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At least 271 records · Page 15

Carbon isotope fractionation by an ancestral rubisco suggests that biological proxies for CO 2 through geologic time should be reevaluated

The history of Earth’s carbon cycle reflects trends in atmospheric composition convolved with the evolution of photosynthesis. Fortunately, key parts of the carbon cycle have been recorded in the carbon isotope ratios of sedimentary rocks. The dominant model used to interpret this record as a proxy for ancient atmospheric CO 2 is based on carbon isotope fractionations of modern photoautotrophs, and longstanding questions remain about how their evolution might have impacted the record. Therefore, we measured both biomass (ε p ) and enzymatic (ε Rubisco ) carbon isotope fractionations of a cyanobacterial strain ( Synechococcus elongatus PCC 7942) solely expressing a putative ancestral Form 1B rubisco dating to ≫1 Ga. This strain, nicknamed ANC, grows in ambient pCO 2 and displays larger ε p values than WT, despite having a much smaller ε Rubisco (17.23 ± 0.61‰ vs. 25.18 ± 0.31‰, respectively). Surprisingly, ANC ε p exceeded ANC ε Rubisco in all conditions tested, contradicting prevailing models of cyanobacterial carbon isotope fractionation. Such models can be rectified by introducing additional isotopic fractionation associated with powered inorganic carbon uptake mechanisms present in Cyanobacteria, but this amendment hinders the ability to accurately estimate historical pCO 2 from geological data. Understanding the evolution of rubisco and the CO 2 concentrating mechanism is therefore critical for interpreting the carbon isotope record, and fluctuations in the record may reflect the evolving efficiency of carbon fixing metabolisms in addition to changes in atmospheric CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Realizing a topological diode effect on the surface of a topological Kondo insulator

Introducing the concept of topology into material science has sparked a revolution from classic electronic and optoelectronic devices to topological quantum devices. The latter has potential for transferring energy and information with unprecedented efficiency. Here, we demonstrate a topological diode effect on the surface of a three-dimensional material, SmB 6 , a candidate topological Kondo insulator. The diode effect is evidenced by pronounced rectification and photogalvanic effects under electromagnetic modulation and radiation at radio frequency. Our experimental results and modeling suggest that these prominent effects are intimately tied to the spatially inhomogeneous formation of topological surface states (TSS) at the intermediate temperature. This work provides a manner of breaking the mirror symmetry (in addition to the inversion symmetry), resulting in the formation of pn-junctions between puddles of metallic TSS. Further, this effect paves the way for efficient current rectifiers or energy-harvesting devices working down to radio frequency range at low temperature, which could be extended to high temperatures using other topological insulators with large bulk gap.

36 MATERIALS SCIENCE↗

A Machine Learning Method for the Forensics Attribution of Separated Plutonium

Plutonium (Pu) source attribution would be a powerful tool to support nuclear nonproliferation efforts. This capability to find the source of a Pu sample would act as a deterrent to smuggling efforts, and also help regulatory agencies verify declared nuclear activities. Work at Texas A&M University yielded a nuclear forensics methodology, which is capable of determining separated Pu’s reactor of origin, fuel burnup, and the time since irradiation (TSI)—three parameters of interest. The methodology used a set of ten intra-element isotopic ratios found in separated Pu, which was compared to a library of isotopic ratio values produced using neutronics simulations for reactors of interest. By calculating the probability that unknown Pu sample’s isotopic ratio set matched a set in the library, the methodology could predict the three parameters of interest of the sample. One shortcoming of this methodology was an inability to correctly attribute spoofed Pu, where Pu sourced from two different reactors or two different fuel burnup levels are mixed. A new methodology to rectify this vulnerability using machine learning (ML) technique is developed, instead of the maximum likelihood calculation previously used and the results are satisfactory. The ML approach leverages the existing simulated data for training the algorithm, but use them efficiently by only using intra-element isotope ratios that contribute to the attribution one of the three parameters at a time. Previously, all isotope ratios were used to attribute all three parameters together. The new methodology attributes the Pu parameters in three steps, one for each parameter, rather than resolving all of the three parameters simultaneously like the previous maximum likelihood approach. First, a support vector machine classifier with a set of seven isotopic ratios finds the reactor of origin and a set of regression models trained using gaussian process predicts the burnup with a different set of seven isotopes. Finally, TSI is calculated analytically using decay equations. Thus far, the new methodology is capable of attributing pure Pu samples and has been validated using experimental data. The next step will to be augment the classifier training data set with spoofed Pu data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Development of coated heat flux gauges for fast responding measurements

Thermal systems often exhibit transient behaviors that have important implications for the operation of the system and can be difficult to predict. For these reasons, experimental testing is often required to ensure system durability requirements are achieved. One important parameter governing the survivability of components in hot, high-stress environments is the heat flux into the part that dictates the temperature distribution for the component. However, sensors required to experimentally characterize heat fluxes in extreme environments must also be resilient. Here, this study presents the development of coated heat transfer gauges capable of robust, high-frequency measurements in turbine research facilities. The addition of a protective coating increases the durability of the gauge, but inherent of that coating is the attenuation of high-frequency temperature penetrations. As a result, this study first outlines the use of analytical solutions to define a gauge design for a specific frequency range and heat transfer, ensuring that subsurface signals can be rectified to surface conditions through inverse methods. Then, the fabrication of polyimide substrate sensors with a parylene-F coating is described. Micro surface heaters added to the custom sensors were used to determine important geometric and thermal properties necessary to calculate accurate surface heat flux. Ultimately, this work shows increased sensor robustness in a turbine test bed and experimentally validates that the frequency response of the fabricated sensors meet the design intent.

47 OTHER INSTRUMENTATION↗

Impurity transport in PISCES-RF

Linear plasma devices (LPD) utilizing a helicon plasma source, a high density light ion source, can generate impurities due to progressive erosion of the radio frequency (RF) transmission window caused by rectified sheath voltage. These source-born impurities can entrain and be transported by the plasma toward a target, affecting plasma-material interaction studies. Earlier work on material testing in Prototype-Materials Plasma Exposure eXperiment at ORNL revealed significant source impurity deposition on downstream targets. However, using a similar RF source, no target impurity deposition is observed in Plasma Interaction Surface Component Experimental Station (PISCES)-RF despite evidence of RF window erosion in the source region, thereby motivating the present work. Experimentally, using various magnetic field configurations upstream of the PISCES-RF plasma source and seeding titanium (Ti) impurities at various axial locations, impurity transport and deposition along the machine axis were investigated. It was found that Ti deposition was localized to the side of the plasma source where the Ti impurity was seeded. In contrast, aluminum (Al) deposition, originating from the sputtering of the helicon window, occurred predominantly upstream of the plasma source, suggesting an asymmetry in the axial transport of eroded RF window material. These observations suggest a stagnation of the parallel plasma flow immediately downstream of the plasma source, with impurity ions remaining unmagnetized near the source upstream. Al deposition in magnetic field-free regions in PISCES-RF indicates that sputtered Al impurities likely remained neutral due to their large ionization mean-free path under PISCES-RF conditions. Plasma modeling and simulation supported this, indicating that Al-neutrals transport toward the helicon source upstream for low electron density cases. It was found that the Larmor radius of the Al ions was greater than the plasma radius towards the source upstream and remained weakly magnetized in PISCES-RF, meaning that plasma source-born impurities are not efficiently entrained in the plasma flow. These findings provide critical insights into impurity transport in helicon plasma-based LPDs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Modeling of convective cells, turbulence, and transport induced by a radio-frequency antenna in the tokamak boundary plasma

The edge turbulence model Hermes (Dudson et al 2017 Plasma Phys. Control. Fusion 59 05401) is set up for plasma boundary simulations with an radiofrequency (RF) antenna, using parameters characteristic of a tokamak edge. Cartesian slab geometry is used with thin plate limiters representing the ion cyclotron range of frequency (ICRF) antenna side-wall limiters. Ad-hoc DC electric biasing of the limiters, motivated by calculations with VSim (Nieter et al 2004 J. Comput. Phys. 196 448), represents an induced RF sheath rectified potential in the plasma turbulence model. Flux-driven turbulence simulations demonstrate a realistic distribution of plasma profiles and fluctuations. There is a clear effect of the antenna sheath voltage leading to formation of convective cells; bias-induced convective transport flattens the scrape-off layer density profile and fluctuations penetrate into the shadow region of the limiters as the bias voltage increases. Turbulent transport for impurity ions is inferred by following ion trajectories in the simulated plasma turbulence fields, showing Bohm-like effective diffusion rates. All in all, the model elucidates the key physical phenomena governing the effects of ICRF-induced antenna biasing on the tokamak boundary plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Effect of net direct current on the properties of radio frequency sheaths: simulation and cross-code comparison

In order to understand, predict and control ion cyclotron range of frequency (ICRF) interactions with tokamak scrape-off layer plasmas, computational tools which can model radio frequency (RF) sheaths are needed. In particular, models for the effective surface impedance and DC rectified sheath potentials may be coupled with full wave RF simulation codes to predict self-consistent wave fields near surfaces and the resulting power dissipation and plasma-material interactions from ion sputtering. In this study, previous work assuming zero net DC current flow through the sheath is generalized to allow the surface to collect net positive or negative current, as is often observed in experiments. The waveforms, DC potential and RF admittance are investigated by means of analytical theory, nonlinear fluid and particle-in-cell (PIC) codes. Cross-code comparisons provide detailed model verification and elucidate the roles of ion and electron kinetics. When the sheath draws negative (positive) DC current, the voltage rectification is reduced (increased) compared with the zero-current case, and the magnitude of both the real and imaginary parts of the admittance are increased (reduced). In conclusion, a previous four-input parametrization of the sheath rectification and admittance properties is generalized to include a fifth parameter describing the DC sheath current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Validation of 2D Te and ne measurements made with Helium imaging spectroscopy in the volume of the TCV divertor

Abstract Multi-spectral imaging of helium atomic emission (HeMSI) has been used to create 2D poloidal maps of T e and n e in TCV’s divertor. To achieve these measurements, TCV’s MANTIS multispectral cameras (Perek et al 2019 Rev. Sci. Instrum. 90 123514) simultaneously imaged four He I lines (two singlet and two triplet) and a He II line (468 nm) from passively present He and He + . The images, which were absolutely calibrated and covered the whole divertor region, were inverted through the assumption of toroidal symmetry to create emissivity profiles and, consequently, line-ratio profiles. A collisional-radiative model (CRM) was applied to the line-ratio profiles to produce 2D poloidal maps of T e and n e . The collisional-radiative modeling was accomplished with the Goto helium CRM code (Zholobenko et al 2018 Nucl. Fusion 58 126006, Zholobenko et al 2018 Technical Report , Goto 2003 J. Quant. Spectrosc. Radiat. Transfer 76 331–44) which accounts for electron-impact excitation (EIE) and deexcitation, and electron–ion recombination (EIR) with He + . The HeMSI T e and n e measurements were compared with co-local Thomson scattering measurements. The two sets of measurements exhibited good agreement for ionizing plasmas: ( 5 eV ⩽ T e ⩽ 60 eV , and 2 × 10 18 m − 3 ⩽ n e ⩽ 3 × 10 19 m − 3 ) in the case of majority helium plasmas, and ( 10 eV ⩽ T e ⩽ 40 eV , 2 × 10 18 m − 3 ⩽ n e ⩽ 3 × 10 19 m − 3 ) in the case of majority deuterium plasmas. However, there were instances where HeMSI measurements diverged from Thomson scattering. When T e ⩽ 10 eV in majority deuterium plasmas, HeMSI deduced inaccurately high values of T e . This disagreement cannot be rectified within the CRM’s EIE and EIR framework. Second, on sporadic occasions within the private flux region, HeMSI produced erroneously high measurements of n e . Multi-spectral imaging of Helium emission has been demonstrated to produce accurate 2D poloidal maps of T e and n e within the divertor of a tokamak for plasma conditions relevant to contemporary divertor studies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Resonance in radio frequency sheath admittance and enhanced impurity emission near the ion cyclotron frequency

Ion cyclotron resonance heating (ICRH) is of considerable interest among all auxiliary heating techniques, because it transfers power directly to ions, targets the high-density core, and involves the cheapest radio-frequency (RF) components. During ICRH operation, RF sheaths form on the ICRH antenna itself, nearby hardware, and far-field surfaces. These sheaths are associated with large hot-spot formation and impurity emissions. This work presents high-resolution numerical modelling of RF sheaths in nuclear fusion scenarios using hPIC2, a Debye-scale particle-in-cell code. The modelling reveals a new RF sheath phenomenon which occurs when the RF is resonant with a species ion cyclotron frequency or harmonic in an oblique magnetic field. This resonance of the RF sheath causes modifications of the energy-angle distributions of the ions impacting on the walls, with consequent increase in wall impurity emission. Due to the 1/ R scaling of the magnetic field in a tokamak, such cases are possible on divertor or vacuum chamber surfaces, depending on the geometry of the tokamak and the RF heating scenario. A simple physics interpretation using a driven damped harmonic oscillator is proposed, where the ion sheath transit time plays the role of damping the RF sheath admittance. Critically, the resonance leads to increased ion heat flux at the wall as well as increased physical sputtering, despite a lack of increase in RF rectified sheath potential.

ICRH antenna↗

Using the Stix finite element RF code to investigate operation optimization of the ICRF antenna on Alcator C-Mod

Abstract As the Ion Cyclotron Radio Frequency range (ICRF) heating becomes more favorable in fusion devices, the urgency of predicting and mitigating impurity generation that arises from it becomes more pressing. In the ICRF regime, rectified Radio Frequency (RF) sheaths are known to form at antenna and material edges that influence negative effects like sputtering and a decrease in heating efficiency. Methods to mitigate the formation of these RF sheaths through RF image currents cancellation have been experimentally studied. A power-phasing scan done on Alcator C-Mod in which the amount of power on the two inner straps ( P in ) versus the total 4 straps ( P tot ) was varied showed a minimization of enhanced potentials between P in / P tot ∼ 0.7–0.9 while impurities were minimized for P in / P tot ∼ 0.5–0.8. New capabilities in the realm of representing the RF sheath numerically now allow for these experiments to be simulated. Given the size of the sheath relative to the scale of the device, it can be approximated as a Boundary Condition (BC). A new parallelized cold-plasma wave equation solver called Stix implements a non-linear sheath impedance model BC formulated by Myra et al (2015 Phys. Plasmas 22 062507) through the method of finite elements using the MFEM library [ http://mfem.org ]. It is seen that Stix shows qualitative agreement with the measured C-Mod enhanced potentials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Integrated modeling of RF-induced tungsten erosion at ICRH antenna structures in the WEST tokamak *

This paper introduces STRIPE (Simulated Transport of RF Impurity Production and Emission), an advanced modeling framework developed to analyze material erosion and the global transport of eroded impurities originating from radio-frequency (RF) antenna structures in magnetic confinement fusion devices. STRIPE integrates multiple physics modules: SolEdge3x for scrape-off-layer plasma profiles, COMSOL for 3D RF rectified sheath potentials, RustBCA for erosion yields and surface interactions, and global impurity transport for 3D ion energy-angle distributions and impurity transport. The framework is applied to an ion cyclotron RF-heated L-mode discharge (#57877) in the WEST tokamak, where it predicts a thirty-fold increase in gross tungsten erosion at antenna limiters during the transition from ohmic to ICRH operation. Additionally, under ICRH conditions, a tenfold enhancement in erosion is observed when comparing RF sheath effects to purely thermal sheath conditions. High-charge-state oxygen ions ($\mathrm{O}$ 6+ and above) are identified as the dominant contributors to tungsten sputtering. To validate the model, a synthetic diagnostic tool based on inverse photon efficiency (S/XB coefficients) from the ColRadPy collisional-radiative model enables direct comparison with spectroscopic measurements. Model predictions using a plasma composition of 1% oxygen and 99% deuterium show good agreement with observed W − I (400.9 nm) emission for discharge #57877, supporting the accuracy of the STRIPE framework. This study focuses specifically on gross erosion calculations to demonstrate STRIPE’s capabilities. Future extensions of this work will incorporate net erosion, re-deposition, self-sputtering effects, and whole-device modeling of sputtered tungsten impurity transport. STRIPE is also being applied to other RF-heated linear and toroidal devices, offering valuable insights for antenna design, impurity control, and performance optimization in next-generation fusion reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comparison between Alcator C-Mod ICRF experiments and 3D full wave simulations

Reliable modeling of ion cyclotron range of frequencies (ICRF) antenna performance is essential for interpreting present experiments and guiding the design of future reactors. In this work, a 3D model of the Alcator C-Mod field-aligned antenna is implemented in the Petra-M finite-element framework [S. Shiraiwa et al 2023 Nucl. Fusion 63 026024] and benchmarked against experimental results. Four experimental cases are examined. First, the simulated rectified sheath potentials on the antenna limiters are compared with measurements from a power tapering experiment. Second, proof-of-principle far-field sheath simulations are performed. In scenarios with low single-pass absorption, simulations predict enhanced sheath potentials on a distant poloidal limiter in the far field of the antenna, consistent with experimental observations. Third, the simulated antenna loading during edge localized modes follows experimental trends and appears to be dominated by the density gradient at the pedestal. Finally, Petra-M predicts the unintended excitation of high-$k$ ∥ modes during monopole phasing operation, in agreement with experimental evidence of poor wave coupling and accessibility to the plasma core. Overall, reasonable agreement is found between the simulations and experiments. At the same time, areas of imperfect agreement are identified. These provide important guidance on the limits of the current state-of-the-art modeling, which should be kept in mind when using it as a predictive tool for future reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nitrogen precooling heat exchanger replacement and control system upgrade in superfluid cryoplant at CMTF

Liquid nitrogen precooling is used in most cryoplants to achieve cooldown to 80 K temperature range. In one such system at Fermilab’s CMTF superfluid cryoplant, where the helium supply directly exchanges heat with liquid nitrogen, freezing of nitrogen occurred inside the heat exchanger due to heat exchanger flow imbalance during a cryoplant trip. Trapped vapor pockets of nitrogen within the frozen heat exchanger channels were formed while warming up the heat exchanger, creating high localized pressure and subsequent damage/rupture of the heat exchanger. Replacement of the heat exchanger was done, and modifications were made in the system to rectify future occurrences. The control system was updated to bypass the heat exchanger entirely if the incoming helium stream temperature drops below 76 K. This was done by repurposing two control valves as heat exchanger bypass valves that were previously used for a redundant 80 K adsorber in the coldbox. Additional modifications were made to further prevent return of large amount of cold helium gas from cold end during abrupt cryoplant shutdown. This modification has ensured high reliability of heat exchanger with prevention of freezing of nitrogen which can damage the heat exchanger.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Integration of Ag-CBRAM crossbars and Mott ReLU neurons for efficient implementation of deep neural networks in hardware

In-memory computing with emerging non-volatile memory devices (eNVMs) has shown promising results in accelerating matrix-vector multiplications. However, activation function calculations are still being implemented with general processors or large and complex neuron peripheral circuits. Here, we present the integration of Ag-based conductive bridge random access memory (Ag-CBRAM) crossbar arrays with Mott rectified linear unit (ReLU) activation neurons for scalable, energy and area-efficient hardware (HW) implementation of deep neural networks. We develop Ag-CBRAM devices that can achieve a high ON/OFF ratio and multi-level programmability. Compact and energy-efficient Mott ReLU neuron devices implementing ReLU activation function are directly connected to the columns of Ag-CBRAM crossbars to compute the output from the weighted sum current. We implement convolution filters and activations for VGG-16 using our integrated HW and demonstrate the successful generation of feature maps for CIFAR-10 images in HW. Our approach paves a new way toward building a highly compact and energy-efficient eNVMs-based in-memory computing system.

Mott insulators↗

A machine learning approach to photometric metallicities of giant stars

ABSTRACT Despite the advances provided by large-scale photometric surveys, stellar features – such as metallicity – generally remain limited to spectroscopic observations often of bright, nearby low-extinction stars. To rectify this, we present a neural network approach for estimating the metallicities and distances of red giant stars with 8-band photometry and parallaxes from Gaia EDR3 and the 2MASS and WISE surveys. The algorithm accounts for uncertainties in the predictions arising from the range of possible outputs at each input and from the range of models compatible with the training set (through drop-out). A two-stage procedure is adopted where an initial network to estimate photoastrometric parallaxes is trained using a large sample of noisy parallax data from Gaia EDR3 and then a secondary network is trained using spectroscopic metallicities from the APOGEE and LAMOST surveys and an augmented feature space utilizing the first-stage parallax estimates. The algorithm produces metallicity predictions with an average uncertainty of $\pm 0.19\, \mathrm{dex}$. The methodology is applied to stars within the Galactic bar/bulge with particular focus on a sample of 1.69 million objects with Gaia radial velocities. We demonstrate the use and validity of our approach by inspecting both spatial and kinematic gradients with metallicity in the Galactic bar/bulge recovering previous results on the vertical metallicity gradient (−0.528 ± 0.002 dex kpc−1) and the vertex deviation of the bar ($-21.29\pm 2.74\, \mathrm{deg}$).

79 ASTRONOMY AND ASTROPHYSICS↗

Signaling and scrambling with strongly long-range interactions

Strongly long-range interacting quantum systems—those with interactions decaying as a power law 1/$r^α$ in the distance $\textit{r}$ on a $\textit{D}$-dimensional lattice for $\textit{α ≤ D}$—have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. In this work, our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\textit{α ≤ D/2}$. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all $\textit{α < D}$. This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Next-to-leading order scalar contributions to 𝜇→𝑒 conversion

Within a class of models in which lepton flavor violation is induced dominantly by scalar particle exchanges, we estimate the 𝜇→𝑒 conversion rate in several nuclei. We include next-to-leading order (NLO) terms in the one- and two-nucleon interactions in chiral effective theory, rectifying some incorrect results in the previous literature. We provide an uncertainty budget for the conversion rates and we find that NLO contributions affect the amplitudes at the level of 10%, which could be larger than the uncertainty on the leading order couplings, dominated by the strange and nonstrange nucleon sigma terms. We study the implications of our results for testing Higgs-mediated charged lepton flavor violation (CLFV) in the future by combining results from various experimental searches, such as 𝜇→𝑒 conversion in multiple target nuclei and 𝜇→𝑒⁢𝛾.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Symmetric Set of Transport Coefficients for Collisional Magnetized Plasma

Braginskii extended magnetohydrodynamics is used to model transport in collisional astrophysical and high energy density plasmas. We show that commonly used approximations to the α ⊥ and β ⊥ transport coefficients [e.g., Epperlein and Haines, Phys. Fluids 29 , 1029 (1986) ] have a subtle inaccuracy that causes significant artificial magnetic dissipation and discontinuities. This is because magnetic transport actually relies on β ∥ - β ⊥ and α ⊥ - α ∥ , rather than α ⊥ and β ⊥ themselves. We provide fit functions that rectify this problem and thus resolve the discrepancies with kinetic simulations in the literature. Furthermore, then implemented in the g orgon code, they reduce the predicted density asymmetry amplitude at laser ablation fronts. Recognizing the importance of α ⊥ - α ∥ and β ∥ - β ⊥ , we recast the set of coefficients. This makes explicit the symmetry of the magnetic and thermal transport, as well as the symmetry of the coefficients themselves.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗