Ion Polarization Current Research Articles

Measurement of small island characteristics using high resolution ECE and CER at DIII-D

Abstract The measurements using the high resolution electron cyclotron emission radiometry and the charge exchange and recombination spectroscopy are processed using analytic formulas to allow for the detection of islands as small as 1.9 cm. In contrast to large, saturated magnetic islands which are relatively well understood to be governed by the loss of bootstrap current inside the island, small islands are less well understood due to the difficulty of their accurate measurement in tokamaks. Here, ‘small’ islands are islands comparable in size to the ion banana width, which can be as small as 0.8 cm at DIII-D. The new measurement methods allow for the detection of small island widths when the predicted increase of mode frequency to match the Doppler shifted ion diamagnetic frequency is observed. Therefore, for the first time, the mode frequency increase can be unambiguously associated to the acceleration of the magnetic island propagation. Such association allows for a further development and validation of the much-debated theory of ion polarization currents, which is thought to govern the small island growth.

Analysis of the role of the ion polarization current on the onset of pre-disruptive magnetic islands in JET

The problem of the trigger of the neoclassical tearing mode is addressed in this work by evaluating the non-linear terms of the generalized Rutherford equation (GRE) for a set of JET disruptions. The linear stability index Δ′0, even for positive values, is not enough to describe the trigger of the mode as the stabilizing non-linear effects tend to prevent the growth of a mode below a certain width. First, an analysis on the contribution of the stabilizing effect of the curvature and the destabilizing effect of the bootstrap is done. Second, the work focuses on the role of the ion polarization current, a return current that flows parallel to the magnetic field due to the difference in the drift motion of the electrons and ions. This contribution is thought to play an important role in the onset of an island of width W, because it scales as 1/W3, making it a dominant term in the GRE when W is small. The assessment is carried out over a subset of pulses, producing interesting observations that were then generalized across the entire database, obtaining consistent results.

Study of stability and rotation of a chain of saturated, freely-rotating magnetic islands in tokamaks

The non-linear dynamics of a chain of stationary, saturated magnetic islands is studied by solving a four-field system of equations that include non-ideal effects, lowest order finite Larmor radius corrections and neoclassical terms. The magnetic island rotation velocity is calculated self-consistently with the fields profiles. The solutions for the island rotation velocity and for the ion polarization current are determined as a function of the characteristic parameters of the system and the results are discussed. The results of the calculations show that island rotation velocity and the ion polarization current depend in a non-trivial way on the parameters characterizing the system, and some clear patterns emerge only in particular cases. An analysis of magnetic island rotation velocity is performed on experiments in COMPASS tokamak. Measured island rotation velocity is compared with the calculated ion and electron flow velocities, for different hypotheses on the toroidal rotation of the plasma. The comparison shows that the island rotation velocity is consistent with the ion flow velocity, under the hypothesis of slow toroidal rotation and low collisionality. Theoretical calculation of the island rotation velocity according to the model here developed suggests that the islands rotate weakly in the ion direction, in the hypothesis of slow toroidal rotation and high collisionality. The impossibility of directly measuring the plasma rotation velocity makes it difficult to distinguish between these different regimes.

Disconnection of scrape off layer turbulence between the outer midplane and divertor target plate in NSTX

The connection between scrape off layer (SOL) turbulence at the outer midplane and at the divertor target plate is characterized in the National Spherical Torus Experiment (NSTX). Divertor fluctuations due to midplane blobs are studied by imaging their helical intersection with the divertor plate. Divertor fluctuation levels gradually decrease approaching the outer strike point. Divertor radial turbulence scale lengths as well as radial and poloidal turbulence propagation velocities are comparable to those on the low field side midplane. Strong correlation between divertor and midplane turbulence is observed in the far SOL. The correlation progressively decreases towards the separatrix, along with the decrease in the measured divertor fluctuations. The reduction in correlation is consistent with an electrostatic two-region blob model (Myra et al 2006 Phys. Plasmas 13 112502) with perpendicular ion polarization currents due to X-point geometry causing filament disconnection.

A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma

A two-fluid, neoclassical theory of the interaction of a single magnetic island chain with a resonant error-field in a quasi-cylindrical, low-β, tokamak plasma is presented. The plasmas typically found in large hot tokamaks lie in the so-called weak neoclassical flow-damping regime in which the neoclassical ion stress tensor is not the dominant term in the ion parallel equation of motion. Nevertheless, flow-damping in such plasmas dominates ion perpendicular viscosity, and is largely responsible for determining the phase velocity of a freely rotating island chain (which is in the ion diamagnetic direction relative to the local E × B frame at the rational surface). The critical vacuum island width required to lock the island chain is mostly determined by the ion neoclassical poloidal flow damping rate at the rational surface. The stabilizing effect of the average field-line curvature, as well as the destabilizing effect of the perturbed bootstrap current, is the same for a freely rotating, a non-uniformly rotating, and a locked island chain. The destabilizing effect of the error-field averages to zero when the chain is rotating and only manifests itself when the chain locks. The perturbed ion polarization current has a small destabilizing effect on a freely rotating island chain, but a large destabilizing effect on both a non-uniformly rotating and a locked island chain. This behavior may account for the experimentally observed fact that locked island chains are much more unstable than corresponding freely rotating chains.

Calculation of the radial electric field with RF sheath boundary conditions in divertor geometry

The equilibrium electric field that results from an imposed DC bias potential, such as that driven by a radio frequency (RF) sheath, is calculated using a new minimal two-field model in the BOUT++ framework. Biasing, using an RF-modified sheath boundary condition, is applied to an axisymmetric limiter, and a thermal sheath boundary is applied to the divertor plates. The penetration of the bias potential into the plasma is studied with a minimal self-consistent model that includes the physics of vorticity (charge balance), ion polarization currents, force balance with , ion diamagnetic flow (ion pressure gradient) and parallel electron charge loss to the thermal and biased sheaths. It is found that a positive radial electric field forms in the scrape-off layer and it smoothly connects across the separatrix to the force-balanced radial electric field in the closed flux surface region. The results are in qualitative agreement with the experiments. Plasma convection related to the net flow in front of the limiter is also obtained from the calculation.

An improved neoclassical drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in tokamak plasmas

The effect of the perturbed ion polarization current on the stability of neoclassical tearing modes in tokamak plasmas is calculated using an improved, neoclassical, four-field, drift-magnetohydrodynamical model. The calculation involves the self-consistent determination of the pressure and scalar electric potential profiles in the vicinity of the associated magnetic island chain, which allows the chain's propagation velocity to be fixed. Two regimes are considered. First, a regime in which neoclassical ion poloidal flow damping is not strong enough to enhance the magnitude of the polarization current (relative to that found in slab geometry). Second, a regime in which neoclassical ion poloidal flow damping is strong enough to significantly enhance the magnitude of the polarization current. In both regimes, two types of solution are considered. First, a freely rotating solution (i.e., an island chain that is not interacting with a static, resonant, magnetic perturbation). Second, a locked solution (i.e., an island chain that has been brought to rest in the laboratory frame via interaction with a static, resonant, magnetic perturbation). In all cases, the polarization current is found to be either always stabilizing or stabilizing provided that ηi≡dlnTi/dlnne does not exceed some threshold value. In certain ranges of ηi, the polarization current is found to have a stabilizing effect on a freely rotating island, but a destabilizing effect on a corresponding locked island.

X-Point Effect on Plasma Blob Dynamics.

Plasma blob dynamics on the high-field side in the proximity of a magnetic field null (X point) is investigated in TORPEX. A significant acceleration of the blobs towards the X point is observed. Close to the X point the blobs break apart. The E×B drifts associated with the blobs are measured, isolating the background drift component from the fluctuating contribution of the blob internal potential dipole. The time evolution of the latter is consistent with the fast blob dynamics. An analytical model based on charge conservation is derived for the potential dipole, including ion polarization, diamagnetic, and parallel currents. In the vicinity of the X point, a crucial role in determining the blob motion is played by the decrease of the poloidal magnetic field intensity. This variation increases the connection length that short circuits the potential dipole of the blob. Good quantitative agreement is found between the model and the experimental data in the initial accelerating phase of the blob dynamics.

Nonlinear error-field penetration in low density ohmically heated tokamak plasmas

A theory is developed to predict the error-field penetration threshold in low density, ohmically heated, tokamak plasmas. The novel feature of the theory is that the response of the plasma in the vicinity of the resonant surface to the applied error-field is calculated from nonlinear drift-MHD (magnetohydrodynamical) magnetic island theory, rather than linear layer theory. Error-field penetration, and subsequent locked mode formation, is triggered once the destabilizing effect of the resonant harmonic of the error-field overcomes the stabilizing effect of the ion polarization current (caused by the propagation of the error-field-induced island chain in the local ion fluid frame). The predicted scaling of the error-field penetration threshold with engineering parameters is , where br is the resonant harmonic of the vacuum radial error-field at the resonant surface, BT the toroidal magnetic field-strength, ne the electron number density at the resonant surface and R0 the major radius of the plasma. This scaling—in particular, the linear dependence of the threshold with density—is consistent with experimental observations. When the scaling is used to extrapolate from JET to ITER, the predicted ITER error-field penetration threshold is (br/BT)crit ∼ 5 × 10−5, which just lies within the expected capabilities of the ITER error-field correction system.

Collisionless inter-species energy transfer and turbulent heating in drift wave turbulence

We reconsider the classic problems of calculating “turbulent heating” and collisionless inter-species transfer of energy in drift wave turbulence. These issues are of interest for low collisionality, electron heated plasmas, such as ITER, where collisionless energy transfer from electrons to ions is likely to be significant. From the wave Poynting theorem at steady state, a volume integral over an annulus r1<r<r2, gives the net heating as ∫r1r2dr〈Ẽ·J̃〉=−Sr|r1r2≠0. Here Sr is the wave energy density flux in the radial direction. Thus, a wave energy flux differential across an annular region indeed gives rise to a net heating, in contrast to previous predictions. This heating is related to the Reynolds work by the zonal flow, since Sr is directly linked to the zonal flow drive. In addition to net heating, there is inter-species heat transfer. For collisionless electron drift waves, the total turbulent energy source for collisionless heat transfer is due to quasilinear electron cooling. Subsequent quasilinear ion heating occurs through linear ion Landau damping. In addition, perpendicular heating via ion polarization currents contributes to ion heating. Since at steady state, Reynolds work of the turbulence on the zonal flow must balance zonal flow frictional damping (∼νii〈Vθ〉2∼|eϕ̃T|4), it is no surprise that zonal flow friction appears as an important channel for ion heating. This process of energy transfer via zonal flow has not previously been accounted for in analyses of energy transfer. As an application, we compare the rate of turbulent energy transfer in a low collisionality plasma with the rate of the energy transfer by collisions. The result shows that the collisionless turbulent energy transfer is a significant energy coupling process for ITER plasma.

Experimental investigation of the trigger problem in magnetic reconnection

Magnetic reconnection releases magnetic energy not only in steady state, but also in time-dependent and often explosive events. Here, we investigate the trigger mechanism for this explosive release by using a toroidal experiment in the strong guide-field regime. We observe spontaneous reconnection events with exponentially growing reconnection rates, and we characterize the full 3D dynamics of these events using multiple internal probes. The reconnection is asymmetric: it begins at one toroidal location and propagates around in both directions. The spontaneous onset is facilitated by an interaction between the x-line current channel and a global mode, which appears in the electrostatic potential. It is this mode which breaks axisymmetry and enables a localized decrease in x-line current. We apply a simple model—which relies on ion polarization currents for current continuity—to reproduce the exponential growth and compute the growth rate. The result agrees well with the experimental growth rate.

Electrostatic instabilities, turbulence and fast ion interactions in the TORPEX device

Electrostatic turbulence, related structures and their effect on particle, heat and toroidal momentum transport are investigated in TORPEX simple magnetized plasmas using high-resolution diagnostics, control parameters, linear fluid models and nonlinear numerical simulations. The nature of the dominant instabilities is controlled by the value of the vertical magnetic field, Bv, relative to that of the toroidal field, BT. For Bv/BT > 3%, only ideal interchange instabilities are observed. A critical pressure gradient to drive the interchange instability is experimentally identified. Interchange modes give rise to blobs, radially propagating filaments of enhanced plasma pressure. Blob velocities and sizes are obtained from electrostatic probe measurements using pattern recognition methods. The observed values span a wide range and are described by a single analytical expression, from the small blob size regime in which the blob velocity is limited by cross-field ion polarization currents, to the large blob size regime in which the limitation to the blob velocity comes from parallel currents to the sheath. As a first attempt at controlling the blob dynamical properties, limiter configurations with varying angles between field lines and the conducting surface of the limiter are explored. Mach probe measurements clearly demonstrate a link between toroidal flows and blobs. To complement probe data, a fast framing camera and a movable gas puffing system are installed. Density and light fluctuations show similar signatures of interchange activity. Further developments of optical diagnostics, including an image intensifier and laser-induced fluorescence, are under way. The effect of interchange turbulence on fast ion phase space dynamics is studied using movable fast ion source and detector in scenarios for which the development from linear waves into blobs is fully characterized. A theory validation project is conducted in parallel with TORPEX experiments, based on quantitative comparisons of observables that are defined in the same way in the data and in the output of numerical codes, including 2D and 3D local and global simulations.

Modelling the effect of cross-field diffusion on tearing mode stability

A non-linear theory of tearing modes in a magnetized plasma which retains the effect of cross-field diffusion on the ion polarization current is presented. This ion polarization current is predicted to influence the tearing mode evolution when its amplitude is small, corresponding to a magnetic island with a width that is comparable to the ion Larmor radius. It is therefore likely to be most relevant for understanding whether tearing modes can drive magnetic turbulence, and for understanding the threshold physics of neoclassical tearing modes, of particular relevance to tokamaks. There are two opposing contributions to the ion polarization current: one from a narrow layer in the vicinity of the island separatrix and one in the opposite direction from outside this layer. These contributions are comparable, so the net effect of the ion polarization current on tearing mode stability requires a quantitative prediction of both. The region outside the layer is relatively well understood. The separatrix layer, on the other hand, must treat a range of complex physics mechanisms, including finite Larmor radius effects and the influence of cross-field diffusion. This paper treats both together for the first time. The cross-field diffusion is found to have the following influences on the separatrix region: (i) the density distribution is smoothed across the separatrix; (ii) density is no longer a flux surface function and (iii) the distribution function is not entirely Maxwellian. The net effect of including cross-field diffusion is a substantial reduction of the contribution of the ion polarization current from the separatrix layer region.

Cross-Field Motion of Plasma Blobs in an Open Magnetic Field Line Configuration

The radial propagation of blobs generated from plasma instabilities is investigated in an open magnetic field line configuration. Blob cross-field velocities and sizes are obtained from internal probe measurements using pattern recognition. By varying the ion mass, the normalized vertical blob scale a[over] is scanned from a[over] < 1 to a[over] > 1. An analytical expression for the blob velocity including cross-field ion polarization currents, parallel currents to the sheath, and ion-neutral collisions is derived and shows good quantitative agreement with the experimental data. In agreement with previous theoretical studies, this scaling shows that, for a[over] < 1, the blob velocity is limited by cross-field ion polarization currents, while for a[over] > 1 it is limited by parallel currents to the sheath.

The influence of rotation on the βN threshold for the 2∕1 neoclassical tearing mode in DIII-D

Utilizing a capability to vary neutral beam torque injection in the DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] tokamak, m∕n=2∕1 neoclassical tearing mode onset thresholds are found to fall by about one unit in βN, from ∼3 to ∼2, in ITER-like sawtoothing high-energy confinement modes of plasma operation [R. Aymar, Plasma Phys. Control. Fusion 42, B385 (2000)] as “co-injected” torque and rotation are reduced. However, increasing levels of torque and rotation in the counter-direction do not lead to corresponding rises in βN thresholds. More encouragingly, error field sensitivity is not found to increase in low rotation plasmas, as might be expected theoretically. These results pose an interesting physics problem, as well as raising concern for future devices such as ITER. Further analyses have explored possible physics origins of the behavior. They suggest many of the usual effects expected to lead to a rotation dependence (mode coupling, wall drag, ion polarization currents) are not significant, with instead models that depend on the size and sign of rotation shear playing a role. Onset behavior suggests the mode is close to being intrinsically (classically) unstable when it appears, and a conceptual explanation is offered for a mechanism by which rotation shear feeds into the onset process through changes to the classical tearing stability index, Δ′. Further parameter extensions and studies are desirable to fully resolve the underlying physics of this interesting process.

Drift-tearing magnetic islands in tokamak plasmas

A systematic fluid theory of nonlinear magnetic island dynamics in conventional low-β, large aspect-ratio, circular cross-section tokamak plasmas is developed using an extended magnetohydrodynamics model that incorporates diamagnetic flows, ion gyroviscosity, fast parallel electron heat transport, the ion sound wave, the drift wave, and average magnetic field-line curvature. The model excludes the compressible Alfvén wave, geodesic field-line curvature, neoclassical effects, and ion Landau damping. A collisional closure is used for plasma dynamics parallel to the magnetic field. Two distinct branches of island solutions are found, namely the “sonic” and “hypersonic” branches. Both branches are investigated analytically, using suitable ordering schemes, and in each case the problem is reduced to a relatively simple set of nonlinear differential equations that can be solved numerically via iteration. The solution determines the island phase velocity, relative to the plasma, and the effect of local currents on the island stability. Sonic islands are relatively wide, flatten both the temperature and density profiles, and tend to propagate close to the local ion fluid velocity. Hypersonic islands, on the other hand, are relatively narrow, only flatten the temperature profile, radiate drift-acoustic waves, and tend to propagate close to the local electron fluid velocity. The hypersonic solution branch ceases to exist above a critical island width. Under normal circumstances, both types of island are stabilized by local ion polarization currents.

Hypersonic drift-tearing magnetic islands in tokamak plasmas

A two-fluid theory of long wavelength, hypersonic, drift-tearing magnetic islands in low-collisionality, low-β plasmas possessing relatively weak magnetic shear is developed. The model assumes both slab geometry and cold ions, and neglects electron temperature and equilibrium current gradient effects. The problem is solved in three asymptotically matched regions. The “inner region” contains the island. However, the island emits electrostatic drift-acoustic waves that propagate into the surrounding “intermediate region,” where they are absorbed by the plasma. Since the waves carry momentum, the inner region exerts a net force on the intermediate region, and vice versa, giving rise to strong velocity shear in the region immediately surrounding the island. The intermediate region is matched to the surrounding “outer region,” in which ideal magnetohydrodynamic holds. Isolated hypersonic islands propagate with a velocity that lies between those of the unperturbed local ion and electron fluids, but is much closer to the latter. The ion polarization current is stabilizing, and increases with increasing island width. Finally, the hypersonic branch of isolated island solutions ceases to exist above a certain critical island width. Hypersonic islands whose widths exceed the critical width are hypothesized to bifurcate to the so-called “sonic” solution branch.

Filamentary Alfvénic structures excited at the edges of equatorial plasma bubbles

Abstract. Recent observations performed by the French DEMETER satellite at altitudes of about 710 km suggest that the generation of equatorial plasma bubbles correlates with the presence of filamentary structures of field aligned currents carried by Alfvén waves. These localized structures are located at the bubble edges. We study the dynamics of the equatorial plasma bubbles, taking into account that their motion is dictated by gravity driven and displacement currents. Ion-polarization currents appear to be crucial for the accurate description of the evolution of plasma bubbles in the high altitude ionosphere. During their eastward/westward motion the bubbles intersect gravity driven currents flowing transversely with respect to the background magnetic field. The circulation of these currents is prohibited by large density depressions located at the bubble edges acting as perfect insulators. As a result, in these localized regions the transverse currents have to be locally closed by field aligned currents. Such a physical process generates kinetic Alfvén waves which appear to be stationary in the plasma bubble reference frame. Using a two-dimensional model and "in situ" wave measurements on board the DEMETER spacecraft, we give estimates for the magnitude of the field aligned currents and the associated Alfvén fields.

The influence of the ion polarization current on magnetic island stability in a tokamak plasma

The influence of the ion polarization current on the stability of a constant-ψ magnetic island in a tokamak plasma is investigated numerically using a reduced two-fluid model in two-dimensional slab geometry. The polarization current is found to be negligibly small when the island is either too narrow or too wide. However, under certain circumstances, there exists an intermediate regime in which the polarization current is appreciable, and has a stabilizing influence on the island. This effect may account for the metastable nature of neoclassical tearing modes in tokamak plasmas.

Study of strong cross-field sheared flow with the vorticity probe in the Large Plasma Device

This work reports evidence for the existence of coherent structures in steady-state shear-flow driven plasmas in the Large Plasma Device [W. Gekelman et al., Rev. Sci. Instrum. 62, 2875 (1991)] facility at UCLA. The measurements are performed with the vorticity probe (VP), a probe that directly measures the plasma vorticity associated with the E×B shear flow by means of a method that is both simpler and more accurate than the methods used in neutral fluids. Because the rate of change of vorticity is a key quantity in nonlinear models, as in the Hasegawa-Mima equation, its direct measurement is critical for verification purposes. The physical origin of the rate of change of plasma vorticity from E×B flow is the divergence of the ion polarization current. Vortex coherent structures occur when the vorticity is a nonlinear function of the stream function. Statistical properties of vorticity are reported and shown to be consistent with the types of coherent structures created by the Kelvin-Helmholtz instability. Comparisons of the measured vortex characteristics with the results from nonlinear simulations of the systems is described.