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NASA NTRS1991

Oscillations of rotating neutron stars

A perturbation technique is used to compute the rotational corrections to the nonradial oscillation spectrum of a realistic neutron star model. The l = l(0) oscillations are coupled to l = l(0) + or - 1 oscillations by the Coriolis force. To calculate the rotational corrections to the quadrupole, l(0) = 2, oscillation modes, previous calculations of the nonradial oscillation spectrum of this neutron star model are extended to include l(0) = 1 and l(0) = 3 modes, as well as many higher overtones at each value of l(o). As an example of this technique, the rotational corrections to two quadrupole toroidal modes are computed. For these modes the coupling to the spheroidal class of oscillations produced by the Coriolis force introduces a nonzero radial component to the velocity field, as well as a nonvanishing Lagrangian density perturbation. This result is used to compute the neutrino damping rates for these toroidal modes of a rotating neutron star. The neutrino damping time can approach the gravitational radiation damping time in rotating neutron stars if the central temperature is high enough. The rotationally induced coupling of spheroidal oscillations to toroidal modes can also produce significant displacements at the stellar surface in some of the toroidal modes. The damping rates due to this process for the rotationally corrected toroidal modes are estimated. The coupling of surface motions to the toroidal modes also have interesting implications for channeling energy, e.g., that associated with a glitch in the crust, to the surface of the star. Perhaps this might produce observable effects in the pulsar emission process or a gamma-ray burst event.

Strohmayer, Tod E.↗

DOE OSTI2025

Conceptual design of ELM control coils for the TCABR tokamak

An upgrade of the Tokamak à Chauffage Alfvén Brésilien (TCABR) is being designed to make it capable of creating a well controlled environment where the impact of resonant magnetic perturbation (RMP) fields on edge localised modes can be addressed over a wide range of (i) plasma shapes, (ii) divertor configurations, (iii) RMP coil geometries and (iv) perturbed magnetic field spectra. To this end, a unique set of in-vessel RMP coils is being designed and, in this work, their conceptual design is presented. This unique set of coils is composed of three toroidal arrays of coils on the low field side and three toroidal arrays of coils on the high field side. Each of these six toroidal arrays is composed of 18 coils thus allowing for the creation of RMP fields with toroidal mode numbers n ≤ 9 and with increased control of the poloidal mode number spectrum. To study dynamical effects of RMP fields of different toroidal mode numbers, all rotating simultaneously with different velocities, each of the 108 RMP coils will be powered independently by power supplies that can provide voltages of up to 4 kV and electric currents of up to 2 kA, with frequencies varying continuously from 0Hz up to 10kHz. A set of physical criteria were used to determine the optimal coil geometry and their respective number of turns to reduce the coil currents and voltages during operation with alternate current. Further, the conceptual design was carried out using both the vacuum approach (no plasma response) and the single-fluid response approach, which accounts for the response of a linear, single-fluid, visco-resistive plasma calculated using the M3D-C 1 code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Measurement of near- and far-field impurity flows during pellet-induced rapid shutdown in DIII-D

Both near-field (<1 m away toroidally from the pellet) and far-field (>1 m away toroidally from the pellet) poloidal and toroidal impurity (carbon ion) flows are measured using visible imaging and fast bolometry during a polypropylene pellet-induced rapid plasma shutdown in the DIII-D tokamak. In the near field, the pellet appears to increase poloidal flow in the ion diamagnetic direction, possibly due to the strong radial temperature gradient caused by the pellet ablation. In the far field, the poloidal impurity flow typically appears slower and in the opposite direction. Toroidal impurity flow appears to be strongly influenced by the plasma initial toroidal rotation, especially in the far field. These results demonstrate that rapid shutdown impurity flows are not necessarily global in structure but can be quite different close to and far from the injected pellet.

Electromagnetic radiation detectors↗

DOE OSTI2025

Conceptual study on using Doppler backscattering to measure magnetic pitch angle in tokamak plasmas

We introduce a new approach to measure the magnetic pitch angle profile in tokamak plasmas with Doppler backscattering (DBS), a technique traditionally used for measuring flows and density fluctuations. The DBS signal is maximised when its probe beam's wavevector is perpendicular to the magnetic field at the cutoff location, independent of the density fluctuations [Hillesheim \emph{et al} 2022 \emph{Nucl. Fusion} \textbf{55} 073024]. Hence, if one could isolate this effect, DBS would then yield information about the magnetic pitch angle. By varying the toroidal launch angle, the DBS beam reaches cutoff with different angles with respect to the magnetic field, but with other properties remaining similar. Hence, the toroidal launch angle which gives maximum backscattered power is thus that which is matched to the pitch angle at the cutoff location, enabling inference of the magnetic pitch angle. We performed systematic scans of the DBS toroidal launch angle for repeated DIII-D tokamak discharges. Experimental DBS data from this scan were analysed and combined with Gaussian beam-tracing simulations using the Scotty code [Hall-Chen \emph{et al} 2022 \emph{Plasma Phys. Control. Fusion} \textbf{64} 095002]. The pitch-angle inferred from DBS is consistent with that from magnetics-only and motional-Stark-effect-constrained (MSE) equilibrium reconstruction in the edge. In the core, the pitch angles from DBS and magnetics-only reconstructions differ by one to two degrees, while simultaneous MSE measurements were not available. The uncertainty in these measurements was under a degree; we show that this uncertainty is primarily due to the error in toroidal steering, the number of toroidally separated measurements, and shot-to-shot repeatability. We find that the error of pitch-angle measurements can be reduced by optimising the poloidal launch angle and initial beam properties. Since DBS has high spatial and temporal resolutions, is non-perturbative, does not require neutral beams, and is likely robust to neutron damage of and debris on the first mirrors, using DBS to measure the pitch angle in future fusion energy systems is especially appealing.

beam tracing↗

NASA NTRS1986

An imaging extreme ultraviolet spectrometer for astrophysical investigations in space

A high-efficiency, extreme ultraviolet (EUV) imaging spectrometer has been constructed and tested. The spectrometer employs a concave toroidal grating illuminated at normal incidence in a Rowland circle mounting and has only one reflecting surface. The toroidal grating has been fabricated by a new technique employing an elastically deformable submaster grating which is replicated in a spherical form and then mechanically distorted to produce the desired aspect ratio of the toroidal surface for stigmatic imaging over the selected wavelength range. The fixed toroidal grating used in the spectrometer is then replicated from this surface. Photographic tests and initial photoelectric tests with a two-dimensional, pulse-counting detector system have verified the image quality of the toroidal grating at wavelengths near 600 A. The basic designs of two instruments employing the spectrometer for astrophysical investigations in space are described, namely, a high-resolution EUV spectroheliometer for studies of the solar chromosphere, transition region, and corona; and an EUV spectroscopic telescope for studies of nonsolar objects.

Huber, M. C. E.↗

NASA NTRS1987

The evaluation of a deformable diffraction grating for a stigmatic EUV spectroheliometer

A high-efficiency, extreme ultraviolet (EUV) imaging spectrometer is constructed and tested. The spectrometer employs a concave toroidal grating illuminated at normal incidence in a Rowland circle mounting and has only one reflecting surface. The toroidal grating has been fabricated by a new technique employing an elastically-deformable sub-master grating replicated in a spherical form and then mechanically distorted to produce the desired aspect ratio of the toroidal surface for stigmatic imaging over the selected wavelength range. The fixed toroidal grating used in the spectrometer is then replicated from this surface. Photographic tests and initial photoelectric tests with a two-dimensional, pulse-counting detector system verify the image quality of the toroidal grating at wavelengths near 600 A. The results of these tests and the basic designs of two instruments which could employ the imaging spectrometer for astrophysical investigations in space are described; i.e., a high-resolution EUV spectroheliometer for studies of the solar chromosphere, transition region, and corona; and an EUV spectroscopic telescope for studies of non-solar objects.

Timothy, J. G.↗

DOE OSTI2025

Dynamics of Downdrafts Around a Growing Convective Cloud: A Numerical Study

We examine the dynamics of cloud-edge downdrafts over the growth phase of isolated cumuli, combining Eulerian and Lagrangian analyses. As in previous studies, our results show that growing cumuli are surrounded by downdrafts linked to cloud-scale quasi-toroidal circulations at all times at middle and upper cloud levels consistent with the thermal chain description of convective clouds. These toroidal circulations are responsible for the most intense cloud-edge downdrafts in our simulations. In the upper cloud half, roughly 30%–50% of the upward mass flux is typically compensated within a radius of about twice the updraft radius in quasi-laminar simulations forced by a warm bubble in an initially quiescent flow. In a turbulent cloud forced by surface fluxes, this compensation fraction is around 10%–30% over the same region. In contrast to the buoyancy-centered view of subsiding shells, Eulerian and Lagrangian vertical momentum budget analyses show that the most intense cloud-edge downdrafts in the turbulent setup, and after spin-up of the toroidal circulation in the quasi-laminar experiments, are predominantly mechanically forced (i.e., driven by dynamic pressure accelerations). This is consistent throughout the entire growth phase of the cumulus clouds and across tests with varying assumptions, including drier and moister environments. Despite dynamic pressure perturbations being the main driver of toroidal downdrafts, the downdraft speed (relative to the corresponding updraft velocity) exceeds the prediction of the non-buoyant Hill's spherical vortex—a simple model frequently used for cloud-scale circulations—by more than 30%.

Pardo, Lianet Hernández [Goethe Univ., Frankfurt (↗

DOE OSTI2025

Experimental demonstration of transient CHI start-up using a floating biased electrode configuration

Transient coaxial helicity injection (CHI) current start-up in a spherical tokamak (ST) has been demonstrated for the first time using a reactor-relevant floating single biased (FSB) electrode configuration on QUEST. Unlike previous applications of CHI on HIT-II and on NSTX in which the entire ST vessel was split in two using two toroidal ceramic rings as vacuum breaks, in the FSB electrode configuration on QUEST, only the lower outer divertor plate is electrically insulated from the rest of the vessel. This is the CHI injector region. A CHI discharge is generated by driving current, using an external power supply, along magnetic field lines that connect the inner and outer divertor plates in the CHI injector region. The CHI plasma evolution and closed flux formation on QUEST are very similar to those on NSTX and have generated toroidal currents of 150 kA with 100 kA of current flowing on closed flux surfaces. An alternate, force-free model approach has been used to derive the CHI scaling relations. The resulting CHI scaling relations from the model are consistent with the conventional CHI scaling relations, which state that the CHI generated toroidal current is proportional to the CHI injector flux and the CHI injector current is inversely proportional to the toroidal field. These results from QUEST bode well for the application of CHI in a new generation of compact high field STs and low aspect ratio tokamaks in which the space for the central solenoid is very restricted.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad–Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.

Physics↗

DOE OSTI2025

Low- n stability and plasma response to RMP in various STEP scenarios

The low-n (n is the toroidal mode number) magnetohydrodynamic (MHD) stability and plasma response are numerically investigated for various scenarios designed for STEP, that are relevant for the H-mode pedestal analysis. Control of the edge-localized modes (ELMs) with externally applied resonant magnetic perturbations (RMPs) is considered. Optimization of the ELM control coil current configuration, based on the computed plasma MHD response and well-established figures of merit validated on present-day experiments, finds reasonable robustness of a fixed coil phasing (for a given n-number) to control ELMs in all five STEP plasmas considered. Based on certain semi-empirical criteria, the required coil current to achieve ELM suppression is estimated to be about 10–20 kAt with the n = 1 or 2 RMP configuration and about 100–200 kAt for the n = 4 RMP. Systematic linear stability calculations are used to map out stability windows for the low-n kink-peeling modes, in terms of the ideal-wall location and variation of the edge safety factor q 95 with respect to the target design. The kink-peeling stability boundary is found to be generally sensitive to the q 95 variation, which has implications for achieving the quiescent H-mode regime in STEP. Full toroidal quasilinear initial-value simulations for these STEP plasmas find that generation of the edge-harmonic oscillations (EHOs) depends sensitively on the plasma scenario, the initial linear stability of the kink-peeling modes, the initial plasma toroidal flow and q 95 . In general, it is easier (more robust) to access the EHO-regime for two of the cases considered with smaller plasma volume and higher on-axis safety factor. Finally, quasilinear simulations find robust density pumpout due to applied RMPs in these STEP plasmas, but the effect on the plasma toroidal flow varies among different cases.

EHO↗

DOE OSTI2026

Radiation asymmetry during shattered pellet and massive gas injection in DIII-D

Infrared thermography of the first wall in DIII-D is used to show the toroidal peaking of plasma radiation during mitigated disruptions with shattered pellet injection (SPI) and with massive gas injection (MGI). During MGI, the radiation peak location is shown to be due to the n = 1 magnetohydrodynamic (MHD) activity and continuously variable in toroidal phase based on externally applied error fields, consistent with previous experimental results. Furthermore, the measured toroidal peaking factor (TPF) is in agreement with the previous estimates based on radiometry, with a total TPF of 1.07 ± 0.05 when integrated over the entire duration of the disruption, and a value of 1.3 ± 0.1 during the thermal quench (TQ). For SPI, the location of the radiation peak is found to be determined predominantly by the particle source location, and thus can be varied on DIII-D by injecting from either of two toroidally separated injectors. 3D non-linear MHD simulations with the NIMROD code support this picture. The localized SPI particle source leads to higher peaking than for MGI, with a total TPF of 1.3 ± 0.1 over the full disruption and a TQ TPF of 1.9 +0.5/−0.3, a value also consistent with the NIMROD simulations. This TQ value is close to or potentially exceeding the allowable limit for the previously planned Be first wall in ITER, pointing to the importance of radiation asymmetries depending on the choice of first wall material.

Physics - Plasma physics↗

DOE OSTI2024

Nonlinear modeling of ELM mitigation with RMP on HL-2A

Abstract Nonlinear modeling of mitigation of the edge localized mode (ELM) with resonant magnetic perturbation (RMP) is performed for the HL-2A tokamak, utilizing the three-dimensional (3D) magnetohydrodynamic code JOREK. Based on the 3D equilibrium established after application of the n = 1 ( n is the toroidal mode number) RMP at 4.9 kAt coil current with odd parity, ELM mitigation is successfully simulated consistent with the experimental result. Nonlinear simulations show strong mode coupling among toroidal Fourier harmonics, allowing redistribution of the magnetic energy such that the most unstable toroidal mode saturates at a lower level. This magnetic energy cascade offers an explanation of the RMP-induced ELM mitigation achieved in HL-2A. Detailed examination of the simulation results shows persistent resonant field screening even during the ELM mitigation phase. Finite plasma resistivity however does enable partial penetration of the resonant field thus modifying the edge magnetic topology and characteristics of the edge transport. Plasma radial profiles undergo pronounced changes around the pedestal region, when the magnetic energy of the most unstable toroidal mode reaches the maximum value. Systematic scans of the applied RMP coil current with the JOREK simulations find a threshold value of around 4.5 kAt required for achieving the ELM mitigation on HL-2A.

Physics↗

DOE OSTI2025

Validation of 3D MHD simulations of Ne/D 2 mixed shattered pellet injection in JET

Nonlinear 3D magnetohydrodynamic (MHD) modeling of shattered pellet injection (SPI) in JET tokamak plasmas is performed with the JOREK code. The study focuses on the validation of simulation result with respect to experimental observations, addressing in particular figures of merit for the efficiency of the SPI, as a technique to mitigate thermal loads by injecting radiative impurities like neon during the thermal quench (TQ) phase of disruptions. A set of JET pulses with neon/deuterium atomic mixture ratio in the shattered pellet varying from 10% to 100% provides the experimental data to be compared with. Simulations using different models for the ablation of solid fragments and the radiation of neon impurities are considered. Synthetic diagnostics are employed for a direct quantitative comparison with key JET diagnostic systems providing in particular radiation, electron temperature and density, and magnetic measurements. 3D radiation structures from MHD simulations are analyzed to estimate the toroidal asymmetry of radiation, which is difficult to measure in JET due to the presence of only two toroidally displaced multi-channel bolometry systems. JOREK simulations show that, before the TQ, the bulk of the radiation is concentrated in a toroidal region enclosing the radiating fragments that is missed by both multi-channel bolometers, suggesting a possible underestimation of the total radiation by such diagnostic systems in the pre-TQ phase. On the other hand, JOREK predicts that during the TQ the radiation becomes more toroidally symmetric, with positive implications for the heat load to plasma facing components.

JOREK↗

NASA NTRS1983

Doubly diffusive magnetic buoyancy instability in the solar interior

An investigation of the buoyancy of diffuse magnetic fields has shown that in the presence of rotation, static equilibrium configurations of the toroidal magnetic field and ambient plasma can exist. In that case, the escape of toroidal magnetic flux from the solar interior may be determined by the growth of instabilities which the equilibrium configuration may be subject to. In connection with the present investigation, it is assumed that in the region of toroidal magnetic flux amplification, the magnetic field has not as yet filamented into flux ropes, and is therefore 'diffuse'. A study is conducted of the MHD stability of an electrically conducting and differentially rotating gas in the presence of a toroidal magnetic field, an external constant gravitational field, and radiance pressure. The full dispersion relation for the magnetic buoyancy problem is developed, and the solutions of the dispersion relation are discussed.

Schmitt, J. H. M. M.↗

NASA NTRS1991

A new solar cycle model including meridional circulation

A kinematic model is presented for the solar cycle which includes not only the transport of magnetic flux by supergranular diffusion and a poleward bulk flow at the sun's surface, but also the effects of turbulent diffusion and an equatorward 'return flow' beneath the surface. As in the earlier models of Babcock and Leighton, the rotational shearing of a subsurface poloidal field generates toroidal flux that erupts at the surface in the form of bipolar magnetic regions. However, such eruptions do not result in any net loss of toroidal flux from the sun (as assumed by Babcock and Leighton); instead, the large-scale toroidal field is destroyed both by 'unwinding' as the local poloidal field reverses its polarity, and by diffusion as the toroidal flux is transported equatorward by the subsurface flow and merged with its opposite hemisphere counterpart. The inclusion of meridional circulation allows stable oscillations of the magnetic field, accompanied by the equatorward progression of flux eruptions, to be achieved even in the absence of a radial gradient in the angular velocity. An illustrative case in which a subsurface flow speed of order 1 m/s and subsurface diffusion rate of order 10 sq km/s yield 22-yr oscillations in qualitative agreement with observations.

Wang, Y.-M.↗

NASA NTRS1994

Force-free fields in thin coronal loops

We solve the force-free equation J x B = 0 for fields which are toroidally symmetric. The technique utilizes an expansion about a cylindrical field and is therefore valid or tori with a large aspect ratio such as long, thin, coronal loops. The calculation is performed in spatial toroidal coordinates, rather than in the flux coordinates used by previous authors; this allows direct calculation of the loci of flux surfaces and of surfaces of constant magnetic pressure. Our solutions differ significantly from toroidal fields in laboratories, which are in general not force-free. They are characterized by field lines whose projections in the poloidal planes are circles with centers displaced by varying distances from the axis of the torus. In general, flux surfaces do not correspond to surfaces of constant magnetic pressure. We have examined solutions corresponding to simple analytic zero-order cylindrical fields. For moderate twists in the zero-order (cylindrical) field, the magnetic pressure is larger on the inner toroidal radius. However, this effect diminishes with twist angle and in fact, for extreme initial twists, the magnetic pressure can be larger on the outer radius. We compare our results with previous work utilizing flux coordinates.

Emslie, A. Gordon↗

NASA NTRS2002

Computational Analysis of Towed Ballute Interactions

A ballute (balloon-parachute) is an inflatable, aerodynamic drag device for application to planetary entry vehicles. Ballutes may be directly attached to a vehicle, increasing its cross-sectional area upon inflation, or towed behind the vehicle as a semi-independent device that can be quickly cut free when the requisite change in velocity is achieved. The aerothermodynamics of spherical and toroidal towed ballutes are considered in the present study. A limiting case of zero towline length (clamped system) is also considered. A toroidal system can be designed (ignoring influence of the tethers) such that all flow processed by the bow shock of the towing spacecraft passes through the hole in the toroid. For a spherical ballute, towline length is a critical parameter that affects aeroheating on the ballute being towed through the spacecraft wake. In both cases, complex and often unsteady interactions ensue in which the spacecraft and its wake resemble an aero spike situated in front of the ballute. The strength of the interactions depends upon system geometry and Reynolds number. We show how interactions may envelope the base of the towing spacecraft or impinge on the ballute surface with adverse consequences to its thermal protection system. Geometric constraints to minimize or eliminate such adverse interactions are discussed. The towed, toroidal system and the clamped, spherical system show greatest potential for a baseline design approach.

Gnoffo, Peter A.↗

NASA NTRS2006

Fast Erase Method and Apparatus For Digital Media

A non-contact fast erase method for erasing information stored on a magnetic or optical media. The magnetic media element includes a magnetic surface affixed to a toroidal conductor and stores information in a magnetic polarization pattern. The fast erase method includes applying an alternating current to a planar inductive element positioned near the toroidal conductor, inducing an alternating current in the toroidal conductor, and heating the magnetic surface to a temperature that exceeds the Curie-point so that information stored on the magnetic media element is permanently erased. The optical disc element stores information in a plurality of locations being defined by pits and lands in a toroidal conductive layer. The fast erase method includes similarly inducing a plurality of currents in the optical media element conductive layer and melting a predetermined portion of the conductive layer so that the information stored on the optical medium is destroyed.

Oakely, Ernest C.↗