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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Solution of the linear wave-particle kinetic equation for global modes of arbitrary frequency in a tokamak

The linear response of a plasma to perturbations of arbitrary frequency and wavelength is derived for any axisymmetric magnetized toroidal plasma. An explicit transformation to action-angle coordinates is achieved using orthogonal magnetic coordinates and the Littlejohn Lagrangian, establishing the validity of this result to arbitrary order in normalized Larmor radius. The global resonance condition for compressional modes is clarified in more detail than in previous works, confirming that the poloidal orbit-average of the cyclotron frequency gives the desired result at lowest order in Larmor radius. The global plasma response to the perturbation at each resonance is captured by a poloidal and gyroaverage of the perturbing potential. A “global gyroaveraging” of the potential is a natural by-product of this analysis which takes into account the changing of the magnetic field over an orbit. The resonance condition depends on two arbitrary integers which completely separately capture the effects poloidal non-uniformity and finite Larmor radius in generating sidebands. We learn that poloidal sidebands generated for compressional modes are dominated by the change in gyrofrequency over the orbit, which is very different to shear modes where the gyrofrequency only contributes via a finite Larmor radius effect. This increases the number of bounce harmonics required to compute the linear drive, giving a more complicated resonance map. An example calculation is given comparing resonance of shear and compressional modes in a published DIII-D case.

Compressional↗
DOE OSTI2025

Final design of outer poloidal field coils for COMPASS Upgrade

The paper aims to provide an overview of the final design of the outer poloidal field coils system for COMPASS Upgrade. Due to a relatively unique combination of design features of the new device (placement in high toroidal magnetic field, copper coils sub-cooled to liquid nitrogen temperature, hot vacuum vessel operation), the poloidal field coils design faced several interesting engineering challenges. Most notably high electromagnetic stress in the coil conductor, compatibility of the insulation to thermal and mechanical stress and design of coil supports with given spatial constraints while able to accommodate coil movements and withstand considerable mechanical stress. In conclusion, the paper describes solution to these challenges together with underlying analyses and mechanical tests.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Uncertainty guided online ensemble for non-stationary data streams in fusion science

Machine Learning (ML) is poised to play a pivotal role in the development and operation of next-generation fusion devices. Fusion data shows non-stationary behavior with distribution drifts, resulted by both experimental evolution and machine wear-and-tear. ML models assume stationary distribution and fail to maintain performance when encountered with such non-stationary data streams. Online learning techniques have been leveraged in other domains, however it has been largely unexplored for fusion applications. In this paper, we investigate online learning for continuous adaptation to drifting data streams in the prediction of Toroidal Field (TF) coils deflection at the DIII-D fusion facility. We further address the short-term performance degradation inherent to standard online learning, which arises because ground truth is unavailable at prediction time. To mitigate this issue, we propose an uncertainty-guided online ensemble framework. The method leverages the Deep Gaussian Process Approximation (DGPA) for calibrated uncertainty estimation and uses these uncertainty measures to guide a meta-algorithm that aggregates predictions from learners trained over different historical horizons. Our results show that online learning reduces prediction error by 80% compared to a static model. The online ensemble and the proposed uncertainty-guided ensemble further reduce error by approximately 6%, and 10% respectively, relative to standard single-model online learning, while also providing calibrated uncertainty estimates to support operational decision-making.

AI↗
DOE OSTI2025

Experiment-modeling studies comparing energy dissipation in the DIII-D SAS and SAS-VW divertors

Recent DIII-D experiments on Small Angle Slot (SAS) divertors have confirmed that a combination of divertor closure and target shaping can enhance cooling across the divertor target and increase energy dissipation, but with significant dependence on B T (toroidal magnetic field) direction. In these novel divertors, the roles of closure, target shaping, drifts, and scale lengths are all interconnected in optimizing dissipation, with the separatrix electron density n eSEP being the key parameter associated with the level of dissipation/detachment. After modifying the original flat-targeted graphite SAS to include a V shape with a tungsten coating on the outer side of the divertor (SAS-VW), matched series of discharges were run to compare to detailed SOLPS-ITER modeling. Experimentally, when run as designed with the outer strike point at the slot vertex, SAS-VW requires nearly identical n eSEP for detachment as the original SAS, with little difference in dissipation for the new geometry. This is in contrast to (1) earlier modeling predictions that a small change of the SAS geometry to a V shape should enhance dissipation at the same n eSEP for magnetic configurations having better H-mode access (ion B × ∇B drift directed into the divertor), and (2) despite the achievement of significantly higher (2-7x) neutral pressures and compression in the SAS-VW slot. Comparisons of experimental density scans to the most recent SOLPS-ITER modeling with ExB drifts show reasonable agreement for dissipation/detachment onset when using separatrix density as the independent parameter. In order to help understand the discrepancy in modeled vs actual performance for the new configuration, additional measurements varying gas injection location and impurity injection were undertaken. In-slot D 2 gas fueling is more effective (5–22 %) in promoting detachment, in accord with modeling. In-slot impurity injection (N 2 or Ne) can yield 30 % lower core Z eff and 15 % less confinement degradation after detachment compared to main chamber puffing, as well as relatively lower tungsten leakage from the divertor. Modeling can also reproduce the improved detachment seen as the strike point moves inboard of the slot vertex. While we can explain the effects of the most important parameters causing energy dissipation in these slot divertors, it remains that many aspects of their behavior cannot be accurately modeled using state-of-art codes such as SOLPS-ITER. This is of concern for future model-driven designs utilizing similar V-shaped geometries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Shock-induced bubble jets: a dual perspective of bubble collapse and interfacial instability theory

Interactions between shock waves and gas bubbles in a liquid can lead to bubble collapse and high-speed liquid jet formation, relevant to biomedical applications such as shock wave lithotripsy and targeted drug delivery. This study reveals a complex interplay between acceleration-induced instabilities that drive jet formation and radial accelerations causing overall bubble collapse under shock wave pressure. Using high-speed synchrotron X-ray phase contrast imaging, the dynamics of micrometre-sized air bubbles interacting with laser-induced underwater shock waves are visualised. These images offer full optical access to phase discontinuities along the X-ray path, including jet formation, its propagation inside the bubble, and penetration through the distal side. Jet formation from laser-induced shock waves is suggested to be an acceleration-driven process. A model predicting jet speed based on the perturbation growth rate of a single-mode Richtmyer–Meshkov instability shows good agreement with experimental data, despite uncertainties in the jet-driving mechanisms. The jet initially follows a linear growth phase, transitioning into a nonlinear regime as it evolves. To capture this transition, a heuristic model bridging the linear and nonlinear growth phases is introduced, also approximating jet shape as a single-mode instability, again matching experimental observations. Upon piercing the distal bubble surface, jets can entrain gas and form a toroidal secondary bubble. Linear scaling laws are identified for the pinch-off time and volume of the ejected bubble relative to the jet’s Weber number, characterising the balance of inertia and surface tension. At low speeds, jets destabilise due to capillary effects, resulting in ligament pinch-off.

Drops and Bubbles: Bubble dynamics↗
DOE OSTI2024

Direct, simple and efficient computation of all components of the virtual-casing magnetic field in axisymmetric geometries with Kapur–Rokhlin quadrature

In a recent publication (Toler et al., J. Plasma Phys., vol. 89, issue 2, 2023, p. 905890210), we demonstrated that for axisymmetric geometries, the Kapur–Rokhlin quadrature rule provided an efficient and high-order accurate method for computing the normal component, on the plasma surface, of the magnetic field due to the toroidal current flowing in the plasma, via the virtual-casing principle. The calculation was indirect, as it required the prior computation of the magnetic vector potential from the virtual-casing principle, followed by the computation of its tangential derivative by Fourier differentiation, to obtain the normal component of the magnetic field. Our approach did not provide the other components of the virtual-casing magnetic field. In this letter, we show that a more direct and more general approach is available for the computation of the virtual-casing magnetic field. The Kapur–Rokhlin quadrature rule accurately calculates the principal value integrals in the expression for all the components of the magnetic field on the plasma boundary, and the numerical error converges at a rate nearly as high as the indirect method we presented previously.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Stellarator equilibrium axis-expansion to all orders in distance from the axis for arbitrary plasma beta

A systematic theory of the asymptotic expansion of the magnetohydrostatics (MHS) equilibrium in the distance from the magnetic axis is developed to include arbitrary smooth currents near the magnetic axis. Compared with the vacuum and the force-free system, an additional magnetic differential equation must be solved to obtain the pressure-driven currents. It is shown that there exist variables in which the rest of the MHS system closely mimics the vacuum system. Thus, a unified treatment of MHS fields is possible. The mathematical structure of the near-axis expansions to arbitrary order is examined carefully to show that the double-periodicity of physical quantities in a toroidal domain can be satisfied order by order. The essential role played by the leading-order Birkhoff–Gustavson normal form in solving the magnetic differential equations is highlighted. Several explicit examples of vacuum, force-free and MHS equilibrium in different geometries are presented.

Physics↗
DOE OSTI2024

Radiative and continuum dampings of reversed shear Alfvén eigenmodes and perturbative analysis limitations for tokamaks

A careful theoretical analysis of the excitation of Alfvén eigenmodes (AEs), such as TAE (toroidicity-induced AE) and RSAE (reversed shear AE), by superalfvenic energetic particles is required for reliable predictions of energetic ion relaxation in present day fusion experiments. This includes the evaluation of different AE damping mechanisms including radiative and continuum dampings which are the focus of this study. A recent comprehensive benchmark of different eigenmode solvers including gyrokinetic, gyrofluid and hybrid magenetohydrodynamics (MHD) has shown that employed models may have deficiencies when addressing some of them (Taimourzadeh et al., Nucl. Fusion, vol. 59, 2019, 066006). Here, in this paper, we are studying the radiative and continuum dampings of RSAEs in details which were missing in hybrid NOVA/NOVA-C calculations to prepare a NOVA-C package with a substantial upgrade. Both dampings require the finite Larmor radius (FLR) corrections to AE mode structures to be accounted for. Accurately calculating different damping rates and understanding their parametric dependencies, we resolve the limitation coming out of the perturbative approach. In particular, here, the radiative damping is included perturbatively, whereas the continuum damping is computed non-perturbatively. Our comparison leads to the conclusion that the non-perturbative treatment of the unstable RSAE modes is needed to find the agreement with the gyrokinetic calculations. We expect that the RSAE mode structure modification plays a dominant role in determining the RSAE stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Turbulence and transport in mirror geometries in the Large Plasma Device

Thanks to advances in plasma science and enabling technology, mirror machines are being reconsidered for fusion power plants and as possible fusion volumetric neutron sources. However, cross-field transport and turbulence in mirrors remains relatively understudied compared with toroidal devices. Turbulence and transport in mirror configurations were studied utilizing the flexible magnetic geometry of the Large Plasma Device (LAPD). Multiple mirror ratios from $M=1$ to $M=2.68$ and three mirror-cell lengths from $L=3.51$ to $L=10.86$ m were examined. Langmuir and magnetic probes were used to measure profiles of density, temperature, potential and magnetic field. The electric field-fluctuation-driven ${\tilde {\boldsymbol{E}}} \times {\boldsymbol{B}}$ particle flux, where $\boldsymbol{B}$ is the background field, was calculated from these quantities. Two probe correlation techniques were used to infer wavenumbers and two-dimensional structure. Cross-field particle flux and density fluctuation power decreased with increased mirror ratio. Core density and temperatures remain similar with mirror ratio, but radial line-integrated density increased. The physical expansion of the plasma in the mirror cell by using a higher field in the source region may have led to reduced density fluctuation power through the increased gradient scale length. This increased scale length reduced the growth rate and saturation level of rotational interchange and drift-like instabilities. Despite the introduction of magnetic curvature, no evidence of mirror-driven instabilities – interchange, velocity space or otherwise – were observed. For curvature-induced interchange, many possible stabilization mechanisms were present, suppressing the visibility of the instability.

Travis, Phil (ORCID:0000000343170432)↗
DOE OSTI2025

Bootstrap current modeling in M3D-C1

Bootstrap current plays a crucial role in the equilibrium of magnetically confined plasmas, particularly in quasi-symmetric stellarators and in tokamaks, where it can represent bulk of the electric current density. Accurate modeling of this current is essential for understanding the magnetohydrodynamic (MHD) equilibrium and stability of these configurations. This study expands the modeling capabilities of M3D-C1, an extended-MHD code, by implementing self-consistent physics models for bootstrap current. It employs two analytical frameworks: a generalized Sauter model (Sauter et al. 1999 Phys. Plasmas vol. 6, no. 7, pp. 2834–2839), and a revised Sauter-like model (Redl et al. 2021 Phys. Plasmas vol. 28, no. 2, pp. 022502). The isomorphism described by Landreman et al. (2022 Phys. Rev. Lett. vol. 128, pp. 035001) is employed to apply these models to quasi-symmetric stellarators. The implementation in M3D-C1 is benchmarked against neoclassical codes, including NEO, XGCa and SFINCS, showing excellent agreement. These improvements allow M3D-C1 to self-consistently calculate the neoclassical contributions to plasma current in axisymmetric and quasi-symmetric configurations, providing a more accurate representation of the plasma behavior in these configurations. A workflow for evaluating the neoclassical transport using SFINCS with arbitrary toroidal equilibria calculated using M3D-C1 is also presented. This workflow enables a quantitative evaluation of the error in the Sauter-like model in cases that deviate from axi- or quasi-symmetry (e.g. through the development of an MHD instability).

fusion plasma↗
DOE OSTI2026

Omnigenous umbilic stellarators

To better understand the dependence of the magnetic field structure in the plasma edge on the plasma boundary shape, in the context of X-point and island divertor designs, we define and develop a class of stellarators called umbilic stellarators. These equilibria are characterised by a single continuous high-curvature edge on the plasma boundary that goes around multiple times toroidally before meeting itself. We develop a technique that allows us to simultaneously optimise the plasma boundary along with a curve lying on the boundary on which we impose a high curvature while imposing omnigenity – a property of the magnetic field that ensures trapped particle confinement throughout the plasma volume. We find that umbilic stellarators naturally tend to favour piecewise omnigenity instead of omnigenity with a specific helicity. After generating omnigenous umbilic stellarators, we design coil sets for some of them and explore the fieldline structure in the edge and its sensitivity to small fluctuations in the plasma. Finally, using single-stage optimisation, we simultaneously modify the plasma and coil shape and propose an experiment to modify an existing tokamak to a finite-𝛽 stellarator using this technique and explore a potentially simpler way to convert a limited tokamak into a diverted stellarator.

fusion plasma↗
DOE OSTI2024

Revealing the three-dimensional arrangement of polar topology in nanoparticles

In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Effect of convective transport in edge and scrape-off-layer plasmas of ADITYA-U tokamak

The 2-D edge plasma fluid transport code, UEDGE has been used to simulate the edge and scrape-off layer regions of circular limiter plasmas of ADITYA-U. The computational mesh defining the limiter geometry of ADITYA-U has been introduced in the UEDGE code through an in-house developed routine. It has successfully been integrated with the UEDGE code and the measured radial profile of electron density (n e ) in the edge region is modelled using the simulations. The plasma discharge for the present study has plasma current I P ~ 130 kA, duration ~ 150 ms, chord-averaged electron density ~ 1.3 x 10 19 m -3 , and central electron temperature ~ 270 eV has been observed. The maximum toroidal magnetic field is ~ 1.2 T. It has been found that an inward convective velocity, v conv ~ 1.5 m/s is required in addition to the constant perpendicular diffusion coefficient, D ⟂ ~ 0.2 m 2 /s to adequately match the measured n e profile in typical discharges of ADITYA-U. The value of D ⟂ ~ 0.2 m 2 /s is found to lie between the estimated neoclassical diffusivity and Bohm diffusivity.

Physics - Plasma physics↗
DOE OSTI2024

3D hybrid fluid-particle jet simulations and the importance of synchrotron radiative losses

Context. Relativistic jets in active galactic nuclei are known for their exceptional energy output, and imaging the synthetic synchrotron emission of numerical jet simulations is essential for a comparison with observed jet polarization emission. Aims. Through the use of 3D hybrid fluid-particle jet simulations (with the PLUTO code), we overcome some of the commonly made assumptions in relativistic magnetohydrodynamic (RMHD) simulations by using non-thermal particle attributes to account for the resulting synchrotron radiation. Polarized radiative transfer and ray-tracing (via the RADMC-3D code) highlight the differences in total intensity maps when (i) the jet is simulated purely with the RMHD approach, (ii) a jet tracer is considered in the RMHD approach, and (iii) a hybrid fluid-particle approach is used. The resulting emission maps were compared to the example of the radio galaxy Centaurus A. Methods. We applied the Lagrangian particle module implemented in the latest version of the PLUTO code. This new module contains a state-of-the-art algorithm for modeling diffusive shock acceleration and for accounting for radiative losses in RMHD jet simulations. The module implements the physical postulates missing in RMHD jet simulations by accounting for a cooled ambient medium and strengthening the central jet emission. Results. We find a distinction between the innermost structure of the jet and the back-flowing material by mimicking the radio emission of the Seyfert II radio galaxy Centaurus A when considering an edge-brightened jet with an underlying purely toroidal magnetic field. We demonstrate the necessity of synchrotron cooling as well as the improvements gained when directly accounting for non-thermal synchrotron radiation via non-thermal particles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Effects of density turbulence on helicon wave propagation in the core plasmas

Radio frequency wave propagation can be significantly affected by density irregularities, such as filaments in the scrape-off layer or instabilities in the core plasma. In this study, we examine the impact of edge turbulence on helicon wave propagation using the Petra-M simulation tool. To analyze the effect of edge turbulence, we utilize a realistic background plasma derived from XGC simulations, which includes spatial density fluctuations at the edge. This focus is particularly relevant for the DIII-D configuration, characterized by edge density turbulence of the core plasmas in a wide pedestal QH-mode. We focus on helicon wave propagation in the core plasma since the slow mode cannot propagate into the core plasma when the density is higher than the lower hybrid resonance, where a wide pedestal QH-mode occurs. The simulation results indicate that edge density fluctuations have a substantial impact on helicon wave coupling due to scattering in the core. We specifically demonstrate that the toroidal mode number and the level of density fluctuations are significant factors influencing scattering. While we have minimized the excitation of slow modes from the antenna, we still observe mode-converted slow modes resulting from the incoming helicon waves. The insights derived from these simulations will inform upcoming tokamak experiments regarding helicon antenna coupling in long pulse scenarios.

Kim, Eun-Hwa [Princeton Plasma Physics Laboratory ↗
DOE OSTI2026

Simulations of ICRF Heating for SPARC during First Campaign and Primary Reference-Like Discharge using the Stix Code

High magnetic field tokamaks, like SPARC, rely on ion cyclotron radio frequency heating (ICRF) to reach fusion relevant temperatures. The SPARC tokamak will have 14 ICRF antennas in 7 toroidal locations delivering > 20 MW of power to the plasma. New capabilities with the full wave cold plasma solver, Stix, now allow for resolving the wave-particle resonances using lower order thermal corrections to capture core absorption of Landau damping and ion resonances in devices like SPARC. Favorable comparisons to the TORIC codes give confidence in the single pass absorption of this model to accurately capture the strength of edge interactions of the RF. Using this new dielectric formulation in the Stix code, simulations of the 2D poloidal cross section of SPARC are completed for the first campaign and primary reference-like discharges (PRD-like). A scan of the minority ion concentrations of helium-3 is performed and shows the expected behavior that as the helium-3 decreases the amount of single pass absorption also decreases which is seen in both scenarios. Additionally, both scenarios show only slight differences in single-pass absorption for the range of 3% to 5% helium-3 allowing for more flexibility in experiments. This study also highlights the differences between the first campaign and PRD-like with the first campaign discharges showing much more multi-pass absorption and an effect of confining the wave to a smaller portion of the cross-section due to the fast wave cut-off. This latter result suggests that far-field sheath rectification at the high-field side would be minimal for the first campaign scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Ion Cyclotron Heating in a Levitated Dipole Fusion Reactor

OpenStar Technologies is pursuing the levitated dipole (LD) as a highly modular, loosely-coupled system that leverages their expertise in high temperature superconductor (HTS) technology. The next generation experiment at OpenStar, Tahi (Ma¯ori for “first”), will demonstrate the generation and confinement of fast ions in a levitated dipole for the first time. Ion cyclotron range of frequency (ICRF) heating is a leading candidate for energetic ion formation in Tahi. A frequency in the 10 MHz range will be used for H minority heating or D majority heating with waves launched from an antenna located above the floating coil. Unlike a tokamak, where the targeted cyclotron resonance is typically a vertical path through the center of the plasma, in a dipole the resonance location follows a C-shaped path from the separatrix to the center of the plasma. The value of B also varies significantly within the confined plasma resulting in a large number of cyclotron harmonics present in the low field region. Furthermore, levitated dipoles contain a “first closed flux surface” surrounding the floating coil, in addition to the traditional separatrix /last closed flux surface. Simulation e ff orts using full-wave ICRF codes show that ICRF heating of a levitated dipole reactor is feasible using a pair of toroidal current straps phased to launch the appropriate parallel ( i.e. poloidal) refractive index.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗