing a medium power RF amplifier

Does the carrier impact the small-signal frequency
response? Test a 50W amplifier
Amplitude Response
15
20W Carrier
No Carrier

Gain (dB) relative (+ approx 30 dB)

14
13
12
11
10
9

FFT klystron output (LR42 Ibeam=1900mA)

8

0

7
ï20

6
5
471

472

473

474

475
476
477
frequency (MHz)

478

479

480

Is this a useful amplifier for a
LLRF amp within the feedback
loop? What impact does thisbehavior have?
John D. Fox (SLAC)

481

ï40

ï60

ï80

ï100

ï120
ï1000

IBIC 2012 - Learning From Beams

ï500

0freq (kHz)500

October 2012

1000

52 / 61

A little knowledge is a dangerous thing

choosing a medium power RF amplifier

A little knowledge is a dangerous thing

Measuring image responses from a two tone test ( large signal carrier,swept small signal)
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201253 / 61

A little knowledge is a dangerous thing

choosing a medium power RF amplifier

Does the carrier impact the image frequencies? Test a
50W amplifier

AmpC (220V AC power) and AmpB
50
AmpC 20W Carrier
AmpC 60W Carrier
AmpB 10W Carrier
AmpB 30W Carrier

40

Output Power (dBm)

30
20
10
0
−10
−20
−30
471

472

473

474

John D. Fox (SLAC)

475

476
477
freq (MHz)

478

479

480

481

Is this a useful amplifier for a
LLRF amp within the feedback
loop? What impact does thisbehavior have?

IBIC 2012 - Learning From Beams

October 201254 / 61

A little knowledge is a dangerous thing
TDS 3054B

18 Oct 2006

choosing a medium power RF amplifier

08:46:55

LTI ideas, time and frequency domains
Amplifier input
0.1

Volts

0.05
0
−0.05
−0.1
−50

0

50
100
time (ns)
Amplifier Coupled Output (−50 dB)

150

200

150

200

150

200

150

200

0.1

Volts

0.05
0
−0.05
−0.1
−50

0

50

100
time (ns)Amp C Input
0.1

Volts

0.05
0
−0.05

John D. Fox (SLAC)

−0.1
−50

0

50
100
time (ns)Amp C Output (−50 dB)

0.1
0.05
Volts

Does the small-signal
frequency response tell you
the large-signal pulse
response? Is this an LTI
system?

0
−0.05
−0.1
−50

IBIC 2012 - Learning From Beams

0

50

100
time (ns)October 201255 / 61

Summary

Summary• Time and frequency domains, transforms• LTI formalism - but are accelerator systems LTI?
• Oscilloscopes, Spectrum analyzers ( Network Analyzers, too)• Signals from Bunched Beams• Ideas on pickups and kickers• Common Control Room needs - tune measurements• Current Measurement - the DDCT

To learn more, look at the various courses of the USPAS ( US Particle
Accelerator School) , the CERN Accelerator School, the course
proceedings from the US-Japan-Russia-CERN accelerator schools,
also in the Beam Instrumentation Workshop ( BIW) and DIPAC
proceedings. The JACOW website has all sorts of reference material
from PAC, EPAC, APAC and IPAC meetings, as well topical meetingson Accelerator Science and Technology
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201256 / 61

Summary

Acknowledgements

It has been a pleasure to think about these issues of Signals fromBeams with colleagues from many labs, who have all contributed tothis talk in their expertise. I particularly want to thank J-L Pellegrin, F.
Pedersen, M. Serio, D. Teytelman, and M. Tobiyama for theircontributions to the field and for so many fun hours in the control room
doing interesting measurements and so freely sharing their expertisewith young scientists.

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201257 / 61

Summary

Signals From Beams - Frequncy Domain BPM
processing

B

LPF

C
D

GaAu
Switches

Oscillator

Filter Amplifier

BPF

LPF
LPF

SwitchDriver

CLK
Ext. Clock
Button Address Test Gate

DRV

LNA

LimiterLO

S/H

FilterAL
AmplifierFilter

BPF

IF

Mixer
21.4 MHZ
Automatic Gain
Control

VCO

LPF

BPF

S/H
S/H

SingleButton Sampling
Reset
AGC

FilterP/H

Peak/ Hold

S/H

A

X

B
Y
C
D

Σ

Analog Output

LPF

Phase Detector
Sample/ Hold

Phase Detector
Frequency
Synthesizer

FKey

Sums & DifferencesA

Plug-in

MUX

Button Signals

1-dB adj.
Attenuators

A multiplexed system, uses single receiver to measure sequentially 4
signals. Can Measure at high harmonic of RF for pickup sensitivity.
Requires multiple turns, measures average orbit ( Bergoz)

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201258 / 61

Summary

Signals From Beams - Time Domain BPM processing

A self-timed system, uses pulse stretching gaussian filters to replicate
amplitudes, sample/hold . Applicable to single pulses ( Pellegrin)
John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201259 / 61

Summary

Signals From Beams - AM/PM BPM processing

A frequency domain system, rings filter to make long quasi-cw pulse.
Measures relative amplitudes in AM-PM conversion, phase detector.
can be applied to single pulses ( Tobiyama)

John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201260 / 61

Summary

Signals From Beams - Log ratio BPM processing

Processing uses log technique, difference amp to compute ratio of
amplitudes. Frequency domain system, can be applied to single pulses(Shafer)John D. Fox (SLAC)IBIC 2012 - Learning From Beams

October 201261 / 61