ABSTRACT
Mathematically, the problem is described by the system of Maxwell equations for the electro magnetic field incorporating terms that take into account the presence of plasma. To reduce exten sive computations and focus ourselves on essential points, we adopt a simplified model assuming a scalar (rather than vector) field and dealing with one-dimensional rather than three-dimensional space. Then the problem is described by the equation
where u is the unknown wave field, c is the light velocity in vacuum, Xb(x) is the so-called plasma frequency, Λq'{t) is the instantaneous source frequency, Λr(t) is the source amplitude, δ(χ) is the Dirac function concentrated at the origin, and 0(t) is the Heaviside step function,
A discussion concerning the derivation of this model can be found in Lewis (1967). Here we adopt the model as being given and study the mathematical and physical consequences that can be derived from it. Let us make a few remarks on the model (11.1).
