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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2020

Curvature of Radial Electric Field Aggravates Edge Magnetohydrodynamics Mode in Toroidally Confined Plasmas

We show that the radial electric field (E r ) plays a dual role in edge magnetohydrodynamics (MHD) activity. While E r shear (first spatial derivative of E r ) dephases radial velocity and displacement, and so is stabilizing, a new finding here is that E r curvature (second spatial derivative of E r ) tends to synchronize the radial velocity and displacement, and so destabilizes MHD. As a highlighted result, we analytically demonstrate that E r curvature can destabilize an otherwise stable kink mode, and so form a joint vortexkink mode. The synergetic effects of E r shear and E r curvature in edge MHD extend the familiar E × B shearing paradigm. This theory thus explains the experimental findings that a deeper E × B well may aggravate edge MHD, and so trigger the formation of the edge harmonic oscillation. Here, a simple criterion linking E r structure and the edge MHD activity is derived.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Three-wave coupling observed between a shear Alfvén wave and a kink-unstable magnetic flux rope

Results from a laboratory experiment are presented in which, for the first time, a shear Alfvén wave is launched using an antenna in a current-carrying plasma column that is tailored to be either stable or unstable to the kink oscillation. As the plasma is driven kink unstable, the frequency power spectrum of the Alfvén wave evolves from a single peak to a peak with multiple sidebands separated by integer multiples of the kink frequency. The main sidebands (one on either side of the launched wave peak in the power spectrum) are analyzed using azimuthal wavenumber matching, perpendicular and parallel wavenumber decomposition, and bispectral time series analysis. The dispersion relation and three-wave matching conditions are satisfied, given each sideband is a propagating Alfvén wave that results from the interaction of the pump Alfvén wave and the co-propagating component of a half-wavelength, standing kink mode. The interaction is shown to generate smaller perpendicular wavelength Alfvén waves that drive energy transport to scales that will approach the dissipation scale of k⊥ρs=1, with k⊥ being the perpendicular wavenumber and ρs being the ion gyroradius at the electron temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2012

Quasi-periodic Fast-mode Wave Trains Within a Global EUV Wave and Sequential Transverse Oscillations Detected by SDO-AIA

We present the first unambiguous detection of quasi-periodic wave trains within the broad pulse of a global EUV wave (so-called EIT wave) occurring on the limb. These wave trains, running ahead of the lateral coronal mass ejection (CME) front of 2-4 times slower, coherently travel to distances greater than approximately solar radius/2 along the solar surface, with initial velocities up to 1400 kilometers per second decelerating to approximately 650 kilometers per second. The rapid expansion of the CME initiated at an elevated height of 110 Mm produces a strong downward and lateral compression, which may play an important role in driving the primary EUV wave and shaping its front forwardly inclined toward the solar surface. The wave trains have a dominant 2 minute periodicity that matches the X-ray flare pulsations, suggesting a causal connection. The arrival of the leading EUV wave front at increasing distances produces an uninterrupted chain sequence of deflections and/or transverse (likely fast kink mode) oscillations of local structures, including a flux-rope coronal cavity and its embedded filament with delayed onsets consistent with the wave travel time at an elevated (by approximately 50%) velocity within it. This suggests that the EUV wave penetrates through a topological separatrix surface into the cavity, unexpected from CME-caused magnetic reconfiguration. These observations, when taken together, provide compelling evidence of the fast-mode MHD wave nature of the primary (outer) fast component of a global EUV wave, running ahead of the secondary (inner) slow component of CME-caused restructuring.

Solar Corona↗
DOE OSTI2021

Characteristics of Ultralow Aspect Ratio Toroidal Plasmas and Non-Solenoidal Startup and Edge Stability Studies at Near-Unity Aspect Ratio (Final Report)

This grant supported a long-term research and development program to explore the physics and technology of spherical tokamak (ST) plasma behavior at near-unity aspect ratio ( A ). The PEGASUS Toroidal Experiment is a university-scale ( R ) ~ 0.40 m, α ~ .35 m, I p ≤ 0.3 MA, B T ≤ 0.15 T) experiment that accesses A → 1, to provide large values of the normalized plasma current, I N = I p /α B T , or equivalently the toroidal field utilization factor I p / I TF . The research activities focused on: 1) developing the technique of Local Helicity Injection (LHI) as a viable means of initiating and growing an ST plasma without the use of a central solenoid; 2) exploring the equilibrium and stability properties of spherical tokamak plasmas at extremely low aspect ratio; and 3) obtaining new insights in the properties of the enhanced confinement H-mode regime at A ~ 1. The initial (Phase I) facility employed a unique high-stress central solenoid Ohmic for current drive and heating with simple magnet current waveforms. A subsequent major upgrade (Phase II) offered more flexible control of the plasma evolution along with a powerful LHI system for plasma initiation, heating and sustainment. The LHI technique consists of injection of high-density current streams into vacuum toroidal and vertical magnetic fields. These streams become unstable and support magnetic reconnection to allow the system to relax into a tokamak-like magnetic configuration. This program focused on: 1) development of electron current sources that provide sufficiently high injection currents in the challenging edge plasma region; 2) validation of theoretical limits to achievable I p arising from magnetic helicity and energy conservation plus absolute limits arising from relaxation to a minimal energy states; 3) tests of a power balance model to describe the evolution of the plasma current I p (t); and 4) study of magnetic fluctuations and their role in the I p evolution. This culminated in the production of toroidal currents of I p ≥ 0.2 MA with only ~8 kA of injected current. Operation with Ohmic induction alone in Phase I created plasmas with soft limits on the achievable I p and field utilization ( I p / I TF ~ 1) due to the onset of large low-order (2/1 or 3/2) internal resonant tearing modes. With the expanded capabilities in Phase II operation, methods employed to mitigate those modes and achieve I p / I TF > 1 were: 1) I TF ramp-downs; 2) non-solenoidal startup via LHI; and 3) extremely low I TF Ohmic operations assisted by LHI current injector pre-ionization. Extensive use of LHI-driven startup and drive for non-solenoidal operation produced favorable current profiles to stably operate tokamak plasmas with unprecedentedly high I N = I p / aB T ~ 15 and I p / I TF > 2. With strong reconnection-driven anomalous ion heating, this in turn provided access to tokamak plasmas with B t up to 100%, a world record 2 times higher than that previously achieved in advanced or spherical tokamaks. This high B t regime had a large fraction (~50%) of the plasma volume in a region of an absolute minimum- B configuration. The MHD stability limit in this regime was the ideal external kink mode without a stabilizing wall. These results provided the first demonstration of access to tokamak plasmas with very high B t , high i N , high elongation κ, and low internal inductance ℓ i , and as such served as a proof-ofprinciple for access to this long-sought ST regime. The naturally low B T needed for stability at A ≤ 1.2 reduces the L-H mode power threshold, P LH , so that H-mode plasmas were achieved with Ohmic heating alone. The power threshold for the transition to the H-mode regime was found to be 10× the accepted values from the ITER international scaling, confirming initial trends indicated by experiments on MAST and NSTX, and suggesting that the physics behind this transition is not yet fully understood. The density dependence of the transition and the observed insensitivity to whether the plasma is bounded by a limiter or magnetic divertor are consistent with the recent FM 3 model. Multiple unstable toroidal magnetic modes were measured during ELM (Edge Localized Mode) crashes, with generally lower toroidal mode numbers than seen at higher A , which was attributed to the larger peeling mode instability drive at low A . First-ever edge current profile measurements through an ELM crash showed current-carrying filaments were generated, as seen in ELM simulations and in electromagnetic blob transport theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Internal short circuit and failure mechanisms of lithium-ion pouch cells under mechanical indentation abuse conditions: An experimental study

Electromechanical structural integrity and thermal stability dictate the safety performance of lithium-ion batteries. Progressive deformation and failure across microscopic and macroscopic lengths scales that are responsible for internal short circuit (ISC) in lithium-ion cells under mechanical abuse conditions remains elusive. In this study, a series of indentation tests were conducted on lithium-ion cells with different capacities up to the occurrence of ISC. The external response and internal configuration of these cells were investigated. It is discovered that cells with different capacities and state of charges exhibited different behaviors. Maximum temperature, which is often regarded as the most important parameter related to thermal runaway (TR), varied considerably due to the complicated contact configurations. X-ray computed tomography (XCT) showed that ISC was a collective result of shear band or other strain-localization modes in the electrode assembly, shear offsets in the granular coatings of electrodes, and the accompanying ductile fracture in the metal foils. We believe that the irregular strain-localization modes (kinks, cusps, and buckles), radical mismatches in mechanical properties of different layers, and geometric features of the indenter eventually lead to the tearing/puncture of cell separator at various locations. Furthermore, the results could provide useful guidance for the micromechanical modeling of lithium-ion cells.

25 ENERGY STORAGE↗
DOE OSTI2020

Stability of a tokamak plasma with diffuse toroidal rotation

The present work considers the stability of a high- $\beta$ , large aspect ratio, circular plasma with diffuse profiles for the safety factor and the angular toroidal frequency (López & Guazzotto, Phys. Plasmas , vol. 24, 032501). An application of the Frieman–Rotenberg formalism results in a system of scalar eigenmode equations whose coupling is retained at the plasma–vacuum transition but is disregarded across the plasma column, which is a standard practice. The solution technique consists of a multidimensional shooting method for the poloidal harmonics; robust initial guesses are constructed by solving the dispersion relation in the static scenario with vanishing magnetic shear. Flow shear appears as a high- $\beta$ toroidal contribution, and we illustrate its destabilizing influence on $n=1$ external kink modes in the presence of ideal and resistive walls. Internal resonances are avoided by means of the selection of appropriate equilibrium parameters. The stabilizing influence of a finite positive average magnetic shear is also exemplified.

Physics↗
DOE OSTI2026

ARC physics basis–magnetohydrodynamics

ARC is designed to produce 400 ⁢MW of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the 𝑚/𝑛 =2/1 and 3/2 surfaces (with poloidal mode number 𝑚, and toroidal mode number 𝑛) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below 0.1% of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the 𝑛 =1 error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting 𝑛 =2 error fields to some degree and creating strong enough 𝑛 =2 or 𝑛 =3 edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Optimization of quasi-axisymmetric stellarators with varied elongation

An optimization study of Quasi-Axisymmetric (QA) stellarators with varied elongation has been carried out using the optimization code STELLOPT. The starting point of our optimization is a previously obtained QA stellarator with 3 field periods and aspect ratio of 6. Here, a series of QA stellarators are obtained at zero plasma beta with varied elongation value ranging from 2.5 to 3.7. Good quasi-symmetry is kept when the elongation value is reduced from the original value of 3.7. The rotational transform profile and aspect ratio are kept fixed. The plasma volume is ether kept fixed or varied linearly with elongation. Furthermore, finite beta QA stellarators are considered. The corresponding bootstrap currents are calculated using the kinetic code SFINCS. A series of kink-stable QA stellarators are obtained via optimization with varied plasma beta up to 5% and self-consistent bootstrap current. This work demonstrates that good QA stellarators with finite beta and varied elongation exist that are stable to external kink modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Improvements to the Faraday cup fast ion loss detector and magnetohydrodynamic induced fast ion loss measurements in Joint European Torus plasmas

Upgrades to electronic hardware and detector design have been made to the JET thin-foil Faraday cup fast ion loss detector in anticipation of the upcoming deuterium–tritium (DT) campaign. An improved foil stack design has been implemented, which greatly reduces the number of foil-to-foil shorts, and triaxial cabling has mitigated ambient noise pickup. Initial tests of 200 kHz digitizers, as opposed to the original 5 kHz digitizers, have provided enhanced analysis techniques and direct coherence measurements of fast ion losses with magnetohydrodynamic activity. Here, we present recent loss measurements in JET deuterium plasmas correlated with kink modes, fishbone modes, edge-localized modes, and sawteeth. Sources of systematic noise are discussed with emphasis on capacitive plasma pickup. Overall, the system upgrades have established a diagnostic capable of recording alpha particle losses due to a wide variety of resonant fast ion transport mechanisms to be used in future DT-experiments and modeling efforts.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Nonlinear magnetohydrodynamic modeling of current-drive-induced sawtooth-like crashes in the W7-X stellarator

Sawtooth-like core electron temperature crashes have been observed in W7-X experiments with electron cyclotron current drive. Here we present nonlinear single-fluid magnetohydrodynamic simulations of this phenomenon using the newly developed stellarator modeling capability of the M3D-C 1 code. The near-axis current drive gives rise to two ι = 1 resonances in the equilibrium rotational transform profile so that two consecutive (1, 1) internal kink modes are seen in the simulations. A small-amplitude crash at the inner resonance occurs first, which may correspond to the sawtooth precursors observed in the experiments. A bigger crash at the outer resonance then flattens the core temperature profile, which shows semi-quantitative agreements with experimental measurements on certain metrics such as the crash amplitude and the inversion radius of the temperature change. These results illustrate a likely mechanism of the current-drive-induced sawtooth-like crashes in W7-X and, to some extent, validate the stellarator modeling capability of M3D-C 1 .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Core-Pedestal Plasma Configurations in Advanced Tokamaks

Here, several configurations for the core and pedestal plasma are examined for a predefined tokamak design by implementing multiple heating/current drive (H/CD) sources to achieve an optimum configuration of high fusion power in a noninductive operation while maintaining an ideally magnetohydrodynamic (MHD) stable core plasma using the IPS-FASTRAN framework. IPS-FASTRAN is a component-based lightweight coupled simulation framework that is used to simulate magnetically confined plasma by integrating a set of high-fidelity codes to construct the plasma equilibrium (EFIT, TOQ, and CHEASE), calculate the turbulent heat and particle transport fluxes (TGLF), model various H/CD systems (TORIC, TORAY, GENRAY, and NUBEAM), model the pedestal pressure and width (EPED), and estimate the ideal MHD stability (DCON). The TGLF core transport model and EPED pedestal model are used to self-consistently predict plasma profiles consistent with ideal MHD stability and H/CD (and bootstrap) current sources. In order to evaluate the achievable and sustainable plasma beta, varying configurations are produced ranging from the no-wall stability to with-wall stability regimes, simultaneously subject to the self-consistent TGLF, EPED, and H/CD source profile predictions that optimize configuration performance. The pedestal density, plasma current, and total injected power are scanned to explore their impact on the target plasma configuration, fusion power, and confinement quality. A set of fully noninductive scenarios are achieved by employing ion-cyclotron, neutral beam injection, helicon, and lower-hybrid H/CDs to provide a broad profile for the total current drive in the core region for a predefined tokamak design. These noninductive scenarios are characterized by high fusion gain (Q ~ 4) and power (P fus ~ 600 MW), optimum confinement quality (H 98 ~ 1.1), and high bootstrap current fraction (f BS ~ 0.7) for Greenwald fraction below unity. The broad current profile configurations identified are stable to low-n kink modes either because the normalized pressure β N is below the no-wall limit or a wall is present.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simulating energetic particle losses in JET plasmas with a reverse integration biasing scheme

We report that an integrated energetic particle transport model has been constructed in JET plasmas constrained by experimental fast ion loss measurements. The model incorporates a synthetic fast ion loss detector identical to JET’s thin-foil Faraday cup fast ion loss detector array. The loss model combines analyses from the TRANSP and ORBIT-kick codes with enhanced features for producing the synthetic diagnostic. Extensions to the ORBIT code framework allow a full-orbit representation within the vacuum region that can map particles directly to an installed detector geometry. Since synthetic fast ion loss detectors are plagued by weak loss statistics, a novel reverse integration biasing scheme has been implemented to boost computational efficiency. The model is validated against experimental loss measurements induced by long-lived kink modes and is found to be in good agreement. This confirms the development of a fully integrated transport/loss model which can be quantitatively verified against experiment allowing for future validation and predictive studies. The model is particularly useful for more complicated plasma scenarios that involve multiple fast ion species such as JET’s 2021 DT-campaign.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Infernal instabilities in negative-triangularity plasmas with negative central shear

Abstract A systematic numerical investigation is carried out to understand magnetohydrodynamic stability of the ideal infernal-kink instability in tokamak plasmas with both negative triangularity (neg-D) shaping and negative central shear for the equilibrium safety factor profile. The latter is motivated by the desire to form the internal transport barrier in the neg-D configuration, which is known to have difficulty in forming the edge transport barrier. The infernal-kink mode is generally found to be more unstable in neg-D plasmas as compared to their positive D-shaped (pos-D) counterpart. This is mainly due to less favorable (or even unfavorable) average magnetic curvature near the radial location of the minimum safety factor ( q min ) as compared to the pos-D configuration. The larger Shafranov shift associated with the neg-D shape helps the mode stabilization but is not sufficient to overcome the destabilizing effect due to bad curvature. Strong poloidal mode coupling due to plasma shaping (toroidicity, elongation, triangularity, etc.) helps explain the slight shift with respect to that predicted by the analytic theory of the peak location of the computed mode growth versus q min .

Zhang, X. M.↗
DOE OSTI2023

AToM: Advanced Tokamak Modeling Environment

Stability constraints play an important role in integrated modeling. The global plasma stability and macro-instabilities such as internal kink modes, neoclassical tearing modes, and edge localized perturbations limit the plasma performance and can result in large-scale transient events and plasma disruptions. These macro-instabilities can be also beneficial to the plasma performance. For example, the peeling models often lead to the edge localized modes (ELMs). However, the formation of stationary edge harmonic oscillations (EHOs) due to nonlinear interaction of peeling modes can result in a transition to the Quiescent H-mode (QH-mode) without ELMs. The profiles predicted with transport models need to be refined using the MHD stability constraints. This is important especially for transient and nonlinear stages of discharges such as ramp-up access to hybrid and steady state operation, and L- to H-mode transition as well as transition to the QH-mode. Several stability and MHD codes are already included in the OMFIT framework. These codes include BALOO, ELITE, GATO, M3DC1, MARS, and NIMROD. However, the verifications of stability constraints are currently mostly excluded from transport modeling workflows. The only exception is the EPED module which includes the ELITE predictions to limit the pedestal height. Here, we improved the OMFIT workflow to include stability calculations. Including the stability conditions to the integrated modeling workflow improved the robustness of the predictive modeling discharges. Being implemented in the workflow, the stability conditions can be also used for the stability analysis of experimental data. This improved the physics understanding of various discharge scenarios and can be used in experiment planning.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Kinetic Simulations of Instabilities and Particle Acceleration in Cylindrical Magnetized Relativistic Jets

Relativistic magnetized jets, such as those from AGN, GRBs, and XRBs, are susceptible to current- and pressure-driven MHD instabilities that can lead to particle acceleration and nonthermal radiation. Here, we investigate the development of these instabilities through 3D kinetic simulations of cylindrically symmetric equilibria involving toroidal magnetic fields with electron–positron pair plasma. Generalizing recent treatments by Alves et al. and Davelaar et al., we consider a range of initial structures in which the force due to toroidal magnetic field is balanced by a combination of forces due to axial magnetic field and gas pressure. We argue that the particle energy limit identified by Alves et al. is due to the finite duration of the fast magnetic dissipation phase. We find a rather minor role of electric fields parallel to the local magnetic fields in particle acceleration. In all investigated cases, a kink mode arises in the central core region with a growth timescale consistent with the predictions of linearized MHD models. In the case of a gas-pressure-balanced (Z-pinch) profile, we identify a weak local pinch mode well outside the jet core. We argue that pressure-driven modes are important for relativistic jets, in regions where sufficient gas pressure is produced by other dissipation mechanisms.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Kinetic Simulations of the Kruskal–Schwarzschild Instability in Accelerating Striped Outflows: Dynamics and Energy Dissipation

Astrophysical relativistic outflows are launched as Poynting-flux dominated, yet the mechanism governing efficient magnetic dissipation, which powers the observed emission, is still poorly understood. We study magnetic energy dissipation in relativistic "striped" jets, which host current sheets separating magnetically dominated regions with opposite field polarity. The effective gravity force g in the rest frame of accelerating jets drives the Kruskal–Schwarzschild instability (KSI), a magnetic analog of the Rayleigh–Taylor instability. By means of 2D and 3D particle-in-cell simulations, we study the linear and nonlinear evolution of the KSI. The linear stage is well described by linear stability analysis. The nonlinear stages of the KSI generate thin (skin-depth-thick) current layers, with length comparable to the dominant KSI wavelength. There, the relativistic drift-kink mode and the tearing mode drive efficient magnetic dissipation. The dissipation rate can be cast as an increase in the effective width Δ eff of the dissipative region, which follows dΔ eff /dt ≃ 0.05 $\sqrt{Δ_{eff} g}$. Our results have important implications for the location of the dissipation region in gamma-ray burst and active galactic nuclei jets.

79 ASTRONOMY AND ASTROPHYSICS↗