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DOE OSTI2022

Stabilization and control of persistent current magnets using variable inductance

Ultra-stable, tunable magnetic fields are desirable for a wide range of applications in medical imaging, electron microscopy, quantum science, and atomic physics. Superconducting magnets operated in persistent current mode, with device current flowing in a closed superconducting loop disconnected from a power source, are a common approach for applications with the most stringent requirements on temporal field stability. In this work, we present a method for active control of this persistent current by means of dynamic inductance change within the superconducting circuit. For a first realization of this general technique, we consider a variable superconducting inductor placed in series with the main magnet. The inductor acts as a dynamic flux storage device capable of transferring flux to or from the main magnet through inductance change. This allows for fine and fast adjustments of the persistent current without the use of thermal switches that limit the speed and accuracy of many present-day methods. With first experiments employing this technique, we demonstrate stabilization of a 1.95 T Nb–Ti round lens for electron microscopy against decay resulting from residual losses in the superconducting circuit, and more generally show flexibility for precise control over the magnitude and waveform of the persistent current.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2016

Effects of magnetic islands on bootstrap current in toroidal plasmas

The effects of magnetic islands on electron bootstrap current in toroidal plasmas are studied using gyrokinetic simulations. The magnetic islands cause little changes of the bootstrap current level in the banana regime because of trapped electron effects. In the plateau regime, the bootstrap current is completely suppressed at the island centers due to the destruction of trapped electron orbits by collisions and the flattening of pressure profiles by the islands. In the collisional regime, small but finite bootstrap current can exist inside the islands because of the pressure gradients created by large collisional transport across the islands. Lastly, simulation results show that the bootstrap current level increases near the island separatrix due to steeper local density gradients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Survey of heating and current drive for K-DEMO

Here, we present calculations of heating and current drive by neutral injection and by electromagnetic waves in the ion cyclotron, helicon, lower hybrid, and electron cyclotron frequency ranges for the steady state burn conditions in a K-DEMO configuration with $I_{\rm p}=12.3$ MA, a = 2.1 m, $R_{\rm o}=6.8$ m, $B_{\rm o}=7.4$ T, $ \newcommand{\nebar}{{\overline{n}_{\rm e}}} \nebar=1.1 \times 10^{20}$ m–3, $T(0)=40$ keV, and $Z_{\rm eff}=1.5$ . Lower hybrid wave current drive calculations comprise a 2D scan over poloidal launcher location and launched $ \newcommand{\Nparallel}{{n_{\Vert}}} \Nparallel$ , at a fixed frequency of 5 GHz. An ICRF frequency scan over 50–100 MHz is based on an ITER-like ICRF midplane antenna; the absorption calculation includes thermal D, T, He, Ar, and W as well as suprathermal beam ions and alphas. Helicon fast wave performance is surveyed by varying frequency over 0.6–2.5 GHz, launched $ \newcommand{\Nparallel}{{n_{\Vert}}} \Nparallel$ from –1.6 to –3, and launcher position from top to bottom on the low-field side. An ITER-like 1 MeV neutral beam system with quasi-tangential geometry is scanned over elevation to vary the targeted minor radius. The electron cyclotron survey varies the frequency (190–300 GHz), launcher poloidal location, and the poloidal and toroidal direction of the launched waves. We report for each system the range of minor radius in which current is driven, the current drive efficiency, the optimal system parameters, and typical profiles of driven current. Electron and ion heating profiles are reported for the ICRF and NBI systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Runaway electron beam dynamics at low plasma density in DIII-D: energy distribution, current profile, and internal instability

Parameters of the post-disruption runaway electron (RE) beam in the collisionless background plasma achieved after deuterium injection are investigated in DIII-D. The spatially resolved RE energy distribution function is measured for the first time during the RE plateau stage by inverting hard X-ray bremsstrahlung spectra. It has maximum energy up to 20 MeV and a non-monotonous feature at 5{6 MeV observed only in the core of the beam supporting the possibility of kinetic instabilities. The RE current profile is reconstructed for the first time using the spatially resolved RE energy distribution. It is found to be more peaked than the pre-disruption plasma current, with higher internal inductance, suggesting preferential formation of REs in the core plasma or potentially a radially inward motion of the REs. The accessed relatively low-current (180 kA) RE beam is found stable, likely due to its elevated q profile. From this base stable equilibrium, instability is accessed by ramping the solenoid current. Under a large applied accelerating loop voltage an internal kink mode is observed. The kink mode leads to sawtooth-like relaxation of the RE current profile, but drives no RE loss. Under conditions of a large decelerating voltage, chirping Alfvénic instabilities driven by REs during the RE plateau stage are observed for the first time. The low-frequency (0.1{7 MHz) Alfvénic instabilities, supposedly compressional Alfvén eigenmodes, are found to be correlated with a RE loss signal. Finally, this provides novel plasma conditions to study these instabilities and investigate opportunities to utilize them for RE control. Bifurcated electron cyclotron emission (ECE) spectrum is measured during the collisionless RE plateau, with a break point at ≈100 GHz suggesting resonant absorption of the ECE at low frequencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

RECONNECTION OF QUASI-SINGULAR CURRENT SHEETS: THE ''IDEAL'' TEARING MODE

A strong indication that fast reconnection regimes exist within resistive magnetohydrodynamics was given by the proof that the Sweet-Parker current sheet, maintained by a flow field with an appropriate inflow-outflow structure, could be unstable to a reconnecting instability which grows without bound as the Lundquist number, S, tends to infinity. The requirement of a minimum value for S in order for the plasmoid instability to kick in does little to resolve the paradoxical nature of the result. Here we argue against the realizability of Sweet-Parker current sheets in astrophysical plasmas with very large S by showing that an ''ideal'' tearing mode takes over before current sheets reach such a thickness. While the Sweet-Parker current sheet thickness scales as ∼S {sup –1/2}, the tearing mode becomes effectively ideal when a current sheet collapses to a thickness of the order of ∼S {sup –1/3}, up to 100 times thicker than S {sup –1/2}, when (as happens in many astrophysical environments) S is as large as 10{sup 12}. Such a sheet, while still diffusing over a very long time, is unstable to a tearing mode with multiple x-points: here we detail the characteristics of the instability and discuss how it may help solve the flare trigger problem and effectively initiate the turbulent disruption of the sheet.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Understanding the impact of an applied axial magnetic field on efficient current coupling on the Z machine

Magnetized liner inertial fusion (MagLIF) is an attractive concept for producing thermonuclear fusion reactions. The MagLIF platform involves the operation of Helmholtz coils to apply a 15 Tesla axial magnetic field to the load region, where a cylindrical, fuel-filled metal liner is imploded by a ∼ 2 0 MA current pulse. The fringe field from these coils extends into the transmission line that delivers the current to the target. We investigated the extent to which this applied field disturbs the nominal power flow within that transmission line. A simplified model of the geometry shows that adding the applied magnetic field results in magnetic field lines that connect the cathode to the anode, suggesting electrons may not be magnetically insulated in this region. Particle-in-cell simulations indicated the addition of the applied magnetic field would not significantly impact the current delivery to the load. Velocimetry was used to experimentally assess the current delivery with and without the applied magnetic field. We find no measurable effects of the applied field on current delivery in the configuration investigated in this study. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Laminated Permanent Magnets Enable Compact Magnetic Components in Current Source Converters

Magnetic components play a key role in determining the size, cost, efficiency of a power converter. They are more significant in current source converters, where the dc-link energy is stored in an inductor/transformer. In such cases, the magnetics have a predominantly DC flux, superimposed by an AC flux at switching frequency. Previously, permanent magnets have been proposed to offset the DC flux and thereby reduce the size, cost, and losses of the inductors/transformers. This paper starts by analyzing the issue of eddy currents when using such standard permanent magnets, especially in medium frequency applications, making them practically unusable. Alternatively, the paper proposes the use of laminated permanent magnets to reduce these eddy currents and thereby realize the benefits of offsetting the DC flux to reduce the size, cost, and loss of inductors/transformers. Using a soft-switching solid-state transformer as an example, experimental results are presented to show the impact of eddy currents in standard permanent magnets when used with a medium frequency transformer. Here, experimental results showing the benefits of using laminated magnets in reducing the eddy currents are presented.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2025

Small-Signal Stability of Grid-Forming Inverters Using Current-Limiting and Frequency Stabilization

This paper presents a small-signal stability analysis of grid-forming (GFM) inverters under current-limiting conditions. It examines how adjustments in virtual impedance angles, implemented through advanced current-limiting and frequency stabilization techniques, influence small-signal stability. This paper studies a GFM inverter control integrating a fictitious power technique stabilizing primary control by adding a virtual power term and a hybrid current limiter integrating virtual impedance in the anti-wind-up feedback with current reference saturation limiting. A small-signal model is developed to assess the impact of virtual impedance angles on GFM inverter dynamics during grid disturbances, such as voltage drops. The findings indicate that although increasing the virtual impedance angle (to make it more inductive) enhances large-signal stability and voltage support during faults, it can induce oscillations and lead to instability if the angle exceeds certain thresholds. Based on the small-signal models, this paper provides design considerations for the current-limiter impedances to ensure reliable GFM inverter behavior under grid disturbances while maintaining small-signal stability.

current limiting↗

DOE OSTI2022

An Inrush Current Limiting Method for Grid-Connected Converters Considering Grid Voltage Disturbances

To support the electric power grid, some grid-connected converters are required to ride through abnormal grid conditions, including voltage disturbances. However, at the moment, when a grid voltage disturbance happens, a large inrush current could be induced due to the large difference between the grid and converter output pulsewidth modulation (PWM) voltages. This inrush current could be more severe in the faster switching SiC-based multilevel converter, which only needs a small filter inductance to meet its normal operation requirements, such as harmonics and peak ripple currents. In this article, a PWM mask method is used to limit the inrush current. With this method, the inrush current can be effectively limited to a preset value and can help the converter ride through grid voltage disturbances. Furthermore, the method is validated through experiments conducted on a single-phase SiC-based five-level converter considering low voltage, high voltage, and phase angle disturbances.

42 ENGINEERING↗

DOE OSTI2025

Analysis of Screening Current Effects in a Hybrid Nb$_{3}$Sn/REBCO Superconducting Accelerator Magnet Using a T - A Formulation

To explore the feasibility of using high-temperature superconducting (HTS) REBCO coated conductors in future accelerator magnets, two REBCO flat racetrack coils were fabricated using 4-mm wide EuBCO tapes at the High Energy Accelerator Research Organization (KEK). These coils were tested as an insert inside a Nb$_{3}$Sn common-coil dipole magnet, which provides a background field of up to $\sim$ 9.5T, at the Brookhaven National Laboratory (BNL). REBCO tapes offer exceptionally high critical current density under strong magnetic fields; however, they also exhibit significant magnetization due to screening currents, leading to magnetic field errors. Here, this study presents a 2D finite element model of screening current-induced fields (SCIF) in REBCO coils using the T-A formulation, along with the results obtained. Simulations were then performed for two KEK test cases: one where the REBCO conductors were oriented with the HTS tapes parallel to the background field, and another where the tapes were perpendicular to it. Since screening currents also influence the stress distribution and increase the peak stress in the coils, the mechanical effects of these currents were analyzed. The implications of these simulation and test results for the design of Nb$_{3}$Sn/REBCO superconducting accelerator magnets are discussed.

Accelerator magnets↗

DOE OSTI2024

Robust Disturbance Rejection Rotor Current Control of Doubly-Fed Induction Generators

This article proposes a robust transient disturbance rejection current controller (TDRCC) to improve the transient performance of doubly-fed induction generators (DFIGs) in wind turbines during grid disturbances, such as short circuits. Here, the proposed robust TDRCC replaces the proportional-integral-derivative (PID) current controllers conventionally used in the vector control scheme of the DFIG rotor side converter (RSC). The TDRCC estimates the transient disturbances caused by grid faults or other external disturbances and provides compensation to the DFIG rotor voltage in the current control loops of the RSC to improve the robustness of the controller to disturbance. A sliding-mode current controller (SMCC) is also designed to highlight the transient performance improvement of the DFIG using the TDRCC over the state-of-the-art control methods during grid short circuit faults. Simulation studies are conducted in PSCAD/EMTDC for a 3.6-MW DFIG wind turbine with the proposed TDRCC, the conventional PI controller, and the SMCC, respectively during the most severe balanced three-phase grid short circuit fault specified by the U.S. grid code as well as an unbalance single-phase grid short circuit fault. Hardware experiments are conducted on a 200-W DFIG wind turbine emulator with the three different controllers for the same three-phase short circuit fault. Simulation and hardware experiment results show that the TDRCC reduces the peak rotor current significantly when compared with the PI and SMCC controlled DFIG system and, therefore, would help prolong the lifespan of the DFIG's power electronics and reduce maintenance costs.

42 ENGINEERING↗

DOE OSTI2024

Efficient Modeling of Floating Wind Arrays Including Current Loads and Seabed Bathymetry

Capabilities for modeling the effects of seabed bathymetry and current drag loads on a floating wind farm are now available in an open-source model for quasi-static analysis. In this model, mooring lines and dynamic cables are represented by a quasi-static solver that can quickly represent complex mooring/cabling arrangements and arrays of floating bodies. To account for seabed bathymetry, we expand the model to include a surface mesh that captures changes in water depth over a rectangular grid. We formulate modifications to the catenary equations that capture a mooring line's profile and tensions when contacting a slope seabed. To account for current drag loads on mooring lines and dynamic cables, we formulate a novel technique that rotates the reference frame so that the vector sum of the the weight and the current force are used in the catenary equations, while accounting for the seabed orientation. To complete the system, current drag loads on floating substructures are handled by inclusion of strip-theory drag calculations. These new capabilities are verified by comparing with results from the established offshore dynamics models MoorDyn and OrcaFlex in equivalent steady-state scenarios. The results show very good agreement for both sloped seabeds and current loads. With computation times of the quasi-static model typically under one second, the model additions are a useful capability toward rapidly evaluating a floating wind array's response to environmental loads under realistic site conditions.

bathymetry↗

DOE OSTI2014

Dose equations for shift-variant CT acquisition modes using variable pitch, tube current, and aperture, and the meaning of their associated CTDI{sub vol}

Purpose: With the increasing clinical use of shift-variant CT protocols involving tube current modulation (TCM), variable pitch or pitch modulation (PM), and variable aperture a(t), the interpretation of the scanner-reported CTDI{sub vol} is called into question. This was addressed for TCM in their previous paper published by Dixon and Boone [Med. Phys. 40, 111920 (14pp.) (2013)] and is extended to PM and concurrent TCM/PM as well as variable aperture in this work. Methods: Rigorous convolution equations are derived to describe the accumulated dose distributions for TCM, PM, and concurrent TCM/PM. A comparison with scanner-reported CTDI{sub vol} formulae clearly identifies the source of their differences with the traditional CTDI{sub vol}. Dose distribution simulations using the convolution are provided for a variety of TCM and PM scenarios including a helical shuttle used for perfusion studies (as well as constant mA)—all having the same scanner-reported CTDI{sub vol}. These new convolution simulations for TCM are validated by comparison with their previous discrete summations. Results: These equations show that PM is equivalent to TCM if the pitch variation p(z) is proportional to 1/i(z), where i(z) is the local tube current. The simulations show that the local dose at z depends only weakly on the local tube current i(z) or local pitch p(z) due to scatter from all other locations along z, and that the “local CTDI{sub vol}(z)” or “CTDI{sub vol} per slice” do not represent a local dose but rather only a relative i(z) or p(z). The CTDI-paradigm does not apply to shift-variant techniques and the scanner-reported CTDI{sub vol} for the same lacks physical significance and relevance. Conclusions: While the traditional CTDI{sub vol} at constant tube current and pitch conveys useful information (the peak dose at the center of the scan length), CTDI{sub vol} for shift-variant techniques (TCM or PM) conveys no useful information about the associated dose distribution it purportedly represents. On the other hand, the total energy absorbed E (“integral dose”) as well as its surrogate DLP remain robust (invariant) with respect to shift-variance, depending only on the total mAs = 〈i〉t{sub 0} accumulated during the total beam-on time t{sub 0} and aperture a, where 〈i〉 is the average current.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2017

Dependence of the maximal superconducting current on the resonance frequency in a shunted Josephson junction

We have analyzed the phase dynamics and current–voltage characteristics of a Josephson junction shunted by an LC circuit. When the Josephson frequency ω{sub J} becomes equal to the natural frequency ω{sub rc} of the formed resonance circuit, the I–V curve acquires additional branches. We have studied the features of the rc branch and the superconducting circuit for different values of the resonance frequency. It is shown that the maximal superconducting current through the Josephson junction on the rc-branch depends on the resonance frequency and is determined by the closeness of the end point of the rc branch to the critical current. We have determined the dependence of the maximal superconducting current on the resonance frequency for different values of the dissipation parameters. The limiting value of the maximal superconducting current is independent (to within 1%) of the parameters of the system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

On the behavior of plasma with a negative current in the L-2M stellarator

The behavior of plasma with a negative current in the range of 5 kA ≤ vertical bar J vertical bar ≤ 16 kA in the L-2M stellarator is studied. Plasma is created and heated by means of electron cyclotron resonance heating (ECRH). Here, the definition “negative” stands for a toroidal current directed in such a way that it reduces the initial rotational transform µ in absolute value. It is shown that, only at relatively small values of the negative current ( vertical bar J vertical bar ∼ 6 kA), the increase in the shear leads to a reduction in electromagnetic turbulence. As vertical bar J vertical bar rises, the average level of magnetic fluctuations in the stationary phase of the discharge gradually increases. After ECRH is switched off (i.e., when plasma cools down), there is a time interval in which the amplitude of magnetic field fluctuations increases. No coherent three-dimensional modes (e.g., double tearing modes) that could accompany the penetration of the current into the plasma were observed. As for axisymmetric perturbations with m ≠ 0, analysis of the experimental data shows that they are absent at vertical bar J vertical bar ≤ 8 kA, appear in some discharges at vertical bar J vertical bar = 9 kA, and are observed in each discharge at vertical bar J vertical bar ≥ 10 kA. The frequency of these oscillations is on the order of 10 kHz, the poloidal mode number is m = 2, and the duration is 4–6 ms. The absence of oscillations with m = 1 and the small value of the external magnetic field for the m = 2 perturbation indicate that the radial size of the magnetic island is less than 1 cm. This, in turn, suggests that the radial profile of the plasma current changes with increasing vertical bar J vertical bar.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Formation of a spark discharge in an inhomogeneous electric field with current limitation by a large ballast Resistance

Results of studies of a spark discharge initiated in argon in a point–plane electrode gap with limitation of the discharge current by a large ballast resistance are presented. It is shown that the current flowing through the plasma channel of such a low-current spark has the form of periodic pulses. It is experimentally demonstrated that, when a low-current spark transforms into a constricted glow discharge, current pulses disappear, the spatial structure of the cathode glow changes abruptly, and a brightly glowing positive plasma column forms in the gap.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Kinetic effects on the currents determining the stability of a magnetic island in tokamaks

The role of the bootstrap and polarization currents for the stability of neoclassical tearing modes is investigated employing both a drift kinetic and a gyrokinetic approach. The adiabatic response of the ions around the island separatrix implies, for island widths below or around the ion thermal banana width, density flattening for islands rotating at the ion diamagnetic frequency, while for islands rotating at the electron diamagnetic frequency the density is unperturbed and the only contribution to the neoclassical drive arises from electron temperature flattening. As for the polarization current, the full inclusion of finite orbit width effects in the calculation of the potential developing in a rotating island leads to a smoothing of the discontinuous derivatives exhibited by the analytic potential on which the polarization term used in the modeling is based. This leads to a reduction of the polarization-current contribution with respect to the analytic estimate, in line with other studies. Other contributions to the perpendicular ion current, related to the response of the particles around the island separatrix, are found to compete or even dominate the polarization-current term for realistic island rotation frequencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Determination of plasma density from data on the ion current to cylindrical and planar probes

To improve probe methods of plasma diagnostics, special probe measurements were performed and numerical models describing ion transport to a probe with allowance for collisions were developed. The current–voltage characteristics of cylindrical and planar probes were measured in an RF capacitive discharge in argon at a frequency of 81 MHz and plasma densities of 10{sup 10}–10{sup 11} cm{sup –3}, typical of modern RF reactors. 1D and 2D numerical models based on the particle-in-cell method with Monte Carlo collisions for simulating ion motion and the Boltzmann equilibrium for electrons are developed to describe current collection by a probe. The models were used to find the plasma density from the ion part of the current–voltage characteristic, study the effect of ion collisions, and verify simplified approaches to determining the plasma density. A 1D hydrodynamic model of the ion current to a cylindrical probe with allowance for ion collisions is proposed. For a planar probe, a method to determine the plasma density from the averaged numerical results is developed. A comparative analysis of different approaches to calculating the plasma density from the ion current to a probe is performed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗