Hi, I have currently been thinking about laser-plasma interaction and I have a simple model in mind. I am going to look for a cylindrically symmetric solution of a cylindrically symmetric laser beam (of radius R) hits a initially charge neutral plasma creating an electron beam in the plasma. For the electron beam I am also going to assume that there is only one component of the magnetic field B_theta and 2 components for the electric field, E_r and E_z. I think this will be the most simple model I can write down whilst giving some information about the 2D case (the 1D case has been completed). Once more assumption which I am not too sure will hold or not (but I think it will) is that the electron beam in the plasma will begin to spread out radially but my assumption will be that it doesn't spread out much and therefore, i can use that idea to reduce the complexity and allow me to linearize the equations, decouple them and solve them. I have my working in the attached PDF document in section 2 - Perturbation idea. Your thoughts are appreciated.