source: ETALON/papers/2016_HDR_ND/Advanced_diags/esculap.tex @ 757

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\chapter{Laser-plasma experiments}
\label{chap:laser-plasma}

Recent results of plasma-acceleration experiments, including laser-plasma experiments have been discussed in section~\ref{sec:plasma_accelerators}. During the past 10 years I have took part in a few laser-driven plasma acceleration experiments~\cite{Ibbotson:2010zz,Kneip:2009zz,Chance:2014mzn,Cros:2017lil}. Coming from the conventional accelerators community my contribution has often been on the instrumentation side. I will describe more in details one of them which we are planning at LAL in Orsay.

\section{ESCULAP}
 \label{sec:ESCULAP}

The ESCULAP (ElectronS CoUrts pour l'Acc\'el\'eration Plasma)~\cite{Delerue:2016tcy} experiment aims at studying external injection of low energy (\SI{10}{MeV}) electrons in a plasma in the quasilinear regime. This experiment will use the photo injector PHIL~\cite{1748-0221-8-01-T01001} and the high power laser LASERIX~\cite{Ple:07,Zimmer:10,Delmas:14}. 

The proposed layout of the experiment is shown on figure~\ref{fig:layout_ESCULAP} and the most recent description of the experiment is in~\cite{EAAC17_ESCULAP}\footnote{This section is based on text that may also appear in~\cite{EAAC17_ESCULAP}.}.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.95\linewidth]{Advanced_diags/figure_PHIL_LASERIX_with_cell.png}
  \caption{The proposed layout for the ESCULAP experiment: the PHIL and Laserix facilities are combined for this external injection laser-driven plasma acceleration experiment as presented in~\cite{EAAC17_ESCULAP}.}
  \label{fig:layout_ESCULAP}
\end{figure}

Preliminary simulations have shown that electrons with an energy of several hundreds of \si{MeV} could be produced in such experiment however there are several challenges associated with such experiment:
\begin{itemize}
\item Make the high power laser and the accelerator work together with a low jitter between the two machines.
\item Compress the electron beam to match it as close as possible to the plasma wavelength.
\item Shape the plasma so that it can compress and accelerate the beam.
\end{itemize}

\subsection{Simulations}
\label{chap:plasma_acceleration_mecanism} 

Preliminary simulations of the ESCULAP experiment have been done and reported in~\cite{Delerue:2016tcy} and more advanced simulations are under way~\cite{EAAC17_simulations}. The description below is taken mostly from~\cite{Delerue:2016tcy}.

\subsubsection{Plasma acceleration in the linear regime}

A high power laser pulse sent in a low density hydrogen or helium gas can ionise it and create a wake characterized by strong electric and magnetic fields. If the pulse is not too intense ($I<\SI{e18}{W/cm^2}$), then the plasma will be weakly driven by the laser pulse, this is called the linear regime~\cite{Gorbunov:1987,Sprangle:1987}. 
% If the plasma is made of hydrogen or helium it will be ionized by the beginning of the pulse, well before the peak intensity is reached. If a certain number of assumptions are met, it is possible to find an analytical solution for the plasma wave. In particular, the perturbation of the plasma by the laser pulse have to be small, the plasma has to be cold and the accelerated electrons' charge has to be low with respect to the total plasma charge.

In such conditions we can use or define the following quantities:
\begin{itemize}
 \item{Maximum Accelerating field} $E_0 = \frac{2 \pi m_e c^2}{e \lambda_p} $ hence  \\ $$E_0 [GV / m]= 96.2 \sqrt{n_e [\SI{e18}{cm^{-3}}]}$$
 \item{Longitudinal accelerating field} \\ $$E_{0z} = \frac{\eta}{4}  a_0^2 \cos(k_p d_l) \exp(- \frac{2 \rho^2}{w_z^2}) \times E_0$$
\item{Radial accelerating field}\\ $$E_{0r} = \frac{\rho}{k_p w_z^2} \eta  a_0^2 \sin(k_p d_l) \exp(- \frac{2 \rho^2}{w_z^2}) \times E_0$$
\end{itemize}
with $m_e$ the electron mass, $e$ the electron charge, $\lambda$ the laser wavelength (in our case  $\lambda=$ \SI{0.8}{\micro \meter}), $n_e$ the plasma density,  $\lambda_p$ the plasma wavelength ($\lambda_p = \lambda \times \sqrt{\frac{n_c}{n_e}}$) , $k_p$ the plasma wave number,  $\eta$ the laser-plasma coupling, $a_0$ the plasma relativistic limit, $d_l$ the laser distance behind the pulse, $\rho$ the radial distance and $w_z$ the laser waist radius at position $z$ (and $w_0$ is the waist at $z=0$, the focal point).

Therefore a density of \SI{4e17}{cm^{-3}} will give a maximum longitudinal accelerating field of more than \SI{10}{GV/m}. This corresponds to a plasma wavelength of about \SI{50}{\micro m} (that is about \SI{180}{fs}). It is important to note also that the radial accelerating field can take either positive or a negative value, that is, it can be either focussing or defocussing.

With a \SI{2}{Joules} laser focused on a \SI{55}{\micro \meter} waist we get a Rayleigh length of about \SI{1}{cm}. This will give a sufficient length to compress and accelerate the electrons. These electrons must also be focussed in a comparable volume.


\subsubsection{Expected electrons distributions}

For our simulations we have considered electrons with an energy of \SI{9.5}{MeV} focussed on a low density $H_2$ plasma. At the entrance of the plasma the electrons have a transverse size of \SI{170}{\micro \meter}, they are converging with an half-angle of \SI{3}{mrad} and the FWHM duration of the bunch is \SI{75}{fs}. The total length of the plasma cell considered is \SI{9}{cm} but the cell has been designed so that it has a varying pressure according to the profile shown on figure~\ref{fig:plasma_density}.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.9\linewidth]{Advanced_diags/WEPMY003f4.png}
  \caption{Density profile along the plasma axis. The maximum density, $n_{e0}$ is \SI{4e17}{cm^{-3}}. Figure taken from~\cite{Delerue:2016tcy}.}
  \label{fig:plasma_density}
\end{figure}

The simultations were done using an adapted version of the numerical code WAKE-EP~\cite{WAKE}.

The aim of this special density profile is to achieve a radial and longitudinal compression of the electron bunch before its acceleration. The first part of the density profile (decreasing pressure gradient) will keep all the electron together in the focussing  phase of the plasma wake. As the electrons have a relatively low $\gamma$ the difference in accelerating gradient experienced between the head and the tail of the bunch will compress them all together. Once this is achieved the second part of the density profile (increasing pressure gradient) will keep the bunch together at the back of the wave to accelerate them with the highest field.


\begin{figure}[tbp]
  \centering
  \begin{tabular}{cccc}
 (a) &  \includegraphics[width=0.45\linewidth]{Advanced_diags/WEPMY003f5a.png} &
 (b) &  \includegraphics[width=0.45\linewidth]{Advanced_diags/WEPMY003f5b.png} \\
 (c) & \includegraphics[width=0.45\linewidth]{Advanced_diags/WEPMY003f5c.png} &
 (d) &  \includegraphics[width=0.45\linewidth]{Advanced_diags/WEPMY003f5d.png} \\
  \end{tabular}
  \caption{Lorentz factor of the electrons (black and left vertical axis) and longitudinal accelerating field divided by $E_0 = mc \omega_p / e = \SI{608}{MV/cm}$ ( blue and right vertical axis), versus the distance behind the laser pulse $\xi$ at different z positions in the plasma.  Figure taken from~\cite{Delerue:2016tcy}. }
  \label{fig:simulations}
\end{figure}


\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.95\linewidth]{Advanced_diags/WEPMY003f6.png}
  \caption{Energy distribution at the end of the acceleration process. Figure taken from~\cite{Delerue:2016tcy}. }
  \vspace*{-0.6 cm}
  \label{fig:energy_dist}
  \end{figure}


On figure~\ref{fig:simulations} (a) one can see the distribution of the electrons (in black) and of the laser wake (in blue) at $z=\SI{-4}{cm}$, the entrance of the plasma cell. We can see that at injection the electron bunch (coming from a conventional accelerator simulated using ASTRA~\cite{astra}) have a large time spread and a small energy spread. As they progress through the decreasing gradient ramp the trailing electrons will experience a higher accelerating field than the electrons  at the front. As at these energy they are barely relativistic this difference will result in these electrons almost catching up with the leading one and the beam will get compressed in time. This is illustrated by figure~\ref{fig:simulations} (b-c). On figure~\ref{fig:simulations} (b) one can see that the distance between the leading and trailing electrons has significantly reduced and the trailing electrons have now more energy than the leading ones. On figure~\ref{fig:simulations} (c) the trailing electrons are even overtaking the leading ones and the bunch is compressed in only a few micrometers. It is important to note that this compression completely erases the initial energy spread of the bunch and its time spread. Once this process is over, after  $z=\SI{-2}{cm}$,  the increase in plasma density and in laser intensity will significantly accelerate the electrons. On figure~\ref{fig:simulations} (d) one can see that at the end of the accelerating process the electrons reach a Lorentz factor $\gamma$ of about 500 with slightly more than 15\% energy spread (figure~\ref{fig:energy_dist}).



\subsection{Synchronisation between PHIL and Laserix}

For this experiment to be possible the two machines, PHIL and LASERIX must fire at the same time. It was first attempted to directly use LASERIX as clock source for PHIL but this did not work. Therefore I proposed to use the same synchronization scheme for ESCULAP than for ThomX. This scheme has already been discussed in section~\ref{sec:ThomXsynchro}. Extensive tests have been made and reported in~\cite{Delerue:2017kxo}.

The layout specific to ESCULAP is shown in figure~\ref{fig:ESCULAP_synchro_scheme}. An example of jitter measurement is shown on figure~\ref{fig:jitter_setup} and the trend of the jitter over several minutes is shown on figure~\ref{fig:synchro_result}.

\begin{figure}[htbp]
        \centering
        \includegraphics*[width=12.4cm]{Advanced_diags/THPAB093f2.png}
        \caption{The ESCULAP synchronization scheme, combining the current LASERIX synchronization system (at the bottom) and the PHIL synchronization system (at the top). The system used to synchronize the two facilities is shown in the middle. Figure taken from~\cite{Delerue:2017kxo}.}
        \label{fig:ESCULAP_synchro_scheme}
\end{figure}


\begin{figure}[htbp]
        \centering
        \includegraphics*[width=8cm]{Advanced_diags/THPAB093f1.png}
        \caption{Example of jitter measurement between the signal coming from a photodiode recording the LASERIX laser pulse (in light blue) and the signal coming from the \SI{3}{GHz} RF of PHIL (in red). An ultra-fast scope is used to measure the time between the rise of the photodiode signal above a predefined level and the zero crossing of the RF. The jitter of this measurement is considered to be the jitter between the two machines.  Figure taken from~\cite{Delerue:2017kxo}.}
        \label{fig:jitter_setup}
\end{figure}



\begin{figure}[htbp]
        \centering
        \includegraphics*[width=7cm]{Advanced_diags/THPAB093f3a.png}
        \includegraphics*[width=6.3cm]{Advanced_diags/THPAB093f3b.png}
        \caption{Jitter between the photodiode signal from the laser pulse and the \SI{3}{GHz} from the PHIL RF. On the left figure, the data are recorded during \SI{50}{min}. On the right figure the data are recorded during \SI{3}{min}. The drop on the right image is due to a safety stop of the frequency feedback.  Figure taken from~\cite{Delerue:2017kxo}.}
        \label{fig:synchro_result}
\end{figure}


\subsection{Compression of the electron bunch}

The current beam specifications of the PHIL accelerator are far from those needed for ESCULAP. To reach these performances a compression dogleg chicane will be necessary. This has been studied extensively by graduate student Ke WANG and reported in~\cite{EAAC17_compression}, the layout of this dogleg is shown on figure~\ref{fig:ESCULAP_dogleg}. 
The principle of a compression chicane is to use the beam chirp induced by RF cavities. Dipole magnets are used to disperse the beam according to this chirp. Optical components (quadrupole magnets and sextupole magnets) then give a different travel length depending on the beam energy and a final dipole gather all the electrons back together with a much shorter time spread than before the chicane.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.90\linewidth]{Advanced_diags/dogleg.eps}
  \caption{Figure taken from~\cite{EAAC17_compression}. }
  \label{fig:ESCULAP_dogleg}
  \end{figure}

It has been shown in~\cite{EAAC17_compression} that bunch length much shorter than~\SI{150}{fs} FWHM can be achieved (with the effects of space-charge and Coherent Synchrotron Radiation taken into account), therefore fulfilling our needs for ESCULAP.


\subsection{The plasma cell}

The next challenge to be addressed is to vary the plasma density along the beam axis to match (or come close from) the density profile shown on figure~\ref{fig:plasma_density}. 
Given the low energy at which we will perform the experiments this shaping will be rather important. 
Several strategies are currently being investigated: either by shaping the channel in which the gas will propagate or by using different gas inlets at different pressures. A preliminary design of such cell is shown on figure~\ref{fig:ESCULAP_cell}.

The gas pressures required to get the densities we need are at the limit between molecular and viscous flow, making simulations more difficult.  We are therefore considering increase the cell dimensions to be in viscous flow, easier to simulate. This work is in progress.

\begin{figure}[htbp]
  \centering
  \includegraphics[width=0.90\linewidth]{Advanced_diags/Cellule_1.pdf}
  \caption{Preliminary design of a plasma cell for ESCULAP. }
  \label{fig:ESCULAP_cell}
  \end{figure}



The design phase of ESCULAP should be completed in the coming months and then we hope to move onto the construction of the facility.


\section{APOLLON and EuPraxia}

The ESCULAP experiment is one small contribution among many to the field of plasma acceleration. I am also contributing to two other initiatives of larger amplitude.
Near Orsay the multi-petawatt laser APOLLON will soon deliver its first beam and I contribute to the conception of the Long Focal Area where laser-driven plasma acceleration will take place. At the European level the Eupraxia \cite{Walker:2017ebq} consortium in which I contribute aims at demonstrating practical applications of plasma accelerators, both as a light source and as a tool for high energy physics.

\section{Perspectives and limitations of plasma acceleration as a particle source}

The success reported in 2004 and 2006 have set very high expectations of what could be done with plasma accelerators. Two directions were foreseen: Free Electron Lasers and Particle Colliders. More than 10 years later the progress has been slower than expected.

The low emittance and high peak current of the bunch produced by plasma accelerators made them a choice candidate as a source for Free Electron Lasers. However to date no group has achieved this. Although the beam has several desirable qualities its phase space is not match to the requirements of a Free Electron Laser and the shot to shot instabilities of such beam make such matching difficult. Several groups are working on this and are regularly reporting progress.


For a collider the main issue is to reach the beam energy of  interest to High Energy Physics. A scheme has been proposed where the beam accelerated by a plasma accelerator is injected in another one~\cite{PhysRevSTAB.13.101301} but staging experiments are still at an early stage.   The large shot to shot instability and the large beam energy spread will also have to be addressed.

The work done at FACET on beam driven acceleration is now pursued at CERN by the AWAKE project~\cite{awake} where protons will be used to accelerate electrons with a very favorable transformer ratio. This could be used to build a lepton collider with hundreds of \si{GeV} in the center of mass.

One should remember that the evolution of particle accelerators has been driven both by user needs but also by what was technologically feasible. The applications of plasma accelerators will  benefit from the high accelerating gradients but will have to take into account the limitations of these beams.


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