Reversed Field Experiment Research Articles

A wave-particle interaction model for tail ion acceleration in reversed field pinch plasmas

In the reversed field pinch plasmas produced by the reversed field experiment (RFX), neutral particle measurements reveal the presence in the radial direction of a small population of non-thermal energetic ions (E = 103 eV to 8 × 103 eV). In this work supra-thermal electrons at the plasma edge are considered to be the free-energy source for the ion acceleration. Fast electrons, moving in the same direction of the main magnetic field, excite an ~pi electrostatic wave which gives energy to the ions which are accelerated in the direction perpendicular to the local equilibrium magnetic field. The theoretical predictions for the neutral particle fluxes are in agreement with the experimental measurements. Moreover, a correlation between the experimental fast-ion and fast-electron energy densities has been found.

Effect of a resistive vacuum vessel on dynamo mode rotation in reversed field pinches

Locked (i.e., nonrotating) dynamo modes give rise to a serious edge loading problem during the operation of high current reversed field pinches. Rotating dynamo modes generally have a far more benign effect. A simple analytic model is developed in order to investigate the slowing down effect of electromagnetic torques due to eddy currents excited in the vacuum vessel on the rotation of dynamo modes in both the Madison Symmetric Torus (MST) [Fusion Technol. 19, 131 (1991)] and the Reversed Field Experiment (RFX) [Fusion Eng. Des. 25, 335 (1995)]. This model strongly suggests that vacuum vessel eddy currents are the primary cause of the observed lack of mode rotation in RFX. The eddy currents in MST are found to be too weak to cause a similar problem. The crucial difference between RFX and MST is the presence of a thin, highly resistive vacuum vessel in the former device. The MST vacuum vessel is thick and highly conducting. Various locked mode alleviation methods are discussed.

Improved confinement and transport studies in the reversed field experiment (RFX)

This paper presents results obtained on the Reversed Field eXperiment, RFX [G. Rostagni, Fusion Engineering and Design 25, 301 (1995)], on the study of local transport properties of the RFP configuration both in the standard regime and during improved confinement phases obtained with poloidal current drive. The plasma core is dominated by magnetic turbulence, as indicated by both energy and particle transport analysis. Diffusivity decreases toward the edge and is reduced in the core at high Lundquist number. The edge region is apparently not affected by dynamo mode turbulence and determines global confinement in standard operation. Particle and heat diffusivity in this region show a favorable dependence with increasing density. The most interesting feature of the edge region of RFX consists of a sheared radial electric field with shearing rate comparable to that observed in tokamaks. Indications of turbulence reduction in the shear layer have been obtained. Enhanced energy confinement has been produced by pulsed poloidal current drive (PPCD). A clear reduction of the dynamo activity has been observed with a decrease of core thermal diffusivity to level comparable to the edge and global confinement improvement up to a factor of 3.

Requirements for an active spectroscopy diagnostic with neutral beams on the RFX reversed field pinch

The conceptual feasibility of an active spectroscopic diagnostic on reversed field experiment (RFX) to measure the radial profiles of ion temperature, toroidal and poloidal drift velocities, and main impurity densities is examined. In particular a charge exchange recombination spectroscopy experiment is simulated for carbon and helium impurities. The motional Stark effect on the beam atoms injected into RFX is estimated as a means to measure the magnetic field pitch and intensity. A modulated beam injector (500 Hz) with 2 A of equivalent current and an energy of 50 keV/amu appears to be adequate to perform the measurements over a reasonable range of operational regimes.

Signal processing and calibration electronics for the metal foil bolometers of RFX

A new signal processing and calibration electronics, expressly designed to be used together with the tomographic diagnostic's metal foil bolometers of RFX (a Reversed Field eXperiment for the study of thermonuclear fusion), is presented in detail. The detectors are Wheatstone bridges, which are unbalanced by the incident radiation originating from the plasma. In this version, a suppressed-carrier amplitude modulation technique is implemented using 50 kHz carrier frequency amplifiers, which permit a signal bandwidth of 10 kHz and a voltage amplification up to 5000. Directly after amplification, filtering and demodulation, the analog signals are sampled in the torus hall and digitized. The digitized signal is optically sent to the VME acquisition boards with a TAXI (Transparent Asynchronous Xmitter/receiver Interface) link. A customized circuitry has also been developed for the absolute calibration of the gain settings and the bandwidths of the electronics. This paper contains a detailed description of the circuits, the results of the bench tests and the analysis of the performances of both the amplification and the calibration electronics. The results obtained during RFX operation, the nature of the noise present in the experimental conditions and possible upgrades of the system are also shown and discussed.

Search for low-dimensional chaos in a reversed field pinch plasma

An analysis of experimental data from the reversed field experiment (RFX) reversed field pinch machine [L. Fellin, P. Kusstatscher, and G. Rostagni, Fusion Eng. Des. 25, 315 (1995)] is carried out to investigate the possible existence of deterministic chaos in the edge plasma region. The mathematical tools used include Lyapunov exponents, Kaplan–Yorke dimension, minimum embedding dimension estimates and nonlinear forecasting. The whole analysis agrees in ruling out the possibility of low-dimensional chaos: The dimension of the underlying dynamical system is estimated to be >10. From a critical rereading of the literature it emerges that the findings of this work are likely to be common to all reversed field pinches.

Plasma rotation and finite Larmor radius losses in a reversed field pinch

A model is proposed to calculate the effect of particle and momentum losses due to unconfined ion orbits at the edge of the plasma in a reversed field pinch device. The value of the shearing rate can be obtained, requiring that the electromagnetic force due to the return current in the confined plasma is equilibrated by the reaction force due to direct ion momentum losses. A natural scaling of the shearing rate with the ion cyclotron frequency is obtained by assuming that this equilibrium is achieved through the effect of orbit squeezing caused by the finite value of the radial electric field gradient. The extension of the shear layer has been obtained requiring that the contribution of charge exchange viscosity to the perpendicular momentum balance is negligible. A shear layer width scaling as the Larmor radius is obtained. The scaling relations derived account for recent observations obtained in the reversed field experiment, RFX [G. Rostagni, Fusion Eng. Des. 25, 301 (1995)]. A quantitative comparison with experimental data indicates that impurities in low ionization stages can play an important role in the shear layer dynamics.

The ultra-soft x-ray multilayer mirror-based duochromator for the reverse field experiment reversed field pinch experiment

The ultra-soft x-ray duochromator based on two multilayer mirrors installed on the reversed field pinch experiment (RFX) reversed field pinch is described. Built at the Budker Institute of Nuclear Physics of Novosibirsk, it has been designed to monitor the time behavior of the hydrogen and helium-like resonant transitions of carbon and oxygen, the main impurities in the RFX emission spectrum, with the possibility of scanning the wavelengths between 16 and 45 Å. The wavelengths can be independently selected for both the mirrors (made of Ni/C and Cr/C layers, respectively) via a Θ–2Θ mechanism, without breaking the vacuum. The detector is based on a scintillator layer deposited on the head of a photomultiplier. Vacuum ultraviolet and visible radiation is cut by means of thin metal films (Fe, Al, Cr) deposited on a mylar substrate and on the scintillator. The wavelength resolution (λ/Δλ) of 40 to 50 in the region of interest is provided by a Soller collimator and a precollimator stage placed in front of the mirror. The relatively large etendue allows one to perform observation in a wide range of experimental conditions. Sample results of the chordal observations are compared in absolute units with the predictions of a collisional–radiative one-dimensional impurity transport code.

Analogue feedback control system of RFX

Abstract The paper deals with the design and the experimental results of the first feedback control system of the main plasma quantitites for a reversed field pinch (RFP) machine. It was designed for RFX (Reverse Field eXperiment), the largest presently operating RFP device. The peculiar aspects of RFP with respect to Tokamaks are highlighted by considering their influence on the specifications of the control system design and the choice of the controlled quantities. Three feedback loops were implemented: the control of the plasma current, the toroidal magnetic field at the wall and the poloidal magnetic field configuration. The main purpose of the last loop is to minimize the field errors at the poloidal cuts of the conducting shell which surrounds the RFX vacuum vessel. The evaluation of the transfer functions of the systems and the regulator design are presented together with the experimental results obtained till now. The validation of the models used for the regulator synthesis was also performed and its results are reported.

Lower hybrid accessibility in a large, hot reversed field pinch

Accessibility and damping of the slow wave in a reversed field pinch (RFP) plasma is investigated theoretically, using projected Reversed Field Experiment (RFX) plasma parameters. By numerically solving the hot plasma dispersion relation, regions of propagation are found and the possibility of mode conversion is analysed. If the parallel index of refraction of the wave is chosen judiciously at the edge of the plasma, the slow wave is accessible to a target region located just inside the reversal surface without mode conversion. Landau damping is also optimized in this region. A representative fast electron population is then added in order to determine its effect on accessibility and damping. The presence of these electrons, whose parameters were estimated by extrapolation of Madison Symmetric Torus (MST) data, does not affect the accessibility of the wave. However, the initial phase velocity of the wave needs to be increased somewhat in order to maintain optimal damping in the target zone

Single chord far-infrared polarimetry experiment on RFX

This paper summarizes the work of the authors in the realization and testing of a pilot single chord polarimetry experiment on the RFX (reversed field experiment) machine, at the far-infrared wavelength of 118.8 μm. The fundamental purpose of this experiment is to demonstrate the feasibility of a Faraday rotation angle measurement on RFX, with the required resolution, and to clarify all the aspects which may be useful for the final six-chord version of the diagnostic. The apparatus which has been developed is described, with emphasis on some of the modifications which proved essential in order to obtain a satisfactory measurement, in spite of the hostile environment of the machine. Typical results of Faraday angle measurements are presented and discussed, and the reliability of the measurement is demonstrated. In particular, the required ±0.2° accuracy is achieved and the results are consistent with magnetic field profiles similar to the ones predicted by the Bessel function model. Suitable design considerations are formulated in order to guarantee the required performance in the six-chord version, even when the machine moves into full regime.

A global analysis of the behaviour of the ZT-40M reversed field pinch

Experimental data from the reversed field experiment, ZT-40M, have been re-examined in an attempt to determine the scaling behaviour of the physical plasma quantities and their fluctuations. A subset of the data is defined, allowing a reduced number of independent variables to describe the behaviour. For flat-top ZT-40M discharges the independent variables are chosen as being the toroidal current, Iϕ, and the dimensionless pinch parameter, Theta , which is proportional to the ratio of the toroidal current to the toroidal magnetic flux. The amplitudes of the dependent variables, including the electron temperature, plasma resistance, toroidal flux, the ratio of Iϕ to the mean electron density and their fluctuation amplitudes, exhibit minima as functions of Θ for constant Iϕ. These minima move towards lower Theta values with increasing Iϕ. Over the range of conditions for acceptable operation, the scaling of variables with Iϕ is not unique but depends on the variation of Θ as Iϕ increases. The Θ variation is governed by the specific conditions (such as constant poloidal β, βp) chosen to set the desired RFP operational constraints. Contour plots of the dependent variables versus the two independent variables, Iϕ and Θ, allow the determination of the Iϕ-Θ trajectory that corresponds to discharges that meet the chosen condition. The analysis shows that the amplitude of the low frequency fluctuations correlates with the mean βp and energy confinement time of ZT-40M. By modifying the external circuits on ZT-40M, low frequency fluctuations were reduced. Comparing the designs of different RFP experiments and their operating behaviour, these modifications suggest design changes for present and future RFP experiments that will benefit their performance

Three dimensional simulation of an FEL amplifier with an axial field

In their reversed field experiment, Conde and Bekefi observed a dramatic decrease in RF power output when the anti-resonance condition was satisfied, i.e., cyclotron frequency =−FEL frequency. They further noticed that even with no injected RF signal, beam transmission also fell at the anti-resonance. We show here that the true cause of the observed orbital instability is not the anti-resonance, but rather the fact that the two independent oscillations about the ideal helical trajectory have frequencies whose ratio is −2. That this would be a source of trouble was pointed out by Cherry in 1925. In the Conde-Bekefi experiment, the condition for anti-resonance coincided with the 2 : −1 ratio. By choosing wiggler parameters such that the two effects are dissociated, we demonstrate convincingly that the 2 : −1 condition causes the instability, and that a generalized version of Cherry's model provides an adequate analytic description of our numerical results.

Kinetic modeling of fast electron dynamics and self-consistent magnetic fields in a reversed field pinch

The dynamics of fast electrons in a reversed field pinch configuration is investigated by numerically solving the appropriate kinetic equation in three dimensions (two dimensions in velocity space and one dimension in real space). To this end, a Fokker–Planck code has been developed, including Coulomb collisions, direct current (dc) electric field, radial diffusion due to magnetic turbulence, ambipolar electric fields, and the self-consistent evaluation of the magnetic fields generated by the plasma itself. This has allowed the theoretical validation of the kinetic dynamo model in a realistic geometry. In contrast to fluid-turbulent theories, such a model predicts that the radial diffusion of fast electrons associated with stochastic magnetic fields might be able to sustain the reversed field configuration. Quantitatively, it is found that the level of magnetic turbulence necessary to obtain the toroidal field reversal at the plasma edge is compatible with levels typically measured in reversed field pinch devices. In particular, the main parameters of standard discharges in the largest existing facility of this type, RFX (reversed field experiment) [Proceedings of the 14th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Würzburg, 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 2, p. 583], have been successfully simulated.

A two color multichord infrared interferometer for RFX

A multichord interferometer designed for the Reversed Field experiment (RFX) (R=2 m, a=0.5 m, I=2 MA) is presented. The high density expected and the rather limited diagnostic access to the plasma motivated the choice of a two-color CO2/CO laser (10.6/5.4 μm) interferometer. Due to the time-varying magnetic fields ≥0.1 T around the torus entailed by the operation of the machine, the system has been mounted on a 3 ton graphite C-shaped optical table supported by a stainless steel structure on pneumatic vibration isolators. This led to long term stability of alignment and a very low level of mechanical vibrations. The interferometer can be moved in and out of the torus with ease by a carriage-rail system for maintenance both of the diagnostic and of the machine. The design foresees eight vertical chords spanning the arms of the C-shaped table and includes more additional measurements using a horizontal port and mirrors mounted inside the vacuum chamber. The expected accuracy in line density units is ≤1×1018 m−2, and the overall concept is that of a reliable system for high density and large size magnetic confinement plasmas.

Synchronization in a PLC/VAX-based control and data-acquisition system of a nuclear-fusion experiment

This paper describes the concept and implementation details of the synchronization mechanisms used in the control and data-acquisition system of the RFX (Reversed-Field Experiment) nuclear-fusion experimental device, at present under construction in Padova, Italy, within the framework of the co-ordinated nuclear-fusion research programme of the European Communities. The system employs industrial PLCs for the “slow” control and monitoring functions, and a VAX-based CAMAC for the “fast” functions of trigger-signal generation and data acquisition during the experiment pulses. All subsystems communicative via Ethernet, using compatible software protocols. The operational sequence of the complete system is governed by a single state machine implemented on a PLC-based supervisor system. Equivalent “slave” state machines are implemented on all other subsystems (PLC-and VAX-based). These state machines are synchronized by means of the exchange of messages via Ethernet. This paper deals in detail with the following components which are involved in system synchronization: • - the Message Exchange System which implements the system-wide exchange of short messages; • - the Scheduler programs which implement the state machine on the various computing nodes, and which make use of the Message Exchange System.

Symmetric toroidal pinch (STP-3(M))

Research on the symmetric toroidal pinch (STP) has been carried out at Nagoya during the past 15 years. From 1970 to 1982, this research concentrated on heating and confinement of screw pinch plasmas with force-free currents. Reversed-field experiments in metal tori started in 1983. The main object of these experiments is to study transport processes in reversed-field pinches with high current density (5–10 MA· m−2) At present, plasma currents up to 15 MA (6.2 MA· m−2) can be driven during 1.6 ms. Toroidal flux enhancement and related phenomena are being investigated.

Financial pinch kills British RFX pinch

The British Atomic Energy Authority has cancelled the Reversed Field Experiment. The £20‐million RFX magnetic‐confinement‐fusion facility, planned for the Culham Laboratory in Oxfordshire, was to have been the world's most ambitious reversed‐field‐pinch machine to date. With its cancellation, for budgetary reasons, American plans for full participation in the RFX have come to a sudden and disappointing end (PHYSICS TODAY, September 1981, page 20).