Self-consistent equilibria in a cylindrical reversed-field pinch

Summary A previous investigation by one of us, concerning the self-consistent equilibria of a two-region (plasma+gas) cylindrical Tokamak, is extended to the similar equilibria of a Reversed-Field Pinch, where a significant current density is driven by a dynamo electric field due to turbulence. The previous model has been generalized under the following basic assumptions:a) to the lowest order, the turbulent dynamo electric fieldE ^t is expressed as a homogeneous function of degree 1 of the magnetic fieldB, sayE ^t =α·B, with α being a 2nd-rank tensor, homogeneous of degree 0 inB, and generally depending on the plasma state;b)E ^t does not appear in the plasma power balance, as if it were produced by a Maxwell demon able to extract the needed power from the plasma internal energy. In particular we show that, in the simplest case when both α and the plasma resistivity η are isotropic and constant, the magnetic field turns out force-free with constant abnormality αμ₀/η for vanishing axial electric fieldE _z . This case has also been solved analytically, for whateverE _z , under circular, besides cylindrical, symmetry.     

Mode locking in reversed-field pinch experiments

The MHD mode trajectory in the Madison Symmetric Torus reversed-field pinch has been found to obey the sine-Gordon equation. Corresponding to experiment, a perturbation analysis predicts the locations of mode locking to be at the vacuum chamber poloidal and/or toroidal gaps. The mode's energy dissipates when it locks, as shown by a decaying spiral phase-plane trajectory. Unlocked modes travel around the torus without an abrupt energy loss. By varying key machine parameters obtained by statistical analysis, the probability of locking in accordance with the experimental results can be predicted.     

Core electrostatic fluctuations and particle transport in a reversed-field pinch

Potential and electron-density fluctuation profiles, phi(r) and ?(e)(r)/n(e), are measured for the first time in the core of a reversed-field pinch using a heavy ion beam probe. It is found that the fluctuations are broadband and correlated with the core resonant m/n=1/6 tearing mode. The electrostatic-fluctuation-induced particle transport in the core of standard RFP plasmas, estimated from measured , is small compared to the total particle flux. Measurements of fluctuations and estimates of fluctuation induced particle transport in improved confinement RFP discharges are also presented.     

Neoclassical transport in the helical reversed-field pinch

Test particle evaluation of the diffusion coefficient in a fusion plasma in the reversed-field pinch (RFP) configuration shows distinct similarities with stellarators when the plasma spontaneously evolves towards a helical shape. The almost total absence of superbanana particles at the levels of helical deformation seen in experiment (Bh/B=10%) causes transport to be proportional to collision frequency (at low collisions). This fact excludes the possibility that the minimum conceivable transport could be inversely proportional to collision frequency, which is typical of unoptimized stellarators. This result strengthens the perspectives of the helical RFP as a fusion configuration.     

Confinement scaling laws for the conventional reversed-field pinch

Mechanical behavior of the Si(111)/Si(3)N4(0001) interface is studied using million atom molecular dynamics simulations. At a critical value of applied strain parallel to the interface, a crack forms on the silicon nitride surface and moves toward the interface. The crack does not propagate into the silicon substrate; instead, dislocations are emitted when the crack reaches the interface. The dislocation loop propagates in the (1; 1;1) plane of the silicon substrate with a speed of 500 (+/-100) m/s. Time evolution of the dislocation emission and nature of defects is studied.     

Control of density fluctuations and electron transport in the reversed-field pinch

Contrary to what has been observed thus far collision-induced light scattering (CILS) can be completely polarized. This exceptional behavior characterizes the very far wing of the binary CILS spectrum by gaseous helium. This conclusion is drawn from an experimental study of the depolarization ratio of He (2) in a much extended, previously unexplored, spectral domain. Our analysis shows that this property, unique thus far, is mainly due to an almost perfect cancellation between polarization and exchange pair polarizability contributions to the depolarized spectrum, taking place at internuclear distances shorter than the atomic diameter.     

Effects of anisotropic thermal conductivity in magnetohydrodynamics simulations of a reversed-field pinch

A compressible magnetohydrodynamics simulation of the reversed-field pinch is performed including anisotropic thermal conductivity. When the thermal conductivity is much larger in the direction parallel to the magnetic field than in the perpendicular direction, magnetic field lines become isothermal. As a consequence, as long as magnetic surfaces exist, a temperature distribution is observed displaying a hotter confined region, while an almost uniform temperature is produced when the magnetic field lines become chaotic. To include this effect in the numerical simulation, we use a multiple-time-scale analysis, which allows us to reproduce the effect of a large parallel thermal conductivity. The resulting temperature distribution is related to the existence of closed magnetic surfaces, as observed in experiments. The magnetic field is also affected by the presence of an anisotropic thermal conductivity.     

Application of microwave reflectometry for plasma density diagnostics in a reversed-field pinch machine

The implementation of reflectometry as a means of measuring plasma density is examined in relation to the reversed-field pinch machine. The effects of magnetic shear and density fluctuations are studied. Ray-tracing and simulation results are presented and the proposed reflectometer system for the RFX reversed-field pinch machine is described.     

Measurements of the MHD dynamo in the quasi-single-helicity reversed-field pinch

The first experimental study of the MHD dynamo in a quasi-single-helicity (QSH) reversed-field pinch toroidal plasma is presented. In QSH plasmas, a dominant wave number appears in the velocity fluctuation spectrum. This velocity component extends throughout the plasma volume and couples with magnetic fluctuations to produce a significant MHD dynamo electric field. The narrowing of the velocity fluctuation spectrum and the single-mode character of the dynamo are features predicted by theory and computation, but only now are observed in experiment.     

Measurement of internal magnetic field fluctuations in a reversed-field pinch by Faraday rotation

Magnetic field fluctuations (and the associated current perturbation) have been measured in the core of a high-temperature reversed-field pinch using a newly developed fast-polarimetry system. Radial magnetic field fluctuation levels of approximately 1% are measured in standard-reversed-field pinch discharges which increase to approximately 4% during the sawtooth crash (enhanced dynamo). The fluctuation level is reduced fourfold for high-confinement plasmas where the core-resonant tearing modes are suppressed.     

Improved particle confinement in transition from multiple-helicity to quasi-single-helicity regimes of a reversed-field pinch

The quasi-single-helicity (QSH) state of a reversed-field pinch (RFP) plasma is a regime in which the RFP configuration can be sustained by a dynamo produced mainly by a single tearing mode and in which a helical structure with well-defined magnetic flux surfaces arises. In this Letter, we show that spontaneous transitions to the QSH regime enhance the particle confinement. This improvement is originated by the simultaneous and cooperative action of the increase of the magnetic island and the reduction of the magnetic stochasticity.     

Measurement of the current-density profile and plasma dynamics in the reversed-field pinch

First measurements of the current-density profile in the core of a high-temperature reversed-field pinch are presented. The current-density profile is observed to peak during the sawtooth cycle and broaden promptly at the crash. This change in profile can be linked to magnetic relaxation and the dynamo which is predicted to drive antiparallel current in the plasma core. For high-confinement discharges, the dynamo is suppressed and the current-density profile is observed to strongly peak.     

Nonambipolar magnetic-fluctuation-induced particle transport and plasma flow in the MST reversed-field pinch

First direct measurements of nonambipolar magnetic fluctuation-induced charge transport in the interior of a high-temperature plasma are reported. Global resistive tearing modes drive the charge transport which is measured in the vicinity of the resonant surface for the dominant core resonant mode. Finite charge transport has two important consequences. First, it generates a potential well along with locally strong electric field and electric field shear at the resonant surface. Second, this electric field induces a spontaneous E x B driven zonal flow.     

Spectroscopic observation of fluctuation-induced dynamo in the edge of the reversed-field pinch

The fluctuation-induced dynamo has been investigated by direct measurement of v and b in the edge of a reversed-field pinch and is found to be significant in balancing Ohm's law. The velocity fluctuations producing the dynamo emf have poloidal mode number m = 0, consistent with MHD calculations and in contrast with the core m = 1 dynamo. The velocity fluctuations exhibit the parity relative to their resonant surface predicted by linear MHD theory.     

Investigation of electron-distribution function and dynamo mechanisms in a reversed-field pinch by analysis of hydrogen-pellet deflection

In reversed-field pinches, two different mechanisms have been proposed to explain the dynamo process which drives the poloidal current needed to sustain the magnetic configuration: the kinetic dynamo theory and the magnetohydrodynamic (MHD) dynamo theory. Experimentally, they can be distinguished by the radial behavior of the electron distribution function. In this Letter the trajectory deflection of frozen hydrogen pellets has been used as a diagnostic of suprathermal electrons in the plasma. The classical Spitzer-Harm distortion of the electron distribution function consistent with the MHD dynamo electric field is found to give a better modeling of the pellet trajectory.     

Transport barrier inside the reversal surface in the chaotic regime of the reversed-field pinch

Magnetic field lines and the corresponding particle orbits are computed for a typical chaotic magnetic field provided by a magnetohydrodynamics numerical simulation of the reversed-field pinch. The m = 1 modes are phase locked and produce a toroidally localized bulging of the plasma which increases particle transport. The m = 0 and m = 1 modes produce magnetic chaos implying poor confinement. However, they also allow for the formation of magnetic islands which induce transport barriers inside the reversal surface.     

The charactization of high-speed swept reflectometer for plasma diagnostics on the RFX reversed-field pinch

An ordinary mode IMPATT-based reflectometer operating over 26.5–110GHz has been developed for density diagnostic application on the RFX reversedfield pinch experimental fusion machine. The reflectometer uses polarization rotators located at the antennas for optimizing the polarization of the emitted E-field A sweep speed of 1.25ms for the full band is possible. Single subbands may be swept at a rate of 200us. The provision of polarization rotators and high-speed solid-state oscillators maximises the immunity of the system to the effects of high fluctuation frequencies and mode mixing due to high magnetic shear. The reflectometer uses an IMPATT oscillator system for the source which has not been used in previous reflectometer circuits. A previously unachievable temporal resulution is therefore available with this system. The reflectometer is the first to be developed for use on a reversed-field pinch (RFP) machine.Verification of reflectometer operation was achieved using plane metal targets to simulate the reflecting plasma cut-off layer. Targets were located at various distances from the antennas to cover the expected spatial reflection range. The theoretical and experimental characteristics were obtained by processing the intermediate frequency output of the detectors. Spurious signals are removed by calibrating the target data using residual fringe data. A zero-crossing detection algorithm was developed to accurately identify the beat fringes and to deduce the phase/frequency characteristic. Single subband and full sweep results are presented.