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landau-damping-1d1v.html
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<!DOCTYPE html>
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/*
* Skeleton V2.0.4
* Copyright 2014, Dave Gamache
* www.getskeleton.com
* Free to use under the MIT license.
* http://www.opensource.org/licenses/mit-license.php
* 12/29/2014
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background-color: #1EAEDB;
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textarea {
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appearance: none; }
textarea {
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padding-top: 6px;
padding-bottom: 6px; }
input[type="email"]:focus,
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th,
td {
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<h1>Linear Landau damping on uniform grid</h1>
<p>Here we perform a linear Landau damping test of the scheme in the case of uniform grid.</p>
<p>Initial conditions for electrons are</p>
<p class="math">\[
f(x, v) = \frac{1}{\sqrt{2\pi}}\exp\left\{-\frac{v^2}{2}\right\}\left(1 + \tilde n\cos kx\right)
\]</p>
<p>where velocities <span class="math">$v$</span> are normalised to a thermal velocity <span class="math">$v_{\rm th}$</span>, concentration <span class="math">$n$</span> is normalized to equilibrium concentration <span class="math">$N_e$</span>, spatial coordinate <span class="math">$x$</span> is normalized to <span class="math">$v_{\rm th} \over \omega_p$</span> where <span class="math">$\omega_p^2 = \frac{4\pi e^2 N_e}{m}$</span> is a plasma frequency (<span class="math">$e$</span> is the elemaentary charge and <span class="math">$m$</span> is the electron mass).</p>
<p class="math">\[
k
\]</p>
<p>normalized to <span class="math">$\omega_p \over v_{\rm th}$</span> is a wave number. Here we verify the case <span class="math">$k \sim 1$</span> for which dispersion and Landau damping are significant.</p>
<p>Ions are supposed to be uniformly distributed and immobile.</p>
<p>For simulations below we choose: <span class="math">$k = 0.5$</span>, <span class="math">$\tilde n = 0.01$</span></p>
<p>Simulations are performed on a uniform grid <span class="math">$x \in (\frac{\pi}{8},8\pi)$</span>, <span class="math">$\Delta x = \frac{\pi}{8}$</span>, <span class="math">$v \in (-4,4)$</span>, <span class="math">$\Delta v = 0.1$</span>, <span class="math">$t \in (0, 70)$</span>, <span class="math">$\Delta t = 0.1$</span></p>
<p>Below we check damping of electric energy calculated as follows</p>
<p class="math">\[
\varepsilon_e = \int \frac{E^2}{2} dx
\]</p>
<p>where <span class="math">$E$</span> is an electric filed normalized to <span class="math">$\frac{m\omega_p v_{\rm th}}{e}$</span>.</p>
<p>We expect it to damp with the rate defined by the following expression:</p>
<p class="math">\[
\gamma = \frac{\pi}{8\sqrt{2}}k^{-3}\exp\left(-\frac{1}{2k^2}\right)
\]</p>
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" />
<p>Here we see the great coincidence between simulations and the theory. We also see a well-known effect of oscillations recursion due to numerical artifact caused by finite resolution of veolcity space. It has been shown that the recursion time is of the order of <span class="math">$\pi/(k\Delta v)$</span> where <span class="math">$\Delta v$</span> is the velocity resolution. In our case this statement gives <span class="math">$t_{recur} \sim 62$</span> which is also in good coincidence with simulation results.</p>
<p>We also can check the dispersion relation for Laingmuir oscillations in warm plasma. We expect that the frequency will be equal to</p>
<p class="math">\[
\omega_L = (\omega_p^2 + 3k^2)^{\frac12}
\]</p>
<p>Here is the spectrum of oscillations in the central point (we take time interval <span class="math">$t \in (0,50)$</span> where oscillations does not contain numerical artifacts).</p>
<img src="data:image/png;base64,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" />
<p>Below we compare theoretical value for oscillations frequency and the one obtained numerically:</p>
<pre class="output">
theoretical: 1.3228756555322954
numerical: 1.382300767579509
</pre>
<p>Again we have a very good coincidence limited only by resolution of time step.</p>
<h1>Linear Landau damping on non-uniform grid</h1>
<p>Now we perform a linear Landau damping test of the scheme in the case of non-uniform grid.</p>
<p>Initial conditions and simulation parameters are the same except for grid along velocity axis. Now it isn't uniform:</p>
<p class="math">\[
v \in (-4,4),
\]</p>
<p class="math">\[
\Delta v = 0.05 \iff |v| < 1,
\]</p>
<p class="math">\[
\Delta v = 0.1 \iff |v| > 1.
\]</p>
<p>We also increase time resolution by factor of two.</p>
<p>Let us again check damping rate of electric energy and compare it to theoretical prediction</p>
<img src="data:image/png;base64,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" />
<p>Again we see a good coincidence between simulations and theory. However for the non-uniform grid the rucursion effect comes to play earlier.</p>
<p>Now we check dispersion relation</p>
<img src="data:image/png;base64,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" />
<pre class="output">
theoretical: 1.3228756555322954
numerical: 1.4660765716752369
</pre>
<p>We again have a good coincidence limited only by time resolition</p>
<h1>Non-linear Landau damping on non-uniform grid</h1>
<p>Finaly we check the case of non-linear (strong) Landau damping using non-uniform grid. For this we increase initial perturbation of electron concentration to <span class="math">$\tilde n = 0.5$</span>. To cope with increasing amplitude of oscillations we also increase the velocity domain to <span class="math">$(-6, 6)$</span></p>
<p>Let us look again to time evolution of electric energy</p>
<img 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" />
<p>There is no analytical solution for strong landau damping. However the result can be compared to what has been obtained by other simulations. Our parameters are essentially the same as in the simulations performed in <a href="https://doi.org/10.1006/jcph.2001.6818">Filbet et al. J. Comp. Phys. 172, 166-187 (2001)</a>. So we can compare the curve presented above with the one plotted at Fig. 6(a) of this paper. It can be easily seen that the quantitative coincidence is almost perfect.</p>
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Published from <a href="landau-damping-1d1v.jmd">landau-damping-1d1v.jmd</a>
using <a href="http://github.com/JunoLab/Weave.jl">Weave.jl</a> v0.10.10 on 2021-11-05.
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