Burning Plasma Regime Research Articles

Characterization of the ELM-free negative triangularity edge on DIII-D

Abstract Tokamak plasmas with strong negative triangularity (NT) shaping typically exhibit fundamentally different edge behavior than conventional L-mode or H-mode plasmas. On DIII-D, every plasma with sufficiently negative triangularity ( δ < δ crit ≃ − 0.12 ) is found to be inherently free of edge localized modes (ELMs), even at injected powers well above the predicted L-H power threshold. It is also possible to access an ELM-free state at weaker average triangularities, provided that at least one of the two x-points is still sufficiently negative. Access to the ELM-free NT scenario is found to coincide with the closure of the second stability region for infinite-n ballooning modes, suggesting that ballooning stability may play a role in limiting the accessible pressure gradient in NT plasmas. Despite this, NT plasmas are able to support small pedestals and are typically characterized by an enhancement of edge pressure gradients beyond those found in traditional L-mode plasmas. Furthermore, the pressure gradient inside of this small pedestal is unusually steep, allowing access to high core performance that is competitive with other ELM-free regimes previously achieved on DIII-D. Since ELM-free operation in NT is linked directly to the magnetic geometry, NT fusion pilot plants are predicted to maintain advantageous edge conditions even in burning plasma regimes, potentially eliminating reactor core-integration issues caused by ELMs.

Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER

For ITER operations, the range of desirable burning-plasma regimes with high fusion power output will be restricted by various operational constraints. These constraints include the saturation of ITER’s various heating and fueling actuators such as the neutral beam injectors, the ion and electron cyclotron heating systems, the gas puffing system, and the deuterium–tritium pellet injectors. In addition to these actuator constraints, the H-mode power threshold, divertor detachment, and the heat load on the divertor targets may apply limitations to ITER’s operational space. In this work, Plasma Operation Contour (POPCON) plots that map the aforementioned constraints to the temperature-density space are used to investigate which constraints are most limiting towards accessing regimes with high fusion power output. The presented POPCON plots are based on a control-oriented core-edge model that couples the nonlinear density and energy response models for the core-plasma region with SOLPS4.3 parameterizations for conditions in the edge-plasma regions (scrape-off-layer and divertor). Using this control-oriented core-edge model, a nonlinear burn controller, which aims to regulate the plasma temperature and density in the core-plasma region, is constructed in this work. This controller is augmented with an online optimization scheme that governs the control references such that the plasma can be guided towards regimes with high fusion powers while protecting the divertor targets from dangerously high heat loads. A closed-loop simulation study illustrates the capability of this burn control scheme.

The impact of low-mode symmetry on inertial fusion energy output in the burning plasma state

Indirect Drive Inertial Confinement Fusion Experiments on the National Ignition Facility (NIF) have achieved a burning plasma state with neutron yields exceeding 170 kJ, roughly 3 times the prior record and a necessary stage for igniting plasmas. The results are achieved despite multiple sources of degradations that lead to high variability in performance. Results shown here, for the first time, include an empirical correction factor for mode-2 asymmetry in the burning plasma regime in addition to previously determined corrections for radiative mix and mode-1. Analysis shows that including these three corrections alone accounts for the measured fusion performance variability in the two highest performing experimental campaigns on the NIF to within error. Here we quantify the performance sensitivity to mode-2 symmetry in the burning plasma regime and apply the results, in the form of an empirical correction to a 1D performance model. Furthermore, we find the sensitivity to mode-2 determined through a series of integrated 2D radiation hydrodynamic simulations to be consistent with the experimentally determined sensitivity only when including alpha-heating.

Measuring and simulating ice–ablator mix in inertial confinement fusion

Fuel–ablator mix has been established as a major performance degrading effect in the burning plasma regime of recent inertial confinement fusion (ICF) experiments. As such, the study of fuel–ablator mix with experiments and simulations can provide valuable insight for our understanding of these experiments and establish a path for even higher yields and increased robustness. We present a novel high-yield experimental ICF design that is motivated by recent experiments measuring ice–ablator mix with a CH ablator instead of a high-density carbon (HDC) ablator [B. Bachmann et al., Phys. Rev. Lett. 129, 275001 (2022)]. We review these experiments in more detail and describe the modeling assumptions and parameters used to obtain agreement with the data from implosion and burn simulations with mix. Using this mix model calibrated a posteriori to the experimental data, we design an implosion that uses a CH ablator that is predicted to achieve better performance than a recent experiment that achieved net target gain of 1.5 in HDC. Because hydrodynamic instabilities are greatly reduced with this new design, we also expect a high reproducibility at the same implosion adiabat as current record yield experiments.

Neutron backscatter edges as a diagnostic of burn propagation

High gain in hotspot-ignition inertial confinement fusion (ICF) implosions requires the propagation of thermonuclear burn from a central hotspot to the surrounding cold dense fuel. As ICF experiments enter the burning plasma regime, diagnostic signatures of burn propagation must be identified. In previous work [A. J. Crilly et al., Phys. Plasmas 27(1), 012701 (2020)], it has been shown that the spectral shape of the neutron backscatter edges is sensitive to the dense fuel hydrodynamic conditions. The backscatter edges are prominent features in the ICF neutron spectrum produced by the 180° scattering of primary deuterium–tritium fusion neutrons from ions. In this work, synthetic neutron spectra from radiation-hydrodynamics simulations of burning ICF implosions are used to assess the backscatter edge analysis in a propagating burn regime. Significant changes to the edge's spectral shape are observed as the degree of burn increases, and a simplified analysis is developed to infer scatter-averaged fluid velocity and temperature. The backscatter analysis offers direct measurement of the increased dense fuel temperatures that result from burn propagation.

Overview of the SPARC physics basis towards the exploration of burning-plasma regimes in high-field, compact tokamaks

The SPARC tokamak project, currently in engineering design, aims to achieve breakeven and burning plasma conditions in a compact device, thanks to new developments in high-temperature superconductor technology. With a magnetic field of 12.2 T on axis and 8.7 MA of plasma current, SPARC is predicted to produce 140 MW of fusion power with a plasma gain of Q ≈ 11, providing ample margin with respect to its mission of Q > 2. All tokamak systems are being designed to produce this landmark plasma discharge, thus enabling the study of burning plasma physics and tokamak operations in reactor relevant conditions to pave the way for the design and construction of a compact, high-field fusion power plant. Construction of SPARC is planned to begin by mid-2021.

Design of inertial fusion implosions reaching the burning plasma regime

In a burning plasma state1–7, alpha particles from deuterium–tritium fusion reactions redeposit their energy and are the dominant source of heating. This state has recently been achieved at the US National Ignition Facility8 using indirect-drive inertial-confinement fusion. Our experiments use a laser-generated radiation-filled cavity (a hohlraum) to spherically implode capsules containing deuterium and tritium fuel in a central hot spot where the fusion reactions occur. We have developed more efficient hohlraums to implode larger fusion targets compared with previous experiments9,10. This delivered more energy to the hot spot, whereas other parameters were optimized to maintain the high pressures required for inertial-confinement fusion. We also report improvements in implosion symmetry control by moving energy between the laser beams11–16 and designing advanced hohlraum geometry17 that allows for these larger implosions to be driven at the present laser energy and power capability of the National Ignition Facility. These design changes resulted in fusion powers of 1.5 petawatts, greater than the input power of the laser, and 170 kJ of fusion energy18,19. Radiation hydrodynamics simulations20,21 show energy deposition by alpha particles as the dominant term in the hot-spot energy balance, indicative of a burning plasma state.

Verification and validation of the high-performance Lorentz-orbit code for use in stellarators and tokamaks (LOCUST)

A novel high-performance computing algorithm, developed in response to the next generation of computational challenges associated with burning plasma regimes in ITER-scale tokamak devices, has been tested and is described herein. The Lorentz-orbit code for use in stellarators and tokamaks (LOCUST) is designed for computationally scalable modelling of fast-ion dynamics, in the presence of detailed first wall geometries and fine 3D magnetic field structures. It achieves this through multiple levels of single instruction, multiple thread parallelism and by leveraging general-purpose graphics processing units. This enables LOCUST to rapidly track the full-orbit trajectories of kinetic Monte Carlo markers to deliver high-resolution fast-ion distribution functions and plasma-facing component power loads. LOCUST has been tested against the prominent NUBEAM and ASCOT fast-ion codes. All codes were compared for collisional plasmas in both high and low-aspect ratio toroidal geometries, with full-orbit and guiding-centre tracking. LOCUST produces statistically consistent results in line with acceptable theoretical and Monte Carlo uncertainties. Synthetic fast-ion D-α diagnostics produced by LOCUST are also compared to experiment using FIDASIM and show good agreement.

Hotspot parameter scaling with velocity and yield for high-adiabat layered implosions at the National Ignition Facility.

This paper presents a study on hotspot parameters in indirect-drive, inertially confined fusion implosions as they proceed through the self-heating regime. The implosions with increasing nuclear yield reach the burning-plasma regime, hotspot ignition, and finally propagating burn and ignition. These implosions span a wide range of alpha heating from a yield amplification of 1.7-2.5. We show that the hotspot parameters are explicitly dependent on both yield and velocity and that by fitting to both of these quantities the hotspot parameters can be fit with a single power law in velocity. The yield scaling also enables the hotspot parameters extrapolation to higher yields. This is important as various degradation mechanisms can occur on a given implosion at fixed implosion velocity which can have a large impact on both yield and the hotspot parameters. The yield scaling also enables the experimental dependence of the hotspot parameters on yield amplification to be determined. The implosions reported have resulted in the highest yield (1.73×10^{16}±2.6%), yield amplification, pressure, and implosion velocity yet reported at the National Ignition Facility.

Reconnection heating experiments and simulations for torus plasma merging start-up

A series of merging experiments, TS-3 (TS-3U), TS-4, MAST and ST-40, made clear the promising characteristics of reconnection heating during merging formation of a high-beta spherical tokamak (ST), spheromak and field-reversed configuration (FRC). We developed the MW-class (<30 MW in TS-3U) ion heating using magnetic reconnection of torus plasma merging. Both the merging experiments and particle-in-cell (PIC) simulations (and also partly solar observation) agree on, (i) ion heating of the reconnection in its downstream, (ii) negative potential formation in the downstream for accelerating ions and (iii) low dependence of ion heating on the guide (toroidal) field Bg. An important finding is that the reconnection heating energy depends on the reconnecting magnetic field Brec but has little dependence on Bg in the tokamak operation region with the safety factor at the magnetic axis q0 > 2. The plasmoid/current sheet ejection promotes ion heating in the high-q region, weakening the Bg dependence of ion heating. Since the reconnection accelerated ions up to 70% of the Alfven speed of Brec, the ion temperature Ti increment (and the reconnection heating energy) scales with Brec squared under the constant plasma density. This promising reconnection heating does not depend on plasma size, as long as the reconnection time is shorter than the plasma confinement time. This scaling law extended over 1.2 keV suggests that the merging start-up may realize the burning plasma temperature Ti > 10 keV by increasing Brec. The merging/reconnection heating can explore a new direct route to burning plasma regimes without using any additional heating, such as neutral beam injection (NBI). This scaling leads us to new reconnection heating experiments for direct access to burning plasma regimes: ST-40 at Tokamak Energy and TS-3U at the University of Tokyo.

On alpha-particle transport in inertial fusion

Analytical theory and models of inertial fusion implosion use parameterized microphysics models. In this paper, we consider the DT alpha-particle transport, and report new parameterizations of the range, heating efficacy, and energy partition using modern stopping-power theory. Our resulting heating efficacy is lower than previously published results, which reduces the temperature and pressure generated by a dynamic implosion hot-spot evolution model, and shifts the burning-plasma regime boundary slightly farther from current experimental results.

Dependence of alpha-particle-driven Alfvén eigenmode linear stability on device magnetic field strength and consequences for next-generation tokamaks

Recently-proposed tokamak concepts use magnetic fields up to 12 T, far higher than in conventional devices, to reduce size and cost. Theoretical and computational study of trends in plasma behavior with increasing field strength is critical to such proposed devices. This paper considers trends in Alfvén eigenmode (AE) stability. Energetic particles, including alphas from deuterium–tritium fusion, can destabilize AEs, possibly causing loss of alpha heat and damage to the device. AEs are sensitive to device magnetic field via the field dependence of resonances, alpha particle beta, and alpha orbit width. We describe the origin and effect of these dependences analytically and by using recently-developed numerical techniques (Rodrigues et al 2015 Nucl. Fusion 55 083003). The work suggests high-field machines where fusion-born alphas are sub-Alfvénic or nearly sub-Alfvénic may partially cut off AE resonances, reducing growth rates of AEs and the energy of alphas interacting with them. High-field burning plasma regimes have non-negligible alpha particle beta and AE drive, but faster slowing down time, provided by high electron density, and higher field strength reduces this drive relative to low-field machines with similar power densities. The toroidal mode number of the most unstable modes will tend to be higher in high magnetic field devices. The work suggests that high magnetic field devices have unique, and potentially advantageous, AE instability properties at both low and high densities.

Toward a burning plasma state using diamond ablator inertially confined fusion (ICF) implosions on the National Ignition Facility (NIF)

Producing a burning plasma in the laboratory has been a long-standing milestone for the plasma physics community. A burning plasma is a state where alpha particle deposition from deuterium–tritium (DT) fusion reactions is the leading source of energy input to the DT plasma. Achieving these high thermonuclear yields in an inertial confinement fusion (ICF) implosion requires an efficient transfer of energy from the driving source, e.g., lasers, to the DT fuel. In indirect-drive ICF, the fuel is loaded into a spherical capsule which is placed at the center of a cylindrical radiation enclosure, the hohlraum. Lasers enter through each end of the hohlraum, depositing their energy in the walls where it is converted to x-rays that drive the capsule implosion. Maintaining a spherically symmetric, stable, and efficient drive is a critical challenge and focus of ICF research effort. Our program at the National Ignition Facility has steadily resolved challenges that began with controlling ablative Rayleigh–Taylor instability in implosions, followed by improving hohlraum-capsule x-ray coupling using low gas-fill hohlraums, improving control of time-dependent implosion symmetry, and reducing target engineering feature-generated perturbations. As a result of this program of work, our team is now poised to enter the burning plasma regime.

Theory of alpha heating in inertial fusion: Alpha-heating metrics and the onset of the burning-plasma regime

A detailed and comprehensive 1-dimensional theory of alpha-heating metrics is developed to determine the onset of burning plasma regimes in inertial fusion implosions. The analysis uses an analytic model of the deceleration, stagnation, and burn phases of inertial confinement fusion implosions combined with the results from a database of radiation-hydrodynamic simulations. The onset of the burning-plasma regime occurs when the alpha-heating rate in the hot spot exceeds the compression power input and is represented by the parameter Qα=1/2 α energy/PdV work. A second burning plasma regime is also identified, where the alpha-heating rate exceeds the compression input to the entire stagnated plasma, including the hot spot and confining shell, and is represented by Qαtot. It is shown that progress towards the burning-plasma regime is correlated with the yield enhancement caused by alpha-heating but is more accurately related to the fractional alpha energy fα=1/2 α energy/hot-spot energy. In the analysis presented here, we develop a method to infer these intermediate metrics from experiments and show that the alpha power produced in National Ignition Facility High-Foot implosions is approximately 50% of the external input power delivered to the hot spot and 25% of the total external power (from compression) delivered to the stagnated core.

Alpha Heating and Burning Plasmas in Inertial Confinement Fusion

Assessing the degree to which fusion alpha particles contribute to the fusion yield is essential to understanding the onset of the thermal runaway process of thermonuclear ignition. It is shown that in inertial confinement fusion, the yield enhancement due to alpha particle heating (before ignition occurs) depends on the generalized Lawson parameter that can be inferred from experimental observables. A universal curve valid for arbitrary laser-fusion targets shows the yield amplification due to alpha heating for a given value of the Lawson parameter. The same theory is used to determine the onset of the burning plasma regime when the alpha heating exceeds the compression work. This result can be used to assess the performance of current ignition experiments at the National Ignition Facility.

Alpha Heating and Burning Plasmas in Inertial Confinement Fusion.

Estimating the level of alpha heating and determining the onset of the burning plasma regime is essential to finding the path towards thermonuclear ignition. In a burning plasma, the alpha heating exceeds the external input energy to the plasma. Using a simple model of the implosion, it is shown that a general relation can be derived, connecting the burning plasma regime to the yield enhancement due to alpha heating and to experimentally measurable parameters such as the Lawson ignition parameter. A general alpha-heating curve is found, independent of the target and suitable to assess the performance of all laser fusion experiments whether direct or indirect drive. The onset of the burning plasma regime inside the hot spot of current implosions on the National Ignition Facility requires a fusion yield of about 50kJ.

Nonlinear control and online optimization of the burn condition in ITER via heating, isotopic fueling and impurity injection

The ITER tokamak, the next experimental step toward the development of nuclear fusion reactors, will explore the burning plasma regime in which the plasma temperature is sustained mostly by fusion heating. Regulation of the fusion power through modulation of fueling and external heating sources, referred to as burn control, is one of the fundamental problems in burning plasma research. Active control will be essential for achieving and maintaining desired operating points, responding to changing power demands, and ensuring stable operation. Most existing burn control efforts use either non-model-based control techniques or designs based on linearized models. These approaches must be designed for particular operating points and break down for large perturbations. In this work, we utilize a spatially averaged (zero-dimensional) nonlinear model to synthesize a multi-variable nonlinear burn control strategy that can reject large perturbations and move between operating points. The controller uses all of the available actuation techniques in tandem to ensure good performance, even if one or more of the actuators saturate. Adaptive parameter estimation is used to improve the model parameter estimates used by the feedback controller in real-time and ensure asymptotic tracking of the desired operating point. In addition, we propose the use of a model-based online optimization algorithm to drive the system to a state that minimizes a given cost function, while respecting input and state constraints. A zero-dimensional simulation study is presented to show the performance of the adaptive control scheme and the optimization scheme with a cost function weighting the fusion power and temperature tracking errors.

Nonlinear Burn Control in Tokamak Fusion Reactors via Output Feedback

The next experimental step in the development of nuclear fusion reactors is the ITER tokamak. It is designed to explore the burning plasma regime in which the plasma temperature is sustained mostly by self-heating from fusion reactions. Burn control, the control of fusion power and other reactor parameters through modulation of fueling and heating, will be essential for achieving and maintaining desired operating points and ensuring stability. Design of burn control strategies is made challenging by the multi-variable, highly nonlinear, uncertain nature of the system. Furthermore, due to the extreme conditions in fusion reactors, diagnostic systems may be limited. To deal with these challenges, we propose the use of a nonlinear, multi-variable output feedback control strategy with a proportional-integral observer. A simulation study is carried out to illustrate the performance of the scheme using a set of diagnostics likely to be available in ITER.

Experimental investigation of the confinement of d(3He,p)α and d(d,p)t fusion reaction products in JET

In ITER, magnetic fusion will explore the burning plasma regime. Because such burning plasma is sustained by its own fusion reactions, alpha particles need to be confined (Hazeltine 2010 Fusion Eng. Des. 7–9 85). New experiments using d(3He,p)α and d(d,p)t fusion reaction products were performed in JET. Fusion product loss was measured from MHD-quiescent plasmas with a charged particle activation probe installed at a position opposite to the magnetic field ion gradient drift (see figure )—1.77 m above mid-plane—in the ceiling of JET tokamak. This new kind of escaping ion detector (Bonheure et al 2008 Fusion Sci. Technol. 53 806) provides for absolutely calibrated measurements. Both the mechanism and the magnitude of the loss are dealt with by this research. Careful analysis shows measured loss is in quantitative agreement with predictions from the classical orbit loss model. However, the comparison with simulated loss radial profile, although improved compared with previous studies in TFTR, Princeton, US (Zweben et al 2000 Nucl. Fusion 40 91), is not fully satisfactory and potential explanations for this discrepancy are examined.

Chapter 5: Physics of energetic ions

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137–664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvénic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfvén eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfvén eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfvén eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.