- #1
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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.
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?
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?