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Stark broadening of hydrogen lines is investigated in low-density magnetized plasmas, at typical conditions of magnetic fusion experiments. The role of time ordering is assessed numerically, by using a simulation code accounting for the evolution of the microscopic electric field generated by the charged particles moving at the vicinity of the atom. The Zeeman effect due to the magnetic field is also retained. Lyman lines with a low principal quantum number

In magnetic fusion, detailed line shapes are of interest for accurate diagnostics or radiative transfer simulations. For plasma conditions and magnetic fields encountered in the divertor of present and future tokamaks, an accurate model for the line shape of the hydrogen isotopes should include Zeeman and Stark effects, and retain the dynamics of the ion-emitter interaction. Since we then have to solve a quantum time-dependent problem, understanding the role of time ordering becomes an important issue both from the fundamental and computational points of view (note, this problem is also investigated in other contexts, e.g., [

According to classical textbooks or review articles (e.g., [

The Schrödinger equation in the interaction representation (

The purpose of ab initio simulations is to numerically reproduce the motion of the charged particles in the plasma so as to obtain the time-dependent electric microfield

Time ordering should play a role on lines which are affected by ion dynamics, that is, with a low upper principal quantum number

Zeeman-Stark profiles of (a)

The underestimation of the Stark effect can be explained by noting that, in the solution of Schrödinger’s equation neglecting time ordering, the matrix exponential essentially involves the time average of the electric field

Profiles of (a)

We have addressed the role of time ordering on hydrogen Zeeman-Stark profiles in low-density plasmas, for typical conditions of tokamak divertors. With numerical simulations, we have shown that neglecting time ordering on lines with a low upper principal quantum number leads to strong deviations, with a systematic underestimate of the Stark width of the Zeeman components. This is interpreted in terms of the time averaged electric field, namely, the latter rapidly vanishes during the decorrelation of the atomic dipole so that the resulting effective Stark effect is reduced. Conversely, we have shown that the deviations are weak on lines with a higher upper quantum number, merely because they are much less affected by ion dynamics. This result, of interest for spectroscopy of magnetic fusion experiments, shows that: (i) the development of line shape models including ion dynamics for Monte Carlo investigations of radiative transfer (e.g., [

This work is supported by an EFDA Fellowship contract, by the French Federation on Magnetic Fusion Research (project “Radiation Absorption Effects”), by the French Research National Agency (Project “PHOTONITER”, Contract ANR-07-BLAN-0187-01), and by the collaboration PIIM/CEA Cadarache (Contract LRC DSM 99-14).