Reversed Field Pinch Device Research Articles

Reconstruction of the plasma surface in a RFP in the presence of non-axisymmetric perturbations

The non-axisymmetric analysis of the vacuum magnetic surface in a toroidal device is discussed assuming that the deviation from axisymmetry is a perturbation. The problem is particularly relevant to study the locked-mode phenomena due to internally resonant resistive magnetohydrodynamic (MHD) modes in reversed field pinch experiments. The general expressions which can be used for the magnetic reconstruction are derived according to two types of formalism: the flux function reconstruction and the magnetic scalar potential representation of the magnetic field. The measurements necessary to obtain a suitable magnetic reconstruction are discussed. In particular, it is found that a sufficient set of Br measurements is key information in obtaining the non-axisymmetric flux function. Such a set of measurements is presently lacking in the RFX reversed field pinch device. Nevertheless, based on an approximate solution of the Laplace equation for the magnetic scalar potential in the vacuum region outside the plasma, a method is derived by which the helical perturbation of the plasma magnetic surface can be computed with sufficient accuracy in RFX based on the measurements of a twin array of B coils only.

Design concept and confinement prediction of TPE-RX reversed-field pinch device

TPE-RX is a large-sized reversed-field pinch machine newly constructed at the Electrotechnical Laboratory. In this paper the design concepts, procedures to determine the machine size and the flux swing to drive the plasma current, and the prediction of the global confinement properties of the TPE-RX are reported. From these considerations, major and minor radii ( R, a) are decided to be R/ a=1.7175/0.45 m, respectively. It is estimated that the flux swing of the iron core of more than 3.9 Wb is necessary to drive 1 MA of plasma current, I p, which is the given constraint of the machine. Energy confinement time in the range of 3–18 ms is predicted to be attained at I p=1 MA depending on the models and assumptions.

Plasma and Mode Rotations in a Reversed-Field Pinch Device, TPE-1RM20

In a reversed-field pinch (RFP) device, TPE-1RM20, the rotation velocities of impurity ions and the magnetic modes are studied in connection to their roles on the dynamo activities. It is observed that the deceleration of the plasma poloidal rotation synchronizes with the deceleration of both poloidal and toroidal mode rotations at a discrete dynamo event. It is shown that the plasma poloidal rotation velocity in the case of high-Θ discharges becomes faster than that in the case of low-Θ discharges (Θ; pinch parameter). The radial electric field is estimated to be positive around r/a∼0.52 under some assumptions. Measurements reveal that the plasma poloidal rotation is in the electron diamagnetic direction around r/a∼0.52. This indicates that the poloidal rotation does not simply depend on Er×B flow. Through the present experimental results, some new subjects in the RFP plasma research are discussed.

Core Transport Improvement during Poloidal Current Drive in the RFX Reversed Field Pinch

We describe plasma profiles evolution during pulsed poloidal current drive experiments performed with the RFX reversed field pinch device. With external drive of edge poloidal current, magnetic fluctuations are reduced suggesting a concomitant reduction of the spontaneous dynamo action. The electron temperature profile is seen to peak in the plasma core, consistently with a reduction of the heat conductivity due to a substantial decrease of MHD dynamo fluctuations. Our results also indicate that the magnetic turbulence due to these fluctuations, which dominates heat transport in the core of the reverse field pinch configuration, does not drive an appreciable heat flux at the edge.

New Scalings of Energy Confinement Time of RFP Plasmas and the Extrapolation to Reactor Relevant Region.

Data bases of reversed field pinch (RFP) plasma have been gradually accumulated by recent experiments of several RFP devices. New confinement scalings τX(X=RFPs1)E=0.024Aa2IP/P1/2heat, τX(X=RFPs2)E=0.04s(IN)Aa2I1.25P/P1/2heat which are consistent to the recent data are presented, where units are in [s], [m], [MA] and [MW] respectively and s(IN) is a correction function of IN≡IP/πa2‹ne›20). From the standpoint of new scalings, dependences among parameters of possible RFP reactors are analyzed to find the conditions for RFP reactors. Hs1 Hs2 are defined by the ratios of necessary energy confinement time for RFP reactors for burning against τX(X=RFPs1) and τX(X=RFPs2) respectively. When confinement time follows τX(X=RFPs1)E scaling, confinement enhancement factor of at least Hs1=23 is necessary for RFP reactors to be realistic. When confinement time follows τX(X=RFPs2)E scaling, data points in IP-a space of RFP reactors are within the region of target.

Atitaniumhydride gun for plasma injection into the T2-reversed field pinchdevice

A study of a plasma gun (modified Bostic type) with titanium hydride electrodes has been carried out. The total number of released hydrogen atoms was in the range 1016-1018 and the maximum plasma flow velocity was 2.5×105 m s-1. The ion density near the gun edge reached 1.8×1020 m-3 and the electron temperature was around 40 eV as estimated from probe measurements. No species other than hydrogen or titanium were seen in the plasma line radiation. The plasma injector was successfully used for gas pre-ionization in the Extrap T2 reversed-field pinch device (ohmic heating toroidal experiment (OHTE)).

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.

A vented pump limiter for the reversed field pinch RFX

The reversed field pinch (RFP) plasma performance, as in the Tokamak, is strongly correlated with the edge neutral particle control. The drawbacks of the conventional magnetic divertors and throat limiters on the RFP plasma have slackened the application of an active particle control system in existing devices. An advanced solution, based on the idea of the `vented pump limiter' experimented on Tore Supra, has been conceived for RFX. This type of pump limiter is very attractive for a RFP. In this paper, the design of a `vented limiter' prototype for RFX is presented. Up to six modules of this limiter can be installed at the equatorial plane of RFX, allowing a particle exhaust efficiency comparable with a divertor or a throat limiter working in a Tokamak. Finally, the optimization of this concept for the next step RFP device is presented.

Toroidal and poloidal plasma rotation in the reversed field pinch RFX

In this paper, the toroidal and poloidal rotation velocities measured in the reversed field pinch device RFX from the Doppler shift of impurity ion lines are presented and their relation with the plasma velocity is discussed. It is found that the toroidal velocity at the edge has the opposite direction with respect to the core toroidal velocity, indicating a shear of the plasma rotation velocity of about . Starting from the rotation measurements and the momentum equation, a one-dimensional impurity diffusion model for the core plasma and a Monte Carlo code for the edge region are used to estimate the radial electric field, that is found to be around outward directed in the plasma core, and about inward directed at the edge, consistent with that measured at the edge by Langmuir probes.

Energy Confinement for Reversed Field Pinch Plasma in Experiment of SWIP-REP Device

The energy confinement of reversed field pinch (RFP) plasmas on SWIP-RFP device is studied, the energy confinement time is quantitatively calculated. The results show that the resistive toroidal voltage is about 50 V and the energy confinement time is about 45 μs for a better discharge. It is consistent with the scaling results of the RFP devices.

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.

Experimental Results with Siliconization in Reversed Field Pinch Device

Reversed field pinch (RFP) and ultralow safety factor plasma experimental performances with pulsed discharge cleaning and siliconization on SWIP-RFP device are presented. The wall siliconization was performed by using the device discharges. The experimental results with siliconization in RFP devices showed that the impurity concentrations were decreased in the plasma and better plasma parameters were obtained in the device.

A study on the buckling behaviour of a bellows-type vacuum vessel with torus shape in a reversed field pinch device

Buckling strength of a thin bellows vacuum vessel with torus shape is studied for design work on a reversed field pinch (RFP) fusion experimental device. In the RFP both toroidal and poloidal magnetic fields must be rapidly changed in the initial setting-up phase of the magnetic field configuration and high one-turn resistances of the vessel in both directions are required. Thus a very thin bellows with shallow convolution has to be used and the mechanical strength of the bellows-type vessel is a crucial design point. Here the buckling strength of the vessel is analysed numerically by applying the finite element method to a half-pitch of the bellows in torus shape. Results show that the buckling strength of the bellows torus is proportional to the third power of the equivalent bending thickness and approximately equal to that for a straight cylindrical tube having the same plate thickness as the equivalent bending thickness. Thus the torus effect seems to be unimportant in a bellows torus. This result is different from the previous study for simple toroidal vessels, where the buckling strength is increased by the torus effect.

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.

Nonlinear optical effects in Raman calibrations of a Thomson scattering system

We present an investigation of the occurrence of stimulated Raman scattering and other nonlinear optical effects during Raman calibrations of Thomson scattering diagnostic systems for magnetic fusion plasmas. When these effects take place, the intensity of the Raman lines is unpredictable, and the calibrations are impossible. In this research Raman scattering from H(2) and D(2) at filling pressures up to 1 atm has been experimentally investigated using the Thomson scattering system of the ETA-BETA II reversed field pinch device. Stimulated Raman Stokes light has been observed at filling pressures above 230 and 500 mbars for H(2) and D(2), respectively, for input laser pulses of 8 J and 30 ns (FWHM) duration. Evidence has been found that the stimulated Raman light does not originate from the observed scattering volume but is detected as light diffused into the vacuum chamber. To explain these results, the Raman gain and the intensity of the stimulated Raman light are calculated, taking into account the multimode structure of the laser beam. We find that significant power conversion from the input laser beam to the Stokes wave takes place near the output window of the vacuum chamber. Part of this radiation is diffused back into the machine, and this part is detected as superimposed on the spontaneous Raman signal. Finally we discuss the Raman calibrations in RFX, a larger plasma device in which the Raman medium will be N(2) at a temperature up to 350°C, and show that a filling pressure of 100 mbar gives a sufficient calibration signal, avoiding any nonlinear effect.

Correlation broadening and the study of turbulence in reversed-field pinch plasmas

The use of the spatial correlation function to describe the structure of turbulence in a plasma is well established. The authors consider the extent to which further information about the turbulence can be obtained from the study of the broadening of the correlation function when a time delay is introduced between the correlated signals. They define an experimentally accessible dimensionless measure of the broadening rate and illustrate its use with data obtained from the ZETA and HBTX reversed-field pinch (RFP) devices. They discuss the interpretation of these results in terms of the random motion of turbulent elements or of the broadening due to resistive diffusion, and show that the true value of the fine-scale correlation length in ZETA was about 2.5 cm, half the value given by the magnetic field fluctuations. The results are compatible with an overall picture of the ZETA discharge as dominated by parallel motion along stochastic field lines near the magnetic axis but by radial convective motions near the edge; it remains to be seen whether other RFP devices show a similar pattern.

Impurity studies on ZT-40M, ZTH and RFX using a zero-dimensional model for the reversed field pinch

A time dependent zero-dimensional model of plasma transport for reversed field pinch devices is developed to perform parametric studies on next generation experiments. The model includes energy balance equations for electrons and ions. Particle density and current are specified quantities. Impurities are treated using a coronal nonequilibrium model. Particle leakage and recycling are included for plasma and impurities. The particle lifetime is a specified parameter. The energy confinement times for electrons and ions are specified as multiplicative coefficients times the Ohmic energy confinement time. Ohmic heating is enhanced by an anomaly factor, and a direct ion heating term is included via anomalous resistive heating represented by a multiplicative coefficient times Ohmic heating. A single set of coefficients is found to simulate a variety of ZT-40M runs with different currents and wall conditions. The resulting model is employed to perform parametric analysis on the behaviour of ZTH at 2 MA operation. A confinement law consistent with the Connor-Taylor scaling is used. Three parameter variations are evaluated: I/N from 3 × 10−14 A·m to 6 × 10−14 A·m, the impurity recycle time from 5 ms to 1000 ms, and the carbon percentage from 1% to 10%. It is found that the temperature at the end of the flat-top phase of the current profile is proportional to I/N, and the proportionality constant increases with the particle confinement time τp. For fixed I/N, the temperature increases with τp largely because a reduction of the impurity recycle reduces the radiation loss. When the model is applied to RFX, the temperatures are almost identical to those in ZTH if τp scales as the square of the plasma radius.

Flux generation in ultra-low-q tokamak discharges

Spontaneous generation of toroidal flux is observed in a reversed-field pinch device operated as an ultra-low-q tokamak with a safety factor on axis of 1/4. An initial toroidal bias field of 150 G is increased to 600 G on axis in 300 μsec while the field at the wall is held nearly constant. Sawteeth are observed, which indicate cyclic magnetic reconnection.

Effect of a gradient in parallel current on field error profiles in a reversed-field pinch

Magnetic perturbations caused by external field errors are an important consideration in both the current operation and future design of reversed-field pinch (RFP) devices. Recently, it has been shown that perturbation profiles calculated in the presence of a relaxed RFP equilibrium (J0 =λB0, λ=const) are amplified when compared to those calculated in vacuum. This work extends the approach to include a partially relaxed equilibrium [λ=λ(r)], which is experimentally realistic, and the effects of finite resistivity, viscosity, and flow. The finite gradient in λ produces an amplification of the radial magnetic field perturbation much larger than that predicted for constant λ. Physically, this is due to the presence of an additional perturbed current associated with the gradient in λ which alters the curvature of the perturbation. Finite resistivity, viscosity, and flow act to reduce this amplification.

Characteristics of the toroidal relaxed state of reversed field pinches and comparison with experimental results

A toroidal equilibrium of a reversed field pinch based on Taylor’s Bessel function model (BFM) is investigated. Characteristics of the toroidal relaxed state for a few reversed field pinch devices are presented in detail. It is shown that the toroidal relaxed state agrees with experimental observations not only in the inner region, like BFM, but also to a good extent in the outer region of a reversed field pinch. Inclusion of toroidal effects in the BFM leads to a decrease of the toroidal reversed flux and an increase of the minor radius at which the toroidal field reverses. The toroidal relaxed state has ‘‘μ’’ decreasing in the outer region when calculated using experimental procedure and a saturation of the on-axis value of the pinch parameter Θ. Toroidal effects and finite plasma pressure lead to enhancement of the pinch parameter Θ. The results in this paper show that the observed departure of experiment from the BFM is partly due to the toroidal geometry.