pff_short_conflict-20170228-183539.tex

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\begin{document}

%\preprint{APS/123-QED}

\title{High Bandwidth Arrival Time Stabilisation of an Electron Beam at 
the 
50~fs Level}
%\thanks{A footnote to the article title}%

\author{J.~Roberts}
\email{Corresponding author Jack.Roberts@cern.ch}
\affiliation{John Adams Institute,University of Oxford}
\affiliation{CERN, Geneva}
%\altaffiliation{CERN, Geneva.}

\author{P.~Burrows}
\affiliation{John Adams Institute,University of Oxford}

\author{G.~Christian}
\affiliation{John Adams Institute,University of Oxford}

\author{R.~Corsini}
\affiliation{CERN, Geneva}

\author{A.~Ghigo}
\affiliation{INFN/LNF, Frascati}

\author{F.~Marcellini}
\affiliation{INFN/LNF, Frascati}

\author{C.~Perry}
\affiliation{John Adams Institute,University of Oxford}

\author{P.~Skowronski}
\affiliation{CERN, Geneva}

\date{\today}

\begin{abstract}
CLIC, a proposed future linear electron-positron collider, and other machines 
such as XFELs, place tight tolerances on the phase stabilities of their beams. 
CLIC proposes the use of a novel, high bandwidth and low latency, `phase 
feedforward' system required to achieve a phase stability of 
\(0.2^\circ\)~at~12~GHz, or 
about 50~fs. This work documents the results from operation of a prototype 
phase 
feedforward system at the CLIC test facility CTF3, with 30~MHz bandwidth and a 
total hardware latency of 100~ns. New phase monitors with 
30~fs resolution, 20~kW amplifiers with 47~MHz bandwidth, and electromagnetic 
kickers have been designed and installed for the system. The system utilises a 
dog-leg chicane in the beamline, for which a dedicated optics have been created 
and 
commissioned. The prototype has demonstrated CLIC-level phase stability, 
reducing an initial rms phase variation of \(0.92\pm0.04^\circ\) to 
\(0.20\pm0.01^\circ\) across a duration of 10~minutes.
\end{abstract}

%\pacs{Valid PACS appear here}% PACS, the Physics and Astronomy
%                             % Classification Scheme.
%\keywords{Suggested keywords}%Use showkeys class option if keyword
                              %display desired
\maketitle

%\tableofcontents

%\section{\label{s:intro}Introduction}

The Compat Linear Collider, CLIC, \cite{CLICCDR} is a proposal for a future 
linear electron--positron collider. It uses a novel two beam acceleration 
concept to achieve a high accelerating gradient of 100~MV/m 
and a collision energy of up to 3 TeV. In this concept the 12~GHz RF power used 
to accelerate each high energy colliding beam is extracted and transferred from 
a high intensity drive beam in 24 decelerator sectors. \textcolor{red}{The 
drive beams are generated by compressing an initial 
\(140~\mathrm{\mu s}\) beam pulse bunched at 0.5~GHz into 24 shorter 240~ns 
beam pulses bunched at 12~GHz, in a bunch recombination process using a 
sequence 
of combiner rings and delay loops [REF]. }

CLIC's luminosity quickly drops if the drive beam phase, or arrival time, 
jitters with respect to the colliding beams, causing energy errors and 
subsequent beam size growth at the interaction point. The drive beam phase 
stability must be \(0.2^\circ\)~at~12~GHz (around 50~fs) rms or better to limit 
the luminosity loss to below 1\% \cite{CLICCDR}.  However, the drive beam phase 
stability cannot be guaranteed to be better than \(2^\circ\)~at~12~GHz [REF]. A 
mechanism to improve the drive beam phase stability by an order of magnitude is 
therefore required. 

\textcolor{red}{Other machines, such as XFELs, have similar beam phase 
	stability 
	requirements to CLIC. At FLASH, DESY, these requirements have been met 
	using an RF phase 
	and power feedback based on the measurement of electro-optic beam arrival 
	time monitors [REF]. However, the CLIC drive beam presents a different set 
	of challenges. In particular, FLASH has 1~MHz bunch spacing and a 500~ms 
	beam pulse, whereas the CLIC drive beam has 12~GHz bunch spacing and 240~ns 
	pulse length. A feedback with a latency of several microseconds is 
	therefore not suitable for CLIC.}

CLIC instead proposes a drive beam ``phase feedforward'' (PFF) 
system. 
A prototype PFF system has been designed, commissioned and operated at 
the CLIC test facility CTF3, at CERN, to prove its feasibility. The prototype 
system follows the same concept as the CLIC scheme, and is the focus 
of this work. CTF3 provides a 135~MeV electron beam bunched at 3~GHz with a 
pulse length of 
1.2~\(\mathrm{\mu s}\) and a pulse repetition rate of 0.8~Hz [REF]. All phases 
quoted in the paper are given in degrees at 12~GHz, as relevant for CLIC.


%\section{\label{s:ctfLayout}System Design}

\begin{figure*}
	\includegraphics[width=\textwidth]{figs/ctfpffLayout}% Here is how to 
	%import EPS art
	\caption{\label{fig:pffLayout}Schematic of the PFF prototype at CTF3, 
	showing the approximate location of the phase monitors (\(\phi_1\) , 
	\(\phi_2\) and \(\phi_3\)) and
		the kickers (K1 and K2). The black box “PFF” represents the calculation 
		and output of the correction, including the phase monitor
		electronics, feedforward controller and kicker amplifiers. A bunch 
		arriving early at \(\phi_1\) is directed on to a longer path in the TL2 
		chicane
		using the kickers (blue trajectory), whereas a bunch arriving late will 
		be directed on to a shorter path (red trajectory). }
\end{figure*}

A schematic of the prototype PFF system is shown in Fig.~\ref{fig:pffLayout}. 
The system corrects the phase using two electromagnetic kickers installed 
before the first and last dipole in a four bend, dog-leg shaped chicane. The 
beam's path length through the chicane depends on the magnitude and polarity of 
the voltage applied to the kickers. The phase is measured using a monitor 
upstream of the chicane, and then corrected by setting the kicker voltage to 
deflect bunches arriving early at the phase monitor on to longer trajectories 
in the chicane, and bunches arriving late on to shorter trajectories. 
Downstream of the chicane another phase monitor is placed to measure the 
effects of the correction.

The beam time of flight between the upstream phase monitor and the first kicker 
in the chicane is 380~ns. By bypassing the \textcolor{red}{combiner ring (CR) 
and TL1 transfer 
line} (see Fig.~\ref{fig:pffLayout}) the total cable length required to 
transport signals between the monitor and kickers is shorter, approximately 
250~ns. The PFF correction in the chicane can therefore be applied to the same 
bunch initially measured at the phase monitor, providing the total system 
hardware latency is less than 130~ns. 

%\textcolor{red}{Some details on CLIC system differences...One PFF system will 
%be installed 
%in each decelerator sector (24 PFF 
%	systems per drive beam)...C-shaped chicane instead...}

%\textcolor{red}{CLIC hardware, bandwidth requirements and how they compare to  
%CTF3. The PFF system poses many challenges, particularly in terms of the 
%hardware 
%	bandwidth (\textgreater17.5~MHz \cite{Gerber2015}), power (500~kW 
%	amplifiers) 
%	and latency requirements.}

The PFF system presents a significant hardware challenge, in particular in 
terms of the power and bandwidth requirements for the kicker amplifiers, and 
the resolution of the phase monitors. As well as the kickers themselves, the 
system utilises a low latency digitiser and feedforward controller. New 
components have been designed and built for the prototype at CTF3, and a 
summary of their parameters in comparison to the CLIC requirements is shown in 
\textcolor{red}{Table~x}. 

\textcolor{red}{Table:
No. Systems
No. Kickers
Phase Monitor Resolution
Amplifier Power
Angular Deflection @ Kicker
Correction Bandwidth}

\textcolor{red}{The main differences between the CTF3 and CLIC systems:
48 systems at CLIC (one per decelerator sector) - synchronisation between 
systems not addressed at CTF3.
C-shaped correction chicane with 16 kickers
CLIC drive beam much higher energy, so much higher power requirements}

\textcolor{red}{Correction bandwidth requirement of 17.5~MHz derived from 
\cite{Gerber2015}... 
Higher frequency errors damped by combination process and accelerating 
cavities...}

%\subsection{\label{ss:hardware}Hardware}

%The PFF system uses three phase monitors, two electromagnetic kickers, kicker 
amplifiers and a digitiser/feedforward controller.

The three phase monitors used at CTF3 \cite{phMonEuCard} are designed and built 
by INFN 
Frascati, with the 
associated electronics built by CERN. The monitors are 12~GHz resonating 
cavities with a dipole and monopole mode present. The output from opposing 
vertical pairs of feedthroughs are summed in hybrids to create a position 
independent signal. This signal is split and mixed with a reference 12~GHz 
signal in eight separate mixers. The output from the eight mixers is combined, 
allowing a resolution of \(0.12^\circ\) to be 
achieved whilst maintaining linearity between \(\pm70^\circ\) [REF]. The quoted 
resolution 
is determined by 
comparing the measurements of the two adjacent upstream monitors (installed in 
the CT 
line, see Fig.~\ref{fig:pffLayout}). \textcolor{red}{More details: cylindrical 
cavities so big with notch filters, mixed with 3GHz reference multiplied to 
12GHz etc.}

The two electromagnetic stripline kickers \cite{kickerIPAC11} were also 
designed and built by INFN 
Frascati,  
and are based on the DAFNE design [REF]. Each kicker is approximately 1~m in 
length, 
with a horizontal strip separation of 40~mm. A voltage of 1.26~kV applied to 
the 
downstream end of the kicker strips yields a horizontal deflection of 1~mrad 
for the 135~MeV CTF3 beam. \textcolor{red}{more details - tapering? Move after 
amplifier and state actual max deflection?}

The kicker amplifiers \cite{RobertsThesis} have been designed and built by the 
John Adams 
Institue/Oxford University. The 20~kW amplifiers consist of low voltage Si FETs 
driving high voltage SiC FETs, and for 
an input voltage of \(\pm2\)~V give an output of up to \(\pm700\)~V. The 
amplifier response is linear within 
3\% for input voltages between \(\pm1.2\)~V, then starts to saturate. The 
output 
has a bandwidth of 47~MHz for small signal variations up to 20\% max output, 
and is slew rate limited for larger variations.

Finally, the Feedforward digitiser and controller (FONT5a board) 
\cite{RobertsThesis} was also 
designed and built by John Adams Institute/Oxford University. This digitises 
the 
processed phase monitor signals and then calculates and outputs the appropriate 
voltage with which to drive the amplifier in order to correct the phase. The 
board consists of a Virtex-5 field programmable gate array (FPGA), nine 14-bit 
analogue to digital converters (ADCs) clocked at 357~MHz, and four digital to 
analogue converters (DACs). The parameters of the correction, such as the 
system timing and gain, are controlled on the board via a LabVIEW data 
acquisition and control system. \textcolor{red}{mention board latency? ref a 
font paper/ip feedback?}

The combined hardware latency for the PFF system is approximately 100~ns. The 
output from the FONT5a board is delayed by 30~ns so that the drive voltage from 
the amplifiers and the beam arrive at the kickers synchronously.

\subsection{\label{ss:optics}Chicane Optics}

The PFF system places additional constraints on the optics of the correction 
chicane, and also on the beam lines between the upstream phase monitor and the 
chicane. These ensure the maximum possible phase shift per volt applied to the 
kickers without degrading the transverse beam orbit and beam size after the 
chicane, and high correlation between the initial (uncorrected) upstream and 
downstream phase.

The correction range of the PFF system is defined by the kicker design, the 
maximum output voltage of the kicker amplifiers, and the optics transfer matrix 
coefficient \(R_{52}\) between the kickers in the chicane, which relates the 
change in path length through the chicane per unit 
deflection at the first kicker. 
For the maximum amplifier output of \(\pm700\)~V the kickers deflect the beam 
by \(\pm0.56\)~mrad. Together with \(R_{52} = 0.74\)~m in the chicane optics 
these define the system correction range of approximately 
\(\pm400~\mathrm{\mu m}\), or \(\pm6^\circ\).

The measured phase shift in the chicane versus the amplifier input voltage is 
shown in Fig.~\ref{fig:corrRange}, and agrees with the expected range. 
However, the response of the amplifier and therefore the phase shift is 
non-linear. The correction algorithm assumes linearity, but this has a 
negligible effect compared to the limitations placed by the
upstream-downstream phase correlation and phase monitor resolution.

%\textcolor{red}{MADX units for R52, R56, i.e. conversion between distance and 
%phase.}

\begin{figure}
	\includegraphics[width=\columnwidth]{figs/corrRange}
	\caption{\label{fig:corrRange}Downstream phase vs. the kicker amplifier 
	input voltage. Standard errors on the measured phase are shown.}
\end{figure}

The PFF system also should not change the beam orbit after the chicane. The 
chicane optics are designed so that the second kicker closes the orbit bump 
created by the first kicker.
Fig.~\ref{fig:orbClos} shows the horizontal beam orbit in the region 
of the chicane for the maximum and minimum kick. The closure in 
the BPMs following the chicane is better than 0.1~mm, compared to a maximum 
offset of 1.5~mm inside the chicane.

\begin{figure}
	\includegraphics[width=\columnwidth]{figs/orbClos}
	\caption{\label{fig:orbClos}Horizontal orbit in and around the TL2 chicane 
	at maximum (blue) and 
	minimum (red) 
	input to the kicker amplifiers. Markers show the measured position in beam 
	position monitors, and dashed lines the predicted orbit using the 
	CTF3 MADX model and hardware parameters.}
\end{figure}

%\textcolor{red}{All this must be achieved whilst keeping dispersion low, 
%matching betas etc. 
%within constraints of pre-existing buildings. Achieved R52 0.74m with max 
%dispersion 1.16m...}

\subsection{\label{ss:r56} Phase Correlation}

\textcolor{red}{The PFF system acts to subtract the measured upstream phase 
(\(\phi_u\)) from 
the initial downstream phase (\(\phi_d\)) with a gain factor (\(g\)):
%\begin{equation*}
\(\phi_{\mathrm{PFF}} = \phi_d - g\phi_u\)
%\end{equation*}
, where \(\phi_{\mathrm{PFF}}\) is the corrected downstream phase. The optimal 
system gain is given by:
\(g = \rho_{ud} \sigma_d/\sigma_u\)
, where \(\sigma_u\) and \(\sigma_d\) are the initial upstream and downstream 
phase jitter respectively, and \(\rho_{ud}\) is the correlation between the 
upstream and downstream phase. The theoretical limit on the corrected 
downstream phase jitter (\(\sigma_{\mathrm{PFF}}\)) with this gain is given by:
\(\sigma_{\mathrm{PFF}}=\sigma_d \sqrt{1-\rho_{ud}^2}\).}

One of the key challenges in operating the PFF prototype at CTF3 has been 
obtaining high correlation between the initial, uncorrected, upstream and 
downstream phase. A correlation of 97\% is required to reduce a typical initial 
phase jitter of \(0.8^\circ\) at CTF3 to the target of \(0.2^\circ\). 

The achievable correlation depends on the phase monitor resolution and any 
additional phase jitter introduced in the beam lines between the upstream and 
downstream phase monitors. The phase monitor resolution of \(0.12^\circ\) 
limits the maximum upstream-downstream phase correlation to
\(98\%\) in typical conditions, and places a theoretical limit of
\(0.17^\circ\) on the \textcolor{red}{measured corrected downstream phase 
jitter.}

Any beam jitter that changes the time of flight of bunches influences the 
resulting downstream phase stability and upstream-downstream phase correlation. 
The dominant source of uncorrelated downstream phase jitter at CTF3 is beam 
energy jitter being transformed in to phase jitter in the transfer lines 
between the upstream and downstream phase monitors.

\begin{figure}
	\includegraphics[width=\columnwidth]{figs/r56Scan}% Here is how to import 
	%EPS art
	\caption{\label{fig:r56Scan}Downstream (red points) and upstream (blue 
		points) phase jitter vs. the \(R_{56}\) value in the set TL1 optics. 
		}
\end{figure}

The first order phase-energy dependence can be described via the optics 
transfer matrix coefficient \(R_{56}\):
\(\phi_d = \phi_u + R_{56}(\Delta p / p)\)
, where \(\Delta p / p\) is the relative beam energy offset.
Optimal conditions for the PFF system are obtained when the total \(R_{56}\) 
between the upstream and downstream monitors is zero.
The \(R_{56}\) value in one of the transfer lines at CTF3, TL1, has been tuned 
in order to achieve this, compensating for \(R_{56}\) terms in other beam lines.
Fig.~\ref{fig:r56Scan} shows that with an \(R_{56}\) of around 10~cm in TL1 the 
downstream phase jitter is reduced to the same level as the upstream jitter. 
The upstream-downstream phase correlation is also increased to above 95\%.

However, a large second order phase-energy dependence was also identified and 
this remains uncorrected. This leads to a degradation in upstream-downstream 
phase correlation if there are drifts in beam energy. Energy drifts resulting 
from klystron trips and RF power drifts at CTF3 have made it difficult to 
maintain high phase correlations for timescales longer than 10~minutes as a 
result.

\section{\label{s:results}Results}

\subsection{\label{ss:gScan}Gain Scan}

With the optimal gain the PFF correction acts to remove all correlation between 
the upstream and downstream phase, reducing the downstream phase jitter. If the 
gain is too small some residual correlation will remain, and if it is too large 
the correlation will flip sign. 

The optimal system gain can be derived empirically by observing the dependence 
of the downstream phase on the upstream phase with the correction on, as seen 
in Fig.~\ref{fig:gScan}. Optimal gain values for the system are typically in 
the range 1.0--1.5, being larger than unity when the downstream jitter is 
larger than upstream, as per the predicted theoretical values. 

\begin{figure}
\includegraphics[width=\columnwidth]{figs/gScan}% Here is how to import EPS art
\caption{\label{fig:gScan}Downstream phase jitter with the PFF system on at 
different gains. Markers show the measured phase jitter with standard error 
bars. The shaded red region shows the expected performance given the initial 
jitter and correlation with the PFF system off.}
\end{figure}

\subsection{\label{ss:shape}Intra-Pulse Phase Variations}

The PFF correction is shaped to remove phase variations along the 
1.2~\(\mathrm{\mu s}\) CTF3 beam pulse. The predominant intra-pulse feature at 
CTF3
is a roughly parabolic ``phase sag'' of \(40^\circ\) peak-to-peak, resulting 
from the use of RF pulse compression. As this is much larger than the 
\(\pm 6^\circ\) range of the PFF system, only approximately a 400~ns portion of 
the pulse can be optimally corrected. The phase sag would not be present at 
CLIC, where in any case the drive beam pulse length is less than 400~ns.

%2015: (Peak-to-peak variation of 5.76 degrees in initial phase reduced to 
%0.65 degrees in corrected phase -- OR -- standard deviation of phases reduced 
%from 1.68 to 0.26 degrees...).

%2016: Std \(0.960\pm0.003^\circ\) reduced to \(0.285\pm0.004^\circ\) across 
%440~ns portion of pulse. Worse absolute but better removal small features 
%compared to 2015.

\begin{figure}
	\includegraphics[width=\columnwidth]{figs/shape}% Here is how to import EPS 
	%art
	\caption{\label{fig:shape}Effect of the PFF system on intra-pulse phase 
		variations. The pulse shape upstream (green), and downstream with the 
		PFF 
		system off (blue) and on (red) is shown.}
\end{figure}

\begin{figure}
	\includegraphics[width=\columnwidth]{figs/flatness}% Here is how to import 
	%EPS art
	\caption{\label{fig:flatness}Distribution of downstream rms phase values, 
		here 
		referred to as the 
		``pulse flatness'', for each beam pulse with the PFF system off (blue) 
		and 
		on (red).}
\end{figure}

Fig.~\ref{fig:shape} shows the effect of the PFF system on the intra-pulse 
phase variations. \textcolor{red}{The convention at CTF3 is to operate the PFF 
system in 
interleaved mode, with 
the correction applied to alternating pulses only. This allows a measurement of 
the initial (`PFF Off') and corrected (`PFF On') downstream phase to be 
performed concurrently.} The upstream (PFF input) phase is also shown for 
comparison. Vertical dashed lines mark a 440~ns portion of the pulse where the 
correction is optimal, and this range is used to calculate statistics on the 
effect of the system. 

In this range the PFF system flattens the phase, 
and almost all variations are removed. Residual offsets in the phase are still 
present where there are small uncorrelated differences between the shape of the 
initial upstream and downstream phase. Fig.~\ref{fig:flatness} shows the rms 
phase variation within the 440~ns range 
for each beam pulse in the dataset, with the PFF system on and off. The PFF off 
pulses have an rms of \(0.960\pm0.003^\circ\) on average, and this is reduced 
to \(0.285\pm0.004^\circ\) by the PFF system.

The PFF system at CTF3 has been verified to reduce the amplitude of 
phase errors up to a frequency of 25~MHz, exceeding the CLIC requirements.


%Limited by variations in phase propagation along the pulse (energy differences 
%etc.).

\subsection{\label{ss:meanJit}Pulse-to-pulse Jitter}

As well as removing intra-pulse phase variations the PFF system simultaneously 
corrects offsets in the overall mean phase, i.e. any pulse-to-pulse jitter. The 
mean phase of each beam pulse is calculated across the 440~ns range in the 
central portion of the pulse, as shown before in Fig.~\ref{fig:shape}.

\begin{figure}
	\includegraphics[width=\columnwidth]{figs/meanJit}% Here is how to import 
	%EPS 
	%art
	\caption{\label{fig:meanJit}Distribution of the mean downstream phase with 
		the 
		PFF system off (blue) and on (red).}
\end{figure}

Fig.~\ref{fig:meanJit} shows the effect of the PFF system on the pulse-to-pulse 
stability across a dataset around ten minutes in length. An 
initial mean downstream phase jitter of \(0.92\pm0.04^\circ\) is reduced to \(0.20\pm0.01^\circ\) by the PFF 
correction. All correlation between the upstream and downstream jitter is removed, from 
\(96\pm2\%\) to \(0\pm7\%\). The achieved stability is consistent with the theoretical prediction (considering the initial correlation and jitter) of \(0.26\pm0.06^\circ\) within error bars.
%\textcolor{red}{NB: upstream PFF off is \(0.76\pm0.03^\circ\), but 
%\(0.68\pm0.03^\circ\) for 
%PFF on. Helps to explain why achieved is better than predicted.}

This level of stability could not be maintained for longer periods due to 
CTF3's drifting RF sources, eventually leading to degraded 
upstream-downstream phase correlation and phase drifts outside the PFF 
correction range, as previously mentioned. \(0.30^\circ\) phase jitter has been 
achieved in 20~minute datasets. With suitable feedbacks to keep the phase 
within the correction range, and a reduction of the higher order phase-energy 
dependences in the machine optics, the PFF system could achieve CLIC-level 
phase stability continuously.

\textcolor{red}{The PFF system has also been operated 
whilst intentionally varying the incoming mean phase, as shown in 
Fig.~\ref{fig:wiggle}. The PFF system removes the additional phase variations 
and achieves more than a factor 5 reduction in downstream phase jitter, from 
\(1.71\pm0.07^\circ\) to \(0.32\pm0.01^\circ\) in this case.}

\begin{figure}
	\includegraphics[width=\columnwidth]{figs/wiggle}
	\caption{\label{fig:wiggle}Mean downstream phase with the PFF system off 
		(blue) and on (red) vs. time, with additional phase variations added to 
		the 
		incoming phase.}
\end{figure}

%\subsection{\label{ss:pbpJit}Point-by-point Jitter}
%
%\textcolor{red}{I would remove this. Don't think it adds any 
%information beyond mean jitter and correction of shape.}
%
%\begin{figure}
%\includegraphics[width=\columnwidth]{figs/BestFF_pbp}% Here is how to import 
%%%%EPS art
%\caption{\label{fig:BestFF_pbp}Point-by-point jitter.}
%\end{figure}
%
%Point-by-point jitter of x~degrees achieved across a x~ns portion of the 
%pulse, agrees with simulated value...

\section{\label{s:conc}Conclusions}

CLIC requires a PFF system to reduce the drive beam phase jitter by an order of 
magnitude, from \(2.0^\circ\) to \(0.2^\circ\)~at~12~GHz, or better than 50~fs 
stability. A prototype of the system has been 
in operation at the CLIC test facility CTF3, and corrects the beam phase by 
varying the path length through a chicane using two electromagnetic kickers. 

As 
well as the kickers, the system uses newly designed phase monitors with 
\(0.12^\circ\) resolution, high bandwidth 20~kW amplifiers and a low latency 
digitiser/feedforward controller. The system latency, including hardware and 
signal transit times, is less than the 380~ns beam time of flight between the 
input phase monitor and the correction chicane. Therefore, the feedforward 
correction can 
be directly applied to the same bunch initially measured at the monitor.

New optics for the correction chicane and other beam lines at CTF3 have been 
developed to yield the desired phase shifting behaviour and ensure high 
correlation between the initial upstream and downstream phase.

The prototype system has demonstrated \(0.20\pm0.01^\circ\) pulse-to-pulse 
phase jitter on a time scale of ten minutes. It has also been shown to be able 
to flatten intra-pulse phase variations up to a frequency of 25~MHz. On longer 
timescales the performance of the system is limited by changes to the incoming 
beam conditions, in particular beam energy, which would be better controlled in 
any future application at CLIC.

%Drifts, in particular in beam energy, degrade the correlation between the 
%upstream and downstream phase and prevent this level of stability from being 
%demonstrated on longer time scales at CTF3. A key consideration for any future 
%system should be to design beam lines and optics with zero phase-energy 
%dependence, including non-linear dependencies, to solve this issue.

%\textcolor{red}{Try to apply to XFELs/something else.}

\section{\label{s:ack}Acknowledgements}
\begin{acknowledgments}
	We wish to acknowledge everyone involved in the operation of CTF3 for their 
	help and support in realising the PFF system.
\end{acknowledgments}

\bibliography{pff_short}% Produces the bibliography via BibTeX.

\begin{comment}
\newpage
\pagebreak
\section{Some Figures}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/ctfpffLayout}% Here is how to 
	%import EPS art
	\caption{}
\end{figure*}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/alt/ctfpffLayout_alt}
	\caption{}
\end{figure*}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/gScan}% Here is how to import EPS 
	%art
	\caption{}
\end{figure*}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/alt/gScan_old}
	\caption{}
\end{figure*}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/alt/gScanFull}
	\caption{}
\end{figure*}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/alt/stdMeanPhase}
	\caption{}
\end{figure*}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/alt/FFTUpDown_20161215_2340}
	\caption{}
\end{figure*}

\pagebreak
\begin{figure*}[h]
	\includegraphics[width=\textwidth]{figs/alt/FFTOnOff_20161215_2340}
	\caption{}
\end{figure*}
\end{comment}

\end{document}