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At least 289 records · Page 16

Cost-efficient finite-volume high-order schemes for compressible magnetohydrodynamics

We present an efficient dimension-by-dimension finite-volume method which solves the adiabatic magnetohydrodynamics equations at high discretization order, using the constrained-transport approach on Cartesian grids. Results are presented up to tenth order of accuracy. The algorithmic architecture of this method is very close to that of commonly employed second-order schemes: it requires only one reconstructed value per face for each computational cell, independently of the scheme's order. This property is highly beneficial for the numerical efficiency. It results from reusing the required values already available in neighboring grid cells, in contrast to standard algorithms that require a number of reconstructions and evaluations which increases with the scheme's order of accuracy. At a given resolution, these high-order schemes present significantly less numerical dissipation than commonly employed lower-order approaches. Thus, results of comparable accuracy are achievable at a substantially coarser resolution, yielding overall performance gains. We also present a way to include physical dissipative terms: viscosity, magnetic diffusivity and cooling functions, respecting the finite-volume and constrained-transport frameworks. Benefits of this method are shown through applications in turbulent flows.

97 MATHEMATICS AND COMPUTING↗

An experimental and computational study of thin-layer Rayleigh–Taylor instability development during deceleration with and without an externally applied magnetic field

The importance of mitigating the Rayleigh–Taylor instability (RTI) in inertial confinement fusion (ICF) is critical to successfully achieve high gain fusion yield. Consequently, understanding the seed mechanisms of RTI and the potential evolution of RTI in ICF relevant conditions is crucial. Single feature perturbations consistently demonstrate non-linear RTI evolution, for which an experimental platform on OMEGA-EP is developed. Manufacturing defects introduced into the target design require exploration of unanticipated changes to RTI development and an identification of targets that will still render quantifiable physics results. Consequently, it is presented that the inherent 3D nature of experimental targets necessitates 3D modeling for accurate design work and predictive modeling of experimental targets, especially when high resolution imaging diagnostics, like Fresnel Zone Plates, are utilized. A study of the morphology of the RTI evolution due to changing initial conditions and the presence of an externally applied magnetic field are also explored. Experimental data show thin-layer RTI morphology comparable to resistive magneto hydrodynamic 3D results. A discussion on the impacts of an externally applied magnetic field makes the case for continued efforts to observe a magnetic field's impact on RTI morphology.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Dark photon superradiance: Electrodynamics and multimessenger signals

We study the electrodynamics of a kinetically mixed dark photon cloud that forms through superradiance around a spinning black hole, and design strategies to search for the resulting multimessenger signals. A dark photon superradiance cloud sources a rotating dark electromagnetic field which, through kinetic mixing, induces a rotating visible electromagnetic field. Standard model charged particles entering this field initiate a transient phase of particle production that populates a plasma inside the cloud and leads to a system which shares qualitative features with a pulsar magnetosphere. We study the electrodynamics of the dark photon cloud with resistive magnetohydrodynamics methods applicable to highly magnetized plasma, adapting techniques from simulations of pulsar magnetospheres. We identify turbulent magnetic field reconnection as the main source of dissipation and electromagnetic emission, and compute the peak luminosity from clouds around solar-mass black holes to be as large as 10 43 erg/s for observationally allowed dark photon parameter space. The emission is expected to have a significant x-ray component and to potentially be periodic, with period set by the dark photon mass. The luminosity is comparable to the brightest x-ray sources in the Universe, allowing for searches at distances of up to hundreds of Mpc with existing telescopes. Finally, we discuss observational strategies, including targeted electromagnetic follow-ups of solar-mass black hole mergers and targeted continuous gravitational wave searches of anomalous pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗

Interactions Between Microturbulence and Magnetohydrodynamic Instabilities in Magnetized Plasmas (Final Technical Report)

This document details the work accomplished during the period 04/15/2012-01/31/2020 for the collaborative project “Interactions Between Microturbulence and Magnetohydrodynamic Instabilities in Magnetized Plasmas,” and serves as the final report on the University of California, San Diego part of this collaborative project for Department of Energy Office of Science - Fusion Energy Sciences Grant No. DE- SC0007783. This project focused on the development of analytic and computational tools, seeking to better understand the mutual interactions between small-scale temperature-gradient driven microturbulence and macroscopic magnetohydrodynamic (MHD) instabilities, particularly tearing modes, in magnetically confined plasmas relevant for the generation of fusion energy. This project advanced understanding through numerical simulations of different sets of model equations, corresponding to different microturbulence instabilities. Questions addressed included how the magnitudes, spatial structures, and scaling's of turbulent forcing's and drags impact magnetic island dynamics, as well as quantifying the “region of influence” of an island on the microturbulence dynamics. A key finding of the project is that the microturbulence fluctuations and associated cross-field particle and energy fluxes exhibit spatial asymmetries for sufficiently large islands. The results have improved our fundamental understanding of plasma dynamics, motivated new experimental investigations, and will help inform future fusion predictive modeling efforts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Engquist, B. E.↗

Modifications of magnetohydrodynamics as applied to the solar wind

The effect of including the Braginskii viscous stress tensor in magnetohydrodynamics is remarked upon. It is shown that semiquantitative agreement with a recently observed anisotropy in the turbulent solar wind spectrum can be achieved in this way. The modifications of the dynamical equations are simple enough to permit their inclusion in numerical codes. The effects of large 'ion parallel viscosities' also may be significant for plasmas in quite different regimes than the solar wind.

Montgomery, David↗

Nonlinear evolution of a large-amplitude circularly polarized Alfven wave: Low beta

The nature of turbulent cascades arising from the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation for the case of low plasma Beta and no wave dispersion. The magnetohydrodynamic code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Anisotropic turbulent cascades, similar to those found in early incompressible two-dimensional simulations, occur after nonlinear saturation of the parallel propagating decay instability. The turbulent spectrum can be divided into three regimes: the lowest wave numbers are dominated by lower sideband remnants of the parametric process, intermediate wave numbers display nearly incompressible dynamics, and the highest wave numbers are dominated by acoustic turbulence.

Ghosh, S.↗

Determination of confinement regime boundaries via separatrix parameters on Alcator C-Mod based on a model for interchange-drift-Alfvén turbulence

The separatrix operational space (SepOS) model (Eich and Manz 2021 Nucl. Fusion 61 086017) is shown to predict the L–H transition, the L-mode density limit, and the ideal magnetohydrodynamic ballooning limit in terms of separatrix parameters for a wide range of Alcator C-Mod plasmas. The model is tested using Thomson scattering measurements across a wide range of operating conditions on C-Mod, spanning $\overline{n}_{\mathrm{e}}$ = 0.3–5.5 $\times 10^{20}\,$m −3 , $B_{\mathrm{t}} = 2.5$–8.0 T, and $B_{\mathrm{p}}$= 0.1–1.2 T. An empirical regression for the electron pressure gradient scale length, $\lambda_{{p}_{\mathrm{e}}}$, against a turbulence control parameter, $\alpha_{\mathrm{t}}$, and the poloidal fluid gyroradius, $\rho_{\mathrm{s,p}}$, is constructed for H-modes and found to require positive exponents for both regression parameters, indicating turbulence widening of near-scrape-off layer widths at high $\alpha_{\mathrm{t}}$ and an inverse scaling with $B_{\mathrm{p}}$, consistent with results on ASDEX Upgrade. The SepOS model is also tested in the unfavorable drift direction and found to apply well to all three boundaries, including the L–H transition as long as a correction to the Reynolds energy transfer term, $\alpha_\mathrm{RS} \lt 1$ is applied. I-modes typically exist in the unfavorable drift direction for values of $\alpha_{\mathrm{t}} \lesssim 0.3$. Finally, an experiment studying the transition between the Type-I ELMy and EDA H-mode is analyzed using the same framework. It is found that a recently identified boundary $\alpha_{\mathrm{t}} = 0.55$ at excludes most EDA H-modes but that the balance of wavenumbers responsible for the L-mode density limit, namely $k_\mathrm{EM} = k_\mathrm{RBM}$, may better describe the transition on C-Mod. The ensemble of boundaries validated and explored is then applied to project regime access and limit avoidance for the SPARC primary reference discharge parameters.

ELM suppression↗

Whistler–Alfvén Turbulence in a Nonneutral Ultrarelativistic Pair Plasma

The large-scale dynamics of most conventional space and astrophysical plasmas are predominantly governed by Alfvén modes, which are low-frequency magnetohydrodynamic modes existing in magnetized media. At scales smaller than the ion gyroscale or frequencies exceeding the ion cyclotron frequency, the Alfvén modes transform into kinetic-Alfvén or whistler modes that significantly contribute to plasma dynamics. However, this scenario reverses in nonneutral pair plasmas, such as those found in the magnetospheres of pulsars and magnetars, around rotating black holes, and in their relativistic jets, as well as in certain laboratory plasmas. In these systems, the large-scale dynamics are governed by hybrid whistler–Alfvén modes, which transform into pure Alfvén modes at smaller scales. We derive the nonlinear equations that describe the dynamics of whistler–Alfvén modes in ultrarelativistic nonneutral magnetically dominated pair plasma and discuss the spectrum of turbulence governed by these equations.

79 ASTRONOMY AND ASTROPHYSICS↗

Localized phase contrast imaging at the Wendelstein 7-X stellarator

In its basic form, phase contrast imaging (PCI) provides line-integrated measurements of electron density fluctuations in plasmas. As turbulent fluctuations in magnetically confined plasmas have wave vectors almost perpendicular to the background magnetic field, the signals scattered by fluctuations from different parts of the PCI line-of-sight (LoS) are spatially separated in focal planes of the plasma. This allows localized PCI measurements by placing a mask in such a plane, to only permit signals from specific parts of the LoS to reach the PCI detectors. The present paper describes modeling and design of localization masks for the PCI system at the Wendelstein 7-X (W7-X) stellarator as well as the first results obtained using the masks in the recent long-pulse W7-X experimental campaign. During this project, we have extended the theory describing the mask response within the Fraunhofer diffraction model. As a novel development, we show from first principles that the mask response is determined by the fraction of power of the scattered beam spots that passes the mask. These insights have been used to select the W7-X mask design, consisting of a circular cutout, allowing the unscattered beam spot to pass the mask, with wedges covering a fixed angular range outside the central cutout. In the recent W7-X experimental campaign, the masks have verified the location of the main turbulence features observed by the PCI system and provided new information about the location of short-wavelength magnetohydrodynamic modes.

Physics↗

Time-resolved turbulent dynamo in a laser plasma

Understanding magnetic-field generation and amplification in turbulent plasma is essential to account for observations of magnetic fields in the universe. A theoretical framework attributing the origin and sustainment of these fields to the so-called fluctuation dynamo was recently validated by experiments on laser facilities in low-magnetic-Prandtl-number plasmas (Pm < 1). However, the same framework proposes that the fluctuation dynamo should operate differently when Pm ≳ 1, the regime relevant to many astrophysical environments such as the intracluster medium of galaxy clusters. This paper reports an experiment that creates a laboratory Pm ≳ 1 plasma dynamo. We provide a time-resolved characterization of the plasma’s evolution, measuring temperatures, densities, flow velocities, and magnetic fields, which allows us to explore various stages of the fluctuation dynamo’s operation on seed magnetic fields generated by the action of the Biermann-battery mechanism during the initial drive-laser target interaction. The magnetic energy in structures with characteristic scales close to the driving scale of the stochastic motions is found to increase by almost three orders of magnitude and saturate dynamically. It is shown that the initial growth of these fields occurs at a much greater rate than the turnover rate of the driving-scale stochastic motions. Here, our results point to the possibility that plasma turbulence produced by strong shear can generate fields more efficiently at the driving scale than anticipated by idealized magnetohydrodynamics (MHD) simulations of the nonhelical fluctuation dynamo; this finding could help explain the large-scale fields inferred from observations of astrophysical systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

CO and [C ii] line emission of molecular clouds: the impact of stellar feedback and non-equilibrium chemistry

We analyse synthetic 12 CO, 13 CO, and [C ii] emission maps of molecular cloud (MC) simulations from the SILCC-Zoom project. We present radiation, magnetohydrodynamic zoom-in simulations of individual clouds, both with and without radiative stellar feedback, forming in a turbulent multiphase interstellar medium following on-the-fly the evolution of e.g. H 2 , CO, and C + . We introduce a novel post-processing routine based on cloudy which accounts for higher ionization states of carbon due to stellar radiation in H ii regions. Synthetic emission maps of [C ii] in and around feedback bubbles show that the bubbles are largely devoid of [C ii], as recently found in observations, which we attribute to the further ionization of C+ into C 2+ . For both 12 CO and 13 CO, the cloud-averaged luminosity ratio, $L_\rm {CO}/L_\rm {[C\, \small {II}]}$, can neither be used as a reliable measure of the H 2 mass fraction nor of the evolutionary stage of the clouds. We note a relation between the $I_\rm {CO}/I_\rm {[C\, \small {II}]}$ intensity ratio and the H 2 mass fraction for individual pixels of our synthetic maps. The scatter, however, is too large to reliably infer the H 2 mass fraction. Finally, the assumption of chemical equilibrium overestimates H2 and CO masses by up to 150 and 50 per cent, respectively, and $L_\rm {CO}$ by up to 60 per cent. The masses of H and C + would be underestimated by 65 and 30 per cent, respectively, and $L_\rm {[C\, \small {II}]}$ by up to 35 per cent. Hence, the assumption of chemical equilibrium in MC simulations introduces intrinsic errors of a factor of 2 in chemical abundances, luminosities, and luminosity ratios.

79 ASTRONOMY AND ASTROPHYSICS↗

Time-resolved turbulent dynamo in a laser plasma

Understanding magnetic-field generation and amplification in turbulent plasma is essential to account for observations of magnetic fields in the universe. A theoretical framework attributing the origin and sustainment of these fields to the so-called fluctuation dynamo was recently validated by experiments on laser facilities in low-magnetic-Prandtl-number plasmas (Pm<1). However, the same framework proposes that the fluctuation dynamo should operate differently when Pm≳1, the regime relevant to many astrophysical environments such as the intracluster medium of galaxy clusters. This paper reports an experiment that creates a laboratory Pm≳1 plasma dynamo. We provide a time-resolved characterization of the plasma’s evolution, measuring temperatures, densities, flow velocities, and magnetic fields, which allows us to explore various stages of the fluctuation dynamo’s operation on seed magnetic fields generated by the action of the Biermann-battery mechanism during the initial drive-laser target interaction. The magnetic energy in structures with characteristic scales close to the driving scale of the stochastic motions is found to increase by almost three orders of magnitude and saturate dynamically. It is shown that the initial growth of these fields occurs at a much greater rate than the turnover rate of the driving-scale stochastic motions. Our results point to the possibility that plasma turbulence produced by strong shear can generate fields more efficiently at the driving scale than anticipated by idealized magnetohydrodynamics (MHD) simulations of the nonhelical fluctuation dynamo; this finding could help explain the large-scale fields inferred from observations of astrophysical systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Laminar and turbulent plasmoid ejection in a laboratory Parker Spiral current sheet

Quasi-periodic plasmoid formation at the tip of magnetic streamer structures is observed to occur in experiments on the Big Red Ball as well as in simulations of these experiments performed with the extended magnetohydrodynamics code, NIMROD. This plasmoid formation is found to occur on a characteristic time scale dependent on pressure gradients and magnetic curvature in both experiment and simulation. Single mode, or laminar, plasmoids exist when the pressure gradient is modest, but give way to turbulent plasmoid ejection when the system drive is higher, which produces plasmoids of many sizes. However, a critical pressure gradient is also observed, below which plasmoids are never formed. A simple heuristic model of this plasmoid formation process is presented and suggested to be a consequence of a dynamic loss of equilibrium in the high- $\beta$ region of the helmet streamer. This model is capable of explaining the periodicity of plasmoids observed in the experiment and simulations, and produces plasmoid periods of 90 minutes when applied to two-dimensional models of solar streamers with a height of $3R_\odot$ . This is consistent with the location and frequency at which periodic plasma blobs have been observed to form by Large Angle and Spectrometric Coronograph and Sun Earth Connection Coronal and Heliospheric Investigation instruments.

Physics↗

Solar Nebula Magnetohydrodynamic Dynamos: Kinematic Theory, Dynamical Constraints, and Magnetic Transport of Angular Momentum

A hydromagnetic dynamo provides the best mechanism for contemporaneously producing magnetic fields in a turbulent solar nebula. We investigate the solar nebula in the framework of a steady-state accretion disk model and establish the criteria for a viable nebular dynamo. We have found that typically a magnetic gap exists in the nebula, the region where the degree of ionization is too small for the magnetic field to couple to the gas. The location and width of this gap depend on the particular model; the supposition is that gaps cover different parts of the nebula at different evolutionary stages. We have found, from several dynamical constraints, that the generated magnetic field is likely to saturate at a strength equal to equipartition with the kinetic energy of turbulence. Maxwell stress arising from a large-scale magnetic field may significantly influence nebular structure, and Maxwell stress due to small-scale fields can actually dominate other stresses in the inner parts of the nebula. We also argue that the bulk of nebular gas, within the scale height from the midplane, is stable against Balbus-Hawley instability.

Stepinski, Tomasz F.↗

Annual Research Briefs, 2004: Center for Turbulence Research

This report contains the 2004 annual progress reports of the Research Fellows and students of the Center for Turbulence Research in its eighteenth year of operation. Since its inception in 1987, the objective of the CTR has been to advance the physical understanding of turbulent flows and development of physics based predictive tools for engineering analysis and turbulence control. Turbulence is ubiquitous in nature and in engineering devices. The studies at CTR have been motivated by applications where turbulence effects are significant; these include a broad range of technical areas such as planetary boundary layers, formation of planets, solar convection, magnetohydrodynamics, environmental and eco systems, aerodynamic noise, propulsion systems and high speed transportation. Numerical simulation has been the predominant research tool at CTR which has required a critical mass of researchers in numerical analysis and computer science in addition to core disciplines such as applied mathematics, chemical kinetics and fluid mechanics. Maintaining and promoting this interdisciplinary culture has been a hallmark of CTR and has been responsible for the realization of the results of its basic research in applications. The first group of reports in this volume are directed towards development, analysis and application of novel numerical methods for ow simulations. Development of methods for large eddy simulation of complex flows has been a central theme in this group. The second group is concerned with turbulent combustion, scalar transport and multi-phase ows. The nal group is devoted to geophysical turbulence where the problem of solar convection has been a new focus of considerable attention recently at CTR.

Moin, Parviz↗

Physics basis for the reference flat-top plasma scenario in the ST–E1 fusion power plant

As part of the U.S. Department of Energy’s Milestone-Based Fusion Energy Development Program, Tokamak Energy has completed the pre-concept design of the ST–E1 fusion power plant. ST–E1 is envisaged to operate in two phases: a pilot plant phase, targeting sustained net power production of 300 - 500 MWe for a duration >1 hr, followed by a commercial power plant phase targeting steady-state operations and a normalised overnight capital cost of ⩽12 000 $\$$/kWe. The design process adopted was highly iterative, integrating all major plant systems and progressing in a phased fidelity approach. At the pre-conceptual stage, the emphasis has been on exploring the design space, identifying the main system-level trade-offs, and making the key decisions that define the overall plant concept, rather than optimising a single operating point. This paper, part of a focused collection detailing the ST–E1 pre-concept design, addresses the development of a series of reference flat-top plasma operating points for the pilot plant phase. A modelling workflow was established to develop and assess candidate plasma design points and explore key dependencies. The workflow includes integrated core plasma modelling, magnetohydrodynamic (MHD) stability assessment, equilibrium generation, scrape-off-layer and exhaust modelling, heating & current drive design and optimisation, and turbulent transport modelling. Using this framework, the impact of several key parameters on the flat-top operating space was investigated, including the density limit, core radiation fraction and divertor power loading, level of external heating and curent drive power and assumed pedestal characteristics. The MHD stability, controllability and micro-stability characteristics of these plasmas were also analysed. These investigations informed the definition of a set of fully non-inductive, flat-top reference operating points that satisfy the high-level ST–E1 mission, including a low and high density case, a case that is stable to resistive wall modes and a case with reduced divertor power loading.

ST–E1↗

High Performance Equilibrium Solvers for Integrated Magnetic Fusion Simulations

With the funding provided by this award, we developed numerical codes for the study of magnetically confined plasmas for fusion applications. Accordingly, our work can be divided into two separate categories: 1) the design and analysis of novel numerical methods providing high accuracy and high efficiency; 2) the study of the equilibrium and stability of magnetically confined plasmas with some of these numerical codes, as well as the study of the nature of the turbulent behavior which may arise in the presence of instabilities. We first developed new numerical schemes based on integral equation methods for the computation of steady-state magnetic configurations in fusion experiments, providing high accuracy for the magnetic field and its derivatives, which are required for stability and turbulence calculations. We employed different integral formulations depending on the application of interest: axisymmetric or non-axisymmetric equilibria, force-free or magnetohydrodynamic equilibria, fixed-boundary equilibria or free-boundary equilibria. While efficient, these methods do not yet apply to plasma boundaries which are not smooth, a situation which is fairly common in magnetic confinement experiments. To address this temporary weakness, we also constructed a new steady-state solver based on the Hybridizable Discontinuous Galerkin (HDG) method, which provides full geometric flexibility. In addition to these numerical tools focused on steady-states, we also contributed to the improvement of the speed and accuracy of codes simulating the plasma dynamics of fusion plasmas, by developing a novel velocity space representation for the efficient solution of kinetic equations, which most accurately describe the time evolution of hot plasmas in fusion experiments. Using the tools discussed above, we studied several questions pertaining to the equilibrium and stability of magnetically confined plasmas. In particular, we derived a new simple model for axisymmetric devices called tokamaks, to predict how elongated a fusion plasma can be before it becomes unstable and collapses. We also looked at the effect of the shape of the outer plasma surface on key properties of the steady-state magnetic configurations, and how these properties impact turbulence in fusion plasmas, and the corresponding transport of momentum. Likewise, we studied the role of large localized flows on the steady-state magnetic configurations, and how they may influence plasma stability and turbulence. Non-axisymmetric steady-state magnetic configurations are inherently more complex than axisymmetric steady-state configurations, and the subject of ongoing controversies regarding the regularity of the equations determining such steady-states, and their solutions. Implementing an existing NYU code in a new geometry, we studied the nature of the singularity of the solutions observed in the code, and methods to eliminate them. Our main conclusion is that by appropriately tailoring the plasma boundary, it is possible to eliminate the singularities otherwise appearing in our simulations, and to obtain steady-states which appear to be smooth. To gain further insights on incompletely understood turbulence phenomena, we proposed a new reduced model capturing most of these phenomena, which is simple enough to not require expensive numerical simulations on massive supercomputers to investigate them. We demonstrated the strong similarity between our simulations and published results obtained from computationally expensive simulations, and plan to rely on our reduced model to identify the key mechanisms determining the evolution and strength turbulent driven transport in fusion plasmas. Finally, we proposed a new framework for tokamak reactor design studies, enabling us to consider the relative merits of steady-state versus pulsed fusion reactors. We found that pulsed fusion reactors may benefit most from recent advances in magnet technology, and the availability of very high field magnets. As such, they may become more desirable than steady-state tokamak reactors for cost efficient electricity generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗