Computation of the electric and magnetic fields induced in a plasma created by ionization lasting a finite interval of time

It has been shown that when an infinite expanse of gas, carrying a linearly polarized electromagnetic wave, is instantly ionized, the initial wave is frequency upshifted. This phenomenon of frequency up-conversion through flash ionization gives rise to steady-state transmitted and reflected electromagnetic waves and, most notably, to a time-independent magnetic field. Here we study the case in which the final state of ionization is achieved not instantly but in a finite turn-on time, 0 less than or equal to t less than or equal to t(sub 0), which is followed by the steady-state t(sub 0) less than or equal to t < infinity. We show that the electric field is obtained from the one-dimensional wave equation F double prime of (t) + omega squared(sub 0)g(t)F(t) = 0 if electrons are born at rest when they are created during ionization. As a result, the instantaneous frequency of the upshifted radiation is omega(t) = omega(sub 0) square root of 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 Faraday's law. We find that the steady-state electric field amplitude depends on the steady-state value of g(t) but does not depend on the ionization time t(sub 0). Conversely, the static magnetic field amplitude decreases with increasing turn-on time.