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I am looking at electron beam going through a plasma. I am modelling it using two regions, the electron beam and external to the electron beam. I am using the potential formulation of electrodynamics and I am modelling a rigid electron beam and assuming cylindrical symmetry for simplicity.

I come down (with my assumption for the current) to solving the following equation:

[tex]

-\nabla^{2}\varphi +\frac{1}{c^{2}}\frac{\partial^{2}\varphi}{\partial t^{2}}+\mu_{0}\sigma\frac{\partial\varphi}{\partial t}=\frac{\rho}{\varepsilon_{0}}

[/tex]

The charge density is constant. I am not too sure how to go about solving this equation, would it be via Green's functions? Can someone provide me with a reference please.

Regards

Mat

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# Inhomogeneous electromagnetic wave equation

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