Simple Magnetized Torus Research Articles

Intermittent structures and quasi-stationary equilibrium in a simple magnetized torus in open field line configuration

A steady regime dominated by intermittent blob and hole structures is identified in the plasma state of a simple magnetized torus by achieving a quasi-stationary equilibrium using an open magnetic field line configuration. The open helical field line configuration is characterized by a connection length, cm, and pitch ratio, This is realized by superposing a vertical magnetic fied, to the toroidal field, and the regime is achieved for mT. The combined effect of plasma rotation, arising from a substantial radial electric field, together with an open field line, results in vertically elongated plasma profile and an asymmetric sheared poloidal flow. The analysis shows the existence of density fluctuations exhibiting universal statistical properties, dominated by non-Gaussian blob events in the edge region and holes in the core plasma, separated by a region ascribed as blob birth zone corresponding to a velocity shear layer. Two-dimensional conditional averaging analyses of fluctuations indicate that blobs form in the sheared layer, when the leading edge of an elongated coherent structure breaks off by differential stretching exerted by the background fluctuating field. Convection of this isolated blob out of the contour corresponding to the maximum radial electric field in the low field side, leads to its ejection while holes move along the same contour driven back into the main plasma. The corresponding potential structure shows counter-rotating velocity field within oppositely charged structures, where the embedded electric field is consistent with the observed structure propagation. A comparison with cross-correlation analysis yields a similar conclusion except for a slight overestimation of the structure size and lifetime.

First results from the NORTH tokamak

NORTH is a small-sized tokamak located at the Technical University of Denmark. It can be operated both as a spherical tokamak and a simple magnetized torus (SMT). Here we show first experimental results. We discuss the setup of the device, including the layout of the vacuum vessel, the magnetic field coils, the power supply systems, the heating sources, diagnostics, and the control system. We present measurements in discharges that have been heated by electron cyclotron resonance heating at the fundamental resonance. The waves have been injected both from the low-field side and the high-field side, and rich fluctuation spectra in Langmuir probe and Rogowski coil signals are presented during the different plasma phases. Finally, we discuss research plans and further installations to be made on NORTH.

Investigating shear flow through continuum gyrokinetic simulations of limiter biasing in the Texas Helimak

Previous limiter-biasing experiments on the Texas Helimak, a simple magnetized torus, have been inconclusive on the effect of flow shear on turbulence levels. To investigate this, the first gyrokinetic simulations of limiter biasing in the Helimak using the plasma physics code Gkeyll have been carried out, and the results are presented here. For the scenarios considered, turbulence is mostly driven by the interchange instability, which depends on gradients of steady-state density profiles. An analysis of both experimental and simulation data demonstrates that shear rates are mostly less than local linear growth rates, and not all requirements for shear stabilization are met. Rather, the mostly vertical shear flow has an important effect on bulk transport and experimental steady-state density profiles, and changes in the gradients correspond to changes in turbulence levels.

Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices

We present algorithms and results from Gkeyll, a full-f continuum, electromagnetic gyrokinetic code, designed to study turbulence in the edge region of fusion devices. The edge is computationally very challenging, requiring robust algorithms that can handle large-amplitude fluctuations and stable interactions with plasma sheaths. We present an energy-conserving high-order discontinuous Galerkin scheme that solves gyrokinetic equations in Hamiltonian form. Efficiency is improved by a careful choice of basis functions and automatically generated computation kernels. Previous verification tests were performed in the straight-field-line large plasma device [Shi et al., J. Plasma Phys. 83, 905830304 (2017)] and the Texas Helimak, a simple magnetized torus [Bernard et al., Phys. Plasmas 26, 042301 (2019)], including the effect of end-plate biasing on turbulence. Results for the scrape-off layer for NSTX parameters with a model helical magnetic geometry with bad curvature have been obtained [Shi et al., Phys. Plasmas 26, 012307 (2019)]. In this paper, we present algorithms for the two formulations of electromagnetic gyrokinetics: the Hamiltonian and the symplectic. We describe each formulation and show results of benchmark tests. Although our scheme works for the Hamiltonian formulation, the presence of spurious numerical modes for high-β and large k⊥2ρs2 regimes shows that the symplectic formulation is more robust. We then review our recent algorithm for the symplectic formulation [Mandell et al., J. Plasma Phys. 86, 905860109 (2020)], along with example application of this new capability. Maintaining positivity of the distribution function can be challenging, and we describe a new and novel exponential recovery based algorithm to address this.

Gyrokinetic continuum simulations of plasma turbulence in the Texas Helimak

The first gyrokinetic simulations of plasma turbulence in the Texas Helimak device, a simple magnetized torus, are presented. The device has features similar to the scrape-off layer region of tokamaks, such as bad-curvature-driven instabilities and sheath boundary conditions on the end plates, which are included in these simulations. Comparisons between simulations and measurements from the experiment show not only similarities, including equilibrium profiles and fluctuation amplitudes that approach experimental values, but also some important quantitative differences. Both experimental and simulation results exhibit turbulence statistics that are characteristic of blob transport.

A solvable model for the basic properties of a simple magnetized plasma torus

A simple magnetized plasma torus is modeled by using a ‘top-hat’ density variation. The benefit of this simplification is an exactly solvable model, allowing for a few additions, such as an externally maintained parabolic steady state potential variation imposed on the plasma. The combined effects of the resulting plasma rotation and the plasma polarization due to magnetic field gradient particle drifts can be described. The stabilizing and confining effects of plasma rotation are explicitly demonstrated. In a special high plasma density limit the results are confirmed by a more general model, indicating that the results of the top-hat model can be used with confidence in more general cases. A small vertical magnetic field component can be included for a plasma with neutral collisions and its influence on the electron dynamics studied. The effects of ion–neutral collisions are also included. The rotation and polarization of the plasma has different effects on the time variations of the plasma density and potential. As a reference we use data from the Blaamann device at the University of Tromsø obtained by a movable multi-probe, measuring variations in density, floating potential and an electric field component. The fluctuations in the plasma are characterized by auto-correlations and by cross-correlations between the signal from a fixed reference probe and data. The model accounts adequately for the phase variations of the signals for varying spatial multi-probe positions.

Effect of magnetic shear on edge turbulence in SOL-like open field line configuration in QUEST

Intensity fluctuations are investigated using the fast camera imaging technique in the slab annular plasma as a function of magnetic shear and connection length in the spherical tokamak QUEST. Note that here QUEST is operated as a simple magnetized torus with a tight aspect ratio. Slab annular plasmas feature open magnetic field lines and can mimic the tokamak edge-scrape off layer (SOL)-like plasma attributes reasonably well. Three magnetic shear regimes are realized using three poloidal magnetic field (PF) coil pairs. A whole range of connection lengths (∼∞ ≥ Lc ≥ 5.5 m) is scanned by varying the PF strength for a given toroidal field for each magnetic shear regime. For the first time a systematic study of the effect of magnetic shear and field line pitch together on edge-SOL-like plasma fluctuations is being reported. Slab plasmas with intermediate magnetic shear are observed to be more susceptible to generate distinct blobs when Lc is reduced by increasing the PF strength. A distinct coherent mode appears only at the lowest magnetic shear slab featuring a deep potential well. Such mode is not apparent at other magnetic shear cases even at the same Lc. Finally, with a combination of PF coil pairs, both the features of intermediate and low magnetic shear slabs are shown to be realizable simultaneously. Significantly stronger blobs are observed with such combination of PF mirror ratios in the presence of a coherent mode. This study may provide better insight into the effect of magnetic configuration in the tokamak edge and SOL turbulence and can help in searching for better tools to control cross-field convective intermittent transport in tokamaks.

Millimeter-Wave Beam Scattering by Field-Aligned Blobs in Simple Magnetized Toroidal Plasmas.

The first direct experimental measurements of the scattering of a millimeter-wave beam by plasma blobs in a simple magnetized torus are reported. The wavelength of the beam is comparable to the characteristic size of the blob. Insitu Langmuir probe measurements show that fluctuations of the electron density induce correlated fluctuations of the transmitted power. A first-principles full-wave model, using conditionally sampled 2D electron density profiles, predicts fluctuations of the millimeter-wave power that are in agreement with experiments.

Tomography of a simply magnetized toroidal plasma

Optical emission spectroscopy is a passive diagnostic technique, which does not perturb the plasma state. In particular, in a hydrogen plasma, Balmer-alpha (Hα) emission can be easily measured in the visible range along a line of sight from outside the plasma vessel. Other emission lines in the visible spectral range from hydrogen atoms and molecules can be exploited too, in order to gather complementary pieces of information on the plasma state. Tomography allows us to capture bi-dimensional structures. We propose to adopt an emission spectroscopy tomography for studying the transverse profiles of magnetized plasmas when Abel inversion is not exploitable. An experimental campaign was carried out at the Thorello device, a simple magnetized torus. The characteristics of the profile extraction method, which we implemented for this purpose are discussed, together with a few results concerning the plasma profiles in a simply magnetized torus configuration.

Three-dimensional simulations of blob dynamics in a simple magnetized torus

The propagation of blobs, structures of localized enhanced plasma pressure, is studied in global three-dimensional simulations of a simple magnetized torus. In particular, we carry out single-seeded blob simulations to explore the dependence of the blob velocity with respect to its size. It is found that the velocity scaling for two-dimensional blobs is satisfied in the parameter space where polarization currents are the dominant damping mechanism. On the other hand, three-dimensional blobs propagate faster than their two-dimensional counterparts in the parallel current damping regime. A detailed analysis of the charge and current balance reveals that, in fact, the difference in speed is due to an overestimation of the strength of the sheath current term in the two-dimensional model compared to the self-consistent three-dimensional model.

Fluctuations and intermittent poloidal transport in a simple toroidal plasma

In a simple magnetized toroidal plasma, fluctuation induced poloidal flux is found to be significant in magnitude. The probability distribution function of the fluctuation induced poloidal flux is observed to be strongly non-Gaussian in nature; however, in some cases, the distribution shows good agreement with the analytical form [Carreras et al., Phys. Plasmas 3, 2664 (1996)], assuming a coupling between the near Gaussian density and poloidal velocity fluctuations. The observed non-Gaussian nature of the fluctuation induced poloidal flux and other plasma parameters such as density and fluctuating poloidal velocity in this device is due to intermittent and bursty nature of poloidal transport. In the simple magnetized torus used here, such an intermittent fluctuation induced poloidal flux is found to play a crucial role in generating the poloidal flow.

Basic investigations of electrostatic turbulence and its interaction with plasma and suprathermal ions in a simple magnetized toroidal plasma

Progress in basic understanding of turbulence and its influence on the transport both of the plasma bulk and of suprathermal components is achieved in the TORPEX simple magnetized torus. This configuration combines a microwave plasma production scheme with a quasi-equilibrium generated by a toroidal magnetic field, onto which a small vertical component is superimposed, simulating a simplified form of tokamak scrape-off layers. After having clarified the formation of blobs in ideal interchange turbulence, TORPEX experiments elucidated the mechanisms behind the blob motion, with a general scaling law relating their size and speed. The parallel currents associated with the blobs, responsible for the damping of the charge separation that develops inside them, hence determining their cross-field velocity, have been measured. The blob dynamics is influenced by creating convective cells with biased electrodes, arranged in an array on a metal limiter. Depending on the biasing scheme, radial and vertical blob velocities can be varied. Suprathermal ion transport in small-scale turbulence is also investigated on TORPEX. Suprathermal ions are generated by a miniaturized lithium source, and are detected using a movable double-gridded energy analyser. We characterize vertical and radial spreading of the ion beam, associated with the ideal interchange-dominated plasma turbulence, as a function of the suprathermal ion energy and the plasma temperature. Experimental results are in good agreement with global fluid simulations, including in cases of non-diffusive behaviour. To investigate the interaction of plasma and suprathermal particles with instabilities and turbulence in magnetic configurations of increasing complexity, a closed field line configuration has recently been implemented on TORPEX, based on a current-carrying wire suspended in the vacuum chamber. First measurements indicate the creation of circular symmetric profiles centred on the magnetic axis, and instabilities driven in the region of strong gradients, with a strong ballooning character.

Suprathermal ion transport in simple magnetized torus configurations

Inspired by suprathermal ion experiments in the basic plasma experiment TORPEX, the transport of suprathermal ions in ideal interchange mode turbulence is theoretically examined in the simple magnetized torus configuration. We follow ion tracer trajectories as specified by ideal interchange mode turbulence imported from a numerical simulation of drift-reduced Braginskii equations. Using the variance of displacements, σ2(t)∼tγ, we find that γ depends strongly on suprathermal ion injection energy and the relative magnitude of turbulent fluctuations. The value of γ also changes significantly as a function of time after injection, through three distinguishable phases: ballistic, interaction, and asymmetric. During the interaction phase, we find the remarkable presence of three regimes of dispersion: superdiffusive, diffusive, and subdiffusive, depending on the energy of the suprathermal ions and the amplitude of the turbulent fluctuations. We contrast these results with those from a “slab” magnetic geometry in which subdiffusion does not occur during the interaction phase. Initial results from TORPEX are consistent with data from a new synthetic diagnostic used to interpret our simulation results. The simplicity of the simple magnetized torus makes the present work of interest to analyses of more complicated contexts ranging from fusion devices to astrophysics and space plasma physics.

Blob current structures in TORPEX plasmas: experimental measurements and numerical simulations

In the simple magnetized torus TORPEX, field-aligned blobs originate from ideal interchange waves and propagate radially outward due to ∇B and curvature induced drifts. Time-resolved two-dimensional measurements of the field-aligned current density J∥ associated with blobs are obtained from conditionally sampled data from a single-sided Langmuir probe and a specially designed current probe. The profile of J∥ exhibits an asymmetric dipolar structure, which originates from the polarization of the blob and is consistent with sheath boundary conditions. The asymmetry results from the non-linear dependence of J∥ at the sheath edge upon the floating potential. Using internal measurements, we directly confirm the existence of two regimes, in which parallel currents to the sheath do or do not significantly damp charge separation and thus blob radial velocity. To investigate the effect of the observed asymmetry of J∥ on the blob motion, we carried out numerical simulations of seeded blobs, using a two-field fluid model, which evolves electron density and vorticity. Simulations are performed spanning a wide range of blob sizes covering both regimes. We use either the complete or a linearized form for the sheath dissipation term in the vorticity equation. The structure of the parallel current density and plasma potential is found to be different in the two cases. Asymmetric profiles are observed in simulations with the complete form, while symmetric profiles are obtained when a linearized form is used. Negligible effects are, however, observed in terms of blob radial velocity. The relevance of the present results for fusion devices is also discussed.

Territorial characteristics of low frequency electrostatic fluctuations in a simple magnetized torus

This paper presents an experimental investigation of turbulence in simple toroidal plasma devices without rotational transform. It is argued that Rayleigh–Taylor (flute interchange) mode may be one of the source mechanisms for the observed turbulence but is not sufficient to explain its observed global characteristics. Taking BETA device as an example, we show that pure Rayleigh–Taylor mode cannot explain (i) the observation of mode maximum at the location other than where density scale length is minimum, (ii) the comparable value of amplitude level of fluctuations in good curvature region, and (iii) the decrease in the mode amplitude with increasing magnetic field. Investigations have revealed that there exists not only poloidal plasma flow but also that it is sheared. Including this effect explains the first observation. However, modification brought about by velocity shear in the Rayleigh–Taylor mode still does not explain our second and third observations. We have taken an approach that since Rayleigh–Taylor is not excited in a good curvature region, it cannot be the source of turbulence there. Nor is it defensible to say that turbulence born in a bad curvature region is carried over through E×B rotation to the good curvature region. Consequently, we have invoked cross-field Simon–Hoh instability for this region. Experimental evidence supporting our proposal is presented. This paper concludes that toroidal devices have simultaneous existence of different self-consistent sources of turbulence in different regions of the device.

Life cycle of density structures in a simple magnetized torus

This paper presents an experimental investigation of spatio-temporal structures embedded in the low-frequency electrostatic fluctuations in a toroidal plasma device without rotational transform. The structures are extracted using the conditional averaging technique. The fundamental features and life cycle of the structures from their evolution to demise have been studied. The dipole structures formed rotate in poloidal cross-section with a propagation velocity of ∼9×104 cm s−1. The direction of propagation is the same as the electron diamagnetic drift direction and the E×B rotation direction. We show that these structures evolve in two phases. In the first phase, the spatial extent and the measure of intensity of the structures increase considerably, indicating that ingestion of plasma is more than the loss to the limiter due to diffusion. In the second phase, decay of the structures begins. There are two time scales; the longer one precedes the shorter one. The decay is exponential, indicating that it is solely due to diffusion of plasma to the limiter. This indicates that what appears to be a perpetual periodicity-dominated time series actually consists of a series of large spatio-temporal structures having a definite life cycle of secular growth and decay phases. We interpret this result to mean that BETA plasma possesses a dynamic equilibrium in which the plasma oscillates between two non-equilibrium states.

Turbulence Phase Space in Simple Magnetized Toroidal Plasmas

Plasma turbulence in a simple magnetized torus (SMT) is explored for the first time with three-dimensional global fluid simulations. Three turbulence regimes are described: an ideal interchange mode regime, a previously undiscovered resistive interchange mode regime, and a drift-wave regime. As the pitch of the field lines is decreased, the simulations exhibit a transition from the first regime to the second, while the third--the drift-wave regime--is likely accessible to the experiments only at very low collisionalities.

Observation of a critical pressure gradient for the stabilization of interchange modes in simple magnetized toroidal plasmas

The existence of a critical pressure gradient needed to drive the interchange instability is experimentally demonstrated in the simple magnetized torus TORoidal Plasma EXperiment [A. Fasoli et al., Phys. Plasmas 13, 055902 (2006)]. This gradient is reached during a scan in the neutral gas pressure pn. Around a critical value for pn, depending on the magnetic configuration and on the injected rf power, a small increase in the neutral gas pressure triggers a transition in the plasma behavior. The pressure profile is locally flattened, stabilizing the interchange mode observed at lower neutral gas densities. The measured value for the critical gradient is close to the linear theory estimate.

Advection of long lived density blobs in the turbulent state of a simple magnetized torus plasma

The turbulent regime of a simple magnetized toroidal plasma column has been studied in the plasma device Thorello. The detection and the study of the spatio-temporal evolution of structures have been performed by means of conditional sampling techniques as well as other statistical tools. As a result the evidence of plasma blob formation and expulsion from the edge of the main plasma column has been obtained. The relation between structure phenomenology and statistical characteristics of the turbulent regime has been investigated. The motion of the density structures in the edge region of our device does not look ballistic but rather driven by the overall potential profile established in the turbulent state. Potential fluctuations are strongly anti-correlated with density structures, located in the same position and somewhat more extended. They provide a shallow potential well with a flat bottom and quite sharp edges surrounding and co-moving with the blobs. Blob lifetime exceeds the residence time associated with the overall E × B drift field. Then such persistent structures provide a means for a net convection of the charged particles to the limiter, across the magnetic field and beyond the edge region of the plasma.

Transport scaling in interchange-driven toroidal plasmas

Two-dimensional fluid simulations of a simple magnetized torus are presented, in which the vertical and toroidal components of the magnetic field create helicoidal field lines that terminate on the upper and lower walls of the plasma chamber. The simulations self-consistently evolve the full radial profiles of the electric potential, density, and electron temperature in the presence of three competing effects: the cross-field turbulent transport driven by the interchange instability, parallel losses to the upper and lower walls, and the input of particles and heat by external plasma sources. Considering parameter regimes in which equilibrium E×B shear flow effects are weak, we study the dependence of the plasma profiles—in particular the pressure profile scale length—on the parameters of the system. Analytical scalings are obtained that show remarkable agreement with the simulations.