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&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Short description|Kinetic equation describing collisionless plasma dynamics}}&lt;br /&gt;
{{Quantum methods backlink|Plasma and kinetic methods}}&lt;br /&gt;
&lt;br /&gt;
The &amp;#039;&amp;#039;&amp;#039;Vlasov equation&amp;#039;&amp;#039;&amp;#039; is a fundamental equation in [[Physics:Quantum kinetic theory|kinetic theory]] describing the evolution of a distribution function in phase space.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;div style=&amp;quot;float:right; border:1px solid #e0d890; background:#fff8cc; padding:6px; margin:0 0 1em 1em; width:420px;&amp;quot;&amp;gt;&lt;br /&gt;
[[File:Vlasov equation phase space.png|400px]]&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
== Equation ==&lt;br /&gt;
&amp;lt;math&amp;gt;&lt;br /&gt;
\frac{\partial f}{\partial t} + \mathbf{v}\cdot\nabla f + \frac{q}{m}(\mathbf{E}+\mathbf{v}\times\mathbf{B})\cdot\nabla_v f = 0&lt;br /&gt;
&amp;lt;/math&amp;gt;&lt;br /&gt;
&lt;br /&gt;
This equation provides the basis for understanding [[Physics:Quantum Drift physics|drift physics]] and [[Physics:Quantum Transport theory|transport processes]].&lt;br /&gt;
&lt;br /&gt;
== Applications ==&lt;br /&gt;
Used in:&lt;br /&gt;
&lt;br /&gt;
* Plasma waves  &lt;br /&gt;
* Instabilities  &lt;br /&gt;
* Collisionless plasmas  &lt;br /&gt;
&lt;br /&gt;
=See also=&lt;br /&gt;
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}&lt;br /&gt;
&lt;br /&gt;
=References=&lt;br /&gt;
{{reflist|3}}&lt;br /&gt;
&lt;br /&gt;
{{Author|Harold Foppele}}&lt;br /&gt;
{{Sourceattribution|Vlasov equation|1}}&lt;/div&gt;</summary>
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