Changeset 594 in ETALON

Timestamp:

May 3, 2016, 12:44:35 AM (8 years ago)

Author:

delerue

Message:

Papier acceleration laser-plasma updated

Location:

papers/2016_IPAC/WEPMY003_Plasma_acceleration

Files:

• WEPMY003.aux (modified) (3 diffs)
• WEPMY003.pdf (modified) (previous)
• WEPMY003.tex (modified) (9 diffs)
• biblio.bib (added)

papers/2016_IPAC/WEPMY003_Plasma_acceleration/WEPMY003.aux

@@ -1 +1 @@
 \relax 
-\citation{}
+\citation{PhysRevLett.113.245002}
 \citation{Gorbunov:1987,Sprangle:1987}
-\citation{PHIL}
-\citation{}
+\citation{Ple:07,Zimmer:10,Delmas:14}
+\citation{1748-0221-8-01-T01001,Vinatier2015222}
 \select@language{USenglish}
 \@writefile{toc}{\select@language{USenglish}}
@@ -11 +11 @@
 \@writefile{toc}{\contentsline {subsection}{Plasma acceleration in the linear regime}{1}}
 \@writefile{toc}{\contentsline {subsection}{Proposed experiment}{1}}
+\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The PHIL beam line. The electrons are produced on the left of the image and travel toward the right. A spectrometer magnet can be seen in the middle of the beam line.\relax }}{1}}
+\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
+\newlabel{PHIL}{{1}{1}}
 \@writefile{toc}{\contentsline {section}{Simulations}{1}}
-\citation{}
-\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces The PHIL beam line. The electrons are produced on the left of the image and travel toward the right. A spectrometer magnet can be seen in the middle of the beam line.\relax }}{2}}
-\providecommand*\caption@xref[2]{\@setref\relax\@undefined{#1}}
-\newlabel{PHIL}{{1}{2}}
+\citation{WAKE}
+\citation{astra}
+\bibcite{PhysRevLett.113.245002}{1}
+\bibcite{Gorbunov:1987}{2}
 \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Scheme of the current LASERIX installation at LAL showing the new high intensity laser beamlines for emerging applications.\relax }}{2}}
 \newlabel{fig:scheme_laserix_lal}{{2}{2}}
@@ -22 +25 @@
 \@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Density profile along the plasma axis. The maximum density, $n_{e0}$ is \SI {4e17}{cm^{-3}}.\relax }}{2}}
 \newlabel{fig:plasma_density}{{4}{2}}
-\bibcite{jacow-help}{1}
-\bibcite{IEEE}{2}
+\@writefile{toc}{\contentsline {section}{Conclusions}{2}}
+\bibcite{Sprangle:1987}{3}
+\bibcite{Ple:07}{4}
+\bibcite{Zimmer:10}{5}
+\bibcite{Delmas:14}{6}
+\bibcite{1748-0221-8-01-T01001}{7}
+\bibcite{Vinatier2015222}{8}
+\bibcite{WAKE}{9}
+\bibcite{astra}{10}
 \@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Propagation of the the electrons (in black) and the laser (in blue) at different $z$ positions in the plasma. The horizontal axis is the comoving frame (that is the distance of the electrons behind the laser pulse). For the electrons the vertical axis is their energy expressed by their Lorentz factor. For the laser it is the longitudinal accelerating field compared to the maximum field $E_0 = mc \omega _p / e = \SI {608}{MV/cm}$. \relax }}{3}}
 \newlabel{fig:simulations}{{5}{3}}
 \@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Energy distribution at the end of the acceleration process.\relax }}{3}}
 \newlabel{fig:energy_dist}{{6}{3}}
-\@writefile{toc}{\contentsline {section}{Conclusions}{3}}

papers/2016_IPAC/WEPMY003_Plasma_acceleration/WEPMY003.tex

@@ -76 +76 @@
 
 \section{Introduction}
-Many important results have been reported over the past years about Laser-driven plasma accelerators~\cite{}, however one of the questions that remain unanswered is that of the acceleration of an  electron beam in the MeV range externally injected. After a few meters of drift space a 
-typical sub-GeV electron beam will be spread over several dizains of femtoseconds or even more. Such duration is comparable to the typical period of plasma oscillations for a plasma with density of the order of \SI{e17}{cm^{-3}}.  This can be a limitation for external injection experiments as the electrons arriving at the wrong phase will not be captured and accelerated. One possible solution to mitigate that effect is to first compress the electrons in time before accelerating them. This compression followed by acceleration is one of the mai niters that we plan to investigate in the ESCULAP experiment.
+Many important results have been reported over the past years about Laser-driven plasma accelerators~\cite{PhysRevLett.113.245002}, however one of the questions that remain unanswered 
+is that of the acceleration of an electron beam in the few tens MeV range externally injected. At such energies,  the electron beam will be spread over several dizains of femtoseconds after few meters of drift space.
+ Such duration is comparable to the typical period of plasma oscillations for a plasma with density of the order of \SI{e17}{cm^{-3}}.  This can be a limitation for external injection experiments as the electrons arriving at the wrong phase will not be captured and accelerated. One  solution to mitigate that effect is to  compress the electrons in time before accelerating them. This compression followed by acceleration is one of the main iters that we plan to investigate in  our experiment.
 
 
@@ -83 +84 @@
 
 
-A high power laser pulse sent in a low density gas can ionise it and create a wake characterized by strong electric and magnetic fields. If the pulse is not too intense ($a_0 < 1 $), then the plasma will be weakly driven by the laser pulse, this is called the linear regime~\cite{Gorbunov:1987,Sprangle:1987}.  If the plasma is made of hydrogen or helium it will be ionized by the beginning of the pulse, well before the peak intensity is reached. If a certain number of assumptions are met, it is possible to find an analytical solution for the plasma wave. In particular, the perturbation of the plasma by the laser pulse have to be small, the plasma has to be cold and the accelerated electrons' charge has to be low with respect to the total plasma charge.
-
-In such plasma we can use or define the following quantities:
+A high power laser pulse sent in a low density hydrogen or helium gas can ionise it and create a wake characterized by strong electric and magnetic fields. If the pulse is not too intense ($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{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{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 (\SI{0.8}{\micro \meter}), $n_e$ the plasma density, $n_c = \frac{1.11 10^{21}}{\lambda^2 [ \si{um^2]}} \si{cm^{-3}}$,  $\lambda_p$ 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 $w_0$ at $z=0$, the focal point).
 
-Therefore a pressure of \SI{4e17}{cm^{-3}} will give an accelerating field of more than \SI{60}{GV/m}. This corresponds to a plasma wavelength of about \SI{50}{\micro m} (that is about \SI{180}{fs}).
+Therefore a pressure 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 the 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 1cm. This will give a sufficient length to compress and accelerate the electrons. These electrons must also be focussed in a comparable volume.
@@ -99 +102 @@
 \subsection{Proposed experiment}
 
-To make this experiment we will use the ESCULAP (ElectronS CoUrts et LAsers Plasmas) installation at LAL. The ESCULAP installation is made of the PHIL photoinjector~\cite{PHIL} and the Laserix Laser. PHIL is a conventional  \SI{5}{MeV} Photoinjector that is currently being upgraded to \SI{10}{MeV}. A layout of PHIL is shown on figure~\ref{PHIL}. Laserix is 50 TW, 50~fs high-power Ti:Sa laser. As part of ESCULAP a small leak from Laserix will be directed on the PHIL photocathode to produce short electron pulses. During the laser-driven plasma acceleration experiment the reminder of the Laserix beam will be sent in the plasma chamber.
-
-
-\begin{figure*}[bthp]
+The proposed experiment will be performed within the ESCULAP  ({\em ElectronS CoUrts et LAsers Plasmas}) installation at LAL, by combining the LASERIX laser~\cite{Ple:07,Zimmer:10,Delmas:14}  with the PHIL photoinjector~\cite{1748-0221-8-01-T01001,Vinatier2015222}. PHIL is a conventional  \SI{5}{MeV} Photoinjector that is currently being upgraded to \SI{10}{MeV}. A layout of PHIL is shown on figure~\ref{PHIL}. Laserix is a 50 TW, 50~fs high-power Ti:Sa laser. As part of ESCULAP a small leak from Laserix will be directed on the PHIL photocathode to produce short electron pulses. Laser-driven plasma acceleration experiment will be performed by injecting simulaneously the high energy laser beam with the PHIL generated relativistic electron beam.
+
+
+\begin{figure}[bthp]
     \centering
     \includegraphics*[width=\linewidth]{PHIL.png}
@@ -108 +111 @@
     \label{PHIL}
 %    \vspace*{-\baselineskip}
-\end{figure*}
+\end{figure}
 
 \begin{figure}[htbp]
@@ -135 +138 @@
 \end{figure}
 
-These simulations were done using the Particle-In-Cell code WAKE\cite{}. XXX More details about WAKE?
-
-The aim of this special density profile is to keep achieve a 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 accelerating 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 and accelerate them.
+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 keep achieve a 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.
 
 
@@ -165 +168 @@
 
 
-On figure~\ref{fig:simulations} (a) one can see the distribution of the electrons (in black) and of the laser wake (in blue) at $z=\SI{-4}{cm}$. We can see that at injection the electron bunch (coming from a conventional accelerator simulated using ASTRA~\cite{}) 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 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) and figure~\ref{fig:simulations} (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 onces 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 (with one quarter of plasma wavelength). Once this process is over, after  $z=\SI{-2}{cm}$,  the increase in plasma density will significantly accelerate the electrons. On figure~\ref{fig:simulations} (d) one can see that the electrons reach a Lorentz factor $\gamma$ of about 500 with slightly more than 15\% energy spread (figure~\ref{fig:energy_dist}).
+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) and figure~\ref{fig:simulations} (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 (with one quarter of plasma wavelength). Once this process is over, after  $z=\SI{-2}{cm}$,  the increase in plasma density will significantly accelerate the electrons. On figure~\ref{fig:simulations} (d) one can see that the electrons reach a Lorentz factor $\gamma$ of about 500 with slightly more than 15\% energy spread (figure~\ref{fig:energy_dist}).
 
 
@@ -172 +175 @@
 
 External injection of electrons with an energy of about \SI{10}{MeV} in a low density plasma excited by a high power laser has the potential of bringing the energy of these electrons up \SI{250}{MeV}. This will require the use of a specially designed plasma cell capable of providing a two gradient ramp over a few centimeters. We plan to investigate this scheme experimentally using the ESCULAP facility installed on the Univ. Paris-Sud campus.
+
+
+%\bibliographystyle{unsrt}
+%\bibliography{biblio}
+
 
 %\begin{figure}[htbp]
@@ -183 +191 @@
 
 %\begin{thebibliography}{99}   % Use for  10-99  references
-\begin{thebibliography}{9} % Use for 1-9 references
+%\begin{thebibliography}{9} % Use for 1-9 references
 
 %\bibitem{accelconf-ref}
@@ -190 +198 @@
 %       EPAC'04, Lucerne, July 2004, THZCH03,  p.~249,
 %       \url{http://www.JACoW.org/e04/papers/THZCH03.PDF}
-
-\bibitem{jacow-help}
-        JACoW,
-        \url{http://www.jacow.org}
-
-\bibitem{IEEE}
-        \textit{IEEE Editorial Style Manual},
-        IEEE Periodicals, Piscataway,
-        NJ, USA, Oct. 2014, pp. 34--52.
+%\end{thebibliography}
+%\null  % this is a hack for correcting the wrong un-indent by package 'flushend' in versions before 2015
+
+\begin{thebibliography}{1}
+
+\bibitem{PhysRevLett.113.245002}
+W.~P. Leemans, {\em et al.} 
+%A.~J. Gonsalves, H.-S. Mao, K.~Nakamura, C.~Benedetti, C.~B. Schroeder, Cs. T\'oth, J.~Daniels, D.~E. Mittelberger, S.~S. Bulanov, J.-L.  Vay, C.~G.~R. Geddes, and E.~Esarey.
+\newblock Multi-gev electron beams from capillary-discharge-guided subpetawatt
+  laser pulses in the self-trapping regime.
+\newblock {\em Phys. Rev. Lett.}, 113:245002, Dec 2014.
+
+\bibitem{Gorbunov:1987}
+L.~M. Gorbunov and V.~I. Kirsanov.
+\newblock Excitation of plasma waves by an electromagnetic.
+\newblock {\em JETP}, 66:290, 1987.
+
+\bibitem{Sprangle:1987}
+P.~Sprangle, E.~Esarey, A.~Ting, and G.~Joyce.
+\newblock Laser wakefield acceleration and relativistic optical guiding.
+\newblock {\em Applied Physics Letters}, 53(22):2146--2148, 1988.
+
+\bibitem{Ple:07}
+Fabien Ple, Moana Pittman, Gerard Jamelot, and Jean-Paul Chambaret.
+\newblock Design and demonstration of a high-energy booster amplifier for a
+  high-repetition rate petawatt class laser system.
+\newblock {\em Opt. Lett.}, 32(3):238--240, Feb 2007.
+
+\bibitem{Zimmer:10}
+Daniel Zimmer , {\em et al.} 
+% Bernhard Zielbauer, Moana Pittman, Olivier Guilbaud, Jamil Habib, Sophie Kazamias, David Ros, Vincent Bagnoud, and Thomas Kuehl.
+\newblock Optimization of a tabletop high-repetition-rate soft x-ray laser
+  pumped in double-pulse single-beam grazing incidence.
+\newblock {\em Opt. Lett.}, 35(4):450--452, Feb 2010.
+
+\bibitem{Delmas:14}
+Olivier Delmas, {\em et al.} 
+% Moana Pittman, Kevin Cassou, Olivier Guilbaud, Sophie Kazamias, Gabriel~V. Cojocaru, Olivier Neveu, Julien Demailly, Elsa Baynard, Daniel  Ursescu, and David Ros.
+\newblock Q-switched laser-assisted grazing incidence pumping (qagrip) for
+  efficient soft x-ray laser generation.
+\newblock {\em Opt. Lett.}, 39(21):6102--6105, Nov 2014.
+
+\bibitem{1748-0221-8-01-T01001}
+M~Alves, {\em et al.} 
+% C~Arnault, D~Auguste, J~L Babigeon, F~Blot, J~Brossard, C~Bruni,
+ % S~Cavalier, J~N Cayla, V~Chaumat, J~Collin, M~Dehamme, M~Demarest, J~P Dugal,
+%  M~Elkhaldi, I~Falleau, A~Gonnin, M~Jore, E~Jules, B~Leluan, P~Lepercq,
+%  F~Letellier, E~Mandag, J~C Marrucho, B~Mercier, E~Mistretta, C~Prevost,
+%  R~Roux, V~Soskov, A~Toutain, A~Variola, O~Vitez, and H~Monard.
+\newblock Phil photoinjector test line.
+\newblock {\em Journal of Instrumentation}, 8(01):T01001, 2013.
+
+\bibitem{Vinatier2015222}
+T.~Vinatier, {\em et al.} 
+%C.~Bruni, R.~Roux, J.~Brossard, S.~Chanc{\'e}, J.N. Cayla,
+ % V.~Chaumat, G.~Xu, and H.~Monard.
+\newblock Performances of the alpha-x RF gun on the PHIL accelerator at
+  LAL.
+\newblock {\em Nuclear Instruments and Methods in Physics Research Section A:
+  Accelerators, Spectrometers, Detectors and Associated Equipment}, 797:222 --
+  229, 2015.
+
+\bibitem{WAKE}
+B.~S. Paradkar, B.~Cros, P.~Mora, and G.~Maynard.
+\newblock Numerical modeling of multi-gev laser wakefield electron acceleration
+  inside a dielectric capillary tube.
+\newblock {\em Physics of Plasmas}, 20(8), 2013.
+
+\bibitem{astra}
+  Klaus Floettmann,
+  \emph{A Space Charge Tracking Algorithm Version 3.0}, DESY, Germany, October 2011(Update April 2014)
+
 \end{thebibliography}
-%\null  % this is a hack for correcting the wrong un-indent by package 'flushend' in versions before 2015
+
 
 \end{document}