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\begin{document}
\title{SYNERGIES BETWEEN X-BAND FOR LINEAR COLLIDERS AND LIGHT SOURCES}

\author{M. Dehler, J.-Y. Raguin, A. Citterio, A. Falone, PSI, Villigen PSI, Switzerland\\
W. Wuensch, G. Riddone, A. Grudiev, R. Zennaro, CERN, Geneva, Switzerland}

\maketitle

\begin{abstract}
To compensate nonlinearities in the longitudinal phase space at the injector prototype of the PSI-XFEL, PSI requires a high frequency RF structure in X band. At the same time CLIC is pursuing a program for producing and testing high gradient RF structures in the X band, exploring the effect of different geometries and materials on break down limits and rates.
This makes it interesting to share work and expense in designing and producing a common
CLIC/PSI-XFEL structure. It would provide new data for the CLIC break down tests 
and at the same time be a safe and low risk solution for the more relaxed operating
gradient used at the PSI-XFEL. In addition the prolonged operation of such a structure in
the PSI FEL injector, albeit not at CLIC parameters, constitutes a good quality test for 
the manufacturing procedures employed.

\end{abstract}

\section{INTRODUCTION}

Within the context of the JLC-X and NLC projects, a considerable effort
has been going on in developing high power X band RF systems for high energy
$e^+ e^-$ colliders\cite{NLCJLC}. After the conclusion of these projects, the recent decision
by CLIC to change their principal RF frequency from 30 GHz to a European X band
frequency near 12 GHz has given a renewed push to X band development. A big
RF structure fabrication and testing program involving major laboratories around the
world is under way, R\&D efforts have been directed in adapting standard RF equipment,
from high power klystrons to splitter and loads, to the new frequency.

Interestingly, X band technology is slowly leaking into other applications.
The LCLS FEL uses a X band structure to compensate nonlinearities in the longitudinal phase space
in order to improve bunch compression. The European FEL projects SPARC, FERMI@ELETTRA
and PSI-XFEL also plan to employ X band RF for the same purpose. There is also
a discussion going on to use X band for compact medical accelerators\cite{Caboto}. 

Where the SPARC project is staying with RF structures at the NLC/JLC frequency
of 11.424 GHz, PSI has decided to follow the new European standard
at 11.992 GHz. That way, an optional future operation of the PSI-XFEL in a few bunch
or multi bunch operation mode is still possible (given that the current setup uses
already European S/L band). Int that context, a klystron is currently under development
by SLAC, an adapted version of type XL4 to be baptized XL5. 
The X band structure is being developed within a collaboration between PSI
and CERN, optimizing synergy on both sides. The structure has several purposes, being submitted to break down
tests at CERN, being used in the PSI-XFEL, which is, despite different
operating parameters, an ultra long performance test quite important for
CLIC.


At the PSI-XFEL, we have only limited power, in the order of 40 MW at the structure
after taking account of waveguide losses, and need to generate beam voltages up to
30 MeV, which requires a fairly efficient structure. On the other hand, the beam
passing through has a relatively modest energy of 250 MeV, so that we are relatively
sensitive to transverse wakes. So the structure needs to make a good
compromise between a high shunt impedance, generally associated with low apertures,
and a low transverse kick, demanding the opposite.

As a generic type, we use a structure with a 5$\pi$/6 phase advance and an active length of 750 mm similar to NLC type H75.
Since the structure should not be used to test higher order mode damping, it will not have any HOM dampers.
On the other hand, two wake field monitors near the beginning and the end of the structure are
foreseen, which will help to align the structure to the beam and to minimize transverse kicks. Wakefield monitors are also planned for CLIC structures and their implementation in the PSI-FEL structures will represent an important performance test. 


\section{FUNDAMENTAL MODE PROPERTIES}
In terms of simplicity and cost a single structure with 750
millimeter active length is the most appropriate solution for the
PSI-XFEL requirements. The NLC structure type H75 (5$\pi$/6 phase
advance) has been chosen as the most suitable candidate for the
testing program. The original H75 design, optimized for iris
aperture, thickness and ellipticity of the iris varying along the
structure, provides an accelerating gradient of 65~MV/m for 80~MW
input power and was successfully tested up to 100~MV/m with a SLAC
mode launcher~\cite{ModeLauncher}.
The relevant parameters of the adopted X-band cavity are
summarized in Table\ref{l2ea4-t1}.

\begin{table}[hbt]
   \centering
   \caption{Specifications}
   \begin{tabular}{lcc}
       \toprule
       \textbf{parameter} & \textbf{value}  \\
       \midrule
           Beam Voltage         & 30 MeV \\
           Max. Power     &    29 MW \\
           Iris diameter & 9.1 mm  (avg.)\\
           Wake field monitors & up/downstream\\
           Operating temp. & 40 deg. C \\
           Fill time &  100 ns  \\
           Repetition rate & 100 Hz\\
       \bottomrule
   \end{tabular}
   \label{l2ea4-t1}
\end{table}

The constraints related to the beam dynamics requirements for the
linearization of  the longitudinal phase space fix the
deceleration of the beam to 30~MeV. The gradient is maintained
constant along the structure: Fig.~\ref{a4-f1} shows that, over 72
cells, the average gradient is 40~MV/m -- The required input power
to achieve such gradient is a modest 29~MW.

\begin{figure}[htb]
   \centering
   \includegraphics*[width=65mm]{DEHLER_SYNERGY_f1.eps}
   \caption{Decelerating gradient along the structure.}
   \label{a4-f1}
\end{figure}


Because of the constant gradient design choice, the iris diameter
changes along the structure, the lower limit being fixed by the
deleterious effects of the short-range wake fields. As can be seen
in Fig.~\ref{a4-f2}, the iris diameter changes linearly with the
number of cells: the mean aperture at 9.1 millimeter makes it a
relatively open structure.

\begin{figure}[htb]
   \centering
   \includegraphics*[width=65mm]{DEHLER_SYNERGY_f2.eps}
   \caption{Variation of the iris aperture along the structure.
   The first cell has 9.986 mm iris diameter, the last one 8.239 mm.}
   \label{a4-f2}
\end{figure}

The large phase advance of 5$\pi$/6 offers two main advantages:
The first, it means an intrinsically lower group velocity even at 
large apertures, providing a relatively high gradient and moderate
required input power, and the second, smaller transverse wakes,
since a longer cell means a smaller number of irises per structure.
The variation of the group velocity
and of the r/Q along the structure are shown in Fig.~\ref{a4-f3}
and Fig.~\ref{a4-f4} respectively.


\begin{figure}[htb]
   \centering
   \includegraphics*[width=65mm]{DEHLER_SYNERGY_f3.eps}
   \caption{Variation of the group velocity along the structure.}
   \label{a4-f3}
\end{figure}


\begin{figure}[htb]
   \centering
   \includegraphics*[width=65mm]{DEHLER_SYNERGY_f4.eps}
   \caption{Variation of the r/Q along the structure.}
   \label{a4-f4}
\end{figure}

Concerning the velocity group variation, the v$_{g}$/c is 3.7\% at
the level of the first regular cell and decreases to 1.6\% at the
last regular cell. The r/Q value increases quasi linearly from 8.5
k$\Omega$/m to 10.2 k$\Omega$/m and the average Q-value computed
is about 7150. The filling time of the structure is about 100~ns.

The input and output coupler design is based on the SLAC mode
launcher design (\cite{ModeLauncher}), which converts a rectangular
TE$_{01}$ waveguide mode into the circular TM$_{01}$ waveguide mode
of the X-band structure. The big advantage of this
design is the reduced surface field, due to
the rounded and thickened iris horns and the
coupling the power through the broad wall of the feed waveguide.  The
dimensions of the cells between the mode launcher and the
structure ends are used to optimize the matching, as can be seen in
Fig.~\ref{a4-f6} and Fig.~\ref{a4-f7}.

\begin{figure}[htb]
   \centering
   \includegraphics*[width=80mm]{DEHLER_SYNERGY_f5.eps}
   \caption{Electric field profile showing the good matching into
   upstream cells.}
   \label{a4-f6}
\end{figure}


\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-00, width=65mm]{DEHLER_SYNERGY_f6.eps}
   \caption{Reflexion coefficient for the input and output matching cells.}
   \label{a4-f7}
\end{figure}


\section{WAKE FIELD MONITOR}

\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-90,width=65mm]{DEHLER_SYNERGY_f7.eps}
   \caption{Dispersion diagram of lowest two dipole bands in cell 36.}
   \label{fig:wake1}
\end{figure}

To measure the beam offset inside the structure, we want to couple to the lowest
dipole mode. A minimum perturbation of the fundamental mode and maximum
information in the output signal, together with an easy post processing, are
the principal design criteria. Where and how to couple, what to expect from the measurement
is explained in the following.


\subsection{Location}

We start by looking at the dispersion of the lowest dipole bands
of a typical cell, shown in figure~\ref{fig:wake1}.
As in a classical 2$\pi$/3 structure we have hybrid HEM type dipole modes; the lower
dipole band starts at zero phase with a strong TE type characteristic morphing into a TM 
characteristic
as the phase approaches 180 degrees. At 5$\pi$/6, the cell is longer, so the speed of light line
and the dispersion curve are crossing at opposite slopes (This holds for all cells in the design), so
the beam will excite a backward wave in the lowest dipole band. 
The synchronous phase is relatively near to 180 degrees.


\begin{figure}[htb]
   \centering
   \includegraphics*[width=65mm]{DEHLER_SYNERGY_f8.eps}
   \caption{Limits of lowest dipole band and synchronous frequency versus cell number. Also shown
     the location of the wake field couplers with their respective bandwidths.}
   \label{fig:wake2}
\end{figure}

The distribution of bandwidths and synchronous frequencies
of the lowest dipole band inside the whole structure is shown in figure~\ref{fig:wake2}.
From this, we can identify three different frequency regions. Dipole modes with resonances
in the region of 15.3 to 16.1 GHz will be trapped modes, which are localized in only part of
the structure, since cells at the beginning and the end can not propagate these frequencies.
These trapped modes start in one of the upstream cells with a field distribution corresponding to
a $\pi$ mode and continue with a decreasing phase advance to the downstream cell, where it goes to
zero. The excitation by the beam is most pronounced in the cell, where the resonance corresponds
to the synchronous frequency and phase, which is close to 180 degrees.
Modes with frequencies below 15.3 GHz (the $\pi$ mode of cell 1) will extend from the input coupler
to the cell where the phase advance goes to zero.  Most of these modes will have only a weak kick
factor, since their frequency does not correspond to one of the synchronous frequencies.
The last region contains modes above 16.1 GHz, the modes extend into the output coupler and have a high 
kick.

With this in mind, we are able to choose suitable locations for the wake field monitors.
We assume that the wake field monitor will couple only weakly to the resonant
fields and will not distort the modal pattern inside the structure. Dipole wakes
excited by offsets in the upstream half of the structure will correspond to modes
which are concentrated in the middle of it. Actually, if we put a monitor
in cell 36, it will have a bandwidth of 14.8 to 15.7 GHz (the width of the
dipole band in cell 36), the corresponding modes have their synchronous phases
in the upstream half and will signal offsets there. For the downstream coupler,
we are restricted of the dipole band there -- a reasonable compromise is putting
it in cell 63, which receives wakes excited in cells 40-63.



\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-90,width=65mm]{DEHLER_SYNERGY_f9.eps}
   \caption{Transverse wake impedance for the structure as calculated via the
     dual resonator model\cite{bib:DDSMethod}.}
   \label{fig:wake3}
\end{figure}
Wake monitor signals and wakes, to be shown in the following, were
obtained from a dual resonator equivalent circuit, where the elements of the 
resonators describing the TE and TM components of the hybrid dipole mode
and their mutual couplings are fitted from the results of numerical computations
This method is described in more detail in~\cite{bib:DDSMethod}, and gives 
valid results for the two lowest dipole bands. The transverse impedance
computed for the whole 72 cell structure is shown in figure~\ref{fig:wake3}. As can be
expected from the distribution of frequencies shown in figure~\ref{fig:wake2}, modes
below 15.3 GHz contribute only weakly to the overall wake, only in the region from
15.3 to 16.2 GHz we see a strong coupling to the beam.


\subsection{Monitor Design}
What are the criteria for the pickup measuring the transverse wakes?
In order to effectively measure the position, the wake monitor should reject
signals coming from the fundamental mode power as well as longitudinal higher
order modes, which are all transverse magnetic fields. This type of field can best
be rejected by selectively coupling to the transverse electric components of the hybrid
dipole modes, something, which is obtained by a suitable orientation of
the coupling waveguide.


\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-00,width=65mm]{DEHLER_SYNERGY_f10.eps}
   \caption{Wake monitor cell 36 -- side coupled output waveguide with electric shorted on one side.}
   \label{fig:wake4}
\end{figure}
One option is to realize it using radially oriented waveguides coupling 
head on to the cavity cell and a second having a waveguide in parallel
to the beam axis being side coupled -- similar to the design of the damped
detuned structure, but coupling only to one select cell. The side coupled
version has the advantage, that we can have a longer wave guide damping
down any residual signal from the fundamental mode, which may enter due
to finite mechanical tolerances. That way, there is also enough space to integrate
a transition from the waveguide to coaxial and use a standard 50 $\Omega$ vacuum
feed through to connect the measurement front end. We went for this option,
the coupler design chosen
is similar to the HOM coupled cells of the damped detuned structures, the difference
being that we couple only to one cell and have the wave guide electrically shorted
on one side as shown in figure~\ref{fig:wake4}. 

The coupling strength corresponds
to a loaded Q in the order of 800 at a phase advance of zero (where the modal
patterns couples best) and gives a sufficient signal strength.
The effect on the fundamental mode parameters is only minor --
a 10 \% drop in group velocity and in Q factor, R/Q stays virtually
unchanged.

\subsection{Signals}

\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-90,width=65mm]{DEHLER_SYNERGY_f11.eps}
   \caption{Output signals from up- and downstream monitors vs. frequency.} 
   \label{fig:wake5}
\end{figure}

Figure~\ref{fig:wake5} shows the signal spectra computed for the 
up- and downstream couplers. As can be expected from the previous discussion, we see 
two distinct frequency bands corresponding to the synchronous frequencies
in the two parts of the structure. 

\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-90,width=65mm]{DEHLER_SYNERGY_f12.eps}
   \caption{Signal envelope from up- and downstream monitors vs. time.}
   \label{fig:wake6}
\end{figure}

Before we look at other properties of these monitors, we should explain
a little more in details, what is going on inside the structure.
A dipole mode is excited by the beam dominantly in the 'synchronous' cells, where his resonant
frequency corresponds to the synchronous one. The mode does not build up
instantaneously, but the energy deposited by the beam in this synchronous cell
needs time to get distributed in the structure -- the distance between the synchronous
cell and the wake field monitor leads to a time delay, before the signal 
shows up in the monitor signal. Signals from different part of the
structure have a different delay. In the time domain (figure~\ref{fig:wake6}),
this shows up as an initial rectangular pulse (with some beating on top) of 2-3 nanoseconds length.

\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-0,width=65mm]{DEHLER_SYNERGY_f13.eps}
   \caption{Signal envelope up- and downstream monitors vs. time assuming
            structure axis tilted to beam axis.}
   \label{fig:wake7}
\end{figure}

The beam offset in individual parts of the structure is correlated to different
synchronous frequencies and this in turn with different delays in the time domain
signal. So it is a valid question, whether it is possible to identify also tilts
with respect to the beam.
In this case, the middle of the structure is aligned with the beam
axis, whereas the extremities would be offset generating a transverse signal. The resultant
wake monitor signals are shown in figure~\ref{fig:wake7}. The upstream monitor is the more 
significant one in this case, since it sees the total front half of the structure. Where a constant
offset gives a more or less rectangular pulse like in fig.~\ref{fig:wake6},
we see now a ramp, starting at zero (no offset in the middle) and growing linearly to the peak
(high offset at beginning). The downstream signal shows a similar slope, which is not as pronounced,
since it sees only part of the structure.

We simulated also the effect of a bend in the structure, but here dispersion effects smearing
out the signal are too strong to obtain a clear pattern in the output signal.


\begin{figure}[htb]
   \centering
   \includegraphics*[angle=-0,width=65mm]{DEHLER_SYNERGY_f14.eps}
   \caption{Signal envelope up- and downstream monitors vs. time assuming
            random, uncorrelated misalignment of individual cells in the structure.}
   \label{fig:wake8}
\end{figure}

A last important topic is the resolution of the monitors. Apart from the usual
suspects -- thermal noise in pickup and front end and
 spurious signals from other sources --
we have a significant contribution from the random non correlated misalignment of 
individual cells. As the beam passes through the structure seeing these random
offsets, it will, independent of the offset, excite wake fields and wake signals, 
which we will see as a noisy background to the measurement. To estimate this
contribution, we implemented this feature into the equivalent circuit model
to simulate it.
Figure~\ref{fig:wake8} shows an example for the output signal. Comparing the
peak random offset signal in the first four nanoseconds, roughly 8 mV/pC/mm/m, by that
of a constant offset signal (fig.~\ref{fig:wake6}), 4 mV/pC/mm/m, gives the impact
on the measurement. Or said otherwise, a structure with a
random cell offset of 1 $\mu$m rms
will create a signal proportional to a systematic offset of 2 $\mu$m --
the wake monitors will have a resolution limit of 2 $\mu$m.
Given, that we would like to see resolutions below 10 $\mu$m, corresponding to
a mechanical cell to cell alignment of better than 5 $\mu$m, which seems
entirely feasible.


\section{CONCLUSION AND OUTLOOK}

A new design X band structure for the new CLIC reference frequency has been 
presented, to be used for high gradient testing at CLIC and as a prototype
structure for the PSI-XFEL injector.
It offers an efficient fundamental mode
performance with a wide aperture minimizing transverse wake field effects. The wake
field monitors included in the design will allow a very high quality alignment to
the beam giving information about offsets and tilts of the structure.

With the RF design finished, we are currently in the transition to the mechanical
design, which will be followed by manufacturing and low level RF tests. Structures
for high power testing are expected to be ready in autumn 2009.



\begin{thebibliography}{9}   % Use for  1-9  references

\bibitem{NLCJLC}
C.E. Adolphsen et al, `` International study group progress report on linear collider development'',
SLAC-R-559, SLAC-R-0559, SLAC-559, SLAC-0559, KEK-REPORT-2000-7, LCC-0042, Apr 2000. 286pp.
ISG Progress Report, April 2000.

\bibitem{Caboto}
R. Zennaro, ``Linacs for Hadrontherapy: CABOTO, a X-band CArbon BOoster for Therapy in Oncology''.
proc. X-Band RF Structure and Beam Dynamics Workshop - 44th ICFA Advanced Beam Dynamics Workshop,
Nov 30 - Dec 04 2008, Daresbury UK, to be published.


\bibitem{ModeLauncher}
C. Nantista, S. Tantami and V. Dolgashev, ``Low-field accelerator
structure couplers and design techniques'', Phys. Rev. Special
Topics - Accelerators and Beams, Vol. 7, 072001 (2004).


\bibitem{bib:DDSMethod}
R.M. Jones, C.E. Adolphsen, J.W. Wang, Z. Li, ``Wakefield damping in a pair of X-band accelerators for
linear colliders'',
Phys.Rev.ST Accel.Beams 9:102001,2006.



\end{thebibliography}

\end{document}
