Linear Stark Effect Due to Resonant Interactions of Static and Dynamic Fields

Abstract

In turbulent plasmas the radiating atoms are subjected to an oscillating high-frequency electric field originating from electronic plasma oscillations. It appears to be generally believed that in hydrogen plasmas the radiation spectrum in this situation is well described by the theory of the dynamical linear Stark effect developed by Blokhintsev. 1 However, the atoms are radiating also under the simultaneous influence of a quasistatic field due to slowly moving ions or to lowfrequency ion-acoustic turbulence. The present paper points out that the Blokhintsev theory is not adequate, as the resonant interactions between the Stark separation induced by the quasistatic field and the oscillations of the dynamic field produce a spectrum quite different from what could be explained as the combination of the independent effects of these fields.The problem thus posed is that of radiation of an atom with degenerate states under the combined effects of static and dynamic electric fields. For a pure high-frequency dynamical field, the Blokhintsev theory predicts the appearance of a series of satellites at the harmonics of the frequency of the applied field. An addition of a static field parallel to the high-frequency field is still readily described by a simple extension (1957). . of this theory and merely produces a symmetric splitting of each satellite with shifts proportional to the static field. However, when the static field has a component perpendicular to the dynamical field, then new results, essentially different from the Blokhintsev theory, emerge. In another sense this situation can be viewed as the formation of static Stark-split states which are connected by the off-diagonal matrix elements of the perpendicular dynamic field. For typical magnitudes of the plasma quasistatic field the energy separation due to the component perpendicular to the dynamic field can be of the same order of magnitude as the plasma frequency and resonance effects will occur. In plasmas of atoms which are not subject to the linear Stark effect, the theories 2 " 5 that only consider the dynamic field work well, because the atomic levels are naturally well separated and are only negligibly shifted by the usual magnitude of the quasistatic field in the plasma.As the important physical effects are related to the perpendicular component of the static field, for simplicity we will ignore the parallel component. The more general case will be discussed elsewhere. We will concentrate on the structure of the hydrogenic Lyman-a line, which possessesWe investigated the line shape of the Lyman-a transition of a hydrogen atom simultaneously subjected to a static and a perpendicular high-frequency electric field. It was found that resonance effects occur, producing a profile substantially different from the Stark spectrum of the fields acting independently. This result shows that the interpretation of turbulent hydrogen plasma spectra by the Blokhintsev (dynamic field only) theory is not generally valid. 324

Calculations and Measurements of the Dynamic Stark Effect in Hydrogen

“…Cohn et al 5 , showed for Lya that resonant effects between high and low frequency fields can influence the intensity profile dramatically. This effect was found experimentally by Gallagher and Levine 6 and by Rutgers and DeKluiver 7 for the Balmer lines.…”

Possible spectral diagnostics for turbulent electric fields in solar flares

“…The idea of position spectroscopy, as suggested here, offers-distinct advantages even for laboratory plasmas where other methods for the determination of field strengths are available. Hydrogenic spectra with discernible positions for various Stark shifted components of Balmer lines have already been observed in fusion related laboratory experiments with a high level of plasma oscillations (Gallagher and Levine, 1973).…”

“…The theory of the Stark effect for combined dynamic and static fields has been developed earlier by the authors Kalman, 1972, Bakshi, Kalman, andBakshi, Hogaboom, Kalman, and Cohn, 1974). A very brief sketch of this theory is given in Section 3, but first we can estimate the order of magnitude effects associated with the turbulent fields and their relation to Doppler broadening.…”

Algebraic theory of the dynamical Stark-Zeeman effect for hydrogenlike atoms

“…[22] was pointed out in Ref. [17],where the L shell ( n = 2) has been considered numerically. Then in the framework of various approximations the time-dependent Schrodinger equation for n=2 (seldom for n=3, 4) was solved analytically [18 -21].…”