Ion-Dynamics Effect on Hydrogenic Stark Profiles in Hot and Dense Plasmas

Abstract

A computer simulation has been applied to the calculation of Stark profiles of hydrogenic ions for the conditions of inertial confinement fusion. Drastic modifications of the Lymanline profiles are observed when ion dynamics is taken into account.PACS numbers: 32.70.Jz, 32.30.Rj, 32.60.+i In most of the early Stark broadening theories, it was assumed that the plasma ions could be treated as stationary during the radiative lifetime of an excited atom or ion in the plasma. However, in recent years it has been shown both experimentally 1 and theoretically 2 " 5 that the motion of these ions can produce significant alterations near line center, particularly for low-lying series members 6 such as Lyman-a (L a ) and Lyman-/3 (L^). For a plasma density of N e =l0 17 cm"" 3 , this so-called "ion dynamics" effect can change the halfwidth by a factor of 2. 6 Since all current tabulations of Stark profiles for hydrogen 7 or hydrogenic ions 8 have employed the static-ion approximation, the use of L a and Lp from these tables could result in serious errors in density diagnostics. The situation becomes especially unsatisfactory for the hot, dense plasmas encountered in inertial confinement fusion (ICF), because the density diagnostics rely heavily on fitting the experimental profiles with the theoretical profiles of hydrogenic ions. 9 ' 10 Attempts have been made recently by Cauble and Griem 11 to include the effect of ion dynamics in an approximate way for the Lyman lines of Arxvm broadened by deuterium-tritium (DT) plasmas. For a density N e = 5 x 10 23 cm" 3 and a temperature T e = 4.6 x 10 6 K, they found roughly a doubling in the halfwidth of L a . In the present work, we use a computer simulation to demonstrate that in ICF conditions, the introduction of ion dynamics has a much larger effect on the profile, producing an order of magnitude increase in the halfwidth of L a .Our computer simulation for the ions in the plasma is based on a model of statistically independent quasiparticles moving in a spherical box, 5, n and interacting with the radiator through a Debye shielded field, T,-(Z,<?r/r 3 )(l + r/X)exp(-r/A),where Z p is the charge number of the perturbing ion and k is a screening length discussed below. In order to evaluate the screening length X, we first used the computer simulation to evaluate microfield distribution functions for various values of X. We then chose the value of X for which the computer simulation agreed with the known microfield distribution. 13,14 This fitting procedure produced better than 10% agreement between the computer simulation and the microfield distribution in Ref. 13, and it was found that k could be given by k = [kT/4Tre 2 N e (l + Z p /2)] l/2 .In these calculations, the effect of the Coulomb repulsion between the radiating ions and the perturbing ions was approximated by excluding the perturbers from a sphere of radius r c = Z e Z p e 2 l\xv 2 where Z e denotes the charge number of the emitting ion while fx and v are the reduced mass and relative velocity for the emitter-pertu...

Influence of correlated collisions on Stark-broadened lines in plasmas

“…Here, τ e and τ i denote the electron and ion collision times, estimated as r 0 /v e , r 0 /v i with v e , v i being the electron and ion thermal velocities, respec-tively, and r 0 = N −1/3 being the characteristic scale for the mean interparticle distance. Ion dynamics effects (that arise, for instance, if τ i ∼ τ dd ) have been observed [11] and have been extensively investigated, using numerical simulations [4,[12][13][14][15] or ad hoc models based on the statistical properties of the electric field (such as the model microfield method "MMM" [16,17] or the frequency fluctuation model "FFM" [18][19][20]). Incomplete electron collisions (that are expected when τ e ≪ τ dd is not satisfied) have also been investigated, in particular by using refined models for the collision operator, either based on kinetic theory (such as the "unified theory" [21,22]) or semiempirical procedures (e.g.…”

Electron density measurement in atmospheric pressure plasma jets: Stark broadening of hydrogenated and non-hydrogenated lines

“…Computer simulations have been used as the basis of computer programs for electron density determination from experimental profiles [78] and to obtain large tabulations of Hydrogen [14,79] or Helium Stark profiles [80,81]. CSM enables line profiles for a wide range of plasma densities, temperatures and compositions to be obtained [82], as well as for cases with plasma unbalances or inhomogeneities that can occur in experimental studies. The profiles obtained considering specific experimental conditions allow researchers to undertake plasma diagnostics by direct comparison of the line profiles obtained in the simulations and those experimentally recorded.…”

Frequency Separation Method for Relaxation Problems

“…It is clear that in this way the ion impact limit is recovered exactly and in as sophisticated a f orm as desired: For example, one may use the perturbative IA [13], the exact semiclassical dipole results [15] (for hydrogenic emitters) or fully non-perturbative results including higher multipole effects [16]. Further, this separation of the ionic field into fast(impact) and slow components improves the performance and/or reliability of every method capable of dealing with the intermediate(ion dynamical) regime, which will now only have to correctly compute the contribution of the slow part: For simulations [17], it is very expensive to have to integrate over sharp peaks. Such peaks are due to fast perturbers, which are correctly included in the impact part and do not appear in a simulation of the slow part.…”