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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<title>Plasma wakefield acceleration</title>
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<p align=right> <a href="main_ru.html">RU</a> </p>
<div id="header">
<div id="menu">
<ul>
<li class="first current_page_item"><a href="main.html">Main</a></li>
<li><a href="team_en.html">Team</a></li>
<li><a href="collaboration_en.html">Collaboration</a></li>
<li class="last"><a href="articles_en.html">Publications</a></li>
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<h2 align="center">LCODE framework</h2>
<!-- <p id="facebook"><span class="auto-style3">Like us on</span> <a href="https://www.facebook.com/cernawake">Facebook</a>
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<p align="center">
LCODE is a freely-distributed code for simulations of particle beam-driven plasma wake eld acceleration.
The code is 2-dimensional (2d3v), with both plane and axisymmetric geometries possible. In the code, the
simulation window moves with the light velocity, and the quasi-static approximation is used for calculating
plasma response. The beams are modeled by fully relativistic macro-particles. The plasma is modeled either
by macro-particles (kinetic solver), or as the electron uid ( uid solver). Transversely inhomogeneous plasmas,
hot plasmas, non-neutral plasmas, and mobile ions are possible with the kinetic solver. The code is furnished
with extensive diagnosing tools which include the possibility of in-flight graphical presentation of the results.
</p>
<p align="center">
The essence of the quasi-static approximation is illustrated by Figure 1. When we calculate the plasma response,
the beam is considered as a rigid (not evolving in time) distribution of charges and currents which propagates
with the speed of light c. The elds generated by this beam depend on the longitudinal coordinate
z and time t only in combination ξ = z - ct.
and can be found layer-by-layer starting from the beam head. Since the beam
is not changing, all particles started from some transverse position r<sub>0</sub> copy the motion of each other, and their
parameters (transverse coordinate and momenta) can be found as functions of ξ. Thus, a plasma macroparticle
in the quasi-static model is not a "big" particle, but a particle tube, i.e., a group of real particles started from
a given radius with a given initial momentum. This greatly reduces the memory required for storing plasma
particles.
</p>
<figure align="center" class="sign">
<p><img src="site-files/f-quasistat.png" alt="" width="950" height="200" ></p>
<figcaption><p align="center" class="auto-style2">Figure 1: Geometry of the problem (a), and trajectory of a plasma particle in the simulation window (b).</p></figcaption>
</figure>
<p align="center">
The calculated fields are then used to modify the beam. For highly relativistic beams, the time step
∆t for beam particles can be made large, which speeds up simulations several orders of magnitude. The quasi-static
approximation is thus useful if and only if the time scale of beam evolution is much longer than the period of
plasma wave.
</p>
<p align="left">
<b>LCODE 2D</b>
</p>
<ul>
<li >Latest stable
<A HREF="site-files/manual.pdf">user's manual</A>
<ul>
<li><A HREF="site-files/palettes.zip">Palettes for colored maps</A></li>
</ul>
</li>
<li>Executable files:
<ul>
<li>
<A HREF="site-files/lcode.exe">Parallel for Windows 64 bit</A>
<A HREF="site-files/README.WINDOWS.txt">(ReadMe)</A>
</li>
<li>
<A HREF="site-files/lcode-mpi-halfbaked.run">Half-build for Linux 64 bit</A>
<A HREF="site-files/README.UNIX.txt">(ReadMe)</A>
</li>
</ul>
</li>
<li>Examples of use:
<ul>
<li>
<A HREF="site-files/awake-baseline.cfg">Baseline variant</A>
for AWAKE experiment
</li>
<li>
<A HREF="site-files/pop20-083119.cfg">Equidistant bunch train</A>
to produce Fig.2b from Phys. Plasmas 20, 083119 (2013)
</li>
</ul>
</li>
</ul>
<p>Feel free to contact us at <code>team@lcode.info</code> for assistance and consultation.</p>
<!--
<br>
<p align="left">
<b>LCODE 3D</b>
</p>
<p align="left">
LCODE 3D is a recent LCODE rewrite for 3D geometry. It aims to offer the same key strengths:
<ul>
<li> quasistatic kinetic plasma response calculation </li>
<li> fully relativistic beam model </li>
<li> efficient parallel calculation of beam evolution </li>
<li> aggressive use of substepping </li>
<li> outstanding numerical stability </li>
<li> inherently simple and straightforward underlying models and equations,
while sacrificing as little performance as possible </li>
</ul>
</p>
<p align="left">
Additionally, LCODE 3D aims to add several more software-specific qualities to the mix, such as:
<ul>
<li> open-source license (AGPLv3) and development model </li>
<li> modern agile implementation language (Python/Cython) </li>
<li> integration into other software as a library </li>
<li> adoption of HDF5 as an input, output and internal format </li>
</ul>
LCODE 3D is currently far from maturity, but you already can get it from
<a href="https://github.com/lotov/lcode3d"> GitHub </a>
Feel free to contact us at <code>team@lcode.info</code> for assistance and consultation.
</p>
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