Princeton Large Torus Research Articles

Wolfgang Stodiek

Wolfgang Stodiek

Neoclassical theory of rotation and electric field in high collisionality plasmas with steep gradients

The equation describing the radial transport of toroidal momentum in a collisional subsonic plasma with steep gradients has been obtained via a systematic expansion of the two-fluid equations. The diffusion rate is classical; the poloidal rotation, driven by the temperature gradient, generates, in turn, a toroidal flow gradient, also in Ohmic discharges. Moreover, important modifications of the parallel momentum equation are found to arise if Λ1≡(νi/Ωi)(q2R2/rLT) is ⩾O(1/3); the poloidal rotation velocity is then no longer unique but obeys a cubic equation which may allow for bifurcated equilibria under certain conditions. The toroidal velocities predicted for Ohmic discharges compare well with those measured in PLT [Princeton Large Torus; S. Suckewer et al., Nucl. Fusion 21, 1301 (1981)]; the relevance of the extended equation providing the poloidal rotation velocity to selected experimental edge plasmas is discussed.

New Applications of ORNL Neutral Beam Injectors

The injection of energetic hydrogen and deuterium atoms has been used to heat plasmas in various fusion experimental devices including tokamaks, mirrors, and stellarators. The neutral beam injection is a proven plasma heating technique for increasing plasma densities, temperatures, and pressures. For this fusion endeavor, scientists at Oak Ridge National Laboratory (ORNL) have developed multimegawatt neutral beam injectors. Various ORNL injectors have been used for studying properties of beam-heated plasmas in Oak Ridge Tokamak (ORMAK), Impurity Study Experiment-B (ISX-B), Advanced Toroidal Facility (ATF), Princeton Large Torus (PLT), and Princeton Divertor Experiment (PDX) in the United States and in Small Tight Aspect Ratio Tokamak (START) in the United Kingdom. By using a 30-cm and 100-A ion source, each ORNL neutral beam injector is capable of injecting > 1.5 MW of hydrogen atoms at 50-keV for a pulse length up to 0.5 s.For increasing plasma densities and raising plasma temperatures in START, one such injector was installed and commissioned during 1995. The initial goal was to provide an injected neutral beam power of more than 0.5 MW at a beam energy of 40 keV for 20 ms. Addition of a getter pump has allowed the beam power to be raised to 1 MW at 33 keV. Recent experiments have demonstrated that neutral beam heating can play a big role in raising plasma pressures to a record volume-average beta value over 30%.ORNL neutral beam injectors have been approved for plasma heating experiments on both the TJ-II stellarator at CIEMAT, Spain, and the Mega-Amp Spherical Tokamak (MAST) at Culham Science Centre (Culham). Two proven ORNL NB injectors are being installed at the TJ-II facility. Additional ORNL beam equipment is being used to implement two 5-s NB injectors at the MAST facility. In this paper, we report and discuss the progress and plans for these neutral beam activities.

Observation and Modeling of High‐nIron L‐Shell Lines from Intermediate Ion Stages

The spectra of highly ionized iron species between 7 and 9 A have been studied using data obtained at the Princeton Large Torus tokamak under plasma conditions similar to those present in solar and stellar flares. The wavelengths of many iron lines are measured with very high accuracy (λ/Δλ up to 4 × 104), along with several other lines in species such as He-like Al XII and Mg XI. Theoretical spectra that predict both the wavelength and the intensity of Fe emission lines are compared with the observed spectra and are used to make accurate line identifications. Virtually all the observed iron lines are found to arise from n = 4, 5, and 6 → 2 transitions in Fe XXI-XXIV, and many lines are identified for the first time. Several transitions are shown to have diagnostic applications, and a detailed analysis of the density sensitivity of Fe XXII lines is presented.

High-resolution measurement, line identification, and spectral modeling of the K beta spectrum of heliumlike Ar16+

High-resolution crystal spectrometer measurements of the K\ensuremath{\beta} spectrum of heliumlike ${\mathrm{Ar}}^{16+}$ covering the wavelength region from 3.34 to 3.50 \AA{} are presented and compared with detailed theoretical analyses. The measurements were made on the Princeton Large Torus tokamak and test the theoretical atomic data in the low-density limit at an electron density ${\mathit{n}}_{\mathit{e}}$\ensuremath{\le}2\ifmmode\times\else\texttimes\fi{}${10}^{13}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ and temperature ${\mathit{T}}_{\mathit{e}}$=2.3 keV. Satellite transitions of the type 1${\mathit{s}}^{2}$2l-1s2l3l' and 1${\mathit{s}}^{2}$3l-1s3l3l' from lithiumlike ${\mathrm{Ar}}^{15+}$ and 1${\mathit{s}}^{2}$2l2l'-1s2l2l'3l'' from berylliumlike ${\mathrm{Ar}}^{14+}$ are identified that are produced by either dielectronic recombination or electron-impact excitation. Good overall agreement between the predicted and measured intensities of the strong dielectronic satellites is found. The agreement demonstrates the utility of K\ensuremath{\beta} spectra as a diagnostic of the electron temperature of low-density plasmas, such as those found in the Sun or magnetic fusion facilities. Poorer agreement is found for the weaker dielectronic satellite transitions, including the 1s3l3l' satellites that play an important role in the analysis of high-density plasma produced in laser fusion. Their intensity is underestimated by the calculations by about 50%. Moreover, it is shown that direct electron-impact excitation rates underestimate the relative intensity of the 1${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}_{0}$--1s2p $^{3}$${\mathit{P}}_{1}$ transition in heliumlike ${\mathrm{Ar}}^{16+}$ by a factor of 2, indicating the need for including additional excitation processes and possible blends with high-lying dielectronic satellites of the type 1${\mathit{s}}^{2}$nl'-1s3lnl' with n\ensuremath{\ge}4 in the theoretical models.

Millimeter wave scattering off a whistler and lower hybrid waves in a tokamak

Obliquely propagating whistler and lower hybrid waves through a plasma cause density perturbations. A high-frequency electromagnetic wave sent into such a perturbed region suffers scattering. Theory of electromagnetic wave scattering has been developed in a tokamak where the density profile is taken as parabolic. The wave equation has been solved to evaluate the expression for the amplitude of a scattered wave. For typical parameters of the Princeton Large Torus (PLT) [Bernabei et al., Bull. Am. Phys. Soc. 26, 975 (1981)], the ratio of the power of the scattered to the incident electromagnetic wave comes out to be of the order of 10−4 and 10−5 in cases of scattering off whistler and off lower hybrid waves, respectively, which can be detected; the method can, hence, be used for the diagnostics of the waves.

Theoretical emission line ratios for carbon-like Ti XVII, Cr XIX and Ni XXIII and a comparison with PLT tokamak observations

Recent electron-impact excitation rates for the C-like ions Ti XVII, Cr XIX and Ni XXIII are used to derive electron density sensitive emission line ratios applicable to the ultraviolet spectra of tokamak plasmas. A comparison of these with ratios measured from the Princeton Large Torus (PLT) tokamak reveals good agreement between theory and observation. These results confirm the validity of the atomic data adopted in the line ratio calculations.

High-resolution measurements, line identification, and spectral modeling of K-alpha transitions in Fe XVIII-Fe XXV

A detailed analysis of the iron K-alpha emission spectrum covering the wavelength region from 1.840 to 1.940 A is presented. Measurements are made with a high-resolution Bragg crystal spectrometer on the Princeton Large Torus (PLT) tokamak for plasma conditions which closely resemble those of solar flares. A total of 40 features are identified, consisting of either single or multiple lines from eight charge states in iron, Fe XVIII - Fe XXV, and their wavelengths are determined with an accuracy of 0.1-0.4 mA. Many of these features are identified for the first time. In the interpretation of our observations we rely on model calculations that determine the ionic species abundances from electron density and temperature profiles measured independently with nonspectroscopic techniques and that incorporate theoretical collisional excitation and dielectronic recombination rates resulting in the excitation of the 1s2sr2ps configurations. The model calculations also include the effect of diffusive ion transport. Good overall agreement between the model calculations and the observations is obtained, which gives us confidence in our line identifications and spectral modeling capabilities. The results are compared with earlier analyses of the K-alpha emission from the Sun.

Electron density sensitive ultraviolet emission line ratios for carbon-like Fe XXI in the PLT tokamak

Recent calculations of electron impact excitation rates in carbon-like Fe XXI are used to derive relative level populations and hence theoretical emission line ratios. These are compared with observed values measured from ultraviolet spectra of the Princeton Large Torus (PLT) tokamak, for which the electron density and temperature have been independently determined. Agreement between theory and observation is good, with typical discrepancies of 20% and differences of 4% for the best observed lines. This provides experimental support for the accuracy of the atomic data used in the line ratio calculations, and implies that they may be applied to the analysis of remote sources for which no independent Ne-estimates exist, such as solar flares.

Spectroscopic measurements of the parameters of the ablation clouds of deuterium pellets injected into tokamaks

Spectroscopic measurements have been made of the parameters of the luminous cloud surrounding deuterium pellets injected into the Princeton Large Torus (PLT) [Phys. Rev. Lett. 55, 1398 (1985)] and the Tokamak Fusion Test Reactor (TFTR) [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1987), Vol. 1, p. 171], with the measurements on the latter described formally here for the first time. The electron densities determined from the Stark broadening of the Balmer alpha and beta lines ranged from 5×1015–1×1018 cm−3, while the temperatures obtained from the line to continuum intensity ratios and the ratio of the intensities of the Balmer alpha and beta lines ranged from 0.9 to 3 eV. Balmer alpha emission powers as high as 100 kW were measured. The electron temperature (1.5±0.2 eV) and density (3±1×1017 cm−3 ) at the time of maximum emission from intact pellets were essentially the same for the two tokamaks, although the volumes of both the discharges and the pellets were roughly ten times larger in TFTR than in PLT. The data were taken in Ohmically heated plasmas, except for a limited number of discharges in PLT with low-power (approximately half the Ohmic heating power) ion cyclotron heating for which the results are the same as with Ohmic heating alone. Various factors that may influence the results of measurements of this type are discussed, including self-absorption, low-density plasma surrounding the most intense region of an ablation cloud, fluctuations in the emission intensity, and non-Maxwellian electron distributions. The results of the present experiments are similar to measurements of the pellet cloud parameters in other machines.

Discrepancies between calculated and observed energies for 4s-4p transitions in highly charged Cu-like ions.

The 4${s}_{1/2}$-4${p}_{1/2}$ and 4${s}_{1/2}$-4${p}_{3/2}$ transitions in the Cu-like ions of the elements Sn, Xe, La, Nd, Eu, Gd, Dy, and Yb (atomic numbers Z=50, 54, 57, 60, 63, 64, 66, and 70) have been observed in the spectra from the Princeton Large Torus tokamak. The experimentally determined transition energies were compared to the transition energies calculated using the multiconfiguration Dirac-Fock technique. By including previously published observations, the experimental and calculated transition energies were compared for the entire Cu i isoelectronic sequence from Ru (Z=44) to U (Z=92). Contrary to the conclusion of Cheng and Wagner [Phys. Rev. A 36, 5435 (1987)], we find significant discrepancies between the experimental and calculated transition energies. The discrepancies are attributable to electron correlation corrections that are not accounted for in the calculation.

High-resolution bent-crystal spectrometer for the ultrasoft x-ray region

A multichannel vacuum Bragg-crystal spectrometer has been developed for high-resolution measurements of the line emission from tokamak plasmas in the wavelength region between 4 and 25 Å. The spectrometer employs a bent crystal in Johann geometry and a microchannel-plate-intensified photodiode diode array. The instrument is capable of measuring high-resolution spectra (λ/Δλ≊3000) with fast time resolution (4 ms per spectrum) and good spatial resolution (3 cm). The spectral bandwidth is Δλ/λ0=15% at λ0=8 Å. A simple tilt mechanism allows access to different wavelength intervals. In order to illustrate the utility of the new spectrometer, time- and space-resolved measurements of the n=3–2 spectrum of selenium from the Princeton Large Torus tokamak plasmas are presented. The data are used to determine the plasma transport parameters and to infer the radial distribution of fluorinelike, neonlike, and sodiumlike ions of selenium in the plasma. The new ultrasoft x-ray spectrometer has thus enabled us to demonstrate the utility of high-resolution L-shell spectroscopy of neonlike ions as a fusion diagnostic.

Oscillating two-stream instability of a lower hybrid wave in an inhomogenous plasma

The effect of the density inhomogeneity on the oscillating two-stream instability of a lower hybrid pump wave with a finite wavelength is investigated. The density inhomogeneity introduces dephasing that restricts the interaction region where the matching conditions hold. The loss of energy due to convection from this region introduces a certain convection threshold for the onset of this instability. The coupled differential equations are solved in Fourier space by converting them into an uncoupled eigenvalue equation and then applying a quantization condition. Expressions are obtained for the growth rate and the convective threshold, and the results are applied to the Princeton Large Torus parameters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Measurements of energetic helium-3 minority distributions during ion cyclotron radiofrequency heating in the princeton Large Torus

Ion cyclotron radiofrequency heating experiments were performed with a 3He minority ion species in a 4He majority plasma in the Princeton Large Torus. The energetic 3He ion ‘tail’ was measured directly with a charge exchange neutral analyser for the first time. Comparisons with bounce averaged quasi-linear calculations suggest a modestly peaked radiofrequency power deposition profile. The double charge exchange process 3He++ + 4He0 → 3He0 + 4He++ demonstrated in these measurements may be useful as part of an alpha particle diagnostic in a fusion reactor experiment.

Measurements with vertically viewing charge exchange analyzers during ion cyclotron range of frequencies heating in TFTR

The utility of charge exchange neutral particle analyzers for studying energetic ion distributions in high-temperature plasmas has been demonstrated in a variety of tokamak experiments. Power deposition profiles have been estimated in the Princeton large torus (PLT) from particle measurements as a function of energy and angle during heating in the ion cyclotron range of frequencies (ICRF) and extensive studies of this heating mode are planned for the upcoming operational period in the tokamak fusion test reactor (TFTR). Unlike the horizontally scanning analyzer on PLT, the TFTR system consists of vertical sightlines intersecting a poloidal cross section of the plasma. A bounce-averaged Fokker–Planck program, which includes a quasilinear operator to calculate ICRF-generated energetic ions, is used to simulate the charge exchange flux expected during fundamental hydrogen heating. These sightlines also cross the trajectory of a diagnostic neutral beam (DNB), and it may be possible to observe the fast ion tail during 3He minority heating, if the DNB is operated in helium for double charge exchange neutralization.

Spectra in the 60345-Å wavelength region of the elements Fe, Ni, Zn, Ge, Se, and Mo injected into the Princeton Large Torus tokamak

High-resolution spectra of the elements Fe, Ni, Zn, Ge, Se, and Mo injected into the Princeton Large Torus tokamak were recorded by the 2-m Schwob–Fraenkel soft-x-ray multichannel spectrometer. Spectra were recorded every 50 msec during the times before and after injection. The spectral lines of the injected element were very strong in the spectrum recorded immediately after injection, and the transitions in the injected element were easily distinguished from the transitions in the intrinsic elements (C, O, Ti, Cr, Fe, and Ni). An accurate wavelength scale was established using well-known reference transitions in the intrinsic elements. The spectra recorded just before injection were subtracted from the spectra recorded after injection, and the resulting spectrum was composed almost entirely of transitions from the injected element. A large number of Δn = 0 transitions between the ground and the first excited configurations in the Li i through K i isoelectronic sequences of the injected elements were identified in the wavelength region 60 to 345 A.

X-ray transitions in highly charged neonlike ions.

Wavelength measurements of n=3 to n=2 transitions in neonlike ${\mathrm{Xe}}^{44+}$, ${\mathrm{La}}^{47+}$, ${\mathrm{Nd}}^{50+}$, and ${\mathrm{Eu}}^{53+}$ have been made using a high-resolution Bragg-crystal spectrometer on the Princeton Large Torus tokamak. The measurements cover the wavelength regions 2.00--3.00 A\r{} and include the electric dipole and the electric and magnetic quadrupole transitions. The measured wavelengths are compared to energy levels obtained from a multiconfigurational Dirac-Fock calculation. Systematic differences between the experimental and theoretical values are found, which vary smoothly with atomic number. The magnitude of the differences depends on the particular type of transition and ranges from -2.8 eV to +2.2 eV. Inclusion of electron correlation corrections due to ground-state correlations and (super-) Coster-Kronig-type fluctuations in the theoretical energies is shown to reduce the differences for some but not all types of transitions.

Wavelengths for the 3s^2 1S_0–3s3p^3P_1 transition of the magnesiumlike ions Fe^14+ through Nd^48+

The wavelengths of the 3s2 1S0–3s3p3P1 transition for the magnesiumlike ions Zn18+, Ge20+, Se22+, Mo30+, Sn38+, and Xe42+ have been measured in spectra from the Princeton Large Torus tokamak. When we compare these and other recently available observations with wavelengths calculated using Grant’s multiconfiguration Dirac–Fock program, wavelengths are predicted for the ions Fe14+ through Nd48+.

Effect on Deuteron Temperature on Iron Forbidden Line Intensities in RF-Heated Tokamak Plasmas

AbstractTwo line ratios, the forbidden line at 845.5 Å to the allowed line at 135.7 Å in Fe XXII and the forbidden line at 592.1 Å to the forbidden line at 1118.2 Å in Fe XIX, have been measured as ion temperature-sensitive line ratios during rf heating in the Princeton Large Torus. The results indicate that deuteron collisions in plasmas of high deuteron temperature have a noticeable effect on the intensity of the forbidden lines. Measured relative intensities are compared with values from level population calculations which include deuteron collisional excitation between the levels of the ground configuration. The agreement between the observed and calculated ratios is within 30%. A method for deuteron (or proton) temperature measurement in tokamak plasmas is discussed.1More details about this experiment can be found in Ref. 2.

Synchrotron radiation from dynamically evolving runaway tails

A quasilinear code (2-D in velocity and wave vector space) based on the Ritz–Galerkin method and finite elements is used to study the synchrotron emission from a dynamically evolving runaway tail. The evolution of runaway tails was studied recently using the same code [Phys. Fluids 28, 3356 (1985)]. The velocity distribution derived from the above code is used to estimate the synchrotron radiation in different time steps. The applicability of these results to the Princeton Large Torus [Phys. Rev. Lett. 49, 1255 (1982)] and solar microwave bursts is also commented on.