Intensities Of Stark Components Research Articles

Local measurements of the pedestal magnetic field profile throughout the ELM cycle on DIII-D

New high speed localized measurements of the pedestal magnetic field during the edge localized mode (ELM) cycle of a DIII-D High confinement mode (H-mode) discharge indicate a temporally and spatial complex redistribution of the edge current density profile, jedge. The measurement technique extracts the magnetic field magnitude, B, via the spectral separation of Stark-split neutral beam radiation in the pedestal. Single spatial channel measurements from a novel spatial heterodyne spectrometer are validated in discharges with core current profile changes. The technique measures Stark-splitting changes that imply B changes as small as 1 mT with high time resolution (50 μs). At normalized poloidal flux ψn=1.0, B appears saturated in the inter-ELM period and then rapidly decreases in <200 μs by ∼1%, before edge recycling emission begins to increase. Radially inboard of jedge, B increases at the ELM crash. The behavior is consistent with a rapid collapse of jedge at the ELM crash and subsequent pedestal recovery. In some discharges, at ψn<0.96, changes in B are observed throughout the ELM cycle. In others, B recovers and is relatively stable until a few ms leading up to the next crash. Measurements of B during the H-mode transition show a large increase at ψn=1 with little change at ψn=0.9, consistent with the formation of the edge bootstrap current density peak. The ψn=0.9 spectrum is complicated by predicted changes to the Stark component intensities with density at the L–H transition.

Atomic Data for Calculation of the Intensities of Stark Components of Excited Hydrogen Atoms in Fusion Plasmas

Motional Stark effect (MSE) spectroscopy represents a unique diagnostic tool capable of determining the magnitude of the magnetic field and its direction in the core of fusion plasmas. The primary excitation channel for fast hydrogen atoms in injected neutral beams, with energy in the range of 25–1000 keV, is due to collisions with protons and impurity ions (e.g., He 2 + and heavier impurities). As a result of such excitation, at the particle density of 10 13 –10 14 cm − 3 , the line intensities of the Stark multiplets do not follow statistical expectations (i.e., the populations of fine-structure levels within the same principal quantum number n are not proportional to their statistical weights). Hence, any realistic modeling of MSE spectra has to include the relevant collisional atomic data. In this paper we provide a general expression for the excitation cross sections in parabolic states within n = 3 for an arbitrary orientation between the direction of the motion-induced electric field and the proton-atom collisional axis. The calculations make use of the density matrix obtained with the atomic orbital close coupling method and the method can be applied to other collisional systems (e.g., He 2 + , Be 4 + , C 6 + , etc.). The resulting cross sections are given as simple fits that can be directly applied to spectral modeling. For illustration we note that the asymmetry detected in the first classical cathode ray experiments between the red- and blue-shifted spectral components can be quantitatively studied using the proposed approach.

A Theoretical Study of Spectral Line Intensities of the Helium Atom in an Alternating Circular Electric Field

In this work, the behavior of the Stark component intensities of spectral lines in the emission spectrum of the helium atom excited by an alternating circularly polarized electric field is studied theoretically. The line intensities of an atom in the electric field are calculated within the framework of the method of energy matrix diagonalization. Based on the calculated results, a number of regularities have been revealed in the behavior of the Stark component intensities of the helium spectral lines with changes of the electric field strength.

Non-statistical populations of magnetic sublevels of hydrogen beam atoms in fusion plasmas

Emission of spectral lines from the excited states of neutral beam atoms in fusion plasmas is the basis of beam emission spectroscopy and motional Stark effect diagnostics. It is well known that the measured intensities of Stark multiplet lines between the n=3 and 2 excited states of hydrogen systematically deviate from the full statistical model. Here we study the H α Stark component intensities using a newly developed collisional-radiative model that is based on the description of magnetic sublevels in a parabolic basis. Proton excitation cross-sections between the parabolic states are calculated in the Glauber (eikonal) approximation. The model incorporates various collisional processes between the hydrogen beam atoms and plasma particles (protons, impurity ions and electrons) as well as the radiative processes. The simulated line component ratios σ 1 / σ 0 , π 2 / π 3 and π 4 / π 3 are found to agree with the measured ratios from JET plasmas within the experimental uncertainties.

Application of the Generalized Theory of Stark Broadening to Experimental Highly-Excited Balmer Lines from a Radio-Frequency Discharge

Experimental widths of high-n hydrogen Balmer lines H n (n = 6-12), emitted from a radio-frequency discharge (T = 1850 K and N e = 1.2 × 10 13 cm -3 ), are systematically lower (up to 20%) than predicted by the Kepple-Griem (KG) line broadening theory [1]. This motivated a new theoretical analysis for Stark broadening of hydrogen lines allowing for direct and indirect couplings of the electron and ion microfields, as well as developing a rigorous analytical treatment of the ion dynamics. The theory was applied in two versions: one - using conventional, statistical intensities of Stark components, and another - using dynamical intensities accounting for the lifetime of the substate. It was found that while both versions are in a better agreement with the experiment than the KG theory, the dynamical-intensity version results in the best agreement: its rms discrepancy with the experimental widths was 5%.

Third- and fourth-order analysis of the intensities and polarization dependence of two-photon absorption lines ofGd3+in LaF3and aqueous solution

A comprehensive report and analysis of our observations of numerous parity-allowed direct two-photon transitions within the $4{f}^{7}$ configuration of the ${\mathrm{Gd}}^{3+}$ ion is presented. The experimental technique is ultraviolet fluorescence detection following optical excitation with a dye-laser beam. Previous results and analyses are extended in three ways. (1) The intensities and polarization dependence of individual Stark components, in addition to integrated multiplet intensities, are reported and analyzed for ${\mathrm{Gd}}^{3+}$:La${\mathrm{F}}_{3}$. In those cases ($^{8}S_{\frac{7}{2}}\ensuremath{\rightarrow}^{6}P_{\frac{5}{2}},^{6}D_{\frac{9}{2},\frac{3}{2},\frac{5}{2}}$) where a second-order theory of two-photon absorption adequately explains the integrated intensity, it also (with the exception of $^{6}D_{\frac{9}{2}}$) explains the Stark-component intensities. The remaining transitions are anomalously strong, and in some cases violate the angular momentum selection rules $\ensuremath{\Delta}L,\ensuremath{\Delta}J\ensuremath{\le}2$ and exhibit strong anisotropies, in contradiction to the second-order theory. It is shown that introduction of third- and fourth-order contributions involving spin-orbit and/or crystal-field interactions among levels of the $4{f}^{6}5d$ configuration, which serve as intermediate states, can account for both the integrated and Stark-component intensities of these transitions. (2) The strong anisotropy observed for the transitions $^{8}S_{\frac{7}{2}}\ensuremath{\rightarrow}^{6}P_{\frac{3}{2}},^{6}I_{J},^{6}D_{\frac{1}{2}}$ in ${\mathrm{Gd}}^{3+}$:La${\mathrm{F}}_{3}$ is explained quantitatively as a polarization-dependent interference between contributions to the intensity which are comparable in magnitude. Interference is destructive for $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\parallel}\stackrel{^}{z}$ and constructive for $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\perp}\stackrel{^}{z}$, creating an order-of-magnitude contrast in the line strength for the two polarizations. (3) A two-photon excitation spectrum of ${\mathrm{Gd}}^{3+}$ in aqueous solution is reported. Linewidths comparable to those of room-temperature solids and Stark splittings which suggest a low-symmetry quasistatic environment are observed.

On the asymmetry of lines emitted by one-electron ions in very dense plasmas

Positions and relative intensities of Stark components of lines are altered in very dense plasmas because free electrons partially screen not only the Coulomb interaction between the radiating ion and perturbing ions, but also the Coulomb interaction within the radiating ion itself. This latter plasma-screening perturbation and the perturbation caused by the ion-field gradient (quadrupole interaction) are comparable. The first-order corrected Stark patterns for Lyman- alpha lines of several ions are presented in order to demonstrate the necessity of considering both of these perturbations and the fine-structure interaction simultaneously in the calculation of line profiles for high-density plasmas.

Stark-component intensities of the hydrogen atom in a coulombic field

Stark-component intensities of the hydrogen atom in a coulombic field

Relative intensities of stark components in helium

Theoretical values for the displacements and relative intensities of Stark components have been calculated by Foster for selected groups of helium lines. These were based on approximate methods in the perturbation theory of quantum mechanics, and on the assumption that the source contains equal numbers of atoms excited to states with a common principal quantum number. Experimental work on this subject has been carried out by Foster, Takamine and Werner, and more extensively by Dewey. The observed displacements agree remarkably well with the theory; but the intensities have shown some variations which cannot be disregarded. This appears surprising at first sight, since the theory reveals close connections between displacements and intensities. It seems, however, well established by Dewey that the P - P (and p - p) combination lines are decidedly too strong for the theory. There appear to be other less striking discrepancies.

Relative intensities of stark components in hydrogen

Introduction .—This quantitative investigation of the intensities of Stark components in hydrogen was started before the advent of the new quantum mechanics. Our original purpose was to obtain a more precise measure of the few serious departures from experimental fact, which one finds in the estimates of these intensities based on the correspondence principle. The somewhat limited measurements in the preliminary report proved to be in excellent agreement, however, with the new theoretical intensities by Schrödinger, which had just appeared. These new calculations claimed not only some modifications in the theoretical estimates, but also a few appreciable variations from the original experimental values given by Stark. In extending the work we have, therefore, paid most attention to the relative intensities of those components for which theory and experiment seemed not to agree. Fortunately, this has not required the re-examination of the very weak components, the majority of which have already been studied in a qualitative way at this laboratory. We find that the more reliable quantitative examination of some of the stronger components is sufficient to make the principal corrections needed to bring the experimental intensities into harmony with Schrödinger. Incidentally, it becomes clear that a consideration of the normal fine structure of the Balmer lines is not essential to a quantitative explanation of their observed Stark effects in high fields. The first satisfactory explanation of Stark displacements in hydrogen was made by Epstein through a development of the quantum theory. This did not include a rational basis for the selection rules or a means of estimating intensities. These were supplied by Prof. Bohr through an application of perturbation theory together with his principle of correspondence. Kramers calculated the so-called “characteristic amplitudes” of the motion of the electron in initial and in final orbits, and used these to explain the observed polarisations of Stark components as well as to make estimates of their intensities. The correspondence principle was indefinite, however, in that there were the two amplitudes in each case which should, perhaps, be averaged in some manner not obviously expressed. Kramers used, for convenience, the arithmetical mean. It has been observed that in this particular application it is much better to entirely neglect the amplitudes in the final orbits, since these give rise to all the estimates which can be considered unsatisfactory. This suppression of the above-mentioned final states as important factors in the determination of the intensities is supported by the more recent perturbation theory of quantum mechanics.

Observed Relative Intensities of Stark Components of Hα

BY means of wave mechanics, Schrodinger (Ann. d. Phys., 4, 80, 437; 1926) has made quantitative calculations of the intensities of Stark components in hydrogen which are commonly considered to be an improvement on the earlier estimates based on the correspondence principle (H. A. Kramers, D.K.D. Vidensk. Selsk., 8, 3, 287; 1919). That this is so in the case of Hβ was shown recently by the writers in a quantitative experimental investigation (NATURE, Oct. 23, 1926).

Observed Relative Intensities of Stark Components in Hydrogen

ATTRACTED by the singularly large observed variations (Astrophys. Jour., 62, 229, 1925) from estimated intensities of certain strong Stark components of Hβ (H. A. Kramers, Copenhagen, 1919) we have recently made quantitative measurements from a suitable source by means of a neutral wedge. It is interesting to compare the results with the new theoretical calculations by Schrodinger (Ann. d. Phys., 80, 437, 1926). Following are the observed, calculated, and estimated ratios of intensities of components having polarisations and displacements as indicated. The displacement Δ is expressed in the unit which appears in the quantum theory of the Stark-effect.