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The confinement of pure electron plasmas in the Columbia Non-neutral Torus (CNT) [T. Sunn Pedersen et al., Fusion Sci. Technol. 50, 372 (2006)] can be enhanced by the large radial electric field due to space charge. However the benefits are limited by two effects: (1) The Evector ×Bvector precession can, at low B-fields, resonate with the particle motion along the magnetic field lines, which gives large excursions in the trajectories. (2) Variations in the electric potential on magnetic surfaces, inherent to CNT equilibrium, add to the complexity of the trajectories and can also lead to large excursions. The second effect is sensitive to the conductive structures outside the plasma boundary. Results from a new code to investigate electron trajectories in the magnetic and electric field expected in CNT are presented. [ABSTRACT FROM AUTHOR]

Measurements of the equilibria of plasmas created by emission from a biased filament located off the magnetic axis in the Columbia Non-neutral Torus (CNT) [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois et al., Fusion Sci. Technol. 50, 372 (2006)] show that such plasmas have equilibrium properties consistent with the inner surfaces being in a state of cross-surface thermal equilibrium. Numerical solutions to the equilibrium equation were used to fit the experimental data and demonstrate consistency with cross-surface thermal equilibrium. Previous experiments in CNT showed that constant temperatures across magnetic surfaces are characteristic of CNT plasmas, implying thermal confinement times much less than particle confinement times. These results show that when emitting off axis there is a volume of inner surfaces where diffusion into that region is balanced by outward transport, producing a Boltzmann distribution of electrons. When combined with the low thermal energy confinement time this is a cross-surface thermal equilibrium. [ABSTRACT FROM AUTHOR]

Measurements of confinement jumps in pure electron plasmas confined on magnetic surfaces are presented and discussed. The experiments were performed in the Columbia non-neutral torus stellarator [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois, Q. Marksteiner, N. Pomphrey, W. Reiersen, F. Dahlgren, and X. Sarasola, Fusion Sci. Technol. 50, 372 (2006)]. The jumps exhibit hysteresis and are associated with a negative differential resistance. The jumps occur at particular emission currents of the biased emissive filaments that create and sustain the electron plasmas independent of the methods used to affect the emission current. This observation, as well as other experimental evidence, supports that the jumps are caused by a cathode instability. The jumps can also be triggered by the application of a bias potential on a nearby mesh. In most circumstances, the jumps occur between two stable but measurably different equilibrium states. These different equilibrium states have substantially different confinement times. The cathode physics is important for the jumps because the cathode instability provides the perturbation that triggers the jump of the whole plasma into the other equilibrium state, but as mentioned, an external electrostatic perturbation is also capable of triggering such a jump. [ABSTRACT FROM AUTHOR]

Significant variations in the density and potential along the axis of a pure electron plasma in the Columbia Non-neutral Torus (CNT) stellarator have now been measured. Large variations along the magnetic field are predicted by three-dimensional equilibrium reconstructions of CNT plasmas and by simple electrostatic and geometric arguments [Lefrancois and Pedersen, Phys. Plasmas 13, 120702 (2006)]. The density variation, naxis,[lowercase_phi_synonym]=0°/naxis,[lowercase_phi_synonym]=90°, is measured directly for several different plasma equilibria, and has a median value of 7.8, consistent with the predicted density variation of 4.4, because the error bars are large. The associated variation in potential predicted from the Boltzmann relation, eΔ[uppercase_phi_synonym]/Te=ln(4.4)=1.5, was also measured experimentally. The median measured, eΔ[uppercase_phi_synonym]/Te, was 1.1, which is of the predicted sign and in rough agreement with the measurements, but smaller than predicted. The difference is statistically significant, but might be related to the imperfect numerical modeling of the complicated electrostatic boundary conditions in CNT. The measured variations reconfirm that the Debye lengths of these plasmas are small. [ABSTRACT FROM AUTHOR]

The Columbia Non-neutral Torus (CNT) [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois, Q. Marksteiner, N. Pomphrey, W. Reiersen, F. Dahlgreen, and X. Sarasola, Fusion Sci. Technol. 50, 372 (2006)] is a stellarator used to study non-neutral plasmas confined on magnetic surfaces. A detailed experimental study of confinement of pure electron plasmas in CNT is described here. Electrons are introduced into the magnetic surfaces by placing a biased thermionic emitter on the magnetic axis. As reported previously, the insulated rods holding this and other emitter filaments contribute to the radial transport by charging up negatively and creating E×B convective transport cells. A model for the rod-driven transport is presented and compared to the measured transport rates under a number of different conditions, finding good agreement. Neutrals also drive transport, and by varying the neutral pressure in the experiment, the effects of rod-driven and neutral-driven transport are separated. The neutral-driven electron loss rate scales linearly with neutral pressure. The neutral driven transport, presumably caused by electron-neutral collisions, is much greater than theoretical estimates for neoclassical diffusion in a classical stellarator with strong radial electric fields. In fact the confinement time is on the order of the electron-neutral collision time. Ion accumulation, electron attachment, and other effects are considered, but do not explain the observed transport rates. [ABSTRACT FROM AUTHOR]

A retractable electron emitter has been constructed for the creation of unperturbed pure electron plasmas on magnetic surfaces in the Columbia Non-neutral Torus stellarator. The previous method of electron emission using emitters mounted on stationary rods limited the confinement time to 20 ms. A pneumatically driven system that can retract from the magnetic axis to the last closed flux surface in less than 20 ms while filling the surfaces with electrons was designed. The motion of the retractable emitter was modeled with a system of dynamical equations. The measured position versus time of the emitter agrees well with the model and the fastest axis-to-edge retraction was measured to be 20 ms with 40 psig helium gas driving the pneumatic piston. [ABSTRACT FROM AUTHOR]

Cold pure electron plasmas confined in Penning-Malmberg traps with mirror fields are known to exhibit density variations along field lines, such that the density is roughly proportional to the magnetic field strength, n∼B. The Columbia Nonneutral Torus (CNT) is the first stellarator designed to study pure electron plasmas, and exhibits substantial mirroring, with Bmax≈1.8Bmin. However, results of a three-dimensional equilibrium solver, presented in this Letter, predict a factor of 5.3 increase in density from the minimum-field cross section to the maximum-field cross section along the magnetic axis, for a 1.5 cm Debye length plasma (a≈15 cm for CNT). In this Letter, it is shown that the density variation of electron plasmas in mirror traps can be significantly enhanced in a device that has a cross section that varies from cylinder-like to slab-like, such as the CNT. A simple analytic expression is derived that describes the axial density variation in such a device, and it is found to agree well with the computational predictions for CNT. [ABSTRACT FROM AUTHOR]

Presented for the first time are numerical solutions to the three-dimensional nonlinear equilibrium equation for single-species plasmas confined on magnetic surfaces and surrounded by an equipotential boundary. The major-radial shift of such plasmas is found to be outward, qualitatively similar to the Shafranov shift of quasineutral plasmas confined on magnetic surfaces. However, this is the opposite of what occurs in the pure toroidal field equilibria of non-neutral plasmas (i.e., in the absence of magnetic surfaces). The effect of varying the number of Debye lengths in the plasma for the three-dimensional (3D) model is in agreement with previous 2D calculations: the potential varies significantly on magnetic surfaces for plasmas with few Debye lengths (a≲λd), and tends to be constant on surfaces when many Debye lengths are present (a>=10λd). For the case of a conducting boundary that does not conform to the outer magnetic surface, the plasma is shifted towards the conductor and the potential varies significantly on magnetic surfaces near the plasma edge. Debye shielding effects are clearly demonstrated when a nonuniform bias is applied to the boundary. Computed equilibrium profiles are presented for the Columbia Non-Neutral Torus [T. S. Pedersen, A. H. Boozer, J. P. Kermer, R. Lefrancois, F. Dahlgren, N. Pomphrey, W. Reiersen, and W. Dorland, Fusion Sci. Technol. 46, 200 (2004)], a stellarator designed to confine non-neutral plasmas. [ABSTRACT FROM AUTHOR]

The equilibrium, stability, and transport of pure electron plasmas confined on magnetic surfaces is reviewed. The prospects for creation of partly neutralized plasmas and electron-positron plasmas confined in a stellarator are discussed. The Columbia Non-neutral Torus, a small ultrahigh vacuum stellarator being constructed at Columbia University, is being built to systematically study non-neutral plasmas confined on magnetic surfaces. The experimental design is discussed in the context of relevant physics parameters, and the initial experimental plans for creation and diagnosis of pure electron plasmas are discussed. [ABSTRACT FROM AUTHOR]

Two-dimensional solutions to the equilibrium equation for finite temperature, low density pure electron plasmas confined on magnetic surfaces [T. S. Pedersen and A. H. Boozer, Phys. Rev. Lett. 88, 205002 (2002)] are presented for the first time. These equilibria are not maximum energy states, in contrast to Penning trap equilibria [J. Notte et al., Phys. Rev. Lett. 69, 3056 (1992)]. By varying the number of Debye lengths in the plasma, a/λ[sub D], from 0.1 to 10, we explore both relatively warm and relatively cold plasma equilibria. The effects of different boundary conditions and the implications for collisional transport rates are discussed. [ABSTRACT FROM AUTHOR]

Reports on the numerical solution of the Hasegawa-Wakatani model equations for resistive drift waves for a range of values of the coupling due to the parallel electron motion. Quantification of turbulent flow using the largest Lyapunov exponent; Recognition of the decomposition of the flow into distinct regions with different relative dispersion as the Weiss decomposition.

Visualizations of magnetic surfaces are a valuable diagnostic in the Columbia Non-neutral Torus (CNT). The CNT is a compact stellarator, which is currently being used to study non-neutral plasmas confined on magnetic surfaces. The full 3-D shapes of magnetic surfaces created by CNT's simple four circular coil geometry are readily visualized by using an electron beam and neutral gas. These visualizations are useful for probe alignment and the confirmation of the magnetic surface topology, and they were necessary for the recent installation of a conducting boundary conforming to the last closed magnetic surface. [ABSTRACT FROM AUTHOR]

Accumulation of ions can alter and may destabilize the equilibrium of an electron plasma confined on magnetic surfaces. An analysis of ion sources and ion content in the Columbia Non-neutral Torus (CNT) [T.S. Pedersen, J.P. Kremer, R.G. Lefrancois, Q. Marksteiner, N. Pomphrey, W. Reiersen, F. Dahlgreen, and X. Sarasola, Fusion Sci. Technol. 50, 372 (2006)] is presented. In CNT ions are created preferentially at locations of high electron temperature, near the outer magnetic surfaces. A volumetric integral of neνiz gives an ion creation rate of 2.8×1011 ions/s. This rate of accumulation would cause neutralization of a plasma with 1011 electrons in about half a second. This is not observed experimentally, however, because currently in CNT ions are lost through recombination on insulated rods. From a steady-state balance between the calculated ion creation and loss rates, the equilibrium ion density in a 2×10-8 Torr neutral pressure, 7.5×1011 m-3 electron density plasma in CNT is calculated to be ni=6.2×109 m-3, or 0.8%. The ion density is experimentally measured through the measurement of the ion saturation current on a large area probe to be about 6.0×109 m-3 for these plasmas, which is in good agreement with the predicted value. [ABSTRACT FROM AUTHOR]

Rotating external kink instabilities have been suppressed as well as excited in a tokamak using active magnetic coils that directly couple to the plasma through gaps in passive stabilizing conducting shells that surround the plasma. The kink instability has a complex growth rate, approximately (3+i2π5)×103 s-1, and is near the ideal wall stability limit when discharges are prepared with a rapid plasma current ramp and adjusted to have an edge safety factor near 3. The active control coils are driven by a digital mode control feedback system that uses multiple field-programmable gate arrays to analyze signals from 20 poloidal field sensors and achieve high-speed feedback control. The feedback coil geometry used was designed to optimize feedback effectiveness. Signal processing is of critical importance to optimize phase transfer functions for control of rotating modes. [ABSTRACT FROM AUTHOR]

In magnetic confinement fusion research, the achievement of high plasma pressure is key to reaching the goal of net energy production. The magnetohydrodynamic (MHD) model is used to self-consistently calculate the effects the plasma pressure induces on the magnetic field used to confine the plasma. Such MHD calculations—usually done computationally—serve as input for the assessment of a number of important physics questions. The variational moments equilibrium code (VMEC) is the most widely used to evaluate 3D ideal-MHD equilibria, as prominently present in stellarators. However, considering the computational cost, it is rarely used in large-scale or online applications (e.g. Bayesian scientific modeling, real-time plasma control). Access to fast MHD equilibria is a challenging problem in fusion research, one which machine learning could effectively address. In this paper, we present artificial neural network (NN) models able to quickly compute the equilibrium magnetic field of Wendelstein 7-X. Magnetic configurations that extensively cover the device operational space, and plasma profiles with volume-averaged normalized plasma pressure ⟨β⟩ (β =) up to 5% and non-zero net toroidal current are included in the data set. By using convolutional layers, the spectral representation of the magnetic flux surfaces can be efficiently computed with a single network. To discover better models, a Bayesian hyper-parameter search is carried out, and 3D convolutional NNs are found to outperform feed-forward fully-connected NNs. The achieved normalized root-mean-squared error, the ratio between the regression error and the spread of the data, ranges from 1% to 20% across the different scenarios. The model inference time for a single equilibrium is on the order of milliseconds. Finally, this work shows the feasibility of a fast NN drop-in surrogate model for VMEC, and it opens up new operational scenarios where target applications could make use of magnetic equilibria at unprecedented scales. [ABSTRACT FROM AUTHOR]

The operational regimes in the first divertor campaign of W7-X were limited by unexpectedly high heat loads on certain baffle tiles. In the high-mirror configuration, a permanent hotspot on the baffle plate was detected by the thermographic system, which was further confirmed during the post-campaign inspections of the plasma-facing components. The maximum heat load on three baffle tiles reached about 4.5 MW m−2, which was almost an order of magnitude above its designed value of 0.5 MW m−2. The paper presents a detailed analysis to understand how the baffle plate, which is originally designed to screen the recycling neutrals and is therefore hidden from the hot plasma, can receive such a high heat load - a level that is expected for target plates. Three main causes have been identified: 1) the three baffle tiles are radially only about 5 mm away from a main heat channel towards a target, which is much shorter than the radial power decay length of several centimeters derived from the thermographic measurements in this region; 2) the three baffle tiles are intersected with field-lines of about 30 m length, which are long enough to collect considerable amount of heat via cross-field transport; 3) the baffle tiles have locally large grazing angles. In addition, the analysis method shown in this paper is of general use to estimate the heat flows in shadow areas of targets and thus to evaluate heat loads on the potentially critical components occurring in these areas, especially required for the design of complex 3D divertors like the one in W7-X. [ABSTRACT FROM AUTHOR]

Following up on earlier work which demonstrated an improved numerical stellarator coil design optimization performance by the use of stochastic optimization (Lobsien et al., Nucl. Fusion, vol. 58 (10), 2018, 106013), it is demonstrated here that significant further improvements can be made – lower field errors and improved robustness – for a Wendelstein 7-X test case. This is done by increasing the sample size and applying fully three-dimensional perturbations, but most importantly, by changing the design sequence in which the optimization targets are applied: optimization for field error is conducted first, with coil shape penalties only added to the objective function at a later step in the design process. A robust, feasible coil configuration with a local maximum field error of 3.66 % and an average field error of 0.95 % is achieved here, as compared to a maximum local field error of 6.08 % and average field error of 1.56 % found in our earlier work. These new results are compared to those found without stochastic optimization using the FOCUS and ONSET suites. The relationship between local minima in the optimization space and coil shape penalties is also discussed. [ABSTRACT FROM AUTHOR]

To improve the reliability of the ASDEX pressure gauges in the plasma vessel of the Wendelstein 7-X stellarator, nine of them were equipped with a LaB6 crystal electron emitter for the first time. These crystal cathode pressure gauges were operated during the last campaign in 2018 (operation phase 1.2b) with only 2 A heating current for over 40 h in a magnetic field of about 2.1 T without failure. Owing to this excellent performance, we have decided to equip all pressure gauges with crystal cathodes for the next campaign of Wendelstein 7-X (operation phase 2). We report on a pretest in a superconducting magnet, show a measurement of the neutral pressure in Wendelstein 7-X, and demonstrate the long-term stability of the crystal cathode pressure gauges. [ABSTRACT FROM AUTHOR]

A multi-purpose overview video system, based on EDICAM cameras, was set up at Wendelstein 7-X stellarator, in order to fulfill both machine protection and scientific observation purposes. Places of strong plasma-wall interaction, which can easily evolve to hot-spots, were detected by the EDICAM operators during plasma operation, based on intense local light emission. The EDICAM system was successfully used to avoid hot-spot formation during the commissioning of magnetic configurations with plasma operation. Featuring non-destructive readout capability, smaller areas of the torus interior could be monitored ca. two orders of magnitude faster, in parallel to the normal full frame overview. These fast measurements could be used to show the presence of plasma turbulence (filaments), also detected by other diagnostic systems. [ABSTRACT FROM AUTHOR]

In the stellarator Wendelstein 7-X with its twisted 3D magnetic field geometry, studies of material migration with respect to first wall components become very important in view of the envisioned long-pulse operation. A variety of erosion/deposition samples were installed on the plasma-facing components exposed at three different nominal heat load levels between 0.1 and 10 MW/m2. After the first successful operation phase in divertor configuration, all the probes at higher and lower load levels were removed, whereas at the intermediate load levels, 352 out of 30 000 screws have been exchanged at selected locations along the toroidal and poloidal directions. The exchanged probes have been analyzed by various measurement techniques. At the higher load levels where the probes were installed within the divertor, heavy erosion has been observed presumably at the strike line positions. Both, erosion and deposition phenomena have been found on the screw heads. The optical reflection measurement profile of the whole plasma vessel show the deposition patterns at similar locations in all the five modules. At the low load level, the Si-wafer probes are under investigation. [ABSTRACT FROM AUTHOR]

The modular stellarator Wendelstein 7-X in Greifswald (Germany) was successfully taken into operation in 2015. In the next experimental campaign in 2017, divertor plasmas are planned up to 80 MJ input power limited by the largely uncooled first wall. In 2020, long pulse plasmas are foreseen once the water cooled first wall has been completed. In long pulses, bootstrap currents gradually develop in the plasma, which causes a shift of the strike lines onto the relatively poorly cooled edge of the divertor. To prevent overloading of these edges, a so-called scraper element can be positioned in front of the divertor, intersecting those strike lines that would otherwise hit the divertor edges. As a result, these edges are protected but as a drawback the pumping efficiency of neutrals is also reduced. To assess the impact, two uncooled scraper elements will be installed in the mid-break of the next campaign, one at the top of module 5 and one at the bottom of module 3. The divertor and scraper elements are monitored with Langmuir probes, neutral gas manometers, thermocouples and IR and VIS cameras viewing the plasma facing surface. This paper describes the integration of the uncooled scraper elements and their diagnostics in Wendelstein 7-X. A dedicated low power plasma scenario was developed to evaluate the uncooled scraper element, allowing for reduced heat loads and design simplifications. It is demonstrated that the diagnostics are still capable of measuring the impact of the scraper element. An easily accessible socket to plug in the cables of the diagnostics integrated in the scraper was designed and installed up front to allow for a fast and simple installation of the scraper element in the short mid-break. [ABSTRACT FROM AUTHOR]

The simulation and experimental optimization of a Kalman filter feedback control algorithm for n=1 tokamak external kink modes are reported. In order to achieve the highest plasma pressure limits in ITER, resistive wall mode stabilization is required [T. C. Hender et al., Nucl. Fusion 47, S128 (2007)] and feedback algorithms will need to distinguish the mode from noise due to other magnetohydrodynamic activity. The Kalman filter contains an internal model that captures the dynamics of a rotating, growing n=1 mode. This model is actively compared with real-time measurements to produce an optimal estimate for the mode’s amplitude and phase. On the High Beta Tokamak-Extended Pulse experiment [T. H. Ivers et al., Phys. Plasmas 3, 1926 (1996)], the Kalman filter algorithm is implemented using a set of digital, field-programmable gate array controllers with 10 μs latencies. Signals from an array of 20 poloidal sensor coils are used to measure the n=1 mode, and the feedback control is applied using 40 poloidally and toroidally localized control coils. The feedback system with the Kalman filter is able to suppress the external kink mode over a broad range of phase angles between the sensed mode and applied control field. Scans of filter parameters show good agreement between simulation and experiment, and feedback suppression and excitation of the kink mode are enhanced in experiments when a filter made using optimal parameters from the scans is used. [ABSTRACT FROM AUTHOR]

The authors report on the first experimental demonstration of active feedback suppression of rotating external kink modes near the ideal wall limit in a tokamak using Kalman filtering to discriminate the n=1 kink mode from background noise. The Kalman filter contains an internal model that captures the dynamics of a rotating, growing n=1 mode. Suppression of the external kink mode is demonstrated over a broad range of phase angles between the sensed mode and applied control field, and performance is robust at noise levels that render proportional gain feedback ineffective. Suppression of the kink mode is accomplished without excitation of higher frequencies as was observed in previous experiments using lead-lag loop compensation [A. J. Klein et al., Phys Plasmas 12, 040703 (2005)]. [ABSTRACT FROM AUTHOR]

Publisher's Note: "Performance of new crystal cathode pressure gauges for long-pulse operation in the Wendelstein 7-X stellarator" [Rev. Sci. Instrum. This article was originally published online on 17 December 2019 with a typographical error on page 4, paragraph 2: "(p = C SP * sp I SB e sb )" should have been "(p = C SP * sp I SB i sb )." All online versions of the article were corrected on 20 December 2019; the article is correct as it appears in the printed version of the journal. [Extracted from the article]