Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “toroidal magnetic fields”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Thermal confinement and transport in spherical tokamaks: a review

Here, we review the thermal plasma confinement and transport properties observed and predicted in low aspect ratio tokamaks, or spherical tokamaks (STs), which can depart significantly from those observed at higher aspect ratio. In particular, thermal energy confinement scalings show a strong, near linear dependence of energy confinement time on toroidal magnetic field, while the dependence on plasma current is more modest, the opposite of what is seen at higher aspect ratio. STs have revealed a very strong improvement in normalized confinement with decreasing collisionality, much stronger than at higher aspect ratio, which bodes well for an ST-based fusion pilot plant should this trend continue at an even lower collisionality than has already been accessed. These differences arise because of fundamental differences in transport in STs due to the more extreme toroidicity (i.e. reduced region of bad curvature), and to the relatively larger $E_r \times B$ shearing rates, both of which can suppress electrostatic drift wave instabilities at both ion and electron gyroradius scales. In addition, electromagnetic effects are much stronger in STs because they operate at high β T . Gyrokinetic (GK) studies, coupled with low- and high-k turbulence measurements, have shed light on the underlying physics controlling transport. At lower β T , both ion- and electron-scale electrostatic drift turbulence may be responsible for transport. At higher β T , microtearing, kinetic ballooning, and hybrid trapped electron/kinetic ballooning modes increasingly play a role, and they have a much stronger impact in the core of ST plasmas than at higher aspect ratio. Flow shear affects the balance between ion- and electron-scale modes. Non-linear GK simulations find regimes where the electron heat flux decreases with decreasing collisionality, consistent with the experimental global normalized confinement scaling. The ST is unique in that the relatively low toroidal magnetic field allows for localized measurements of electron-scale turbulence, and this coupled with turbulence measurements at ion-scales has facilitated detailed comparisons with GK simulations. These data have provided compelling evidence for the presence of ion temperature gradient and electron temperature gradient turbulence in some plasmas, and direct experimental support for the impact of experimental actuators like rotation shear, density gradient and magnetic shear on turbulence and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Design study of an edge current density diagnostic using new high-performance single-channel beam emission spectrometers at DIII-D

A novel Motional Stark Effect spectroscopy system has been designed for application at the DIII-D tokamak. The system is optimized for studies of the poloidal and toroidal magnetic field in the plasma pedestal region with frame rates of up to 10 kHz. Further, light from an existing high-photon-throughput collection lens is analyzed using four single-channel f/2.8 Czerny–Turner spectrometers that use custom-made lens systems instead of mirrors. Each spectrometer has two separate outgoing legs and is operated in a positive grating order, which allows for simultaneous observations of D-alpha and D-beta spectra. Forward modeling using the code FIDASIM shows a radial resolution of the system close to 0.6 cm and sufficiently good spectral resolution when masking the high throughput light collection lens in the horizontal direction to avoid overly strong Doppler broadening of beam emission lines. Moreover, a detailed sensitivity study considering realistic levels of readout and photon noise shows that the poloidal and toroidal magnetic field strengths can be inferred with an uncertainty of less than 1%, which will allow the inference of changes of the plasma current during transient events.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Design of an arrangement of cubic magnets for a quasi-axisymmetric stellarator experiment

The usage of permanent magnets to shape the confining magnetic field of a stellarator has the potential to reduce or eliminate the need for non-planar coils. As a proof-of-concept for this idea, here we have developed a procedure for designing an array of cubic permanent magnets that works in tandem with a set of toroidal-field (TF) coils to confine a stellarator plasma. All of the magnets in the design are constrained to have identical geometry and one of three polarization types in order to simplify fabrication while still producing sufficient field accuracy. We present some of the key steps leading to the design, including the geometric arrangement of the magnets around the device, the procedure for optimizing the polarizations according to the three allowable magnet types, and the choice of magnet types to be used. We apply these methods to design an array of rare-Earth permanent magnets that can be paired with a set of planar TF coils to confine a quasi-axisymmetric plasma with a toroidal magnetic field strength of about 0.5 T on axis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Inferring the scrape-off layer heat flux width in a divertor with a low degree of axisymmetry

Plasma facing components (PFCs) in the next generation of tokamak devices will operate in challenging environments, with heat loads predicted to exceed 10 MWm -2 . The magnitude of these heat loads is set by the width of the channel, the ‘scrape-off layer’ (SOL), into which heat is exhausted, and can be characterised by an e-folding length scale for the decay of heat flux across the channel. It is expected this channel will narrow as tokamaks move towards reactor relevant conditions. Understanding the processes involved in setting the SOL heat flux width is imperative to be able to predict the heat loads PFCs must handle in future devices. Measurements of the SOL width are performed on the high-field spherical tokamak, ST40, using a newly commissioned infrared thermography system. With its high on-axis toroidal magnetic field (≥1.5 T) ST40 is uniquely positioned to investigate the influence of toroidal field on the heat flux width in spherical tokamaks, whilst also extending measurements of the SOL width in spherical tokamaks to increased poloidal field (≥0.3 T). Due to the divertor on ST40 having a low degree of axisymmetry, it is necessary for a set of radial measurements of the heat flux to be taken across the divertor, made possible using an automated toolchain that fully incorporates its 3D geometry. These radial profiles are combined with the magnetic geometry of the plasma to infer the width of the SOL, with both Eich and double exponential profiles of heat flux observed. A reduction in the heat flux is observed toroidally across part of the divertor, along with increased heat loads observed locally around the edges of the tiles. Future work in characterising the impact of tile misalignment and uncertainties in the reconstructed divertor magnetic geometry is required in order to further understand the observed heat flux patterns, as are additional investigations into the role potentially being played by an inhomogeneous sheath electric field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Quasi-linear toroidal simulations of resonant magnetic perturbations in eight ITER H-mode scenarios

Abstract Both linear and quasi-linear aspects of the plasma response to the resonant magnetic perturbation (RMP) field are numerically investigated for various H-mode scenarios in ITER, covering the pre-fusion power operation and the fusion power operation phases. Linear response computations for eight ITER scenarios, with varying plasma current and toroidal magnetic field, reveal that the best coil current phasing for controlling the type-I edge localized modes (ELMs) scales roughly linearly with the edge safety factor. The coil phasing is defined as the relative toroidal phase of the coil currents between different rows, for a given toroidal harmonic. Quasi-linear initial value simulation, which is the focus of the present study, shows that application of the n = 3 ( n is the toroidal mode number) RMP field has a minimum side effect on the plasma core momentum confinement but potentially a large effect on the global particle transport. Generally, the RMP field with the best (worst) coil phasing for ELM control produces the strongest (weakest) effect on the plasma edge flow and the overall density. This robustly holds for all eight ITER scenarios. Consequently, in order to minimize the RMP induced side effects while achieving ELM control (suppression) in ITER, a compromise is necessary in choosing the coil current configuration.

Physics↗
DOE OSTI2024

Upgrade of DIII-D radial interferometer–polarimeter for large bandwidth, low noise, and toroidal mode number measurements

Near ion-cyclotron frequency (f ci ) fluctuations, such as those originating from Global and Compressional Alfvén Eigenmodes (GAEs/CAEs), are expected to be present in future fusion reactors but are not well understood due to the limited availability of core measurements in present-day tokamaks. The measurement bandwidth of the Radial Interferometer–Polarimeter (RIP) diagnostic has been upgraded from 1 to 5 MHz to detect these fluctuations in DIII-D. RIP adopts the three-wave technique for simultaneous polarimetric and interferometric measurements. Solid-state microwave sources operating at 650 GHz are used as probe beams and provide 5 MHz bandwidth for both polarimetric and interferometric measurements. Bandwidths of related hardware, including mixer amplifier, signal cable, and digital phase demodulator, are increased correspondingly. Measurement noise is minimized by reducing the time delay between reference and probe signals to nanosecond level and employing correlation-based techniques. Using the upgraded diagnostic, CAE/GAE-like bursting fluctuations are observed in neutral-beam heated plasmas with toroidal magnetic field B φ ≈ 1 T. Current upgrades being undertaken would enable the evaluation of toroidal mode number for these modes. Furthermore, this work opens the possibility of better understanding near ion-cyclotron frequency fluctuations in fusion relevant plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Overview of physics results from the ADITYA-U tokamak and future experiments

The ADITYA upgrade (ADITYA-U), a medium-sized (R 0 = 75 cm, a = 25 cm) conventional tokamak facility in India, has been consistently producing experiments findings by usingcircular and shaped-plasmas. Recognizing the plasma parameters aligning closely with the design parameters of circular limited plasmas, ADITYA-U shifted its focus toward exploring the operational regime for experimentation on saw-tooth and MHD phenomena. Moreover, ADITYA-U has made consistent advancements toward conducting preliminary plasma shaping experiments through the activation of top and bottom divertor coils utilizing hydrogen as well as deuterium fuels. Confinement is improved by a factor of ~1.5 in D 2 plasmas when compared to H 2 plasmas of ADITYA-U. Further, ADITYA-U operations emphasize preventing disruptions and runaway electrons (REs) to ensure safe operations for future fusion devices. Significant suppression of REs has been achieved in ADITYA-U with the application of pulsed localized vertical magnetic field (LVF) perturbation, thereby establishing the technique's independence from the tokamak device. The successful RE mitigation requires a critical threshold of LVF pulse magnitude, which is approximately 1% of the toroidal magnetic field, and a minimum duration of ~5 ms. Apart from this, several novel findings have been achieved in the ADITYA-U experiments, including the modification of sawtooth duration through gas-puff, the emergence of MHD-induced geodesic acoustic mode-like oscillations, the propagation of fast heat pulses induced by MHD activity, the control of RE dynamics through Gas-puffs, the propagation of pinch-driven cold-pulses, the transport and core accumulations of argon impurities, the mass dependency of plasma toroidal rotation and the detection of 'RICE' scaling, as well as the characterization of edge plasma using wall conditioning methods, such as glow discharge cleaning using a combination of Ar-H 2 mixture, localized wall cleaning by electron cyclotron resonant plasma, and the development of machine learning-based disruption predictions, will be discussed in this paper.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 OSTI2022

Precise stellarator quasi-symmetry can be achieved with electromagnetic coils

Magnetic fields with quasi-symmetry are known to provide good confinement of charged particles and plasmas, but the extent to which quasi-symmetry can be achieved in practice has remained an open question. Recent work [M. Landreman and E. Paul, Phys. Rev. Lett. 128, 035001, 2022] reports the discovery of toroidal magnetic fields that are quasi-symmetric to orders-of-magnitude higher precision than previously known fields. We show that these fields can be accurately produced using electromagnetic coils of only moderate engineering complexity, that is, coils that have low curvature and that are sufficiently separated from each other. Our results demonstrate that these new quasi-symmetric fields are relevant for applications requiring the confinement of energetic charged particles for long time scales, such as nuclear fusion. The coils’ length plays an important role for how well the quasi-symmetric fields can be approximated. For the longest coil set considered and a mean field strength of 1 T, the departure from quasi-symmetry is of the order of Earth’s magnetic field. Additionally, we find that magnetic surfaces extend far outside the plasma boundary used by Landreman and Paul, providing confinement far from the core. Simulations confirm that the magnetic fields generated by the new coils confine particles with high kinetic energy substantially longer than previously known coil configurations. In particular, when scaled to a reactor, the best found configuration loses only 0.04% of energetic particles born at midradius when following guiding center trajectories for 200 ms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

On the Geometry of the Near-core Magnetic Field in Massive Stars

It is well-known that the cores of massive stars sustain a stellar dynamo with a complex magnetic field configuration. However, the same cannot be said for the field's strength and geometry at the convective–radiative boundary, which are crucial when performing asteroseismic inference. In this Letter, we present 3D magnetohydrodynamic (MHD) simulations of a 7 M ⊙ mid-main-sequence star, with particular attention given to the convective–radiative boundary in the near-core region. Our simulations reveal that the toroidal magnetic field is significantly stronger than the poloidal field in this region, contrary to recent assumptions. Moreover, the rotational shear layer, also important for asteroseismic inference, is specifically confined within the extent of the Brunt–Väisälä frequency peak. These results, which are based on the inferred properties of HD 43317, have widespread implications for asteroseismic studies of rotation, mixing, and magnetism in stars. While we expect our results to be broadly applicable across stars with similar Brunt–Väisälä frequency profiles and stellar masses, we also expect the MHD parameters (e.g., Re m ) and the initial stellar rotation rate to impact the geometry of the field and differential rotation at the convective–radiative interface.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Multimachine analysis of intermittent fluctuations in the scrape-off layer of magnetically confined fusion plasmas

Far scrape-off layer fluctuations, also known as blobs/filaments, are compared for the first time across six tokamaks: Alcator C-Mod, DIII-D, TCV, KSTAR, MAST, and MAST-U, under the context of stochastic modeling in Ohmic and low confinement mode scenarios. In this model, which well describes these fluctuations, measurements from Langmuir probes are modeled as a superposition of uncorrelated, two-sided exponential temporal pulses. The key parameters of this model are the mean waiting times between consecutive pulses, the pulse duration times and the mean of the pulse amplitudes. The study examines the influence of line-averaged density, plasma current, magnetic field and aspect ratio. The mean amplitudes and pulse waiting times increase with the line-averaged density across devices, while the pulse duration times remain constant. Whereas the variation in waiting times is gradual across the density scan, the mean amplitudes increase abruptly as the density profile broadens and flattens for Alcator C-Mod. The blob waiting times decrease with increasing plasma current and the toroidal magnetic field, while they increase with aspect ratio for conventional tokamaks. The duration times follow the same trends as the waiting times in these parameters but vary more slowly, resulting in the trends in the waiting times dominating the intermittency level of the fluctuations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Status of DMRadio-50L and DMRadio-m$^3$

Recent theoretical advancements have made the QCD axion a stronger dark matter candidate, especially in the sub- \mu μ eV range. While cavity haloscopes have made significant progress in excluding QCD axions in the 1-100 \mu μ eV region, the 1 peV- 1 \mu μ eV region remains unexplored. The DMRadio program consists of a series of experiments designed to probe low mass axions. DMRadio-50L uses a 1 T average field toroidal magnet and a high-Q LC-oscillator with target sensitivity to axions of g_{a\gamma\gamma} < 5 \times 10^{-15}\text{ GeV}^{-1} g a γ γ < 5 × 10 − 15 GeV − 1 between 5 kHz and 5 MHz. DMRadio-m ^3 3 consists of a higher frequency LC-oscillator in a 4 T peak field solenoidal magnet with sensitivity to the DFSZ model of QCD axions between 30 MHz and 200 MHz. In this work, we present the status of DMRadio-50L and DMRadio-m ^3. 3 .

Rapidis, Nicholas Marcos↗
DOE OSTI2026

Divertor detachment characterization in negative triangularity discharges in DIII-D via 2D edge-plasma transport modeling

Edge fluid modeling of the first divertor-plasma detachment experiments in negative triangularity (NT) discharges in the DIII-D tokamak is presented using the 2D multifluid edge transport code UEDGE, including cross-field particle drifts. Experiments were performed where the lower single-null magnetic equilibrium had a strong NT (δ≈−0.5), that is, where the magnetic X-point is at a larger major radius than the core magnetic axis. Divertor-plasma detachment was induced by increasing the core plasma density in DIII-D via intrinsic gas puffing. Here density scans are performed with UEDGE to reach a detached plasma and to quantitatively recover the experimental rollover of the ion saturation current on the outer divertor target plate. The simulations cover experiments with both signs of the toroidal magnetic field, B T , where the ion magnetic Grad-B drifts are directed into (forward B T ) and out of (reverse B T ) the divertor region. Consistent with experiments with neutral beam power injection, the NT simulations reproduce: 40% higher density is needed to reach detachment onset with forward B T compared with reverse B T , and the absence of deep detachment is found with reverse B T . Similarly, comparison between Ohmic discharges in NT and positive triangularity (PT) shaping confirms that a substantially higher density is needed to achieve detachment in NT than in PT, with NT requiring an line-average density of at least the Greenwald density or higher. Simulation results suggest that higher densities are needed to reach detachment in negative compared to PT because these discharges have a shorter midplane-to-target distance along the total magnetic field B, a shorter outer divertor poloidal leg length (0.06 m vs 0.2 m), and reduced radial transport [near-scrape-off layer (SOL) D ⊥ /χ ⊥ =0.3/0.5 vs D ⊥ /χ ⊥ =1.0/1.0, all in (m 2 /s)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Mode structure measurements of ion cyclotron emission and sub-cyclotron modes on DIII-D

We report mode structure measurements of coherent ion cyclotron emission (ICE) and sub-cyclotron modes on DIII-D. Through a dedicated experiment, we aimed to characterize a variety of modes via the upgraded ICE diagnostic in both L- and H-mode plasmas. In the L-mode plasmas, autopower spectrum peaks at harmonics of the ion cyclotron frequency fci were observed and are localized in the core of the plasma. Sub-cyclotron modes (f ~ 0.5f ci ) were also observed in L-mode plasmas when the toroidal magnetic field strength was lowered from B T = 2.17 T. In H-mode plasmas, many ICE harmonics localized to the plasma edge were observed, with some exceeding the nominal ICE diagnostic bandwidth of f ϵ [0, 100] MHz. Polarization estimates made using an orthogonal pair of vertical and horizontal magnetic pickup loops on the outer wall of the machine indicate that ICE and sub-cyclotron modes have compressional polarization at the plasma edge, the latter being consistent with simulation efforts for comparable DIII-D plasmas. For all modes, the same harmonics are observed on both the centerpost and outer wall loops, indicating that ICE is poloidally extended. Finally, toroidal mode numbers were calculated using three outer wall loops for both core ICE and sub-cyclotron modes in L-mode plasmas. Furthermore, the sub-cyclotron case served as a benchmark for our calculation method, with measured numbers of n ϵ [–24, –18] roughly agreeing with heuristic estimates of n ϵ [–20, –13]. Core ICE mode numbers were measured to be n ϵ [–10, 5], which is comparable to measurements made on other machines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Large-scale Evolution of Seconds-long Relativistic Jets from Black Hole–Neutron Star Mergers

We present the first numerical simulations that track the evolution of a black hole–neutron star (BH–NS) merger from premerger to r ≳ 10 11 cm. The disk that forms after a merger of mass ratio q = 2 ejects massive disk winds (3–5 × 10 –2 M ⊙ ). We introduce various postmerger magnetic configurations and find that initial poloidal fields lead to jet launching shortly after the merger. The jet maintains a constant power due to the constancy of the large-scale BH magnetic flux until the disk becomes magnetically arrested (MAD), where the jet power falls off as L j ~ t –2 . All jets inevitably exhibit either excessive luminosity due to rapid MAD activation when the accretion rate is high or excessive duration due to delayed MAD activation compared to typical short gamma-ray bursts (sGRBs). This provides a natural explanation for long sGRBs such as GRB 211211A but also raises a fundamental challenge to our understanding of jet formation in binary mergers. One possible implication is the necessity of higher binary mass ratios or moderate BH spins to launch typical sGRB jets. For postmerger disks with a toroidal magnetic field, dynamo processes delay jet launching such that the jets break out of the disk winds after several seconds. We show for the first time that sGRB jets with initial magnetization σ0 > 100 retain significant magnetization (σ $\gg$ 1) at r > 10 10 cm, emphasizing the importance of magnetic processes in the prompt emission. The jet–wind interaction leads to a power-law angular energy distribution by inflating an energetic cocoon whose emission is studied in a companion paper.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Experimental progress and future plans on spherical tokamak, QUEST

QUEST (Q-shu university experiment with steady state spherical tokamak) aims at effective plasma current start-up and stable maintenance of plasma discharge. To solve the inherent problems in a spherical tokamak (ST) arising from insufficient space for placing the inductive center solenoid, electron cyclotron current drive (ECCD) and transient coaxial helicity injection (T-CHI) are implemented as a non-inductive plasma start-up method in QUEST. Efficient ECCD assisted by energetic electrons could be achieved. By combining control of the wave injection angle and application of a negative toroidal electric field, the bulk electron temperature could be raised up to 1 keV due to selective wave power absorption in the bulk electrons. The plasma current of over 50 kA contained within the closed flux surface could be obtained with a floating single biased electrode placed on lower divertor plates for T-CHI. Long-pulse operations on QUEST are impeded frequently due to wall saturation and subsequent density runaway caused by fuel particle imbalance. Since 2014, a unique tool called the ‘hot wall’ has been implemented to overcome the imbalance. The hot wall has a capability to regulate its surface temperature using a heater and two water cooling channels. With the help of the hot wall, 6 h discharges were obtained in 2020. Cooling down of the surface of the hot wall was significantly effective in recovering the wall pumping and was useful to extend the pulse duration. Augmentation of the toroidal magnetic field, B T up to 0.5 T from 0.25 T and a continuous wave (CW) gyrotron of 28 GHz are planned for QUEST in the near future. As raising B T provides a fundamental resonance of electron cyclotron waves (ECWs) with 28 GHz, more effective plasma current start-up and heating will be performed. Long-pulse operations with higher plasma parameters are expected.

QUEST↗
DOE OSTI2025

Role of E × B Drift in Divertor Detachment Control via Boron Powder Injection on EAST

Here, the effects of B powder injection on plasma detachment about EAST discharge were studied by using SOLPS-ITER code package with the effects of E × B drifts considered. The simulation results show that plasma detachment occurs at the inner target in favourable toroidal magnetic field (B t ) direction at a relatively low B powder flow rate, one order of magnitude lower than that at the outer target. In a similar scenario with unfavourable B t , it is found that the detachment thresholds of B flow rate for both the inner and outer targets are close and of the same order as that for the outer target with favourable Bt. In favourable B t direction at B powder flow rate of 1.2 × 10 21 atoms/s, a localized, broadened high-density region is formed near the inner target benefitted by the injection location and the E × B drift, and a radiation-intensified zone, mostly contributed by B 1+ and B 2+ , occurs there. The E × B drift facilitates plasma detachment at the inner target and simultaneously amplifies the in–out divertor asymmetry. In addition, the simulation results with three different injection locations show that the injection from outer strike point leads to the lowest Z eff inside the separatrix and has an intermediate flow rate for detachment at the outer target, comparing with the X-point and upstream locations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗