I have been working with someone on plasma physics. We have a simple model of a laser hitting a charge neutral plasma. The laser promotes the electrons in the plasma into a high energy electron beam. We have been looking at the problem in 1D using the Lorentz force law, the conservation of number density and Ampere's law, these form a set of first order hyperbolic PDEs.(adsbygoogle = window.adsbygoogle || []).push({});

My colleague is concerned with conservation of charge, he says that as the plasma was initially charge neutral then the total charge (included in the electron beam) must remain zero. I thought that all we had to show was that:

[tex]

\nabla\cdot\mathbf{J}+\frac{\partial\rho}{\partial t}=0

[/tex]

He calculated

[tex]

Q=\int_{0}^{\infty}\rho dx

[/tex]

He wanted this to be zero. Is this right?

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# Charge conservation

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