A 4-line computer code to evaluate the Incoherent Scattering Spectrum

Several authors have employed quite different physical principles to derive expressions for the spectrum of Incoherent Scatter signals. Surprisingly, the final formulas have, seemingly, quite different analytical expressions. However, on closer analysis they all turn out to be equivalent. For the usual situation of thermal equilibrium for each plasma component, the spectrum can be expressed in terms of various singular functions, the traditional choice being the Plasma Dispersion function. Yet another function favoured here is the Error Function of Imaginary argument (Erfi). The recent availability via the Internet or via some commercial packages of computer implementations for the numerical evaluation of the Erfi function has made it possible to implement the numerical calculation of the IS spectrum in just a few lines of code. It is argued in this work that the expression obtained by using the "dressed particle principle" adapts itself to this purpose exceedingly well since it needs just 4 lines of code. Moreover, this expression, by depending only on the plasma susceptibilities, lends itself to an intuitive and exceedingly illuminating physical explanation term by term. For instance, why the cross section of the high frequency component (plasma line) is small, or why the cross section of the low frequency component (ion line) is about one half the Thomson cross section, can both questions be answered readily by simple physical interpretations of different terms of the "dressed particle" formula.