Magnetohydrodynamic Activity Research Articles

A submillimeter polychromator for plasma spectroscopy

A 12-channel grating polychromator for the measurement of electron cyclotron emission on the Frascati tokamak upgrade (FTU) has been built. Three gratings can be exchanged remotely, to allow the instrument to cover three different spectral ranges (between 200 and 600 GHz) which correspond to the second harmonic of electron cyclotron emission for tokamak magnetic fields of 4, 6, and 8 T. Three sets of low-pass filters, whose cut-off frequencies are optimized for each grating, are used to cut the high diffraction orders. In order to exchange the filters together with the grating it was necessary to integrate the groups of filters with the polychromator itself. This has been done reducing the grating sizes and assembling them all closely on a moveable structure. The exchange of gratings and filters can be performed remotely via computer in few seconds without any lost of the alignment. InSb cryogenic hot-electron bolometers are used as detectors. The cryostat hold-time is more than 30 days. Spectral resolution λ/δλ is about 40 corresponding to a spatial resolution of δR≊2.3 cm. The minimum detectable temperature is about 10 eV at 20 kHz bandwidth. The spatial structure and temporal evolution of several kinds of fast temperature perturbations (as the ones due to magnetohydrodynamic activity, temperature fall during pellet injection and plasma disruption) have been measured on FTU by means of this diagnostic system.

Absence of magnetohydrodynamic activity in the voltage-driven sheet pinch.

We have numerically studied the bifurcation properties of a sheet pinch with impenetrable stress-free boundaries. An incompressible, electrically conducting fluid with spatially and temporally uniform kinematic viscosity and magnetic diffusivity is confined between planes at ${\mathit{x}}_{1}$=0 and 1. Periodic boundary conditions are assumed in the ${\mathit{x}}_{2}$ and ${\mathit{x}}_{3}$ directions and the magnetofluid is driven by an electric field in the ${\mathit{x}}_{3}$ direction, prescribed on the boundary planes. There is a stationary basic state with the fluid at rest and a uniform current J=(0,0,${\mathit{J}}_{3}$). Surprisingly, this basic state proves to be stable and apparently to be the only time-asymptotic state, no matter how strong the applied electric field and irrespective of the other control parameters of the system, namely, the magnetic Prandtl number, the spatial periods ${\mathit{L}}_{2}$ and ${\mathit{L}}_{3}$ in the ${\mathit{x}}_{2}$ and ${\mathit{x}}_{3}$ directions, and the mean values ${\mathit{B}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}_{2}$ and ${\mathit{B}\mathit{\ifmmode\bar\else\textasciimacron\fi{}}}_{3}$ of the magnetic-field components in these directions. \textcopyright{} 1996 The American Physical Society.

Ballooning instability precursors to high β disruptions on the Tokamak Fusion Test Reactor

Toroidally localized ballooning modes have been found as precursors to high β disruptions in many regimes on the Tokamak Fusion Test Reactor (TFTR) [D. Meade et al., Proceedings of the International Conference on Plasma Physics and Controlled Nuclear Fusion, Washington, DC, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, pp. 9–24]. Lower frequency, global magnetohydrodynamic (MHD) activity, typically an ideal n=1 kink mode, causes the toroidal localization. Larger-amplitude n=1 modes result in stronger toroidal localization of the ballooning modes. The modes are typically localized to a region spanning about 90°–120° in the toroidal direction.

Fast detection of 14 MeV neutrons on the TFTR neutron collimator

Current mode operation of the NE451 ZnS scintillation detectors of the TFTR neutron collimator has enabled us to record the development of radial neutron emission profiles with much faster speed and higher accuracy than in the pulse counting mode. During high power deuterium–tritium (DT) operation, the intrinsic shot noise on the detector traces was so low that we could observe sawtooth instabilities and disruptions with good precision and, in addition, were able to identify precursor magnetohydrodynamic (MHD) activity and fishbone instabilities. These results demonstrate that in future tritium burning machines like ITER or TPX, the neutron collimator should be designed not only as a monitor of radial fusion power profiles but also as a wave detector for MHD activity.

High-frequency core localized modes in neutral beam heated plasmas on TFTR

A band of high-frequency modes in the range 50–150 kHz with intermediate toroidal mode numbers 4<n<10 are commonly observed in the core of supershot plasmas on TFTR [R. Hawryluk, Plasma Phys. Controlled Fusion 33, 1509 (1991)]. Two distinct varieties of magnetohydrodynamic (MHD) modes are identified, corresponding to a flute-like mode predominantly appearing around the q=1 surface and an outward ballooning mode for q≳1. The flute-like modes have nearly equal amplitude on the high-field and low-field side of the magnetic axis, and are mostly observed in moderate performance supershot plasmas with τE<2τL, while the ballooning-like modes have enhanced amplitude on the low-field side of the magnetic axis and tend to appear in higher performance supershot plasmas with τE≳2τL, where τL is the equivalent L-mode confinement time. Both modes appear to propagate in the ion diamagnetic drift direction and are highly localized with radial widths Δr∼5–10 cm, fluctuation levels ñ/n, T̃e/Te<0.01, and radial displacements ξr∼0.1 cm. Unlike the toroidally localized high-n activity observed just prior to major and minor disruptions on TFTR [E. D. Fredrickson et al., Proceedings of the 15th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville, Spain (International Atomic Energy Agency, Vienna, 1995), No. IAEA-CN-60/A-2-II-5], these modes are typically more benign and may be indicative of MHD activity excited by resonant circulating beam ions.

High spatial resolution interferometry and polarimetry in hot plasmas

Interferometry is a standard technique for measuring the line-integrated electron density of magnetically confined plasmas. It is based on the fact that an electromagnetic wave, on its passage through a plasma, experiences a phase change with respect to the vacuum situation. Moreover, the plane of polarization of the wave will in general rotate because the plasma is birefringent. The total (Faraday) rotation angle of the wave, which can be measured by polarimetric techniques, is proportional to the line-integrated value of the magnetic field component parallel to the beam. The optimum wavelength for interferometry/polarimetry, for diagnosing magnetically confined plasmas is in the far-infrared and infrared spectral region. To invert the line-integrated data of the electron density and magnetic field component to local values, without using too stringent assumptions on the plasma symmetry, it is necessary to probe the plasma along multiple chords. In many confinement devices this is done by using a limited number of discrete probing chords. In recent years much attention has been devoted to the development of multichannel interferometer/polarimeter systems with a much better coverage of the plasma, which could be achieved by expanding the probing beam either to a slab- or a fanlike beam, covering almost the complete minor cross section of the plasma. A much higher number of detectors can be implemented in this way, thus substantially improving the spatial resolution of the measurements. In this paper the present status of interferometer/polarimeter systems featuring slablike or fanlike probing beams will be reviewed. Results of detailed measurements that have been performed to study the effect of magnetohydrodynamic activity (in particular sawteeth), disruptions, additional heating, and pellet injection on the electron density distribution, will be used to illustrate the merits of interferometry/polarimetry with high spatial resolution.

Control of magnetohydrodynamic activities by electron cyclotron heating in WT-3

Abstract Control of the m = 2, n = 1, magnetohydrodynamic mode in an ohmically heated plasma by localized electron cyclotron heating is studied systematically in the WT-3 tokamak. It is found that both m = 2 and m = 2 modes can be simultaneously suppressed by electron cyclotron heating near the q = 1 surface as well as the q = 2 surface, where q is the safety factor.

Magnetohydrodynamic stabilization through rotation.

Rotation of a cylinder of current-carrying magnetofluid is shown to stabilize it against helical magnetohydrodynamic activity, much as rotation can "stiffen" a Navier-Stokes fluid. The (viscous, resistive) magnetofluid is in a periodic cylinder bounded by a rigid wall; it contains an externally supported axial magnetic flux and a driven axial current. The suppressed activity is that known to result in paired helical vortices and helical current-channel distortions. The method used is fully three-dimensional, spectral-method computation. The stabilization is global and not confined to the outer edge of the plasma.

Ion-temperature-gradient-driven instability and anomalous ion heating in reversed-field pinches

A possible mechanism is suggested for direct ion heating in reversed-field pinches (RFP). The ion temperature gradient mode induces collisionless ion perpendicular viscosity which damps the velocity fluctuations associated with resistive magnetohydrodynamic (MHD) mode activity. It is found that the growth rate of the ηi instability is much larger than that in a tokamak, because the effects of both bad magnetic curvature and negative compressibility are enhanced in a RFP configuration. The anomalous perpendicular viscosity coefficient is estimated from the mixing length argument and the corresponding ion heating power due to viscous dissipation is found sufficient to balance the ion conductive losses.

Anomalous losses of deuterium–deuterium fusion products in the Tokamak Fusion Test Reactor*

In the Tokamak Fusion Test Reactor (TFTR) [International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Wurzburg, Paper No. A-2-2 (International Atomic Energy Agency, Vienna, 1993)] there have been at least three types of anomalous loss of alpha-like deuterium–deuterium (D–D) fusion products: (1) a magnetohydrodynamic (MHD)-induced loss of D–D fusion products correlated with Mirnov and fishbone-type oscillations and sawtooth crashes, (2) a slow ‘‘delayed’’ loss of partially thermalized D–D fusion products occurring without large MHD activity, and (3) ion cyclotron resonance heating (ICRH)-induced loss of D–D fusion products ions observed during direct electron heating experiments, and possibly also during 3He minority heating. In this paper each of these will be reviewed, concentrating on those due to MHD activity, which are the largest of these anomalous losses. The experimental results are compared with numerical models of various fusion product transport mechanisms.

Evolution of high βp plasmas with improved stability and confinement*

Experiments to explore the long-time evolution of noninductive, high βp plasmas in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159], have identified a new, quiescent, high performance regime. The experiments were carried out at low current (400–800 kA) with medium power neutral beam injection (3–10 MW). This regime is characterized by high q0 (≳2) and moderate li(∼1.3). It is reached by slow relaxation of the current profile, on the resistive time scale. As the profiles relax, q0 rises and li falls. When q0 goes above 2 (approximately), magnetohydrodynamic (MHD) activity disappears, and the stored energy rises. Most dramatic is the strong peaking of the central density, which increases by as much as a factor of 2. The improved central confinement appears similar to the PEP/reversed central shear/second stable core modes seen in tokamak experiments, but in this case without external intervention or transient excitation. At high current, a similar, but slower relaxation is seen. Also notable in connection with these discharges is the behavior of the edge and scrape-off layer (SOL). The edge localized modes (ELM’s) as seen previously, are small and very rapid (to 1 kHz). The SOL exhibits high density (≥1×1019 m−3), which shows little or no falloff with radius. Also the power deposition at the divertor surface is very broad, up to four times the width usually seen. This regime is of particular interest for the development of steady-state tokamak operating scenarios, for the Tokamak Physics Experiment (TPX), and following reactors.

Ion Cyclotron Emission — a Natural Diagnostic for Fusion Alpha Particles

There exist strong observational links between ion cyclotron emission (ICE) and fusion reactivity in tokamak plasmas. These links originally emerged from deuterium discharges in the Joint European Torus (JET) and were demonstrated most recently in the Preliminary Tritium Experiment. They include the proportionality of ICE intensity to measured fusion reactivity over six decades in signal intensity; correlations in the time evolution of the ICE signal and neutron flux during discharges; the matching of the spectral peak frequencies to successive local ion cyclotron harmonics at the outer midplane edge; and correlations between ICE and the observed impact of magnetohydrodynamic activity, such as sawteeth and edge-localized modes, on energetic ions. The observations are broadly consistent with the excitation of the fast Alfvén wave through cyclotron resonance with the local non-Maxwellian fusion product population — the so-called magnetoacoustic cyclotron instability. The theory of this instability is extended to the regime of arbitrary k||, in which it is necessary to include both wave-particle cyclotron damping and the positive-energy loading due to resonant cyclotron harmonic waves supported by the thermal ions. The consequences of arbitrary k|| for the instability thresholds are described. An outline is given of the close similarities between ICE from tokamaks and signals at multiple ion cyclotron harmonics observed in the Earth’s magnetosphere, which apparently originate from regions where there is a ring-type population of energetic protons. This emission also appears to be explicable in terms of the magnetoacoustic cyclotron instability, and comparison with tokamak observations yields information on the distinction between features generic to the emission mechanism and those specific to particular magnetic geometries.

Superkimberlites: A geodynamic diamond window to the Earth's core

Carbon is the fourth most abundant element in the solar system. In the Earth carbon is in atmospheric CO 2, limestone, other organic products, graphite and trace diamond; interstellar diamond, however, is ubiquitous. Diamond is well known for some unique physical and chemical properties, but it is perhaps less well known that the mineral is geologically ancient (3.3 Ga), that its origins are deep in the mantle (> 180 km), and that diamonds are among the deepest solid objects to reach the surface of the Earth; rare diamonds are from the transition zone (400–670 km), and other diamonds possibly nucleated in the lower mantle (> 670 km). Transport to the surface is in volatile (C O H N S)-charged highly explosive kimberlite and lamproite volcanoes. These volcanoes are sited exclusively in the oldest (> 1.7 Ga), tectonically most stable, and thickest (∼ 200 km) regions of crust and upper mantle lithosphere. The energetics required for volcanism are so exceptional and the sources so deep that possible connections between and among the core, geomagnetism, plumes and diamonds are explored. Some correlations are established and others are implied. The results are sufficiently enticing to propose that kimberlites and geographically and temporally associated carbonatites are continental recorders of plumes dating back to at least 2.8 Ga, and that some diamonds may have recorded core events dating back to 3.3 Ga, or possibly earlier. Peaks in kimberlite magmatic activity correlate, on average, with normal and reverse superchron and subchron behavior of the geomagnetic field. The time lag between magnetohydrodynamic activity in the core and kimberlite eruptive cycles at the Earth's surface is of the order of 25–50 Ma, consistent with the travel times modeled for the passage of plumes from D′' layer to the subcontinental lithosphere. Although the existence of plumes and the nature of D′' are debated, the correlations established for the past 500 Ma between and among superchrons, subchrons, kimberlites and entrained diamonds weigh heavily in favor of the following scenario: solid core growth, the consequent release of Si, O, C, H, S, K and possibly N and B to D′', disruption of D′' at some critically unstable threshold thickness (200–300 km), enhanced core convection and the stabilization of a constant non-reversing magnetic dipole field, rising plumes and subsequent volcanism. If protokimberlitic magma and entrainment begin at the core-mantle boundary, a number of geochemical and mineralogical anomalies in diamonds are at present best satisfied if D′' is invoked. These include but are not limited to intensely reduced (i.e., oxygen deficient) SiC, metallic Fe, an abundance of sulfides, silicate perovskite and wüstite-periclase mineral inclusions in diamonds. The most abundant source of diamonds is unequivocally from cratonic root zones with C possibly implanted by ancient plumes; eclogitic suite diamonds are equivocal, and diamonds transported from the transition zone and the lower mantle are best explained by entrainment in highly reduced plumes. Carbon in the overwhelming majority of diamonds appears to be primordial. By analogy with a chondritic Earth and chondrites, carbon was acquired during accretion in gaseous complexes, in the form of nanometer-size amorphous C, and as hydrocarbon particles; but carbon was possibly also added as crystalline nanodiamonds that served as seeds for subsequent diamond growth.

Neutral beam driven global Alfvén eigenmodes in the Wendelstein W7-AS stellarator.

During neutral beam injection coherent magnetohydrodynamic activity occurs at low and medium \ensuremath{\beta}, which is driven by the energetic beam particles. As interpretation is given in terms of marginally stable global Alfv\'en eigenmodes (GAE), which are destabilized by Landau resonances of the far circulating particles. Toroidicity induced gaps for toroidal Alfv\'en eigenmodes do not occur in W7-AS but GAE modes in gaps below the shear Alfv\'en continua can be excited. This is investigated within a gyrofluid model, which has been used sucessfully for tokamak cases previously.

Proton acceleration in flares and magnetohydrodynamic solar activity

The possibility of accelerated protons in solar flares having a sharp change in their spectral index is discussed. The analysis is based on the Tsytovich (1982, 1984, 1987a, b, c) acceleration model by MHD turbulence, which is shown to have different resonant conditions for non-relativistic and relativistic particles. The different resonant condition is shown to result in a sharp change in the accelerated proton spectral index, even in the absence of any peculiarity in the spectra of the MHD turbulence. Time scales for accelerated protons to relativistic energies are also derived, and shown to be consistent with observations. We also show that the threshold energy for electron acceleration by low frequency MHD turbulence is much greater than for proton acceleration. The turbulence therefore preferentially accelerates protons.

Suppression of m=2 islands by electron cyclotron heating in the Texas Experimental Tokamak: Experiment and theory

Electron cyclotron heating (ECH) is used to suppress m=2 magnetohydrodynamic (MHD) oscillations in the Texas Experimental Tokamak (TEXT) [Nucl. Technol. Fusion 1, 479 (1981)]. The location of ECH power deposition is controlled by a movable antenna. The MHD activity is suppressed when the ECH beam is directed close to the q=2 surface. The experiment is simulated using a three-dimensional resistive MHD code in cylindrical geometry. For fixed plasma current, the saturated m=2 island width is found to depend on the value of the safety factor at the magnetic axis (q0). The simulation suggests that the observed saturated m=2 island in the pre-ECH plasma, which typically occupies 25% of the minor radius, corresponds to q0∼1.3. The suppression of the island in the presence of ECH is attributed to current profile modification. In some discharges, the m=2 activity does not resume even after the ECH pulse is turned off.

Macroscopic behavior and discrete dynamo in high-Θ reversed-field pinch discharges

The magnetohydrodynamic (MHD) activity and the discrete dynamo in high-Θ reversed-field pinch (RFP) discharges are studied through comparisons with those in normal-Θ RFP discharges, where Θ=Bθ(a)/〈Bz〉 is the pinch parameter. In high-Θ RFP discharges, the mode coupling of m=1 is enhanced by the high magnetic shear configuration, and the MHD activity is more turbulent as compared with that in normal-Θ RFP discharges. Furthermore, the discrete increase of the toroidal magnetic flux is obviously observable. The increase of the toroidal magnetic flux generated by the discrete dynamo, which has an asymmetric structure in the toroidal direction, is only 1%–2% of the whole toroidal magnetic flux. The experimental results indicate that the discrete dynamo does not play an essential role in the RFP dynamo.

On the role of the Hartmann number in magnetohydrodynamic activity

Magnetohydrodynamic activity near the threshold of instability is studied numerically for resistive equilibria in periodic cylinders. Attention focuses on the role of the viscosity (and its reflection in the Hartmann number) in determining the existence and nonlinear evolution of instabilities. Three identical axisymmetric resistive equilibria without flow are investigated, with three viscosities. The highest viscosity leads to stability of the axisymmetric state. The intermediate value leads to a helically deformed equilibrium with flow, with an (m,n)=(2,1) deformation. The lowest viscosity leads to a 'mixed' helically deformed, final, approximately steady state with flow, with (m,n)=(2,1) and (3,2) deformations and their harmonics, plus other, adjacent, modes near m=2n. It is concluded that it is likely that the numerical value of the viscosity, and possibly the form of the viscous stress tensor, must never be ignored in discussions of near-threshold incompressible MHD activity in driven, dissipative MHD plasmas.

Internal magnetic and electrostatic fluctuation measurements of magnetohydrodynamic modes in the Texas Experimental Tokamak (TEXT)

A heavy ion-beam probe has been used to make the first internal measurements of magnetic fluctuations in a hot tokamak. The magnetic vector potential fluctuation, Ãφs, is measured during magnetohydrodynamic (MHD) activity and is in reasonable agreement with the prediction of a three-dimensional, resistive, compressible, nonlinear MHD code. Associated density and potential fluctuation measurements and magnetic island widths are also presented.

Free boundary resistive modes in tokamaks

There exist a number of observations of magnetohydrodynamic (MHD) activity that can be related to resistive MHD modes localized near the plasma boundary. To study the stability of these modes, a free boundary description of the plasma is essential. The resistive plasma–vacuum boundary conditions have been implemented in the fully toroidal resistive spectral code castor (Complex Alfvén Spectrum in Toroidal Geometry) [Proceedings of the 18th Conference on Controlled Fusion and Plasma Physics, Berlin, edited by P. Bachmann and D. C. Robinson (European Physical Society, Petit-Lancy, Switzerland, 1991), p. 89]. The influence of a free boundary, as compared to a fixed boundary on the stability of low-m tearing modes, is studied. It is found that the stabilizing (toroidal) effect of a finite pressure due the plasma compression is lost in the free boundary case for modes localized near the boundary. Since the stabilization due to the favorable average curvature in combination with a pressure gradient near the boundary is small, the influence of the pressure on the stability is much less important for free boundary modes than for fixed boundary modes.