Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “first wall”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Influence of fatigue precracking and specimen size on Master Curve fracture toughness measurements of EUROFER97 and F82H steels

EUROFER97 and F82H steels are two leading reduced-activation ferritic-martensitic (RAFM) steels for fusion first wall and blanket applications. Exposure to the harsh environment of fusion reactors can result in severe degradation of fracture toughness. Thus, the post-irradiation evaluation of fracture toughness is critical for understanding the material behavior. Due to the space constraints of irradiation facilities and challenges in controlling a uniform irradiation condition for large size specimens, the development of small specimen test techniques (SSTT) is indispensable to evaluate the performance of irradiated materials. In this study, we evaluated specimen size effects on the Master Curve fracture toughness of EUROFER97 and F82H steels. A wide variety of specimens, including 0.5 T compact tension (C(T)) specimens, 0.16 T mini-compact tension (miniC(T)) specimens, and 1.65 mm miniature bend bar specimens, were tested. The testing methodology was based on the Master Curve method in the ASTM E1921 standard. No specimen size effect was observed in 0.5 T C(T) and 0.16 T miniC(T) specimens on the Master Curve reference temperature T0, while 1.65 mm miniature bend bar specimens yielded a higher T 0Q . A strong effect of fatigue precracking on T 0 for 0.5 T C(T) and 0.16 T miniC(T) specimens was observed, such that testing on specimens with skewed fatigue precrack fronts resulted in lower T 0 than for specimens with ASTM standard qualified straight fatigue precrack fronts. The results highlight the importance of experimental quality control in developing SSTT for Master Curve fracture toughness testing. Lastly, we also evaluated and provided recommendations on the minimum number of specimens needed for each specimen type for yielding reliable T 0Q values.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Initial design concepts for solid boron injection in ITER

As part of ITER’s consideration to change its first wall material from beryllium to tungsten, the ITER Organization has proposed studying the feasibility of real-time solid boron injection (SBI) into the plasma to coat the walls and divertor to supplement glow discharge boronization (GDB). Boron deposits getter oxygen and reduce sputtering of tungsten from plasma facing components (PFCs). Particularly in areas with significant plasma wall interactions, boron coatings are expected to be short-lived under high performance plasma conditions. The proposed SBI system aims to maintain boron layers in these areas to avoid excessive radiation from tungsten in the plasma as a risk mitigation to ensure ITER will be able to reach and sustain Q = 10 conditions. The system will be used sparingly, as redeposition of boron can lead to significant tritium retention, which must be minimized in ITER to comply with nuclear safety concerns. SBI is proposed to limit and precisely control the amount of boron injected in real-time during plasma operation. Here, some of the design requirements and initial concepts for an SBI system in ITER are presented based on previous results carried out with SBI systems on a number of tokamaks and stellarators around the world. Previous results using SBI systems installed by PPPL have injected boron particles from 5 µm–2 mm diameter at calibrated rates of 2–200 mg/s in real-time during plasma operation on AUG, DIII-D, EAST, KSTAR, LHD, TFTR, WEST, and W7-X, leading to improved wall conditions with reduced plasma impurity concentrations and radiated power and improved plasma performance. The boron is ionized in the plasma edge and then deposited on plasma-wetted surfaces. On AUG, EAST and WEST reduced tungsten sputtering sources were observed following several discharges with SBI. Extrapolation of these SBI results are presented to estimate the amount of boron needed for wall conditioning in ITER. Real-time SBI control requirements and plasma operation scenarios for ITER are also described.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Power and particle exhaust for the ARC fusion power plant

To successfully show that fusion is an attractive energy source, the ARCTM fusion power plant will need to operate with a robust, integrated power and particle exhaust solution. To maximise ARC’s fusion power output while avoiding excessive erosion of the plasma-facing components, we will need to radiatively dissipate most of the power crossing the last-closed flux surface, injecting radiating impurities such as argon or neon to access divertor detachment. Divertor detachment will need to be integrated with a high-performance core plasma, and with efficient impurity pumping to prevent the accumulation of helium ash in the core. To access and control detachment in high-performance plasmas, we have designed ARC with up–down-symmetric divertors, with secondary X-points in long, tightly baffled outer legs. Using a core-edge modelling workflow, we predict that with this divertor design, ARC will access detachment with modest argon seeding in the divertor (c Ar,div ∼0.9%), which should have minimal impact on the core ( Z eff,core <0.5) for reasonable argon enrichment (c Ar,div /c Ar,core =6). Due to the high predicted divertor neutral pressure (p div ∼20 Pa), we predict that ARC will sufficiently pump helium to limit ash accumulation in the core (c He,core <2%) for a helium enrichment of c He,div /c He,core =0.4. ARC’s divertor design is expected to increase the stability of a detachment front in the outer divertor leg, helping to prevent divertor reattachment during smaller heat-flux transients such as scrape-off-layer filaments associated with the quasi-continuous exhaust regime. However, this buffering will not be sufficient to prevent divertor reattachment during large type-I edge-localised modes (ELMs), and as such these will need to be avoided on ARC. Experiments on SPARC will be used to select an integrated scenario which avoids or mitigates type-I-ELMs while maintaining access to detachment, good core fusion performance and sufficient impurity exhaust. SPARC experiments will also be used to finalise ARC’s divertor design, by studying the impact of magnetic and first-wall geometry on detachment stability, impurity enrichment and neutral baffling under conditions similar to those expected for ARC. In conclusion, our analysis finds that ARC will have a viable power and particle exhaust solution which is compatible with high-power operations, and this solution will be validated in experiments on SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

ARC disruption physics and strategy

Commonwealth Fusion Systems (CFS) plans to operate a tokamak power plant called ARC in the early 2030s. Tokamak plasmas have stability limits that, if crossed, lead to a rapid termination of the plasma, referred to as a disruption. Disruptions pose a melt risk to the first wall resulting from thermal and non-thermal particle heat fluxes, and an electromagnetic loading risk on all metal components within the equilibrium coils. A comprehensive set of models is used herein to provide an assessment of both mitigated and unmitigated ARC disruption loads. A preliminary massive gas injection system is baselined and a runaway electron mitigation coil option is proposed to close possible gaps in the baseline. It is predicted that all ARC disruption loads are within a factor of 2 of the disruption loads in SPARC, a tokamak presently under construction by CFS, and therefore SPARC provides an opportunity to calibrate models, test solutions and inform the design of ARC. The goal for ARC is disruption-free operation, however, the pragmatic design target is to withstand one mitigated disruption per day, and to restart the plasma following mitigation in tens of seconds without interrupting the power output. Unmitigated disruptions must be rare, and experience with unmitigated disruption impacts in SPARC will better define what rare means. The implications of this strategy for plasma disruptivity and disruption prediction are discussed, and operating the ARC scenario on SPARC is expected to refine the ARC final design and operational plan.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Taming harmful bursts and heat flux in high-confinement tokamak plasmas

A major challenge in tokamak fusion research is first-wall erosion caused by steady heat loads and sudden energy bursts known as edge-localized modes. Divertor detachment reduces steady-state heat flux, while resonant magnetic perturbations can suppress these instabilities. However, integrating the two has been difficult because they require conflicting operating conditions. Here we demonstrate simultaneous achievement of resonant magnetic perturbations mitigated small edge-localized modes and impurity seeded partial divertor detachment in plasmas with an ITER-similar shape on the DIII-D tokamak. Experiments and simulations show that resonant magnetic perturbations facilitate detachment by redistributing particles, lowering the core density and increasing the scrape-off layer density, thereby reducing the amount of injected gas required. Cooling-gas injection eliminates the secondary heat-flux peak created by three-dimensional magnetic lobes, while edge cooling weakens the plasma response to the applied magnetic fields. These advances illustrate a viable pathway for integrating edge stability control with power exhaust in future fusion reactors.

magnetically confined plasmas↗
DOE OSTI2022

Liquid lithium as divertor material to mitigate severe damage of nearby components during plasma transients

The successful operation of thermonuclear fusion reactors such as ITER, DEMO, and future commercial plants is mainly determined by the optimum choice of materials for various components. The objective of this work is to accurately and comprehensively simulate the entire device in 3D to predict pros and cons of various materials, e.g., liquid lithium in comparison to tungsten and carbon to predict future ITER-like and DEMO divertor performances. We used our comprehensive HEIGHTS simulation package to investigate ITER-like components response during transient events in exact 3D geometry. Starting from the lost hot core plasma particles through SOL, deposition on the divertor surface, and the generation of secondary plasma of divertor materials. Our simulations predicted significant reduction in the heat loading and damage to the divertor nearby and internal components in the case when lithium is used on the divertor plates. While if tungsten or carbon are used on the divertor plate, significant melting areas and vaporization spots can occur (less for carbon) on the reflector, dome, and stainless steel tubes, and even parts of the first walls can melt due to the high radiation power of the secondary divertor plasma. Lithium photon radiation deposition into the divertor and nearby surfaces was decreased by two orders of magnitude compared to tungsten and by one order of magnitude compared to carbon. This analysis showed that using liquid lithium for ITER-like surfaces and future DEMO can lead to significant enhancement in components lifetime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Density functional theory calculation of helium segregation and decohesion effect in W110/Ni111 interphase boundary

Density functional theory (DFT) is employed to study the preferential distribution and decohesion effect of He in a W-NiFe composite consisting of W particles embedded in an Ni-based solid solution matrix. A slab containing {110}<100>W//{111}<110>Ni interface is employed as a surrogate model for the W-NiFe system. Firstly, the fracture energy of the W/Ni interphase boundary (IB) (4.37 J/m 2 ) is higher than the cleavage energy of Ni{111} (3.82 J/m^2) and lower than the cleavage energy of W{110} (6.60 J/m 2 ). The comparison shows that the cohesion of the IB is stronger than the Ni{111} planes that are away from the IB. However, the cohesion between the Ni{111} planes adjacent to the IB is found to be the weakest in this system, with a cleavage energy of 3.11 J/m 2 . Subsequently, formation energy of He is calculated in the Ni slab, W slab, and various interstitial sites in the IB. The DFT calculations show that He is significantly more stable in Ni than in W, by about 1.75 eV. Interestingly, He does not prefer to segregate at the IB as compared to bulk Ni. Nevertheless, it prefers to segregate to the region between the Ni{111} planes adjacent to the IB, and decreases the cohesion of the already weakest region. Based on an estimated amount of He gas production in 5 years under first wall neutron irradiation (neutron flux of 1.04x10 15 n/cm 2 /s), the He will decrease the cleavage energy of the weakest region by 21.2%, 15.4%, and 12.2% at 800, 1000, and 1200 C, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Thermal gradient effect on helium and self-interstitial transport in tungsten

First-wall materials in a fusion reactor are expected to withstand harsh conditions, with high heat and particle fluxes that modify the materials microstructure. These fluxes will create strong gradients of temperature and concentration of diverse species. Besides the He ash and the hydrogenic species, neutron particles generated in the fusion reaction will collide with the material creating intrinsic defects, such as vacancies, self-interstitials atoms (SIAs), and clusters of such point defects. These defects and the He atoms will then migrate in the presence of the aforementioned gradients. In this study, we use nonequilibrium molecular dynamics to analyze the transport of He and SIAs in the presence of a thermal gradient in tungsten. We observe that, in all cases, the defects and impurity atoms tend to migrate toward the hot regions of the tungsten sample. The resulting species concentration profiles are exponential distributions, rising toward the hot regions of the sample, in agreement with irreversible thermodynamics analysis. For both He atoms and SIAs, we find that the resulting species flux is directed opposite to the heat flux, indicating that species transport is governed by a Soret effect (thermal-gradient-driven diffusion) characterized by a negative heat of transport that drives species diffusion uphill (from the cooler to the hot regions of the sample). Here, we demonstrate that the steady-state species profiles obtained accounting for the Soret effect vary significantly from those where temperature-gradient-driven transport is not considered and discuss the implications of such a Soret effect on the response to plasma exposure of plasma-facing tungsten.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Evidence on the effects of main-chamber neutrals on density shoulder broadening

Evidence that density shoulder broadening is dependent on high main-chamber neutral density is presented. Shoulder broadening does not occur when the sources for main-chamber neutrals are minimized using divertor baffles and wide gaps to the first wall (~3× the density decay length). Removing the baffles or reducing the gap to the inner wall both act to increase the density shoulder amplitude in otherwise identical TCV discharges. Radial turbulent transport is correlated with shoulder amplitude.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Development of pebble-based extruded carbon rods for extreme plasma heat flux environments

This work presents first experiments toward the development of continuously renewable (extrudable) pebble-based carbon rods for use as plasma-facing components in extreme steady-state plasma flux environments. The primary envisioned application of this work is a first wall that can survive long-term in future magnetic fusion power reactors while also improving recovery of the reactor fuel (tritium and deuterium atoms). Bench tests applying extreme steady-state front-surface heat loads of up to 50 MW/m 2 are presented. Continuous pebble rod front-surface recession and intact pebble recovery are successfully demonstrated, at a rate of order 0.2 cm/s. Numerical simulations of the pebble rod front-surface recession are able to match observations reasonably well, indicating that the recession mechanism can be understood as occurring due to pebble thermal expansion and resulting shock and cracking of the inter-pebble binder. Tests of the pebble rod extrusion demonstrate that friction between the rods and the stainless-steel extrusion channel is tolerably low (<50 N for the expected channel length) over a wide range of temperatures. Front-surface outgassing rates below 1000 Torr L/s/m 2 are achieved, believed to be sufficiently low for use in magnetic fusion reactors. In conclusion, initial parametric scans over pebble rod size and binder fraction to vary front-surface recession rates are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Filamentary velocity scaling validation and spin dynamics in the DIII-D tokamak

Measured filament velocities in the DIII-D tokamak are compared against theoretical scalings, finding that the latter often represents an upper limit on experimental velocity distributions with most filaments possessing lower velocity. Filament spin from internal E × B drift is experimentally demonstrated to alter filament radial velocity. A critical spin velocity, where filament radial velocity peaks, is observed and corresponds to approximately 5 km/s. This transition is corroborated using a less direct measure of filament spin in the form of a temperature ratio. These techniques are combined to find that the critical spin velocity closely aligns with transport times along and across filaments becoming comparable. The normalized filament size distribution is consistent with the most stable size as dictated by Kelvin–Helmholtz and curvature-driven instabilities. Overall, the findings suggest filament stability and spin alter filamentary transport that may threaten the integrity of first walls in fusion devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Design Overview of a High-Pressure Helium Flow Visualization Apparatus for Blanket Cooling Studies

Cooling of the fusion blanket first wall remains a significant challenge given the adverse conditions of heat and particle flux encountered near the plasma. Helium emerges as an attractive cooling candidate because of its chemical and neutronic inertness and separability from hydrogenic species (e.g. tritium). Because of the low thermal mass of helium, optimization of these coolant channels is warranted to provide high heat transfer performance at low pumping costs. Increasingly, computational fluid dynamics (CFD) simulations are employed to model and optimize these flow channels, and accompanying experimental data are needed to validate the predictions of these models. To provide the aforementioned experimental data, a high-pressure helium flow visualization upgrade has been designed for the Helium Flow Loop Experiment facility. This apparatus was built to American Society of Mechanical Engineers boiler and pressure vessel standards to withstand operating pressure of 4 MPa and mated to high-pressure glass windows. Seedless flow visualization is performed via high-speed background oriented schlieren (BOS), with image correlation used for time-resolved two-dimensional velocimetry at frequencies in excess of 60 kHz. Rectangular flow channel test articles are additively manufactured via laser powder bed fusion and installed into this visualization apparatus, with one-sided heating supplied by resistive heaters. In conclusion, the chosen test geometries were informed by prior CFD simulations, and the helium flow structures observed via BOS (detachment, recirculation, etc.) will be used for the validation of these accompanying models, in support of the design and optimization of blanket cooling channel configurations.

Helium flow↗
DOE OSTI2023

Scenario optimization for the tokamak ramp-down phase in RAPTOR: Part B. safe termination of DEMO plasmas

An optimized plasma current ramp-down strategy is critical for safe and fast termination of plasma discharges in a tokamak demonstration fusion reactor (DEMO), both in planned and emergency scenarios, avoiding plasma disruptions and excessive heat loads to the first wall. Plasma stability limits and machine-specific technical requirements constrain the stable envelope through which the plasma must be navigated. Large amounts of auxiliary heating are required throughout the ramp-down phase, to avoid a radiative collapse in the presence of intrinsic tungsten and seeded xenon impurities, as quantitatively estimated in this work. As the plasma current is reduced, the current density becomes increasingly peaked, reflected by a growing value of the internal inductance $\ell$ $i3$ , resulting in reduced controllability of the vertical position of the plasma. The feasibility of different plasma current ramp-down rates is tested by applying an automated optimization framework embedding the RAPTOR core transport solver. Optimal time traces for plasma current $I$ $p$ $(t)$ and plasma elongation $κ(t)$ are proposed, to satisfy an $I$ $p$ -dependent upper limit on the plasma internal inductance, as obtained from vertical stability studies using the CREATE-NL code, as well as a constraint on the time evolution of $q$ 95 , to avoid an ideal MHD mode. A negative current density near the plasma edge is observed in our simulations, even for the most conservative $I$ $p$ ramp-down rate, indicating significant transient dynamics due to a large resistive time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Measurement of post-disruption runaway electron kinetic energy and pitch angle during final loss instability in DIII-D

Post-disruption runaway electron (RE) kinetic energy K and pitch angle sin$\vartheta$ are critical parameters for determining resulting first wall material damage during wall strikes, but are very challenging to measure experimentally. During the final loss instability, confined RE K and sin$\vartheta$ are reconstructed during center-post wall strikes for both high impurity (high-Z) and low impurity (low-Z) plasmas by combining soft x-ray, hard x-ray, synchrotron emission, and total radiated power measurements. Deconfined (wall impacting) RE sin$\vartheta$ is then reconstructed for these shots by using time-decay analysis of infra-red imaging. Additionally, deconfined RE K and sin$\vartheta$ are reconstructed for a low-Z downward loss shot by analyzing resulting damage to a sacrificial graphite dome limiter. The damage analysis uses multi-step modeling simulating plasma instability, RE loss orbits, energy deposition, and finally material expansion (MARS-F, KORC, GEANT-4, and finally COMSOL). Overall, mean kinetic energies are found to be in the range $\langle$$K$$\rangle$ $≈ 3-4$ MeV for confined REs. KORC simulations indicate that the final loss instability process does not change individual RE kinetic energy K. In conclusion, confined RE pitch angles are found to be fairly low initially pre-instability, $\langle$sin$\vartheta$$\rangle$ $≈ 0.1 – 0.2$, but appear to increase roughly 2x, to $\langle$sin$\vartheta$$\rangle$ $≈ 0.3 – 0.4$ for both confined and deconfined REs during instability onset in the low-Z case; this increase is not observed in the high-Z case.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Routes to high-performance operation in Wendelstein 7-X: turbulence suppression with shaping of the density profile

Steep density gradients generally lead to improved plasma performance in the neoclassically optimized stellarator W7-X. This is evident in the global energy confinement time as well as in the ion temperature and can be explained by a strong reduction of the ion temperature gradient turbulence. Such conditions can experimentally be realized by several methods: injection of cryogenic hydrogen pellets, appropriate combination of neutral beam and electron cyclotron resonance heating (ECRH) and, in some cases, with low power of ECRH after preconditioning of the first wall. The duration of the improved phases is determined by the ability to sustain the steep density gradient, by technical limitations of the involved systems and, eventually, by the plasma stability. This paper gives an overview of relevant experimental results and presents example discharges where the improved confinement conditions could be extended to multiple seconds: up to 4 s using neutral beam injection and from 14 to 40 s with steady state pellet injection. In these plasmas the turbulent thermal diffusivity is reduced by a factor of 3 to 4 in a broad radial range, which allows high ion temperatures of up to 3 keV at the densities of about 1.5 • 10 20 m −3 .

high performance plasma↗
DOE OSTI2026

Post-puff SOL broadening on MAST-U under high-recycling conditions: evidence consistent with cross-field transport changes

Transient broadening of the scrape-off layer (SOL) density profile can modify main-chamber first-wall particle fluxes and divertor loading, yet its control parameters remain debated between divertor-regime transitions, neutral dynamics and changes in cross-field transport. We investigate fueling-driven SOL density-profile evolution and post-fueling relaxation on MAST-Upgrade (MAST-U) in ohmic L-mode, using two otherwise similar double-null Conventional Divertor discharges (I p = 450 kA, B T = 0.33 T) with identical 50 ms low-field side gas puffs; the only intentional difference is the puff start time. Upstream Thomson scattering shows that both discharges develop a transient far-SOL density profile modification, expressed as an increased SOL-width metric λ n e and a far-SOL enhancement consistent with a shoulder-like signature. In the earlier-puff case, the SOL-width metric remains elevated after puff termination and the post-puff decay time scales are systematically longer across the analysed radii. Outer-target Langmuir probes indicate high-recycling conditions during the analysed window (few-eV T e with radially peaked j sat,∥ and q ∥ profiles, without signatures of deep detachment). The outer-divertor collisionality proxy Λ div is elevated in both cases and does not discriminate between the different post-puff persistence. The target-integrated ion flux proxy ∫ J sat dA evolves nearly identically in both discharges when aligned to the puff start. Taken together, these observations suggest that the late/post-puff upstream SOL evolution is not set by parallel exhaust to the outer targetalone and is more consistent with upstream cross-field redistribution, with a possible role for plasma–neutral coupling and fueling geometry.

MAST-U↗
DOE OSTI2023

Initial study on thermal stability of cold spray tantalum coating irradiated with deuterium for fusion applications

Abstract Removal of neutral hydrogen atoms in the plasma edge reduces the number of charge exchange events and thus, the net energy losses in the plasma, significantly improving performance of fusion devices. Effective control of the residual pressure of hydrogen isotopes (HIs) in the plasma edge may be achieved by utilizing a hydrogen absorbing first wall interface capable of withstanding the harsh fusion environment. In this study, we have investigated tantalum (Ta) coating deposited by cold spray technology on 316L stainless steel substrate as a potential plasma-facing material surface. High fluence low energy deuterium plasma irradiation experiments and subsequent thermal annealing cycles associated with thermal desorption spectrometry (TDS) demonstrated superior structural stability of the Ta coating. TDS experiments revealed the outgassing of deuterium (as measure of its retention) for cold spray Ta coatings to be three times higher than bulk Ta and two orders of magnitude greater than bulk polycrystalline W. X-ray photoelectron spectroscopy revealed evolution of oxidation states upon deuterium irradiation and a partial recovery of the metallic signature of Ta after the thermal treatment at 1100 K.

Physics↗
DOE OSTI2020

Simulation of MHD instabilities with fluid runaway electron model in M3D- C 1

Runaway electrons are generated in a tokamak during the start up, during normal operation and during a plasma disruption. During a disruption, runaway electrons can be accelerated to high energies, potentially damaging the first wall. To predict the consequences of runaway generation during a disruption, it is necessary to consider resonant interactions of runaways with the bulk plasma. Here we consider the interactions of runaways on low mode number tearing modes. We have developed a fluid runaway electron model for the 3D MHD code M3D-C1[Jardin,et al. J Comput. Sci Discovery 6 014002 (2012)]. To benchmark, we have reproduced the MHD linear tearing mode results (with runaway electrons) in a circular cylinder presented in previous analytic studies[[Helander, P., et al, Phys. Plasmas 14 144102 (2007)] and extended here with a numerical eigenvalue calculation. Furthermore, we find that the low mode number tearing mode has a rotation caused by the MHD - runaways interaction, and the toroidal current scale length is much smaller with runaways than that for without and decreases as the runaway speed increases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗