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Transport and confinement physics: Chapter 2 of the special issue: on the path to tokamak burning plasma operation

Progress in physics understanding and theoretical model development of plasma transport and confinement (TC) in the ITPA TC Topical Group since the publication of the ITER Physics Basis (IPB) document (Doyle et al 2007 Nucl. Fusion 47 S18) was summarized focusing on the contributions to ITER and burning plasma prediction and control. This paper provides a general and streamlined overview on the advances that were mainly led by the ITPA TC joint experiments and joint activities for the last 15 years (see JEX/JA table in appendix). This paper starts with the scientific strategy and scope of the ITPA TC Topical group and overall picture of the major progress, followed by the progress of each research field: particle transport, impurity transport, ion and electron thermal turbulent transport, momentum transport, impact of 3D magnetic fields on transport, confinement mode transitions, global confinement, and reduced transport modeling. Cross references with other Topical Groups are given in order to highlight overlapped topics, such as the 3D effect on the plasma transport in the edge and L-H transition physics. The increasing overlap between the topical groups is a reflection of the progress on integrating the known physics into comprehensive models that are better and better able to reproduce the plasma transport. In recent years, such integration has become increasingly prevalent when considering transport from the SOL, through the edge pedestal, and into the plasma core. In the near future, increased collaboration also with the magneto-hydrodynamic and energetic particles community will be important as we approach burning plasma conditions in next-step fusion devices. A summary of remaining challenges and next steps for each research field is given in the Summary section.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Magneto-gravity waves

Small amplitude low frequency waves in plasma of infinite conductivity under influence of constant external gravitational and magnetic fields

ATMOSPHERIC CONDUCTIVITY↗

Benchmarking magnetised three-wave coupling for laser backscattering: analytic solutions and kinetic simulations

Understanding magnetised laser–plasma interactions is important for controlling magneto-inertial fusion experiments and developing magnetically assisted radiation and particle sources. For nanosecond pulses at non-relativistic intensities, interactions are dominated by coherent three-wave interactions, whose nonlinear coupling coefficients became known only recently when waves propagate at oblique angles with the magnetic field. In this paper, backscattering coupling coefficients predicted by warm-fluid theory are benchmarked using particle-in-cell simulations in one spatial dimension, and excellent agreements are found for a wide range of plasma temperatures, magnetic field strengths and laser propagation angles, when the interactions are mediated by electron-dominant hybrid waves. Systematic comparisons between theory and simulations are made possible by a rigorous protocol. On the theory side, the initial boundary value problem of linearised three-wave equations is solved, and the transient-time solutions allow the effects of growth and damping to be distinguished. On the simulation side, parameters are carefully chosen and calibration runs are performed to ensure that comparisons are well controlled. Fitting simulation data to analytical solutions yields numerical growth rates that match theory predictions within error bars. Although warm-fluid theory is found to be valid for a wide parameter range, genuine kinetic effects have also been observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Efficient Optimization of Plasma Radiation Detector Configurations using Imperfect Inference Models

The configurations of instruments fielded on an experiment affect the amount of information captured and the quality of subsequent inference. Here, we investigate the problem of optimizing plasma x-ray radiation detectors in a magneto-inertial fusion experiment at Sandia National Laboratories. It is impossible to directly measure properties such as the temperature of the thermonuclear fusion plasma produced in these experiments because of the extreme environment and destructive nature of the experiment. Among other diagnostics, several detectors are placed with significant standoff from the fusion target to capture the x-rays emitted by the fusion plasma, which can be used to infer some of its properties. To optimize the configuration of these detectors, a high-fidelity model (HFM) is used for simulating outputs and a low-fidelity model (LFM) is used for inference. We develop methods based on A- and L-optimality criteria that are efficient to compute while explicitly accounting for the discrepancy between the HFM and the LFM. The method allows us to find detector configurations that perform similarly to or better than the configuration obtained using an existing sampling-based optimization method while decreasing computational time by a factor of 50. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Bayesian optimization↗

Guiding center equations for the magnetic dipole

Since the discovery of Van Allen radiation belts in the 1960s, observations of energetic ions trapped in the Earth's dipole magnetic field have illustrated the remarkable confinement properties of this configuration. As such, it has been used for confining a hot plasma for nuclear fusion studies, starting from the pioneering work of Bo Lehnert and Akira Hasegawa, in the Levitated Dipole Experiment (LDX) at MIT until 2011 and in the RT-1 experiment at the University of Tokyo. More recently, the dipole has been subject to a renewed interest for fusion studies by a couple of startups and for smaller applications as a cold plasma source. While the equilibrium and magneto-hydrodynamic stability of the dipole have been investigated quite in detail, neoclassical properties of the dipole are comparatively much less known: the dipole is more known in geophysics than in fusion science. For this reason, in this paper, we propose a set of Hamiltonian, guiding-center equations to describe the motion of electrons and ions in a magnetic dipole configuration. We also developed a code, and we show the main features of particle motion, benchmarking our results with the analytical solutions for the bounce and precession motion, which are well documented in the literature. We also draw some general conclusions for the neoclassical transport in usual toroidal confinement schemes, such as the tokamak and the stellarator, pointing out the unique advantages of the dipole in confining energetic particles.

Hamiltonian mechanics↗

FNAS: The magnetic configuration leading to solar flares

We present a method for solving plasma magnetohydrodynamic (MHD) problems arising from the interaction of plasmas with magnetic fields in stellar atmospheres. Our approach, in contrast to previous methods, is not based on solving equations for the magnetic field and plasma velocity but rather studies the evolution of the electric current and density (and the related gas pressure). We have applied the method to several studies involving linearized departures from static, current-free equilibria. The applications show explicit solutions for cases found in astrophysics and to problems encountered with earlier studies where the gas pressure was neglected. The method is particularly well suited for studying situations which involve a transition between high and low plasma-beta regions. It shows precisely how electric currents, and magnetic free-energy, build up in the plasma as a result of the slow stressing of a potential magnetic field configuration. The method also demonstrates how transverse-current waves, a mix of Alfven and magneto-acoustic modes, propagate in a low-beta plasma for any density stratification and background field geometry.

Fontenla, Juan M.↗

Similarity considerations and conservation laws for magneto-static atmospheres

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

Webb, G. M.↗

Thermomagnetic instability of plasma composition gradients

In this paper, we show that, under Braginskii magneto-hydrodynamics, anti-parallel gradients in an average ion charge state and electron temperature can be unstable to the growth of self-generated magnetic fields. The instability is analogous to the field-generating thermomagnetic instability, although it is driven by the collisional thermal force magnetic source term rather than the Biermann battery term. The gradient in ion charge state causes a gradient in collisionality, which couples with temperature perturbations to create a self-generated magnetic field. This magnetic field deflects the electron heat flux in a way that reinforces the temperature perturbation. The derived linearized growth rate, typically on hydrodynamic timescales, includes resistive and thermal smoothing. It increases with large ion composition gradients and electron heat flux, conditions typical of the hohlraum walls or contaminant mix jets in inertial confinement fusion implosions. However, extended magneto-hydrodynamic simulations indicate that the instability is usually dominated and stabilized by nonlinear Nernst advection, in a similar manner to the standard thermomagnetic instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Z-Pinch Pulsed Plasma Propulsion Technology Development

Fusion-based propulsion can enable fast interplanetary transportation. Magneto-inertial fusion (MIF) is an approach which has been shown to potentially lead to a low cost, small reactor for fusion break even. The Z-Pinch/dense plasma focus method is an MIF concept in which a column of gas is compressed to thermonuclear conditions by an axial current (I approximates 100 MA). Recent advancements in experiments and the theoretical understanding of this concept suggest favorable scaling of fusion power output yield as I(sup 4). This document presents a conceptual design of a Z-Pinch fusion propulsion system and a vehicle for human exploration. The purpose of this study is to apply Z-Pinch fusion principles to the design of a propulsion system for an interplanetary spacecraft. This study took four steps in service of that objective; these steps are identified below. 1. Z-Pinch Modeling and Analysis: There is a wealth of literature characterizing Z-Pinch physics and existing Z-Pinch physics models. In order to be useful in engineering analysis, simplified Z-Pinch fusion thermodynamic models are required to give propulsion engineers the quantity of plasma, plasma temperature, rate of expansion, etc. The study team developed these models in this study. 2. Propulsion Modeling and Analysis: While the Z-Pinch models characterize the fusion process itself, propulsion models calculate the parameters that characterize the propulsion system (thrust, specific impulse, etc.) The study team developed a Z-Pinch propulsion model and used it to determine the best values for pulse rate, amount of propellant per pulse, and mixture ratio of the D-T and liner materials as well as the resulting thrust and specific impulse of the system. 3. Mission Analysis: Several potential missions were studied. Trajectory analysis using data from the propulsion model was used to determine the duration of the propulsion burns, the amount of propellant expended to complete each mission considered. 4. Vehicle Design: To understand the applicability of Z-Pinch propulsion to interplanetary travel, it is necessary to design a concept vehicle that uses it -- the propulsion system significantly impacts the design of the electrical, thermal control, avionics and structural subsystems of a vehicle. The study team developed a conceptual design of an interplanetary vehicle that transports crew and cargo to Mars and back and can be reused for other missions. Several aspects of this vehicle are based on a previous crewed fusion vehicle study -- the Human Outer Planet Exploration (HOPE) Magnetized Target Fusion (MTF) vehicle. Portions of the vehicle design were used outright and others were modified from the MTF design in order to maintain comparability.

Polsgrove, Tara↗

ELM control optimization for various ITER scenarios based on linear and quasi-linear figures of merit

For the purpose of better understanding type-I edge localized mode (ELM) control in ITER with resonant magnetic perturbation (RMP) fields, the plasma response to RMP is computed by a resistive full magneto-hydrodynamic model in toroidal geometry. Five scenarios designed for ITER are considered, ranging from the pre-nuclear to nuclear phases. The plasma response to RMP is quantified by the plasma surface displacement near the X-point of the divertor plasma and at the outboard mid-plane. The optimal coil configurations between two high- Q deuterium-tritium (DT) scenarios (at the same plasma current of 15 MA and the same magnetic field of 5.3 T but different fusion gains, Q = 5 and 10) are predicted to be similar. For the other ITER scenarios with similar edge safety factor q 95 ~ 3 to that of the baseline scenario, the optimal coil phasing is also similar. The optimization results are different for a half-current full-field (7.5 MA/5.3 T) scenario, largely due to the difference in q 95 . The RMP coil currents are also optimized to tailor the core vs edge toroidal torques exerted by the 3D RMP fields on the plasma column. Torque optimization, with various objective functions proposed in the study, is useful for minimizing the side effects of RMP on the plasma core flow in ITER, while still maintaining the ELM control capability. Full utilization of three rows of ELM control coils in ITER is found to be essential to ensure both flexibility and robustness of ELM control, in terms of both linear and quasilinear plasma responses.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Toroidal modeling of runaway electron loss due to 3D fields in ITER

Mitigation of runaway electrons (REs) by three-dimensional (3D) magnetic field perturbations is numerically investigated for the ITER 15 MA baseline D–T scenario, utilizing the MARS-F code (Liu et al Phys. Plasmas 7 3681) with a drift orbit test particle tracing module. Considered are two types of 3D fields: the n = 3 (n is the toroidal mode number) resonant magnetic perturbation (RMP) utilized for the purpose of controlling the edge localized modes in ITER, and perturbations generated by the n = 1 magneto-hydrodynamic (MHD) instabilities in a post-disruption plasma. The RMP field, applied to a pre-disruption plasma, is found to be moderately effective in mitigating the RE seeds in ITER when vacuum field model is assumed. Up to ~40% loss fraction is possible at 90 kA-turn coil current. The mitigation efficiency is however substantially reduced, down to less than 5%, when the plasma response is taken into account. This is due to strong screening of the resonant magnetic field components by the plasma response resulting in much less field line stochasticity. On the other hand, the MARS-F modeling, based on the DINA-simulated post-disruption equilibria, shows that the n = 1 resistive kink instabilities develop in these plasmas, as the edge safety factor qa evolves and drops below integer numbers. RE mitigation by these MHD instabilities is sensitive to the eigenmode structure. The best mitigation is achieved as q a drops below 3, when a global kink instability occurs that encompasses both internal and external components. This global instability is found to be capable of mitigating over 80% MeV-level passing RE orbits at a field perturbation |δB|/B 0 that is comparable to that observed in DIII-D experiments, and full mitigation if the perturbation amplitude is doubled. The 'wetted' area on the ITER limiting surface, due to MHD instability induced RE loss, generally increases with the perturbation amplitude (together with increasing loss fraction). At the highest perturbation level assumed in this study, the wetted area reaches ~60% of the total limiting surface area. Lastly, the lost RE orbits mainly strike the outer divertor region of the limiting surface, with some fraction also hitting a wide area along the inboard side of the surface.

3D fields↗

Steady detonation propagation in thin channels with strong confinement

We examine asymptotically the dynamics of two-dimensional, steady detonation wave propagation and failure for a strongly confined high explosive (HE), in which the width of the explosive is small relative to the reaction zone length. An energy balance equation is derived, which shows how the longitudinal acceleration of subsonic flow behind the detonation shock is influenced both by chemical reaction and by the effects of HE boundary streamline deflection, specifically via the induced rate of change of mass flux through the detonation wave. The latter serves to either counteract or reinforce the acceleration of longitudinal flow, depending on the sign of the gradient of the boundary streamline deflection at the detonation shock. The analysis is valid for general equations of state and chemical reaction rates in the HE. The asymptotically derived form of the energy equation represents an eigenvalue problem for the determination of the steady detonation propagation speed, solved via a shooting method. We explore specific results for ideal and stiffened equations of state, along with a pressure-dependent reaction rate for which changes in the pressure exponent and reaction order are also studied. We consider the influences of both straight and curved HE boundary streamline shapes. The asymptotic analysis reveals significant physical insights into how detonation propagation and failure are affected by strong confinement.

42 ENGINEERING↗

Automated Bayesian high-throughput estimation of plasma temperature and density from emission spectroscopy

Here, this paper introduces a novel approach for automated high-throughput estimation of plasma temperature and density using atomic emission spectroscopy, integrating Bayesian inference with sophisticated physical models. We provide an in-depth examination of Bayesian methods applied to the complexities of plasma diagnostics, supported by a robust framework of physical and measurement models. Our methodology is demonstrated using experimental observations in the field of magneto-inertial fusion, focusing on individual and sequential shot analyses of the Plasma Liner Experiment at LANL. The results demonstrate the effectiveness of our approach in enhancing the accuracy and reliability of plasma parameter estimation and in using the analysis to reveal the deep hidden structure in the data. This study not only offers a new perspective of plasma analysis but also paves the way for further research and applications in nuclear instrumentation and related domains.

Bayesian inference↗

Role of turbulent separatrix tangle in the improvement of the integrated pedestal and heat exhaust issue for stationary-operation tokamak fusion reactors

Abstract The magnetic separatrix surface is designed to provide the final and critical confinement to the hot stationary-operation core plasma in modern tokamak reactors in the absence of an external magnetic perturbation (MP) or transient magneto-hydrodynamic perturbation, while diverting the exhaust heat to divertor plates. All the stationary operational boundary plasma studies and reactor designs have been performed under this assumption. However, there has been a long-standing suspicion that a stationary-operation tokamak plasma even without external MPs or edge localized modes (ELMs) activities may not have a stable closed separatrix surface, especially near the magnetic X-point. Here, the first gyrokinetic numerical observation is reported that the divertor separatrix surface, due to homoclinic tangles caused by intrinsic electromagnetic turbulence, is not a stable closed surface in a stationary operation phase even without MPs or ELMs. Unlike the MP- or ELM-driven homoclinic tangles that could cause deleterious effects to core confinement or divertor plates, it is found that the micro-turbulence driven homoclinic tangles could connect the divertor plasma to the pedestal plasma in a constructive way by broadening the divertor heat-exhaust footprint and weakening the pedestal slope to the ELM-safe direction. Micro-turbulent homoclinic tangles can open a new research direction in understanding and controlling these two most troublesome and non-locally connected edge-plasma issues in a tokamak fusion reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Enhanced tuneable rotatory power in a rotating plasma

We report that the gyrotropic properties of a rotating magnetized plasma are derived analytically. Mechanical rotation leads to a new cutoff for wave propagation along the magnetic field, and polarization rotation above this cutoff is the sum of the classical magneto-optical Faraday effect and the mechanico-optical polarization drag. Exploiting the very large effective group index near the cutoff, we expose here that polarization drag can be 10 4 larger than Faraday rotation at GHz frequency. The rotation leads to weak absorption while allowing direct frequency control, demonstrating the unique potential of rotating plasmas for nonreciprocal elements. The very large rotation frequency of a dense non-neutral plasma could enable unprecedented gyrotropy in the THz regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Rotation of electrothermal-instability-driven overheating structure due to helically oriented surface magnetic field on a high-current-density aluminum rod

Experiments on the 1-MA, 100-ns-rise-time Mykonos Facility demonstrate rotation of electrothermal instability (ETI)-driven overheating structure on 1.00-mm-diameter, 10-nm-surface roughness, 99.999%-pure aluminum rods, which are pulsed with helically polarized surface magnetic field. Rods are machined to include pairs of 10-micron-scale quasi-hemispherical voids or “engineered defects (ED)” which provide the dominant current density perturbation from which ETI grows most rapidly. Experiments include an axial magnetic field component through the addition of a helically wound return-current electrode or “helical return can (HRC).” For a given HRC design, azimuthal field (B ɵ ) and axial field (B z ) components rise at a prescribed and fixed ratio, driving an increasing magnetic field of constant polarization at the rod's surface; most experiments generated surface magnetic field at a 15-degree field polarization angle (from horizontal) defined as ɸ B = arctan(B z /B ɵ ). ETI-driven emission patterns from individual ED are observed to rotate along ɸ B , while emission patterns from dielectric-coated ED pairs are shown to elongate and preferentially merge along ɸ B , in qualitative agreement with 3D-magnetohydrodynamic simulations. These data strongly support that for a randomized distribution of current density perturbations on a high-current density conductor, nearby perturbations will favorably merge about ɸ B , with the degree of merging increasing with current. Such observations offer fundamental new understanding of the seeding mechanisms of the helical magneto-Rayleigh Taylor (MRT) instabilities observed from axially magnetized magnetically driven imploding liners.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗