Equilibrium Field Research Articles

Implementation of a non-axisymmetric magnetic configuration in SOLEDGE3X to simulate 3D toroidal magnetic ripple effects: Application to WEST

The fluid-drift code SOLEDGE3X, developed by CEA/IRFM in collaboration with Aix-Marseille University, is a powerful tool for simulating transport and turbulence in tokamak edge plasmas with axisymmetric magnetic configurations. In tokamaks such as WEST, the pronounced toroidal magnetic ripple significantly affects plasma confinement and power exhaust, modulating both the poloidal and toroidal components of the equilibrium field. Using a discrete Biot–Savart law, the ripple field is calculated as a magnetic perturbation on the SOLEDGE3X mesh. The transport model and parallel gradient solvers have been enhanced to incorporate the new radial magnetic field component. Preliminary simulations of a WEST scenario reveal a heat deposition pattern in the divertor region consistent with observations from infrared camera experiments.

Gyrokinetic linear simulation of feedback instability in dipole magnetosphere

We perform a novel linear simulation of the feedback instability by applying a gyrokinetic model to the magnetosphere, where the geomagnetic field is modeled by a dipole magnetic field. In order to avoid huge numerical calculation costs, the effect of the fluctuating mirror force is neglected. It is found that kinetic effects, such as the finite Larmor radius effect and the electron Landau damping, strongly stabilize the feedback instability and form a peak in the perpendicular wave number spectrum of the growth rate. During the linear growth, it is observed that electron free energy has a much larger value than the electromagnetic field perturbation energy. Since such large electron free energy may lead to electron heating and acceleration, it is important to understand its generation mechanism. Analyses based on the energy conservation reveal that the coupling of the non-uniformity of the equilibrium fields along the geomagnetic field and the fluctuating electron distribution gives rise to thermodynamic power generating the electron free energy. A fine velocity space structure around an average Alfvén velocity of the fluctuating electron distribution mainly contributes to drive the thermodynamic power.

Recent progress of JT-60SA project toward plasma operation

Abstract Superconducting tokamak JT-60SA plays an essential role in fusion research and development by supporting and complementing ITER project, providing directions to the DEMO design activity and fostering next generation scientists and engineers. Since the incident of the Equilibrium Field coil #1 during the Integrated Commissioning (IC) in March 2021, both EU and JA Implementing agencies (IAs) have examined how to ensure safety operation of JT-60SA by mitigating the risk of possible discharge occurrence inside the cryostat. Based on the experience of the Global Paschen tests, the IAs have established a strategy of risk mitigation measures, which is a combination of (i) reinforcement of insulation, (ii) avoiding unnecessary voltage application to the coil systems and (iii) immediate de-energization of the coils when deteriorated vacuum condition is detected. Thanks to the considerable efforts of the Integrated Project Team (IPT) members, the IC restarted in May 2023. After the confirmation of superconducting state of coil systems (TF, EF and CS), the coil energization test and the plasma operation (OP-1) starts. The first plasma was successfully achieved on 23 October 2023 with a limited value of applied voltage and current to the coils. The plasma configuration control will be also confirmed with low plasma current and low auxiliary heating power conditions. Based on the IO-F4E-QST collaboration, activities of JT-60SA have been shared with the IO and provided an important lesson learned for ITER assembly and commissioning, and will provide an outstanding contribution to fusion research at large. After OP-1, Maintenance & Enhancement phase 1 (M/E-1) starts from January 2024, in which in-vessel components are installed, and heating system and diagnostic system are extensively upgraded to allow high power heating experiment planned in OP-2. In order to make the best use of JT-60SA, newly organized JT-60SA experiment team will refine the research plan in the future high heating power operation phase.

Deconfinement of runaway electrons by local vertical magnetic field perturbation

Runaway electron (RE) deconfinement and subsequent suppression is of prime importance for successful long-term operation of any tokamak. In this work, to deconfine and mitigate REs, the efficacy of local vertical field (LVF) perturbation has been explored numerically. LVF perturbation-assisted RE loss studies are carried out by simulating the drift orbits of the REs in magnetostatic perturbed fields and estimating the resulting orbit losses for different initial energies and magnitudes of LVF perturbation. To this end, the pre-existing PARTICLE code has been extended to the relativistic full-orbit-following code PARTICLE-3D (P3D) integrated with the magnetic field calculation code EFFI and plasma equilibrium field calculation code IPREQ to include the required fields for studying particle dynamics in general; this is then used to numerically model LVF perturbation-assisted RE deconfinement experiments conducted in the ADITYA tokamak. Simulation results show a significant (∼90%) deconfinement of REs with the application of LVF perturbation of a suitable amplitude (∼0.1% of the total magnetic field) in a preferred direction. The existence of a threshold magnitude of the applied field is also established, which is observed to be dependent on the energy of the REs. The simulation results reproduce all the experimental observations and reveal other interesting features of RE mitigation using LVF perturbation. The temporal map of orbiting time of REs shows that REs originating from the inboard side edge region ( ψ N > 0.5) of the plasma are relatively more prone to be lost with the application of suitable LVF perturbation than those originating from the plasma core. Interestingly, the simulation results demonstrate the existence of strong correlation between the safety factor (q) profile in the plasma edge region ( ψ N > 0.7) and the level of RE deconfinement using LVF perturbation.

Modified Viscosity Iterative Algorithm for Solving Variational Inclusion and Fixed Point Problems in Real Hilbert Space

This paper introduces a new iterative algorithm, called the Modified Viscosity Iterative algorithm, designed to solve problems related to Variational Inclusion and Fixed point in real Hilbert spaces. The algorithm is specifically tailored to handle Multivalued Quasi-Nonexpansive and Demicontractive operators. The convergence properties of the algorithm are analyzed and established, ensuring its effectiveness in finding solutions for complex mathematical problems in the field of optimization and equilibrium.

Performance of Chat GPT on Equilibrium Field of the Otorhinolaryngology Head and Neck Surgery Specialty Certificate Examinations

Performance of Chat GPT on Equilibrium Field of the Otorhinolaryngology Head and Neck Surgery Specialty Certificate Examinations

Recycling of beryllium, manganese, and zirconium from secondary alloys by magnesium distillation in vacuum

One of the methods for processing secondary magnesium raw materials containing rare refractory metals can be a distillation with the extraction of magnesium into condensate and the accumulation of rare metals in the distillation residue. The residue can be used as a master alloy for special alloys. To justify the possibility of this process, we calculated the boundaries of the vapor-liquid equilibrium fields for the regions of liquid solutions existence in the Mg – Be, Mg – Mn, and Mg – Zr systems at atmospheric pressure (101.33 kPa) and in vacuum (1.33 kPa). The value of the vacuum is due to the fact that a further increase in rarefaction will lead to the magnesium crystallization from the melt, and it will complicate the technology.We established that in the distillation process of magnesium removal from Mg – Be and Mg – Zr alloys, the vapor phase will be represented by more than 99.95 of magnesium. The presence of 0.45 mass.% Mn is possible in the Mg – Mn system at 1000 °C in thevapor phase – condensate . However, results of preliminary tests of the evaporation intensity established that the process conducted at 850-900 °C provides an acceptable evaporation rate of the volatile component (Mg) for technological conditions.Thus, we confirmed the possibility of the proposed method to process secondary light alloys containing beryllium, manganese, and zirconium, which can be involved in the main process intended to produce special alloys in the form of a master alloy with magnesium.

An Approach for Control of Equilibrium Field Profile Through the Real-Time Plasma Current in ADITYA-U and SST-1 Tokamaks

An Approach for Control of Equilibrium Field Profile Through the Real-Time Plasma Current in ADITYA-U and SST-1 Tokamaks

Thermodynamics of antimony—selenium alloys formation and evaporation

The thermodynamic functions of alloy formation and evaporation were considered for two particular systems — Sb – Sb2Se3 and Sb2Se3 – Se in connection with the presence of congruently melting compound Sb2Se3 in the antimony—selenium system. The calculations are based on the partial vapor pressure values of the components forming the particular systems. The thermodynamic activity of antimony selenide and selenium as the most volatile components in the systems was calculated based on the saturated vapor pressure values of antimony selenide over the Sb – Sb2Se3 and selenium melts over Sb2Se3 – Se liquid alloys determined by the boiling point method (isothermal variant). Similar functions of the low volatile components in the above systems: Sb in the first system and Sb2Se3 in the latter one was calculated by numerical integration of the Gibbs—Duhem equation using the substitution proposed by Darken. The partial pressures of antimony selenide and antimony over Sb – Sb2Se3 and Sb2Se3 – Se melts were approximated by temperature—concentration relationships. The system is distinguished with a positive deviation from ideality due to the presence of a delamination region in the first system. The partial and integral entropies and enthalpies of the formation of liquid alloys were calculated based on the values of component activities found as the ratio of the partial vapor pressure of an element or compound above the solution to the saturated vapor pressure of a pure element or compound. The partial and integral functions of alloy formation are presented in the form of graphical dependences on the selenium amount in the melt. The obtained thermodynamic constants will replenish the physical and chemical data base and will be used to calculate the boundaries of the vapor— liquid equilibrium fields on the diagram of state, allowing to determine the possibility and completeness of distillation separation of molten systems.

Development of prototype power supply for ohmic transformer system of SSST

The conceptual design of Small Scale Spherical Tokamak (SSST) has been completed at Institute for Plasma Research (IPR). It consists of poloidal field (or Equilibrium) field coils, Toroidal field coils and Ohmic Transformer (OT) system. The poloidal magnets are used for the plasma shaping and equilibrium. The plasma current ramp up and sustenance up to 20 ms is achieved by OT system. The OT system comprises of Central Solenoid (CS) and compensating coils TR1, TR2 & TR3. The Preliminary design for power supply for OT system has been finalized and a prototype OT power supply has been developed at IPR. The conceptual design of prototype Ohmic Transformer Power Supply (OTPS), its philosophy of operation, simulation results and experimental results are presented in this paper.

Non-CES Aggregators: A Guided Tour

The constant-elasticity-of-substitution (CES) aggregator and its demand system are ubiquitous in business cycles theory, macroeconomic growth and development, international trade and other general equilibrium fields; this is because the CES aggregator has many knife-edge properties that help to keep the analysis tractable in the presence of many goods and factors. However, this also makes it hard to tell which properties of CES are responsible for certain results. Furthermore, it is necessary to relax some of those properties for certain applications. In this article, I review several classes of non-CES aggregators, each of which removes some properties of CES and keeps the rest to introduce some flexibility while retaining the tractability of CES as much as possible. These classes are named after the properties of CES they keep. I explain how these classes are related to each other and discuss their relative strengths and weaknesses to indicate which classes are suited for which applications.

Study on Resonance Phenomenon Caused by Voltage Fluctuation of Power Supply in JT-60SA EF Coil

For the large research Tokamak JT-60SA, evaluating the withstand voltage between conductors is one of the most critical factors for the coil design. The power supply feeding the coil injects a wide spectrum of frequency components. The transient response and resonance phenomena induce a non-uniform voltage distribution in the coil. The transiently concentrated voltage can cause the insulation breakdown between conductors, and JT-60SA may not be able to operate safely. This study conducted an impulse test to evaluate the withstand voltage between adjacent conductors for an equilibrium field (EF) coil. The actual power supply voltage for the EF coil was measured to investigate the ramp rate (dv/dt) and frequency spectrum. In addition, based on the results of a resonance test of the EF dummy coil, a circuit simulation model for the EF coil was developed to evaluate the effect of the transient response and resonance phenomenon on the voltage in the coil. The results of this study provide fundamental data that can be used to ensure that the EF coil does not cause insulation breakdown.

Loss of energetic ions due to n = 1 internal kink instability in HL-2M

Effects of three-dimensional (3D) perturbations due to an unstable n = 1 (n is the toroidal mode number) internal kink (IK) on the energetic particles (EPs) are systematically investigated for the HL-2M tokamak, utilizing the MARS-F/K code [Liu et al., Phys. Plasmas 7, 3681–3690 (2000)] and a recently developed test particle tracing module. A high-beta sawteething HL-2M scenario, simulated by the TRANSP code [Breslau et al., Transp Computer Software (2018)], is chosen for this study. In general, the 3D perturbation associated with an unstable IK is found to affect the EP drift orbit, confinement, and loss in HL-2M. The instability-induced EP loss fraction is found to be typically less than 10%, without counting for the prompt orbit loss associated with the 2D equilibrium field for counter-current particles. The latter reaches about 16% in HL-2M. For co-current EPs, a 100 G 3D magnetic field (inside the plasma) due to the IK does not induce any EP loss assuming a static perturbation. A sawtooth-like time-varying perturbation field, with the peak amplitude reaching 1000 G, can however produce about 30% loss for the co-current EPs in HL-2M. The majority of lost EPs tend to strike the lower divertor region, with a small fraction of particles striking the low-field side mid-plane region of the limiting surface.

Generalized chiral kinetic equations

We derive the generalized chiral kinetic equations which are applicable to the fermions with arbitrary mass. We show how the dynamical magnetic-moment distribution function could lead to spin polarization and electric charge separation. We also show how the electric/magnetic moment distribution and pseudoscalar distribution could be induced by vorticity and electromagnetic field in global equilibrium.

Virial theorem for a cloud of stars obtained from the Jeans equations with second correlation moments

A hydrodynamic model for small acoustic oscillations in a cloud of stars is built, taking into account the self-consistent gravitational field in equilibrium with a non-zero second correlation moment. It is assumed that the momentum flux density tensor should include the analog of the anisotropic pressure tensor and the second correlation moment of both longitudinal and transverse gravitational field strength. The non-relativistic temporal equation for the second correlation moment of the gravitational field strength is derived from the Einstein equations using the first-order post-Newtonian approximation. One longitudinal and two transverse branches of acoustic oscillations are found in a homogeneous and isotropic star cloud. The requirement for the velocity of transverse oscillations to be zero provides the boundary condition for the stability of the cloud. The critical radius of the spherical cloud of stars is obtained, which is precisely consistent with the virial theorem.

Comparing metrics for mixed quantum states: Sjöqvist and Bures

It is known that there are infinitely many distinguishability metrics for mixed quantum states. This freedom, in turn, leads to metric-dependent interpretations of physically meaningful geometric quantities such as complexity and volume of quantum states. In this paper, we first present an explicit and unabridged mathematical discussion on the relation between the Sjoqvist metric and the Bures metric for arbitrary nondegenerate mixed quantum states, using the notion of decompositions of density operators by means of ensembles of pure quantum states. Then, to enhance our comprehension of the difference between these two metrics from a physics standpoint, we compare the formal expressions of these two metrics for arbitrary thermal quantum states specifying quantum systems in equilibrium with a reservoir at non-zero temperature. For illustrative purposes, we show the difference between these two metrics in the case of a simple physical system characterized by a spin-qubit in an arbitrarily oriented uniform and stationary external magnetic field in thermal equilibrium with a finite-temperature bath. Finally, we compare the Bures and Sjoqvist metrics in terms of their monotonicity property.

Charged compact stars in extended [formula omitted] gravity

The purpose of this paper is to study charged compact stars using extended gravitational theory, also known as f(R,G,T) gravity. Alternatively, this theory is also called f(R,T,G) gravity. The symbols R,G, and T denote the Ricci Scalar, the Gauss–Bonnet invariant, and the trace of the energy–momentum tensor, respectively. We suggested several plausible models in the framework of this new gravity theory, and then used these models to explore several physical properties of compact objects of relativistic nature. This research also takes into account three famous compact stars: Vela X-1 (CS1); SAXJ1808.4-3658 (CS2); and 4U1820-30 (CS3). Moreover, using the suggested models, the physical nature of anisotropic stress, energy density, various energy conditions (ECs), the state of equilibrium, interior stability, mass variations, compactness, anisotropy, electric charge, and electric field intensity are analysed for considered compact stars. Different plots of the above-mentioned quantities are presented for this analysis. Conclusively, the ECs are satisfied, and the compact stars have a significant dense core.

A statistical field theory underlying the thermodynamics of Ricci flow and gravity

This paper proposes a statistical field theory of quantum reference frame underlying Perelman’s analogies between his formalism of the Ricci flow and the thermodynamics. The theory is based on a [Formula: see text] quantum nonlinear sigma model (NLSM), interpreted as a quantum reference frame system which a to-be-studied quantum system is relative to. The statistic physics and thermodynamics of the quantum frame fields is studied by the density matrix obtained by the Gaussian approximation quantization. The induced Ricci flow of the frame fields and the Ricci–DeTurck flow of the frame fields associated with the density matrix are deduced. In this framework, the diffeomorphism anomaly of the theory has a deep thermodynamic interpretation. The trace anomaly is related to a Shannon entropy in terms of the density matrix, which monotonically flows and achieves its maximal value at the flow limit, called the Gradient Shrinking Ricci Soliton (GSRS), corresponding to a thermal equilibrium state of spacetime. A relative Shannon entropy with respect to the maximal entropy gives a statistical interpretation to Perelman’s partition function, which is also monotonic and gives an analogous H-theorem to the statistical frame fields system. A temporal static three-space of a GSRS four-spacetime is also a GSRS in lower three-dimension, we find that it is in a thermal equilibrium state, and Perelman’s analogies between his formalism and the thermodynamics of the frame fields in equilibrium can be explicitly given in the framework. By extending the validity of the Equivalence Principle to the quantum level, the quantum reference frame fields theory at low energy gives an effective theory of gravity, a scale-dependent Einstein–Hilbert action plus a cosmological constant is recovered. As a possible underlying microscopic theory of the gravitational system, the theory is also applied to understand the thermodynamics of the Schwarzschild black hole.

3D simulation of orbit loss and heat load on limiters of ICRF-NBI synergy induced fast ions on EAST

Fast ions synergy induced by ion-cyclotron range of frequency (ICRF) and neutral beam injection (NBI) are of interest not only because of their advantage of heating the plasma and drive currents, but also because of their disadvantage of damaging plasma surface components and driving MHD instabilities. In this paper, we calculate the fast ion loss and the deposition distribution of the lost particles on the limiters in EAST under the synergistic effect of the ripple field and collisions with the full-orbit-following simulation program ISSDE for the first time. The previous models to study the NBI fast ion loss by the action of ICRF are relatively simple and consider fewer influencing factors. Most studies on fast ion loss have used toroidal uniform boundaries. In this work, we consider the distribution of ICRF-NBI synergy induced fast ions with different minority H concentrations. After setting the limiter boundary, we consider the prompt fast ion loss caused by the equilibrium field and the fast ion loss caused by the ripple field and collision. Under the action of minority-ion ion-cyclotron resonant heating, the NBI fast ion distribution function has spread in the high-energy part, especially for the minority H concentration of 1%, and the fast ions show each anisotropic distribution near the resonance band on the poloidal dimension. The synergistic loss caused by the ripple field and collision will first be greater than the loss caused by either factor, and then reach a final loss fraction of 3.8%. The heat load power density of the lost fast ions on different limiters is not uniform, as well as on each limiter, which is related to the distance from the limiter to the plasma, the relative position between the limiters and the parallel direction of most fast ions. Once the study of ICRF-NBI synergy induced fast ion loss caused by the action of ripple and collision has been done, we can do optimization in a targeted manner. Such as adding ferromagnetic inserts to reduce the ripple loss and optimizing the limiters’ position to reduce or control the generation of impurities.

Nuclear volume isotope fractionation of europium and other lanthanide elements

The nuclear volume component of equilibrium field shift isotope fractionations in europium and other lanthanide elements is estimated using Mössbauer spectroscopy and electronic structure calculations. This effect goes in the opposite direction from equilibrium mass-dependent fractionation, and in the case of europium is predicted to dominate over mass dependent fractionation for most materials. Including both effects, Eu2+-bearing species will have approximately 0.4-1‰ higher 153Eu/151Eu than Eu3+-bearing species at 25ºC (298 K), and about 0.3‰ higher 153Eu/151Eu at 700ºC (973 K). Field shift fractionation mainly depends on oxidation state; differences in coordination structure without changes in oxidation state appear to have much weaker associated fractionations. Nuclear volume isotope fractionation will become even more dominant over mass dependent fractionation at higher temperatures because nuclear volume effects scale with 1/T (K), vs. 1/T2 for mass-dependent fractionation. Fractionation favoring high 153Eu/151Eu in minerals that preferentially incorporate Eu2+, such as plagioclase, is consistent with recent measurements on igneous rocks showing low 153Eu/151Eu in samples with large negative europium anomalies (Lee and Tanaka, 2021). The present results agree with the recent conclusion that equilibrium fractionation cannot explain cosmochemical REE fractionations in primitive meteoritical materials (Hu et al., 2021), because the net fractionation is too small (~0.2‰ or less) at temperatures >1200 K where vapor-phase REE species are relevant.