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We describe an improvement on the magnetic scalar potential approach to design an electromagnet, which incorporates the need to wind the coil as a helix. Any magnetic field that can be described by a magnetic scalar potential is produced with high fidelity within a Target region; all fields are confined within a larger Return. The helical winding only affects the field in the Return.
Overview of University of Colorado Efforts: The University of Colorado group has focused on two primary fronts during the grant period: development of a variety of multi-point diagnostic and/or imaging analysis techniques, and momentum-transport related experiments on a variety of devices (NSTX at PPPL, CSDX at UCSD, LAPD at UCLA, DIII-D at GA). Experimental work has taken advantage of several diagnostic instruments, including fast-framing cameras for imaging of electron density fluctuations (either directly or using injected gas puffs), ECEI for imaging of electron temperature fluctuations, and multi-tipped Langmuir and magnetic probes for corroborating measurements of Reynolds and Maxwell stresses. Mode Characterization in CSDX: We have performed a series of experiments at the CSDX linear device at UCSD, in collaboration with Center PI G. Tynan's group. The experiments included a detailed study of velocity estimation techniques, including direct comparisons between Langmuir probes and image-based velocimetry from fast-framing camera data. We used the camera data in a second set of studies to identify the spatial and spectral structure of coherent modes, which illuminates wave behavior to a level of detail previously unavailable, and enables direct comparison of dispersion curves to theoretical estimates. In another CSDX study, similar techniques were used to demonstrate a controlled transition from nonlinearly coupled discrete eigenmodes to fully developed broadband turbulence. The axial magnetic field was varied from 40-240 mT, which drove the transition. At low magnetic fields, the plasma is dominated by drift waves. As the magnetic field is increased, a strong potential gradient at the edge introduces an ExB shear-driven instability. At the transition, another mode with signatures of a rotation-induced Rayleigh–Taylor instability appears at the central plasma region. Concurrently, large axial velocities were found in the plasma core. For larger magnetic fields, all of the instabilities co-exist, leading to rich plasma dynamics and fully developed broadband turbulence. Edge-Turbulence and Flow Experiments in NSTX: A series of Gas Puff Imaging (GPI) observations on NSTX revealed a quasi-periodic oscillation in the plasma edge preceding the L-H transition in a limited set of neutral beam heated plasmas. These ~3 kHz flow oscillations exhibit both long wavelength and long correlation lengths, suggesting they are zonal-flow-like. The flow oscillations are strongly correlated with modulations of the level of edge turbulence, thus the system appears to undergo a predator--prey-type limit-cycle preceding the L-H transition. However, a clear trigger for the L-H transition was not observed. Reynolds stress profiles were obtained directly from image velocimetry for L-mode periods ELM-Precursor Studies in NSTX: A separate study based on NSTX-GPI data captured the two-dimensional evolution of edge-localized mode (ELM) precursors. Precursor events were observed preceding ELMs and ELM-induced H–L back-transitions in radio-frequency heated H-mode plasmas, and the growth of the precursor mode through the ELM filamentation was imaged in the plane perpendicular to the local B-field. Strong edge intensity modulations appeared to propagate in the electron diamagnetic direction while steadily drifting radially outwards. Intensity fluctuations were observed at frequencies around 20 kHz and wavenumbers of 0.05-0.2 cm -1 . Upon growing to a trigger point, precursor fluctuations were seen to form filamentary structures and move into the scrape-off layer (SOL) explosively with radial velocities peaking at 8 km/s. Once in the SOL, filaments reverse their propagation direction and travel in the ion diamagnetic direction. Edge intensity fluctuations were strongly correlated with magnetic signals from Mirnov coils, and toroidally distributed coils estimated toroidal mode numbers of n=5-10. Quantitatively similar precursors have been observed in ohmic H-mode plasmas as well, though significantly fewer events are seen in the ohmic cases and none were observed in the near-threshold NBI H-modes studied. Development of Velocimetry and Image Analysis Techniques: Along with the experiments listed above, the Colorado group has continued to explore various velocimetry techniques and their range of validity. We have developed a “linear optical flow” code, which calculates smooth velocity maps while accurately assessing local regions of high curl. This is critical for separating spatial scales of velocity behavior, and thus transport. This code has recently come on-line, and we are currently using it to revisit a number of older datasets. Additionally, we have worked on developing pattern-recognition techniques for imaging diagnostics, based on established digital image compression algorithms. This has the potential to open the analysis of turbulent plasma behavior beyond the well-trodden Fourier and wavelet approaches. Finally, we have extended several of these image-analysis routines to multiple other diagnostic sets, including GPI datasets in NSTX and ECEI imaging on DIII-D. In one study, correlation maps were used to measure the full 2-D mode structure of drift-wave level structures using ECEI for the first time. This enabled direct comparison to gyrokinetic simulations using the GEM code, from which is was determined that TEM modes were being measured in DIII-D.
The impact of externally applied magnetic perturbations (MPs) on fast-ion losses has been investigated by means of the light ion beam probe (LIBP) technique in the ASDEX Upgrade tokamak. The LIBP technique allows to experimentally infer the fast-ion orbit displacement induced by MPs via first-orbit losses using scintillator based fast-ion loss detector (FILD) measurements. The fast-ion orbit displacement against different applied MP spectra has been studied. These shots were conducted in ELM mitigated H-mode plasmas. A rigid rotation of the MP coils was applied with a frequency of 1 Hz, with an n = 2 configuration and changing the differential phase between the upper and lower set of coils (ΔΦ ul ) on a shot-to-shot basis. Beam sources Q7 (tangential) and Q8 (radial) were used to probe different fast-ion orbits with FILD1. The measured fast-ion orbit displacement ranges from 3 to 20 mm approximately, and no qualitative difference is observed between ions from beam sources Q7 and Q8. The minimum is found for a ΔΦ ul ~ 50°, which is shifted with respect to the minimum of the plasma boundary displacement, found at ΔΦ ul ~ 0°. A first attempt to validate the orbit following code ASCOT—including the plasma response calculated with the MARS-F code—against these experimental measurements is performed. Finally, while the dependence of the first-orbit fast-ion displacement with ΔΦ ul does not match the experimental measurements, these simulations do capture other features such as the order of magnitude of the orbit displacement and the importance of the toroidal spectrum of the applied perturbation.
A national ICF laboratory workshop on requirements for a magnetized target capability on NIF was held by NIF at LLNL on October 12 and 13, attended by experts from LLNL, SNL, LLE, LANL, GA, and NRL. Advocates for indirect drive (LLNL), magnetic (Z) drive (SNL), polar direct drive (LLE), and basic science needing applied B (many institutions) presented and discussed requirements for the magnetized target capabilities they would like to see. 30T capability was most frequently requested. A phased operation increasing the field in steps experimentally can be envisioned. The NIF management will take the inputs from the scientific community represented at the workshop and recommend pulse-powered magnet parameters for NIF that best meet the collective user requests. In parallel, LLNL will continue investigating magnets for future generations that might be powered by compact laser-B-field generators (Moody, Fujioka, Santos, Woolsey, Pollock). The NIF facility engineers will start to analyze compatibility of the recommended pulsed magnet parameters (size, field, rise time, materials) with NIF chamber constraints, diagnostic access, and final optics protection against debris in FY16. The objective of this assessment will be to develop a schedule for achieving an initial Bfield capability. Based on an initial assessment, room temperature magnetized gas capsules will be fielded on NIF first. Magnetized cryo-ice-layered targets will take longer (more compatibility issues). Magnetized wetted foam DT targets (Olson) may have somewhat fewer compatibility issues making them a more likely choice for the first cryo-ice-layered target fielded with applied Bz.
Application of three-dimensional (3-D) resonant magnetic perturbations, for the purpose of controlling edge localized modes (ELMs) in high confinement (H-mode) tokamak fusion operations, routinely leads to significantly reduction of the plasma density during the discharge, a phenomenon termed 'density pump-out'. Understanding the density pump-out phenomenon due to 3-D fields is a longstanding challenging issue. This work discusses a self-consistent toroidal model that allows initial value simulation of the density pump-out effect. The model successfully reproduces pump-out phenomenology in DIII-D ELM suppression experiments. The radial particle flux, associated with the 3-D neoclassical effects (the neoclassical toroidal viscosity, NTV), is discovered to play an important role in producing the observed large density pump- out. The key physics is associated with the drift kinetic Landau resonances between the toroidal precession of trapped thermal ions and electrons from one side, and the magnetic field perturbation from the other side. Such resonances, occurring near the top of the pedestal region, substantially enhances the radial particle flux associated with NTV. As a general consequence of the resonant NTV flux, larger density pump- out occurs in plasmas with lower collisionality and slower toroidal rotation.
In the Alcator C-Mod tokamak, runaway electron (RE) experiments have been performed during low density, flattop plasma discharges at three magnetic fields: 2.7, 5.4, and 7.8 T, the last being the highest field to-date at which REs have been generated and measured in a tokamak. Time-evolving synchrotron radiation spectra were measured in the visible wavelength range (λ ≈ 300-1000 nm) by two absolutelycalibrated spectrometers viewing co- and counter-plasma current directions. In this paper, a test particle model is implemented to predict momentum-space and density evolutions of REs on the magnetic axis and q = 1, 3/2, and 2 surfaces. Drift orbits and subsequent loss of confinement are also incorporated into the evolution. These spatiotemporal results are input into the new synthetic diagnostic SOFT [M. Hoppe, et al., Nucl. Fusion 58(2), 026032 (2018)] which reproduces experimentally-measured spectra. For these discharges, it is inferred that synchrotron radiation dominates collisional friction as a power loss mechanism and that RE energies decrease as magnetic field is increased. Additionally, the threshold electric field for RE generation, as determined by hard X-ray and photo-neutron measurements, is compared to current theoretical predictions.
Increases of ion fluxes in the keV–MeV range are sometimes observed near the heliospheric current sheet (HCS) during periods when other sources are absent. These resemble solar energetic particle events, but the events are weaker and apparently local. Conventional explanations based on either shock acceleration of charged particles or particle acceleration due to magnetic reconnection at interplanetary current sheets (CSs) are not persuasive. We suggest instead that recurrent magnetic reconnection occurs at the HCS and smaller CSs in the solar wind, a consequence of which is particle energization by the dynamically evolving secondary CSs and magnetic islands. The effectiveness of the trapping and acceleration process associated with magnetic islands depends in part on the topology of the HCS. We show that the HCS possesses ripples superimposed on the large-scale flat or wavy structure. We conjecture that the ripples can efficiently confine plasma and provide tokamak-like conditions that are favorable for the appearance of small-scale magnetic islands that merge and/or contract. Particles trapped in the vicinity of merging islands and experiencing multiple small-scale reconnection events are accelerated by the induced electric field and experience first-order Fermi acceleration in contracting magnetic islands according to the transport theory of Zank et al. We present multi-spacecraft observations of magnetic island merging and particle energization in the absence of other sources, providing support for theory and simulations that show particle energization by reconnection related processes of magnetic island merging and contraction.
Colloidal, two-dimensional semiconductor nanoplatelets (NPLs) exhibit quantum confinement in only one dimension, which results in an electronic structure that is significantly altered compared to that of other quantum-confined nanomaterials. Whereas it is often assumed that the lack of quantum confinement in the lateral plane yields a spatially extended exciton, reduced dielectric screening potentially challenges this picture. Here, we implement absorption spectroscopy in pulsed magnetic fields up to 60 T for three different CdSe NPL thicknesses and lateral areas. Based on diamagnetic shifts, we find that the exciton lateral extent is comparable to NPL thickness, indicating that the quantum confinement and reduced screening concomitant with few-monolayer thickness strongly reduces the exciton lateral extent. Atomistic electronic structure calculations of the exciton size for varying lengths, widths, and thicknesses support the substantially smaller in-plane exciton extent.
We study the emission spectra of single self-organized InP/GaInP QDs (size 100-220 nm) using high-spatial-resolution, low-temperature (5 K) near-field scanning optical microscope (NSOM) operating at magnetic field strength B=0-10 T. The dots contain up to twenty electrons and represent natural Wigner molecules (WM). We observed vibronic-type shake-up structure in single electron QDs manifesting formation of two electron (2e) WM in photo-excited state. We found that relative intensities of the shake-up components described well by vibronic Frank-Condon factors giving for dots having parabolic confinement energy ħω{sub 0}=1.2-4 meV molecule bond lengths 40-140 nm. We used measurements of magnetic-field-induced shifts to distinguish emission of 2e-WM and singly charged exciton (trion). We also observed magnetic-field-induced molecular-droplet transition for two electron dot, emitting through doubly charge exciton (tetron) at zero magnetic field.
Coils misalignment in a magnetic mirror can produce additional particle transport. The magnetic field non axi-symmetry is responsible for radial and longitudinal drifts in a way much similar to the neo-classical transport in a tandem mirror cell distorted by end plugs. Accordingly, a regime exhibiting large radial displacements--similar to the resonant regime in tandem mirrors--can be obtained by confining ions azimuthally, for example by means of a properly tuned radial electric field. Because of the mass dependence of the magnetic field non-homogeneity drift velocities, the azimuthal trapping is mass specific, allowing, in principle, the filtering of a specific species based on its mass.
The Lithium Tokamak eXperiment is a small, low aspect ratio tokamak [Majeski et al., Nucl. Fusion 49, 055014 (2009)], which is fitted with a stainless steel-clad copper liner, conformal to the last closed flux surface. The liner can be heated to 350 °C. Several gas fueling systems, including supersonic gas injection and molecular cluster injection, have been studied and produce fueling efficiencies up to 35%. Discharges are strongly affected by wall conditioning. Discharges without lithium wall coatings are limited to plasma currents of order 10 kA, and discharge durations of order 5 ms. With solid lithium coatings discharge currents exceed 70 kA, and discharge durations exceed 30 ms. Heating the lithium wall coating, however, results in a prompt degradation of the discharge, at the melting point of lithium. These results suggest that the simplest approach to implementing liquid lithium walls in a tokamak—thin, evaporated, liquefied coatings of lithium—does not produce an adequately clean surface.
A drift-reduced Braginskii fluid model is used to carry out a linear and non-linear study of ideal ballooning modes in the tokamak scrape-off layer. First, it is shown that the scrape-off layer finite connection length and boundary conditions modify the ideal stability limit with respect to the closed flux-surface result. Then, in a two-fluid description, it is found that magnetic induction effects can destabilize long wavelength resistive ballooning modes below marginal ideal stability. Non-linear simulations confirm a gradual transition from small scale quasi-electrostatic interchange turbulence to longer wavelength modes as the plasma beta is increased. The transition to global ideal ballooning modes occurs, roughly, at the linearly obtained stability threshold. The transport levels and the pressure gradient as a function of plasma beta obtained in non-linear simulations can be predicted using the non-linear flattening of the pressure profile from the linear modes as a turbulent saturation mechanism.
We present a comparison study of 3-D pressureless resistive MHD (rMHD) and 3-D presureless two-fluid MHD models of the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI). HIT-SI is a current drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The comparable size of the collisionless ion skin depth d{sub i} to the resistive skin depth predicates the importance of the Hall term for HIT-SI. The simulations are run with NIMROD, an initial-value, 3-D extended MHD code. The modeled plasma density and temperature are assumed uniform and constant. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification (I{sub tor}/I{sub inj}) and formation time τ{sub f} demonstrated by HIT-SI with similar internal magnetic fields. rMHD underestimates (I{sub tor}/I{sub inj}) and exhibits much a longer τ{sub f}. Biorthogonal decomposition (BD), a powerful mathematical tool for reducing large data sets, is employed to quantify how well the simulations reproduce the measured surface magnetic fields without resorting to a probe-by-probe comparison. BD shows that 2fl-MHD captures the dominant surface magnetic structures and the temporal behavior of these features better than rMHD.
The need to understand the structure of magnetic fluctuations in H-1NF heliac [S. Hamberger et al., Fusion Technol. 17, 123 (1990)] plasmas has motivated the installation of a sixteen former, tri-axis helical magnetic probe Mirnov array (HMA). The new array complements two existing poloidal Mirnov arrays by providing polarisation information, higher frequency response, and improved toroidal resolution. The helical placement is ideal for helical axis plasmas because it positions the array as close as possible to the plasma in regions of varying degrees of favourable curvature in the magnetohydrodynamic sense, but almost constant magnetic angle. This makes phase variation with probe position near linear, greatly simplifying the analysis of the data. Several of the issues involved in the design, installation, data analysis, and calibration of this unique array are presented including probe coil design, frequency response measurements, mode number identification, orientation calculations, and mapping probe coil positions to magnetic coordinates. Details of specially designed digitally programmable pre-amplifiers, which allow gains and filters to be changed as part of the data acquisition initialisation sequence and stored with the probe signals, are also presented. The low shear heliac geometry [R. Jiménez-Gómez et al., Nucl. Fusion 51, 033001 (2011)], flexibility of the H-1NF heliac, and wealth of information provided by the HMA create a unique opportunity for detailed study of Alfvén eigenmodes, which could be a serious issue for future fusion reactors.
Characteristics of a rotation of passing particles in a tokamak with radial electric field are calculated. The expression for time-averaged toroidal velocity of the passing particle induced by the electric field is derived. The electric-field-induced additive to the toroidal velocity of the passing particle appears to be much smaller than the velocity of the electric drift calculated for the poloidal magnetic field typical for the trapped particle. This quantity can even have the different sign depending on the azimuthal position of the particle starting point. The unified approach for the calculation of the bounce period and of the time-averaged toroidal velocity of both trapped and passing particles in the whole volume of plasma column is presented. The results are obtained analytically and are confirmed by 3D numerical calculations of the trajectories of charged particles.
The classical dynamics of ballistic non-interacting electrons confined to a narrow electrostatic potential well with corrugated barriers in uniform magnetic field was numerically studied. Trajectories in phase space were analyzed and longitudinal and transversal resistivities were calculated. Commensurability oscillations and negative magnetoresistance similar to those found in antidot lattice devices were observed.
The VMEC nonlinear ideal MHD equilibrium code [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] is compared against analytic linear ideal MHD theory in a screw-pinch-like configuration. The focus of such analysis is to verify the ideal MHD response at magnetic surfaces which possess magnetic transform (ι) which is resonant with spectral values of the perturbed boundary harmonics. A large aspect ratio circular cross section zero-beta equilibrium is considered. This equilibrium possess a rational surface with safety factor q = 2 at a normalized flux value of 0.5. A small resonant boundary perturbation is introduced, exciting a response at the resonant rational surface. The code is found to capture the plasma response as predicted by a newly developed analytic theory that ensures the existence of nested flux surfaces by allowing for a jump in rotational transform (ι=1/q). The VMEC code satisfactorily reproduces these theoretical results without the necessity of an explicit transform discontinuity (Δι) at the rational surface. It is found that the response across the rational surfaces depends upon both radial grid resolution and local shear (dι/dΦ, where ι is the rotational transform and Φ the enclosed toroidal flux). Calculations of an implicit Δι suggest that it does not arise due to numerical artifacts (attributed to radial finite differences in VMEC) or existence conditions for flux surfaces as predicted by linear theory (minimum values of Δι). Scans of the rotational transform profile indicate that for experimentally relevant levels of transform shear the response becomes increasing localised. Furthermore, careful examination of a large experimental tokamak equilibrium, with applied resonant fields, indicates that this shielding response is present, suggesting the phenomena is not limited to this verification exercise.
Wendelstein 7-X (W7-X) aims to demonstrate the reactor capability of the stellarator concept, by creating plasmas with pulse lengths of up to 30 min at a heating power of up to 10 MW. The divertor plasma facing components will see convective steady state heat flux densities of up to 10 MW/m 2 . These high heat flux target elements are actively cooled and are covered with carbon fibre reinforced carbon (CFC) as plasma facing material. The CFC is bonded to the CuCrZr cooling structure. Over the life time of the experiment this interface may weaken and cracks can occur, greatly reducing the heat conduction between the CFC tile and the cooling structure. Furthermore, there is not only the need to monitor the divertor to prevent damage by overheating but also the need to detect these fatigue failures of the interface. A method is presented for an early detection of fatigue failures of the interface layer, solely by using the information delivered by the IR-cameras monitoring the divertor. This was developed and validated through experiments made with high heat flux target elements prior to installation in W7-X.