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We can solve the electron equations of motion, (295) and (296), as a set
of coupled first-order ODEs using the RK4 methods discussed in Sect. 3.
However, in order to evaluate the right-hand sides of these equations we need to know
the electric field at each time-step.
We can achieve this by solving Poisson's equation, (298), every time-step.
However, in order to determine the source term for this equation we need to calculate the
electron number density , which is, of course, a function of the instantaneous