Stabilization of ideal pressure gradient driven edge modes during pulsed parallel current drive in reversed field pinch

Coupling to the electron Bernstein wave (EBW) via a phased array of waveguides is experimentally investigated in the Madison symmetric torus reversed field pinch (RFP). EBWs promise to provide localized heating and current drive in overdense plasmas such as those in the RFP, provided a technique can be developed to efficiently couple power from an externally launched electromagnetic wave to the electrostatic EBW. The choice of antenna structure and launched wave polarization are important factors in coupling waves with frequencies in the electron cyclotron range to EBW, especially on the RFP where the mode conversion to the EBW can take place in the near-field of the antenna. In this paper, a recently developed theory of coupling to EBW from a phased array of waveguides is tested against experiment. The theory predicts that coupling efficiency will vary with launch angle and that coupling depends sensitively upon the edge density profile. Amplitudes and phases of reflected power in each of the waveguides are measured experimentally and compared with predictions based upon density profiles measured by a Langmuir probe in the edge of the plasma. The parametric dependence of reflection has been studied for different polarizations, different launch angles, time varying density profiles and several frequencies of the launched wave. An asymmetry in reflection versus the launch angle predicted by theory was found experimentally for the X-mode, while the O-mode was symmetric. The dependence on density scale length predicted by theory was confirmed in the experiment. The phase of the reflected signal is shown to contain reflectometry-based information about the edge density profile. For appropriate phasing, measurements show that the total power reflection coefficient can be lower than 15%.

In magnetic fusion plasmas, a significant fraction of the kinetic pressure is contributed by superthermal charged particles produced by auxiliary heating (fast ions and electrons) and fusion reactions (a-particles). Since these energetic particles are often far away from thermal equilibrium due to their non-Maxwellian distribution and steep pressure gradients, the free energy can excite electromagnetic instabilities to intensity levels well above the thermal fluctuations. The resultant electromagnetic turbulence could induce large transport of energetic particles, which could reduce heating efficiency, degrade overall plasma confinement, and damage fusion devices. Therefore, understanding and predicting energetic particle confinement properties are critical to the success of burning plasma experiments such as ITER since the ignition relies on plasma self-heating by a-particles. To promote international exchanges and collaborations on energetic particle physics,

Theoretical investigation on r.f. current drive in reversed-field pinch plasma

Reversed field pinches (RFPs) share with tokamaks and stellarators the experimental evidence of an upper limit for the maximum value of the electron density at which they can operate. Above a certain density level, well described by the Greenwald law for tokamaks and RFPs, a radiative collapse with strong plasma cooling is observed, predominantly due to processes occurring at the plasma boundary. In the RFX-mod RFP close to the density limit a radiating belt, poloidally symmetric and toroidally localized, develops in the region where the plasma is shrunk as an effect of the m = 0 tearing modes. The phenomenology recalls that of MARFES or plasma detachment, though, unlike tokamaks, the appearance of the radiating belt is associated with a soft landing of the plasma discharge.The paper reports the experimental pattern of the RFX-mod plasmas close to the density limit, including density and radiation profiles, plasma flow and turbulence. Particles are toroidally conveyed towards the region of maximum shrinking of the plasma column where they accumulate. The interpretation is related to the topology of MHD m = 0 and m = 1 modes: the reconstruction of the magnetic topology shows that the highly radiating region corresponds to the presence of peripheral m = 0 magnetic islands well detached from the wall. The emerging indication is that in RFPs a reduction of the m = 0 activity could be a way to overcome the density limit.

The problem of drift stabilization of the internal resistive-wall modes (RWMs) in tokamaks is theoretically investigated. The basic assumption of the model is that, when the drift effects are neglected, these modes are unstable in the absence of a conducting wall and stable in the presence of a close-fitting perfectly conducting wall. In the former case, the instability condition is expressed as Δ′∞>0, where Δ′∞ is the matching parameter calculated under the assumption that the wall is removed to infinity. In the latter case, one has ΔW′<0, where ΔW′ is the external matching parameter of tearing modes calculated assuming a perfectly conducting wall at the plasma boundary. In the case with a resistive wall, the relevant parameter can be either Δ′∞ or ΔW′, depending on whether the value of the dimensionless parameter ωτs/2m is small or large, respectively (here ω is the mode frequency, τs is the resistive time constant of the wall, and m is the poloidal mode number). In the presence of drift effects, the mode frequency ω is approximately equal to the electron drift frequency, ω≈ω*e. The value of the parameter ω*eτs/2m, which therefore determines the behavior of internal RWMs, is estimated for several existing tokamaks, namely, AUG (ASDEX-Upgrade), DIII-D, JET, TFTR, and JT-60U, as well as for the projected ITER-FEAT. It is shown that, although drift effects do not stabilize internal RWMs in current devices, they should be efficient in suppressing these modes in reactor-grade tokamaks.

Edge Localized Mode Control in TCV

The effect of boundary conditions on plasma confinement in the reversed field pinch (RFP) was studied. Early theoretical studies of the magnetohydrodynamic stability of the reversed field pinch had shown that the pinch was unstable unless it was surrounded by a conducting shell which prevented the penetration of the magnetic field during the lifetime of the pinch. The presence of the sheer, however, complicated construction and prevented control of the plasma equilibrium by feedback systems. This research project was undertaken to determine the effect on confinement of varying the magnetic penetration time of the shell. A reversed field pinch, the Reversatron, was constructed so that shells of varying thickness could be installed. Shells were made with magnetic penetration times both longer and shorter than the duration of the plasma discharge. These shells allowed the performance to be determined as a function of the magnetic penetration time of the shell. This research showed that a shell with a short penetration time degraded the discharges. Diagnostic measurements showed reductions in plasma current, discharge duration, and the Doppler temperature of impurity ions and showed increases in the plasma resistivity and loop voltage. The greater power input and lower temperature implied a reduced energy confinement time. Magnetic diagnostics showed that two classes of MHD instabilities with poloidal mode number m = 1 were responsible for the degraded confinement. These were the dynamo modes resonant on the magentic axis (with toroidal mode numbers -9, -10, -11, -12) and the external kink modes (with toroidal mode numbers 3, 4, 5, and 6).

We report on the first results of charge exchange recombination spectroscopy (CHERS) and motional Stark effect (MSE) measurements in the Madison Symmetric Torus reversed field pinch. A 30 keV, 4 A neutral H beam is used in combination with visible and ultraviolet spectroscopy to make the measurements. For CHERS, we find that the C VI line at 3433.69 Å yields the largest charge-exchange signal/background ratio and is most clearly resolved from other nearby lines. Equilibrium ion temperature measurements have been made with an existing fast Doppler spectrometer and a higher throughput spectrometer is being designed to do velocity and temperature fluctuation measurements. MSE measurements are made by recording the Doppler shifted Hα spectrum emitted by the beam with a charge coupled device and imaging spectrometer. We have observed separation of the π components of the Stark manifold at magnetic fields of about 0.5 T and are considering options for increasing measurement accuracy.

As a consequence of recent improvements to the far-infrared (FIR) interferometer time response, from bandwidth of 10 kHz up to 1 MHz, high-frequency density fluctuations can now be resolved on the Madison symmetric torus (MST) reversed-field pinch. The phase measurement allows absolute calibration of the fluctuation amplitude while eleven chords generate information on the spatial distribution. Density fluctuations up to 200 kHz are observed. A unique feature of the MST interferometer is that six chords are toroidally displaced 5° from the remaining five. Hence, besides information on the poloidal structure, i.e., m=1, toroidal information is also available. By computing the cross power, coherence, and cross phase between two toroidally displaced chords, one can determine the toroidal rotation speed, dispersion, and correlation length.

The frequencies of the fluctuations near the relaxed state of reversed field pinch (RFP) plasma in the presence of a stationary toroidal flow are investigated using magneto-hydrodynamical (MHD) theory in the approximation of the infinite aspect ratio and finite resistivity. We treat the fluctuations as MHD waves and derive their dispersion relations at the edge plasma. It is shown that there exists a new fluctuation mode with low frequency in the presence of a stationary toroidal flow, and that with the plasma resistivity it can be unstable. The dispersion relations of the new fluctuation mode and other MHD modes of the compressible plasma are obtained. The magnitudes of the frequencies are estimated using the parameters of TPE-RX, MST and RFX devices.

A diagnostic procedure is proposed that displays the toroidal and poloidal magnetic field profiles in the form of power series, through r/sup 6/. In addition to the usual external measurements, only one internal point magnetic measurement is required, if cylindrical symmetry and pressure balance are assumed. (The plasma pressure profile is also assumed to be measured nonintrusively; alternatively, it might be ignored if beta is known to be sufficiently small). The (zero-beta) method is tested here against full magnetic-profile shot-averaged data obtained from a multiple-probe device in ZT-40 with a ceramic liner. The agreement is quite good. The procedure seems simple enough for on-line use in RFP experiments. The availability of such profiles should enhance the effective application of theory to the RFP.

Understanding plasma stability and confinement in a reversed-field pinch (RFP), or any toroidal confinement device, requires detailed information on the poloidal magnetic field and current density distribution. The stability of the plasma to tearing modes and other MHD events such as the sawtooth perturbation or dynamo are closely related to the current density profile. In RFP’s, resistive MHD instabilities can produce magnetic islands on rational surfaces that are closely spaced in radius causing magnetic stochasticity resulting from island overlap. Energy transport in conventional RFP plasmas is believed to arise mainly from particles streaming along these stochastic magnetic field lines. For the Madison Symmetric Torus (MST), a major goal is to reduce magnetic fluctuations through current density profile control. Elucidating the physics of this interplay requires high-resolution measurement of both the current density profile time evolution and magnetic fluctuations.

Scaling laws for reversed field pinch (RFP) confinement parameters versus plasma current and density are found from computer simulations. The RFP dynamics at high Lundquist numbers approaching 106 is studied using a high resolution, 3-D, resistive MHD numerical code. Optimum plasma conditions are attained by assuming that the transport coefficients are classical, and by ignoring radiation losses and resistive wall effects. Anomalous global transport results from classical parallel heat conduction along stochastic field lines in the plasma core. The pinch parameter is Θ = 1.8 and the aspect ratio is R/a = 1.25. Poloidal beta is found to scale as βθ ∝ (I/N)-0.40I-0.40 and energy confinement time as τE ∝ (I/N)0.34I0.34. On-axis temperature scales as T(0) ∝ (I/N)0.56I0.56. Experimental results from T2, RFX and MST agree well with the above numerical results and also with the obtained magnetic fluctuation scaling ∝ S-0.14, where S is the Lundquist number. Thus stochastic core field lines appear to persist also at higher, reactor relevant currents and temperatures in the conventional RFP, indicating the need to further pursue confinement enhancement techniques.

The local electron energy flux produced by magnetic fluctuations has been measured directly in the edge plasma of the Madison symmetric torus (MST) reversed field pinch (RFP), continuous current tokamak (CCT), and the scrape-off layer of the TEXT-U tokamak. The flux produced by electrons travelling parallel to a fluctuating magnetic field is obtained from correlation between the fluctuations in the parallel heat flux and the radial magnetic field. The fluctuations in the parallel heat flux were measured with a fast insertable pyrobolometer. The measurements reveal fundamental differences in the nature of electron energy transport in the RFP and the tokamak. In the RFP the fluctuation-induced energy flux is large (, comparable to the total ohmic heating power) inside the reversal surface where the magnetic field is expected to be stochastic, and small in the edge. The magnetic fluctuation induced radial energy flux Q and radial particle flux (measured independently) are related by a `convective' formula . The electron heat transport is significantly lower than the value predicted by the Rechester - Rosenbluth transport model. This feature of the electron energy transport can be explained using self-consistent calculations that account for clumping of electrons streaming along the magnetic field. In the tokamak the magnetic fluctuations do not contribute to the total energy transport except in the vicinity of the q = 2 magnetic surface, where the transport is associated with large amplitude Mirnov oscillations.

In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed-field pinches are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations, however, `optimized' discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary: thus, it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available.