COMPUTATION OF THE ELECTRIC AND MAGNETIC-FIELDS INDUCED IN A PLASMA CREATED BY IONIZATION LASTING A FINITE INTERVAL OF TIME

It has been shown [1] that when an infinite expanse of gas, carrying a linearly polarized electromagnetic wave, is instantly ionized, the in itial wave is frequency upshifted. This phenomenon of frequency up-con version through flash ionization gives rise to steady-state transmitte d and reflected electromagnetic waves and, most notably, to a time-ind ependent magnetic field. Here we study the case in which the final sta te of ionization is achieved not instantly but in a finite turn-on tim e, o less-than-or-equal-to t less-than-or-equal-to t(o), which is foll owed by the steady-state t(o) less-than-or-equal-to t < infinity. We s how that the electric field is obtained from the one-dimensional wave equation F''(t)+omega(o)2g(t)F(t) = o if electrons are born at rest wh en they are created during ionization. As a result, the instantaneous frequency of the upshifted radiation is omega(t) = omega(o) square-roo t g(t). The electric field can be solved exactly for specific choices of g(t). We solve for the electric field using WKB approximations for arbitrary g(t). We then solve for the magnetic field by integrating Fa raday's law. We find that the steady-state electric field amplitude de pends on the steady-state value of g(t) but does not depend on the ion ization time t(o). Conversely, the static magnetic field amplitude dec reases with increasing turn-on time.