Non-axisymmetric Plasma Research Articles

Z eff profile diagnostics using visible bremsstrahlung continuum for nonaxisymmetric plasmas with finite β in large helical device

An astigmatism-corrected Czerny–Turner-type visible spectrometer coupled with a charge-coupled device has been installed in large helical device (LHD) to measure visible bremsstrahlung continuum. A full vertical profile has been observed from the elliptical plasmas at horizontally elongated plasma cross section through a 44 fiber parallel array with vertical observation length of ∼1 m. Line emissions can be easily eliminated by use of the visible spectrometer instead of an interference filter. A nonmonotonic bremsstrahlung emission profile, which is originated in the thick ergodic layer surrounding the main plasma, has been observed for normal discharges in all the magnetic configurations of LHD. After analyzing the detailed structure, the lower half of the vertical bremsstrahlung emission profile is found to be free of the strong edge bremsstrahlung emission in inwardly shifted magnetic configurations (Rax≤3.60 m). The nonmonotonic bremsstrahlung emission disappeared in extremely high-density discharges (ne≥1014 cm−3) because of the reduction of the plasma outside boundary. When the local emissivity is calculated using Abel inversion, the solution is very sensitive to the distortion of the magnetic surface structure. The influence of the magnetic surface distortion based on the finite β effect is examined as error estimation in addition to unclear edge plasma boundary due to the presence of the ergodic layer. The result indicates that the determination of the normalized minor radius for each observation chord gives a larger influence on the Abel inversion rather than the determination of the chord length. When the observed chord-integrated bremsstrahlung intensity profile is flat, the resultant uncertainty seen in the bremsstrahlung emissivity profile becomes large, in particular, at the plasma center. The Zeff profile calculated with consideration of density and temperature profiles is verified in neutral-beam-heated discharges with H2 and C pellet injections, where the Zeff values should be close to 1 and 6, respectively. Analysis on the flat and hollow electron density profiles results in a fairly flat Zeff profile.

Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria

The first quantitative comparison of linear ideal magnetohydrodynamic (MHD) theory with external magnetic measurements of the nonaxisymmetric plasma perturbation driven by external long-wavelength magnetic fields in high-temperature tokamak plasmas is presented. The comparison yields good (within 20%) agreement for plasma pressures up to ∼75% of the ideal stability limit calculated without a conducting wall. For higher plasma pressures, the ideal MHD model tends to overestimate the perturbed field indicating the increasing importance of stabilizing nonideal effects.

Phase diagram for non-axisymmetric plasma balls

Plasma balls and rings emerge as fluid holographic duals of black holes and black rings in the hydrodynamic/gravity correspondence for the Scherk-Schwarz AdS system. Recently, plasma balls spinning above a critical rotation were found to be unstable against m-lobed perturbations. In the phase diagram of stationary solutions the threshold of the instability signals a bifurcation to a new phase of non-axisymmetric configurations. We find explicitly this family of solutions and represent them in the phase diagram. We discuss the implications of our results for the gravitational system. Rotating non-axisymmetric black holes necessarily radiate gravitational waves. We thus emphasize that it would be important, albeit possibly out of present reach, to have a better understanding of the hydrodynamic description of gravitational waves and of the gravitational interaction between two bodies. We also argue that it might well be that a non-axisymmetric m-lobed instability is also present in Myers-Perry black holes for rotations below the recently found ultraspinning instability.

Moment approach to the bootstrap current in nonaxisymmetric toroidal plasmas using δf Monte Carlo methods

To evaluate the bootstrap current in nonaxisymmetric toroidal plasmas quantitatively, a δf Monte Carlo method is incorporated into the moment approach. From the drift-kinetic equation with the pitch-angle scattering collision operator, the bootstrap current and neoclassical conductivity coefficients are calculated. The neoclassical viscosity is evaluated from these two monoenergetic transport coefficients. Numerical results obtained by the δf Monte Carlo method for a model heliotron are in reasonable agreement with asymptotic formulae and with the results obtained by the variational principle.

Recycling studies based on two-dimensional visible light measurements and Monte-Carlo simulation in mirror and helical systems

Analysis of neutral particle behavior in the GAMMA 10 tandem mirror with open magnetic field and the Heliotron J device with non-axisymmetric plasma confining system is described based on the results of Monte-Carlo neutral transport simulation. Three-dimensional (3-D) Monte-Carlo code DEGAS was applied to both devices in order to investigate precisely the spatial distribution of neutral particle density. In GAMMA 10, a detailed structure of inner components of the central-cell is modeled in the simulation space. In Heliotron J, a carbon limiter inserted into the plasma for investigation of plasma-material interactions is also modeled in addition to the helically twisted vacuum vessel and plasma. In both devices, 2-D images of light-emission from the plasma captured with CCD cameras near the limiters are compared with the simulation results and a good agreement between experiment and simulation is recognized. Comparison of the decay length in the emissivity of Hα/Dα line-emission also showed that neutral transport in SOL region plays a significant influence on the emission profile.

Three-dimensional modeling of the plasma arc in arc welding

Most previous three-dimensional modeling on gas tungsten arc welding (GTAW) and gas metal arc welding (GMAW) focuses on the weld pool dynamics and assumes the two-dimensional axisymmetric Gaussian distributions for plasma arc pressure and heat flux. In this article, a three-dimensional plasma arc model is developed, and the distributions of velocity, pressure, temperature, current density, and magnetic field of the plasma arc are calculated by solving the conservation equations of mass, momentum, and energy, as well as part of the Maxwell’s equations. This three-dimensional model can be used to study the nonaxisymmetric plasma arc caused by external perturbations such as an external magnetic field. It also provides more accurate boundary conditions when modeling the weld pool dynamics. The present work lays a foundation for true three-dimensional comprehensive modeling of GTAW and GMAW including the plasma arc, weld pool, and/or electrode.

High accuracy plasma density measurement using hybrid Langmuir probe and microwave interferometer method

High spatial resolution plasma density measurements have been taken as part of an investigation into magnetic nozzle physics at the NASA/MSFC Propulsion Research Center. These measurements utilized a Langmuir triple probe scanned across the measurement chord of either of two stationary rf interferometers. By normalizing the scanned profile to the microwave interferometer line-integrated density measurement for each electrostatic probe measurement, the effect of shot-to-shot variation of the line-integrated density can be removed. In addition, by summing the voltage readings at each radial position in a transverse scan, the line density can be reconstituted, allowing the absolute density to be determined, assuming that the shape of the profile is constant from shot to shot. The spatial and temporal resolutions of this measurement technique depend on the resolutions of the scanned electrostatic probe and the interferometer. The measurement accuracy is 9%-15%, which is on the order of the accuracy of the rf interferometer. The measurement technique was compared directly with both scanning rf interferometer and standard Langmuir probe theory. The hybrid technique compares favorably with the scanning rf interferometer, and appears more accurate than probe theory alone. Additionally, our measurement technique is generally applicable even for nonaxisymmetric plasmas.

A 3-D Integral formulation coupled to a rigid nonaxisymmetric plasma model

In this paper, we analyze the initial phase of an asymmetric plasma displacement event in a tokamak. We assume a rigid model of the plasma and a three-dimensional model of the conducting structures. A volume-integral eddy current formulation is coupled to force and torque balance in the plasma

Reconstruction of laser-induced plasma spectral emissivity in non-axisymmetric conditions

The problem of determining the spectral emissivity in each spatial position of a laser induced plasma is extremely important in order to calculate the spatial distributions of physical and thermodynamical parameters characterizing the plume. Supposing that the plume is optically thin and axisymmetric, the problem is theoretically solved by the Abel inversion of the integral spectral emission. The work presented here is a generalization of the Aguilera et al. method of solving the Abel inversion, based on the modelization of the plume by discrete shells of constant emissivity, in the case of slightly non-axisymmetric plasmas. Some tests and examples of the application of the new algorithm are given.

Three-dimensional plasma structure reconstruction from mutually orthogonal streaks of nonaxisymmetric laser-produced plasma plumes

A method is developed for structure reconstruction of an arbitrary plasma from two luminosity streaks and a front-view snapshot as a weighting function (WF). Two scaling relations link the pressure and temperature to the local specific emission intensity. A trial plasma structure is proposed in terms of specific intensity, and the luminosity streaks are calculated according to the Saha equilibrium. Plasma absorption is included. Error signals between the calculated and measured luminosity are allocated according to the WF to find corrections to local specific intensities. Minimization of the errors completes the reconstruction at a given time, which in turn updates the WF for the next time step. Summing over the full plasma over time facilitates calculation of the total plasma mass, energy and beam attenuation through the plasma. When agreement with their measured counterparts is maximized, the scaling relations are calibrated.

Shear Alfvén mode resonances in nonaxisymmetric toroidal low-pressure plasmas. I. Mode equations in arbitrary geometry

Field line coordinates are used to obtain a concise set of three coupled partial differential equations for the modes in ideal magnetohydrodynamic plasmas of arbitrary geometry. Zero plasma pressure is assumed throughout. The shear Alfvén continuum and the pressureless remnant of the ballooning continuum are readily obtained in a unifying manner. The qualitative differences and similarities of both spectra are discussed. The equations are suitable, in particular, for the study of the spatial dependence of continuum modes close to singular magnetic surfaces or field lines.

Shear Alfvén mode resonances in nonaxisymmetric toroidal low-pressure plasmas. II. Singular modes in the shear Alfvén continuum

The spatial dependence of modes in the shear Alfvén continuum of nonaxisymmetric toroidal magnetohydrodynamic plasma equilibria of zero pressure is investigated theoretically. As in configurations with plane or axial symmetry it is found that these modes may exhibit a singularity extended across whole “singular” magnetic surfaces. However, with nonaxisymmetry in the zero pressure approximation a logarithmic singularity appears in general rather than the oscillatory singularity of an axisymmetric plasma. If the nonaxisymmetry is too strong, the surface-covering property of the singular modes may be lost.

Overview of large helical device diagnostics (invited)

The Large Helical Device (LHD) is the largest helical machine with superconducting coils. Key diagnostics issues for LHD are: (a) capability for multidimensional measurements because of the nonaxisymmetric toroidal plasma; (b) measurements of the electric field; (c) cross check of fundamental parameters using different methods; (d) advanced measurements appropriate for steady-state operation; and (e) a satisfactory data acquisition system. The design and research and development of plasma diagnostics were carried out taking these issues into consideration. As a result, the present status of diagnostics is described: diagnostics for LHD operation, fundamental diagnostics for plasma performance, diagnostics for physics subjects, innovative diagnostics and diagnostics for long-pulse operation. The LHD experiment started in March, 1998. Since then, the development of diagnostics has kept pace with the experimental campaigns.

Reconstruction of time-resolved continuum intensity profile of nonaxisymmetric laser-produced plasma

A single laser pulse is used to produce weakly nonideal plasma from a metallic aluminum target immersed in a dense neutral gas. The attendant increase in plasma density due to neutral gas confinement precipitates interfacial instability when the gas density exceeds a threshold value. This is accompanied by large fluctuations in the total attenuation of the laser beam by the laser-produced plasma plume. We have developed a new diagnostic method utilizing two mutually orthogonal side-view streak photographs of plasma continuum luminosity at a fixed distance from the target surface. The lack of axial symmetry is overcome by using a front-view luminosity image of the plasma at time zero as a two-dimensional weighting factor. The resulting profile at one time is used as the weighting factor for the next time segment. The time-resolved reconstructed plasma profiles clearly exhibit the near-threshold behavior of Rayleigh–Taylor type instability.

5-D simulation study of suprathermal electron transport in non-axisymmetric plasmas

ECRH driven transport of suprathermal electrons is studied in non-axisymmetric plasmas using a new Monte Carlo simulation technique in 5-D phase space. Two different phases of the ECRH driven transport of suprathermal electrons can be seen. The first is a rapid convective phase due to the direct radial motion of trapped electrons and the second is a slower phase due to the collisional transport. The important role of the radial transport of suprathermal electrons in the broadening of the ECRH deposition profile in W7-AS is clarified. The ECRH driven flux is also evaluated and considered in relation to the `electron root' feature recently observed in W7-AS. It is found that, at low collisionalities, the ECRH driven flux due to the suprathermal electrons can play a dominant role in the condition of ambipolarity, and thus the observed electron root feature in W7-AS is thought to be driven by the radial (convective) flux of ECRH generated suprathermal electrons. A possible scenario for this type of electron root is considered for the LHD plasma.

Drift wave simulations with reduced stellarator equilibria

A three-field model to study drift-resistive, low-frequency waves in low-β, nonaxisymmetric plasmas [J. L. V. Lewandowski, Phys. Plasmas 4, 4023 (1997)] is used to analyze the effect of the inhomogeneities in the stellarator magnetic field on the fastest (linear) growth rate, γ. Extensive numerical calculations for a toroidal heliac show that not all Fourier components in the representation of the equilibrium configuration are important as far as γ is concerned.

Neoclassical Heat Flux Due to Poloidally and Toroidally Varying Electrostatic Potential in Nonaxisymmetric Toroidal Plasmas

A poloidally and toroidally varying electrostatic potential due to the perpendicular ion drift and its effect on the radial heat flux are studied in the plateau regime for a nonaxisymmetric toroidal plasma. This potential produces an enhancement by one order of magnitude in the electron heat flux, whereas an increase of the ion heat flux is modest. Moreover, these radial electron and ion heat fluxes due to this potential are found to be inward in a stellarator satisfying the conditions m e 2 h >2 e t 2 and n q - m >0, where q is the safety factor, n and m are the numbers of the toroidal field periods and the helical field coils, and e t and e h are the toroidal and the helical magnetic field modulations.

A method for calculating neoclassical transport coefficients with momentum conserving collision operator

A method for calculating the neoclassical transport coefficients in a nonaxisymmetric multispecies plasma is developed by employing a momentum conserving collision operator. In this method, the parallel current, and the radial particle and heat fluxes are expressed in terms of the transport coefficients which can be obtained by solving the drift kinetic equations with the pitch-angle scattering collision operator. These expressions can be easily incorporated into the existing numerical codes including the pitch-angle scattering collisions only.

On the definition of Pfirsch–Schlüter and bootstrap currents in toroidal systems

In the plasma physics literature there appear two different definitions of Pfirsch–Schlüter current. One of them is predominantly used in equilibrium calculations and satisfies the condition IT=0. The other definition appears commonly in transport calculations and requires that the surface average of the dot product of the Pfirsch–Schlüter current density with the magnetic field vanish, i.e., 〈JPS⋅B〉=0. The difference between the definitions is a surface function. Within the framework of the moment equation approach, the total parallel current is completely determined through a surface average of Ohm’s law; thus different definitions of Pfirsch–Schlüter current imply different expressions for the bootstrap current. Understanding the different implications of these two definitions is of particular importance when designing toroidal devices with minimized Pfirsch–Schlüter current or studying tokamaks with optimized bootstrap current. In this paper the definitions of Pfirsch–Schlüter and bootstrap current, as well as the expressions for the corresponding Pfirsch–Schlüter diffusion flux, are analyzed and discussed for the case of axisymmetric and nonaxisymmetric plasmas. Although in cases like a current-free stellarator or a large-aspect-ratio tokamak both definitions are equivalent, they are in general different, and in order to avoid misunderstandings it is therefore important to use only one. The most appropriate definition is IT=0. In this paper the equations for determining the bootstrap current within the framework of the fluid equations are also analyzed.

Introduction to Confinement of Toroidal Plasma. 2. MHD Equilibrium of Toroidal Plasmas and Properties of Magnetic Surfaces.

MHD equilibrium of toroidal plasmas is discussed for both axisymmetric toroidal plasmas such as tokamak and reversed field pinch, and non-axisymmetric toroidal plasmas such as stellarator, heliotron and torsatron. The contents are; 1) Production of rotational transform, 2) Three-dimensional MHD equilibrium and Grad-Shafranov equation which includes (i) a generalized Grad-Shafranov equation, (ii) Grad-Shafranov equation under stellarator approximation, (iii) FCT equilibrium and currentless equilibrium, and (iv) Solove'v-Shafranov equilibrium equation, 3) Magnetic shear and magnetic well, 4) MHD equilibrium and magnetic islands, and 5) MHD equilibrium and equilibrium data analysis.It is emphasized that MHD equilibrium of stellarator/heliotron can be studied by generalizing Grad-Shafranov equation for tokamaks. MHD equilibrium of spatial axis stellarator is also discussed based on Solove'v-Shafranov equilibrium equation.