Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.
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Plasma Physics and Controlled Fusion is a monthly publication dedicated to the dissemination of original results on all aspects of plasma physics and associated science and technology.
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T D Arber et al 2015 Plasma Phys. Control. Fusion 57 113001
R J Groebner and S Saarelma 2023 Plasma Phys. Control. Fusion 65 073001
This paper reviews current understanding of key physics elements that control the H-mode pedestal structure, which exists at the boundary of magnetically confined plasmas. The structure of interest is the width, height and gradient of temperature, density and pressure profiles in the pedestal. Emphasis is placed on understanding obtained from combined experimental, theoretical and simulation work and on results observed on multiple machines. Pedestal profiles are determined by the self-consistent interaction of sources, transport and magnetohydrodynamic limits. The heat source is primarily from heat deposited in the core and flowing to the pedestal. This source is computed from modeling of experimental data and is generally well understood. Neutrals at the periphery of the plasma provide the dominant particle source in current machines. This source has a complex spatial structure, is very difficult to measure and is poorly understood. For typical H-mode operation, the achievable pedestal pressure is limited by repetitive, transient magnetohydrodynamic instabilities. First principles models of peeling–ballooning modes are generally able to explain the observed limits. In some regimes, instability occurs below the predicted limits and these remain unexplained. Several mechanisms have been identified as plausible sources of heat transport. These include neoclassical processes for ion heat transport and several turbulent processes, driven by the steep pedestal gradients, as sources of electron and ion heat transport. Reduced models have successfully predicted the pedestal or density at the pedestal top. Firming up understanding of heat and particle transport remains a primary challenge for developing more complete predictive pedestal models.
A Pavone et al 2023 Plasma Phys. Control. Fusion 65 053001
This article reviews applications of Bayesian inference and machine learning (ML) in nuclear fusion research. Current and next-generation nuclear fusion experiments require analysis and modelling efforts that integrate different models consistently and exploit information found across heterogeneous data sources in an efficient manner. Model-based Bayesian inference provides a framework well suited for the interpretation of observed data given physics and probabilistic assumptions, also for very complex systems, thanks to its rigorous and straightforward treatment of uncertainties and modelling hypothesis. On the other hand, ML, in particular neural networks and deep learning models, are based on black-box statistical models and allow the handling of large volumes of data and computation very efficiently. For this reason, approaches which make use of ML and Bayesian inference separately and also in conjunction are of particular interest for today's experiments and are the main topic of this review. This article also presents an approach where physics-based Bayesian inference and black-box ML play along, mitigating each other's drawbacks: the former is made more efficient, the latter more interpretable.
M Giacomin et al 2024 Plasma Phys. Control. Fusion 66 055010
In this work, we present first-of-their-kind nonlinear local gyrokinetic (GK) simulations of electromagnetic turbulence at mid-radius in the burning plasma phase of the conceptual high-β, reactor-scale, tight-aspect-ratio tokamak Spherical Tokamak for Energy Production (STEP). A prior linear analysis in Kennedy et al (2023 Nucl. Fusion63 126061) reveals the presence of unstable hybrid kinetic ballooning modes (KBMs), where inclusion of the compressional magnetic field fluctuation, , is crucial, and subdominant microtearing modes (MTMs) are found at binormal scales approaching the ion-Larmor radius. Local nonlinear GK simulations on the selected surface in the central core region suggest that hybrid KBMs can drive large turbulent transport, and that there is negligible turbulent transport from subdominant MTMs when hybrid KBMs are artificially suppressed (through the omission of ). Nonlinear simulations that include perpendicular equilibrium flow shear can saturate at lower fluxes that are more consistent with the available sources in STEP. This analysis suggests that hybrid KBMs could play an important role in setting the turbulent transport in STEP, and possible mechanisms to mitigate turbulent transport are discussed. Increasing the safety factor or the pressure gradient strongly reduces turbulent transport from hybrid KBMs in the cases considered here. Challenges of simulating electromagnetic turbulence in this high-β regime are highlighted. In particular the observation of radially extended turbulent structures in the absence of equilibrium flow shear motivates future advanced global GK simulations that include .
Nathan Mackey et al 2024 Plasma Phys. Control. Fusion 66 055018
In curved magnetic geometries, field-aligned regions of enhanced plasma pressure and density, termed 'blobs,' move as coherent filaments across the magnetic field lines. Coherent blobs account for a significant fraction of transport at the edges of magnetic fusion experiments and arise in naturally-occurring space plasmas. This work examines the dynamics of blobs with a fully kinetic electromagnetic particle-in-cell code and with a drift-reduced fluid code. In low-beta regimes with moderate blob speeds, good agreement is found in the maximum blob velocity between the two simulation schemes and simple analytical estimates. The fully kinetic code demonstrates that blob speeds saturate near the initial sound speed, which is a regime outside the validity of the reduced fluid model.
D Hachmeister et al 2024 Plasma Phys. Control. Fusion 66 055016
In tokamaks, radial transport is ballooning, meaning it is enhanced at the low-field side (LFS). This work investigates the effect of the magnetic configuration on the high-field side (HFS) scrape-off layer. Our experiments involved L-mode and H-mode discharges at ASDEX Upgrade, in which we scanned the magnetic configuration from a lower to an upper single-null shape, thus varying the location of the secondary separatrix. We show that the secondary separatrix determines the width of the HFS scrape-off layer, meaning that the density is much lower in the region that is magnetically disconnected from the LFS scrape-off layer, outside the secondary separatrix. Furthermore, we observe that the large density often seen in the HFS divertor drastically decreases as the separation between the primary and secondary separatrices falls below a particular value. This value is different for L-mode and H-mode plasmas and closely matches the power decay length measured at the LFS midplane. We also show how the HFS scrape-off layer density is smaller in an upper single-null than in a lower single-null, when the ionic grad-B drift points down. This difference is likely caused by reversing the drifts in the active divertor when switching the active X-point from the bottom to the top. We further observe that the neutral density in the lower divertor also correlates with the plasma shape and the high-density region in the HFS scrape-off layer. During the shape scans analyzed here, the HFS divertor remained partially detached throughout, with transitory reattachment modulated by ELM activity in H-mode. This work provides novel experimental data that can be leveraged to further the modeling capabilities and understanding of scrape-off layer physics in highly shaped plasmas.
Yinlong Guo et al 2024 Plasma Phys. Control. Fusion 66 055012
The discrete and stochastic nature of the processes in the strong-field quantum electrodynamics (SF-QED) regime distinguishes them from classical ones. An important approach to identifying the SF-QED features is through the interaction of extremely intense lasers with plasma. Here, we investigate the seeded QED cascades driven by two counter-propagating laser pulses in the background of residual gases in a vacuum chamber via numerical simulations. We focus on the statistical distributions of positron yields from repeated simulations under various conditions. By increasing the gas density, the positron yields become more deterministic. Although the distribution stems from both the quantum stochastic effects and the fluctuations of the environment, the quantum stochastic effects can be identified via the width of the distribution and the exceptional yields, both of which are higher than the quantum-averaged results. The proposed method provides a statistical approach to identifying the quantum stochastic signatures in SFQED processes using high-power lasers and residual gases in the vacuum chamber.
Y Andrew et al 2024 Plasma Phys. Control. Fusion 66 055009
DIII-D plasmas are compared for two upper divertor configurations: with the outer strike point on the small angle slot (SAS) divertor target and with the outer strike point on the horizontal divertor target (HT). Scanning the vertical distance between the magnetic null point and the divertor target over a range 0.10–0.16 m is shown to increase the threshold power, , and edge plasma power, , for the low-to-high confinement (L–H) and H–L transitions respectively, by up to a factor of 1.4. The X-point height scans were performed at three L-mode core plasma line average electron densities, 1.2, 2.2 and 3.6 , to investigate the density dependence of divertor magnetic configuration influence on . The X-point height, , was further extended across the range 0.16–0.22 m with the more open HT divertor configuration, for which a clear decrease in with increasing is observed. The dependence of on divertor magnetic geometry is further investigated using a time-dependent probability density function (PDF) model and information geometry to elucidate the roles played by pedestal plasma turbulence and perpendicular velocity flows. The degree of stochasticity of the plasma turbulence is observed to be sensitive to the plasma heating rate. The calculated square of the information rate shows changes in the relative density fluctuations and perpendicular velocity PDFs begin 2–5 ms prior to the L–H transition for three plasmas; providing a crucial measurement of the dynamic timescale of external transport barrier formation. Additionally, both information length and rate provide potential predictors of the L–H transition for these plasmas.
O P Bardsley et al 2024 Plasma Phys. Control. Fusion 66 055006
Power exhaust is a critical challenge for spherical tokamak reactors, making the design, optimisation and control of advanced divertor configurations crucial. These tasks are greatly simplified if the poloidal magnetic fields in the core and divertor regions can be varied independently. We present a novel method which facilitates decoupling of the core plasma equilibrium from the divertor geometry optimisation and control, using vacuum spherical harmonic (SH) constraints. This has the advantage that it avoids iterative solution of the Grad–Shafranov equation, making it easy to use, rapid and reliable. By comparing a large number of MAST-U equilibrium reconstructions against their approximations using SHs, a small number () of harmonics is found to be sufficient to closely reproduce the plasma boundary shape. We show experimentally that poloidal field changes designed to leave harmonics unaffected indeed have no effect on the core plasma shape. When augmented with divertor geometry constraints, this approach gives a powerful tool for creating advanced magnetic configurations, and its simplicity brings improvements in speed and robustness when solving coil position optimisation problems. We discuss the clear benefits to real-time feedback control, feed-forward scenario design and coilset optimisation with a view to future reactors.
G L Derks et al 2024 Plasma Phys. Control. Fusion 66 055004
This paper extends a 1D dynamic physics-based model of the scrape-off layer (SOL) plasma, DIV1D, to include the core SOL and possibly a second target. The extended model is benchmarked on 1D mapped SOLPS-ITER simulations to find input settings for DIV1D that allow it to describe SOL plasmas from upstream to target—calibrating it on a scenario and device basis. The benchmark shows a quantitative match between DIV1D and 1D mapped SOLPS-ITER profiles for the heat flux, electron temperature, and electron density within roughly 50% on: (1) the Tokamak Configuration Variable (TCV) for a gas puff scan; (2) a single SOLPS-ITER simulation of the Upgraded Mega Ampere Spherical Tokamak; and (3) the Upgraded Axially Symmetric Divertor EXperiment in Garching Tokamak (AUG) for a simultaneous scan in heating power and gas puff. Once calibrated, DIV1D self-consistently describes dependencies of the SOL solution on core fluxes and external neutral gas densities for a density scan on TCV whereas a varying SOL width is used in DIV1D for AUG to match a simultaneous change in power and density. The ability to calibrate DIV1D on a scenario and device basis is enabled by accounting for cross field transport with an effective flux expansion factor and by allowing neutrals to be exchanged between SOL and adjacent domains.
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A Bierwage et al 2024 Plasma Phys. Control. Fusion 66 065012
It was recently shown that there exists a narrow parameter window where benign sawtooth crashes cause only mixing of bulk plasma and slowed-down alpha particle 'ash', while leaving MeV-class fast alphas largely unperturbed (Bierwage et al 2022 Nat. Commun.13 3941). Here, we revisit the underlying physical picture and reframe it in a manner that may be suitable for systematic analyses of this phenomenon in modeling, simulation and experimental studies. In particular, we propose a graph that we call 'time-helicity de-resonation diagram' (short: T-H diagram) that captures the physical essence of energy-selectivity of sawtooth-particle interactions and visualizes it in a compact, intuitive way. Moreover, the regimes of good confinement and strong mixing during a sawtooth crash can be discerned via a single figure of merit: the T-H radius. The concept is introduced here on the basis of simulation results and would eventually benefit from further validation when applied to suitable empirical data.
R W Brzozowski III and T Stoltzfus-Dueck 2024 Plasma Phys. Control. Fusion 66 065011
The modulated transport model, a model kinetic ion transport equation for the pedestal and scrape-off layer (SOL), is generalized to self-consistently include effects of a single neutral particle species. The neutrals contribute additional transport terms, modifying the -dependent orbit-averaged ion diffusivities of the original work and the resulting predicted intrinsic rotation of the ions. After making simplifying assumptions of the neutral transport, in particular taking the continuous transport limit via a short charge-exchange step expansion, we derive relatively simple analytic expressions that capture the diffusive neutral physics. Within the scope of the model's validity, the neutral-driven intrinsic rotation can compete with the turbulence-driven intrinsic rotation. However, for physically motivated parameters, the neutral-driven intrinsic rotation appears negligible, either on a term-by-term basis or due to a strong cancellation between the neutral-driven momentum diffusion and pinch terms. It appears that a treatment containing finite charge-exchange steps is necessary to capture neutral transport of strong flow momentum into the confined region from the SOL.
Sen Xu et al 2024 Plasma Phys. Control. Fusion 66 065010
This paper presents a novel uncertainty optimization algorithm for the design of line-of-sight (LOS) systems used in tomographic inversion. By extending Gaussian process tomography from discrete pixel space to continuous function space through Bayesian inference, we introduce an uncertainty function and analyze its typical distributions. We develop an algorithm to minimize the uncertainty, which is then applied to optimize the LOS configuration of the internal camera in the ITER project. Uncertainty analysis and phantom testing are conducted to validate the effectiveness of the proposed algorithm. The results demonstrate improved accuracy and stability in tomographic reconstructions. This study contributes to the advancement of LOS design for tomographic inversion, offering a practical solution for optimizing diagnostic systems in complex experimental settings.
Huasheng Xie and Xueyun Wang 2024 Plasma Phys. Control. Fusion 66 065009
Fusion reactivity represents the integration of fusion cross-sections and the velocity distributions of two reactants. In this study, we investigate the upper bound of fusion reactivity for a non-thermal reactant coexisting with a thermal Maxwellian background reactant while maintaining a constant total energy. Our optimization approach involves fine-tuning the velocity distribution of the non-thermal reactant. We employ both Lagrange multiplier and Monte Carlo methods to analyze Deuterium–Tritium (D–T) and proton-Boron11 (p-B11) fusion scenarios. Our findings demonstrate that, within the relevant range of fusion energy, the maximum fusion reactivity can often surpass that of the conventional Maxwellian–Maxwellian reactants case by a substantial margin, ranging from 50% to 300%. These enhancements are accompanied by distinctive distribution functions for the non-thermal reactant, characterized by one or multiple beams. These results not only establish an upper limit for fusion reactivity but also provide valuable insights into augmenting fusion reactivity through non-thermal fusion, which holds particular significance in the realm of fusion energy research.
Yang Li et al 2024 Plasma Phys. Control. Fusion 66 065008
The mission of negative ion-based neutral beam injection (NNBI) is to conduct experiments with pulses lasting thousands of seconds. It is crucial to develop a simplified physical calculation model for the long-pulse negative ion source in the current NNBI device. This model will be used to evaluate the advantages and disadvantages of the selected parameters prior to the experiment, and to assist in adjusting and establishing the experimental parameters for the long-pulse ion source experiment. This paper presents the development of a static performance prediction model using a back propagation neural network. The model assesses the yield of negative hydrogen ions and the quantity of electrons in the ion source under specific parameter conditions, utilizing various experimental parameters as input. The experimental data used for this model are derived from historical data generated during the operation of the 2022 NNBI experiment. The test results indicate that under the current optimal hyperparameter condition, the prediction accuracy of H− ion current (I_H−) is 80.84%, and the prediction accuracy of extraction grid electronic current (I_EG) is 77.57%. This can effectively prevent invalid shots, accurately assess the advantages and disadvantages of the input parameters, and enhance the performance of the long-pulse NNBI device.
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R J Groebner and S Saarelma 2023 Plasma Phys. Control. Fusion 65 073001
This paper reviews current understanding of key physics elements that control the H-mode pedestal structure, which exists at the boundary of magnetically confined plasmas. The structure of interest is the width, height and gradient of temperature, density and pressure profiles in the pedestal. Emphasis is placed on understanding obtained from combined experimental, theoretical and simulation work and on results observed on multiple machines. Pedestal profiles are determined by the self-consistent interaction of sources, transport and magnetohydrodynamic limits. The heat source is primarily from heat deposited in the core and flowing to the pedestal. This source is computed from modeling of experimental data and is generally well understood. Neutrals at the periphery of the plasma provide the dominant particle source in current machines. This source has a complex spatial structure, is very difficult to measure and is poorly understood. For typical H-mode operation, the achievable pedestal pressure is limited by repetitive, transient magnetohydrodynamic instabilities. First principles models of peeling–ballooning modes are generally able to explain the observed limits. In some regimes, instability occurs below the predicted limits and these remain unexplained. Several mechanisms have been identified as plausible sources of heat transport. These include neoclassical processes for ion heat transport and several turbulent processes, driven by the steep pedestal gradients, as sources of electron and ion heat transport. Reduced models have successfully predicted the pedestal or density at the pedestal top. Firming up understanding of heat and particle transport remains a primary challenge for developing more complete predictive pedestal models.
A Pavone et al 2023 Plasma Phys. Control. Fusion 65 053001
This article reviews applications of Bayesian inference and machine learning (ML) in nuclear fusion research. Current and next-generation nuclear fusion experiments require analysis and modelling efforts that integrate different models consistently and exploit information found across heterogeneous data sources in an efficient manner. Model-based Bayesian inference provides a framework well suited for the interpretation of observed data given physics and probabilistic assumptions, also for very complex systems, thanks to its rigorous and straightforward treatment of uncertainties and modelling hypothesis. On the other hand, ML, in particular neural networks and deep learning models, are based on black-box statistical models and allow the handling of large volumes of data and computation very efficiently. For this reason, approaches which make use of ML and Bayesian inference separately and also in conjunction are of particular interest for today's experiments and are the main topic of this review. This article also presents an approach where physics-based Bayesian inference and black-box ML play along, mitigating each other's drawbacks: the former is made more efficient, the latter more interpretable.
Annick Pouquet 2023 Plasma Phys. Control. Fusion 65 033002
Nonlinear phenomena and turbulence are central to our understanding and modeling of the dynamics of fluids and plasmas, and yet they still resist analytical resolution in many instances. However, progress has been made recently, displaying a richness of phenomena, which was somewhat unexpected a few years back, such as double constant-flux cascades of the same invariant for both large and small scales, or the presence of non-Gaussian wings in large-scale fields, for fluids and plasmas. Here, I will concentrate on the direct measurement of the magnitude of dissipation and the evaluation of intermittency in a turbulent plasma using exact laws stemming from invariance principles and involving cross-correlation tensors with both the velocity and the magnetic fields. I will illustrate these points through scaling laws, together with data analysis from existing experiments, observations and numerical simulations. Finally, I will also briefly explore the possible implications for the validity and use of several modeling strategies.
J Citrin and P Mantica 2023 Plasma Phys. Control. Fusion 65 033001
In recent years tokamak experiments and modelling have increasingly indicated that the interaction between suprathermal (fast) ions and thermal plasma can lead to a reduction of turbulence and an improvement of confinement. The regimes in which this stabilization occurs are relevant to burning plasmas, and their understanding will inform reactor scenario optimization. This review summarizes observations, simulations, theoretical understanding, and open questions on this emerging topic.
S M Kaye et al 2021 Plasma Phys. Control. Fusion 63 123001
In this paper, we review the thermal plasma confinement and transport properties observed and predicted in low aspect ratio tokamaks, or spherical tokamaks (STs), which can depart significantly from those observed at higher aspect ratio. In particular, thermal energy confinement scalings show a strong, near linear dependence of energy confinement time on toroidal magnetic field, while the dependence on plasma current is more modest, the opposite of what is seen at higher aspect ratio. STs have revealed a very strong improvement in normalized confinement with decreasing collisionality, much stronger than at higher aspect ratio, which bodes well for an ST-based fusion pilot plant should this trend continue at an even lower collisionality than has already been accessed. These differences arise because of fundamental differences in transport in STs due to the more extreme toroidicity (i.e. reduced region of bad curvature), and to the relatively larger shearing rates, both of which can suppress electrostatic drift wave instabilities at both ion and electron gyroradius scales. In addition, electromagnetic effects are much stronger in STs because they operate at high βT. Gyrokinetic (GK) studies, coupled with low- and high-k turbulence measurements, have shed light on the underlying physics controlling transport. At lower βT, both ion- and electron-scale electrostatic drift turbulence may be responsible for transport. At higher βT, microtearing, kinetic ballooning, and hybrid trapped electron/kinetic ballooning modes increasingly play a role, and they have a much stronger impact in the core of ST plasmas than at higher aspect ratio. Flow shear affects the balance between ion- and electron-scale modes. Non-linear GK simulations find regimes where the electron heat flux decreases with decreasing collisionality, consistent with the experimental global normalized confinement scaling. The ST is unique in that the relatively low toroidal magnetic field allows for localized measurements of electron-scale turbulence, and this coupled with turbulence measurements at ion-scales has facilitated detailed comparisons with GK simulations. These data have provided compelling evidence for the presence of ion temperature gradient and electron temperature gradient turbulence in some plasmas, and direct experimental support for the impact of experimental actuators like rotation shear, density gradient and magnetic shear on turbulence and transport.
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Rueda-Rueda et al
In this paper we demonstrate how the inversion, in energy and major radius (E, R) coordinates, of imaging
neutral particle analyser (INPA) measurements can be used to obtain the fast-ion distribution. The INPA is
most sensitive to passing ions with energies in the range (20-150) keV and pitches near 0.5 in the core and 0.7
near the plasma edge. Inversion of synthetic signals, via 0th -order Tikhonov and Elastic Net regularization,
were performed to demonstrate the capability of recovering the ground truth fast-ion 2D phase-space distri-
bution resolved in major radius and energy, even in the presence of moderate noise levels (10%). Finally,
we apply our method to measure the 2D phase-space distribution in an MHD quiescent plasma at ASDEX
Upgrade and find good agreement with the neoclassical fast-ion distribution predicted by TRANSP.
Qiu et al
In 2021, EAST was equipped with a full-ring divertor coil to facilitate research on the fish tail divertor (FTD) concept. Initially, it was observed that the coil current had a negligible ability to sweep the strike point. Conversely, when the amplitude and frequency of the alternating current were marginally increased, there was a significant interruption to plasma control. This perturbation was attributed to the poloidal control field's limited response rate to the coil's fluctuations. To address this issue, novel control methodologies were devised to ensure stable and effective sweeping of the strike point using the divertor coil. The devised methods are twofold: For high-frequency strike point control, a low-pass filter decoupling technique based on ISOFLUX control strategy enabled achieving a sweeping frequency of 100 Hz. This strategy allowed for consistent plasma management without compromising average stored energy or density regulation. Resulting from this proficient manipulation of the strike point, a reduction in the peak temperature of the divertor plate was observed. For low-frequency sweeping, a static Multi-Input Multi-Output (MIMO) decoupling approach was developed, facilitating concurrent sweeping of both the outer and inner strike points.
Habib et al
A magnetized nonthermal electron-positron-ion (e-p-i) plasma is considered to study the propagation properties of ion-acoustic solitary and shock waves in the presence of trapped positrons and electrons for the first time. The Schamel-$\kappa$ (kappa) distribution function describing the plasma nonthermality as well as particle trapping is assumed to consider electrons and positrons. The diffusive effect of ion plasma fluid, which is responsible for shock dynamics is taken into account. A nonlinear Schamel-Korteweg-de Vries-Burgers' (SKdVB) equation is derived by employing the reductive perturbation approach, and the solitary and shock wave solutions of the SKdVB equation have also been derived for different limiting cases. It is found that only positive potential nonlinear structures (for both solitary and shock waves) are formed in the proposed plasma system. The condition for stable solitons in the absence of dissipation is analysed and the nature of arbitrary amplitude solitary waves (obtained via the Sagdeev potential approach) is discussed. It is investigated theoretically and numerically that different plasma compositional parameters [such as the trapping effect of electrons ($\beta_e$) and positrons ($\beta_p$), the obliquity effect ($\theta$), electron-to-ion number density ratio ($\mu_e$), the magnetic field effect (via $\Omega$) and the viscous effect ( via $\eta$)] have significant influence on the dynamics ion-acoustic solitary and shock waves. The theoretical and numerical investigations in this study may be helpful in describing the nature of localised structures in different plasma contexts, e.g., space and astrophysical plasmas, experimental plasmas where electron-positron-ion plasmas exist.
Munaretto et al
Achieving ELM suppression in spherical tokamaks by applying resonant magnetic perturbations (RMP) has proven challenging. The poloidal spectrum of the applied RMP is a key parameter that has an impact on the capability to mitigate and eventually suppress ELMs. In this work the resistive magnetohydrodynamic (MHD) code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681 ) is used to evaluate the possibility of directly measuring the plasma response in MAST-U, and particularly its variation as function of the applied poloidal spectrum, in order to guide the experimental validation of the predicted best RMP configuration for ELM suppression. Toroidal mode number n=2 RMP is considered to minimize the presence of sidebands, and to avoid the deleterious core coupling of n=1. Singular Value Decomposition is used to highlight linearly independent structures in the simulated magnetic 3D fields and how those structures can be measured at the wall where the magnetic sensors are located. Alternative ways to measure the multimodal plasma response and how they can be used to infer the best RMP configuration to achieve ELM suppression are also presented, including the plasma displacement and the 3D footprints at the divertor plates.
Robinson
It is argued that fusion chain reactions in the D-D system is feasible with
supra-thermal deuterons in the MeV regime, with new generations of deuterons being
generated either via neutron-deuteron or proton-deuteron collisions. The propagation of
supra-thermal deuterons in an infinite, hot, dense deuterium target was studied using a
Monte Carlo method that includes multiple nuclear reactions, electron and ion stopping,
along with neutron and proton knock-ons. Over a wide range of densities we observed
significant, albeit sub-critical chain reactions in the multi-keV temperature regime. At very
high densities (over 1000 gcm −3 ) and temperatures (over 40keV) we observed chain reactions
that reached criticality. These results suggest that there is a case to re-assess the potential
of ICF based on deuterium-heavy targets.
Open all abstracts, in this tab
A Bierwage et al 2024 Plasma Phys. Control. Fusion 66 065012
It was recently shown that there exists a narrow parameter window where benign sawtooth crashes cause only mixing of bulk plasma and slowed-down alpha particle 'ash', while leaving MeV-class fast alphas largely unperturbed (Bierwage et al 2022 Nat. Commun.13 3941). Here, we revisit the underlying physical picture and reframe it in a manner that may be suitable for systematic analyses of this phenomenon in modeling, simulation and experimental studies. In particular, we propose a graph that we call 'time-helicity de-resonation diagram' (short: T-H diagram) that captures the physical essence of energy-selectivity of sawtooth-particle interactions and visualizes it in a compact, intuitive way. Moreover, the regimes of good confinement and strong mixing during a sawtooth crash can be discerned via a single figure of merit: the T-H radius. The concept is introduced here on the basis of simulation results and would eventually benefit from further validation when applied to suitable empirical data.
Jose Rueda-Rueda et al 2024 Plasma Phys. Control. Fusion
In this paper we demonstrate how the inversion, in energy and major radius (E, R) coordinates, of imaging
neutral particle analyser (INPA) measurements can be used to obtain the fast-ion distribution. The INPA is
most sensitive to passing ions with energies in the range (20-150) keV and pitches near 0.5 in the core and 0.7
near the plasma edge. Inversion of synthetic signals, via 0th -order Tikhonov and Elastic Net regularization,
were performed to demonstrate the capability of recovering the ground truth fast-ion 2D phase-space distri-
bution resolved in major radius and energy, even in the presence of moderate noise levels (10%). Finally,
we apply our method to measure the 2D phase-space distribution in an MHD quiescent plasma at ASDEX
Upgrade and find good agreement with the neoclassical fast-ion distribution predicted by TRANSP.
R W Brzozowski III and T Stoltzfus-Dueck 2024 Plasma Phys. Control. Fusion 66 065011
The modulated transport model, a model kinetic ion transport equation for the pedestal and scrape-off layer (SOL), is generalized to self-consistently include effects of a single neutral particle species. The neutrals contribute additional transport terms, modifying the -dependent orbit-averaged ion diffusivities of the original work and the resulting predicted intrinsic rotation of the ions. After making simplifying assumptions of the neutral transport, in particular taking the continuous transport limit via a short charge-exchange step expansion, we derive relatively simple analytic expressions that capture the diffusive neutral physics. Within the scope of the model's validity, the neutral-driven intrinsic rotation can compete with the turbulence-driven intrinsic rotation. However, for physically motivated parameters, the neutral-driven intrinsic rotation appears negligible, either on a term-by-term basis or due to a strong cancellation between the neutral-driven momentum diffusion and pinch terms. It appears that a treatment containing finite charge-exchange steps is necessary to capture neutral transport of strong flow momentum into the confined region from the SOL.
Qinglai Qiu et al 2024 Plasma Phys. Control. Fusion
In 2021, EAST was equipped with a full-ring divertor coil to facilitate research on the fish tail divertor (FTD) concept. Initially, it was observed that the coil current had a negligible ability to sweep the strike point. Conversely, when the amplitude and frequency of the alternating current were marginally increased, there was a significant interruption to plasma control. This perturbation was attributed to the poloidal control field's limited response rate to the coil's fluctuations. To address this issue, novel control methodologies were devised to ensure stable and effective sweeping of the strike point using the divertor coil. The devised methods are twofold: For high-frequency strike point control, a low-pass filter decoupling technique based on ISOFLUX control strategy enabled achieving a sweeping frequency of 100 Hz. This strategy allowed for consistent plasma management without compromising average stored energy or density regulation. Resulting from this proficient manipulation of the strike point, a reduction in the peak temperature of the divertor plate was observed. For low-frequency sweeping, a static Multi-Input Multi-Output (MIMO) decoupling approach was developed, facilitating concurrent sweeping of both the outer and inner strike points.
Stefano Munaretto et al 2024 Plasma Phys. Control. Fusion
Achieving ELM suppression in spherical tokamaks by applying resonant magnetic perturbations (RMP) has proven challenging. The poloidal spectrum of the applied RMP is a key parameter that has an impact on the capability to mitigate and eventually suppress ELMs. In this work the resistive magnetohydrodynamic (MHD) code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681 ) is used to evaluate the possibility of directly measuring the plasma response in MAST-U, and particularly its variation as function of the applied poloidal spectrum, in order to guide the experimental validation of the predicted best RMP configuration for ELM suppression. Toroidal mode number n=2 RMP is considered to minimize the presence of sidebands, and to avoid the deleterious core coupling of n=1. Singular Value Decomposition is used to highlight linearly independent structures in the simulated magnetic 3D fields and how those structures can be measured at the wall where the magnetic sensors are located. Alternative ways to measure the multimodal plasma response and how they can be used to infer the best RMP configuration to achieve ELM suppression are also presented, including the plasma displacement and the 3D footprints at the divertor plates.
Alex P L Robinson 2024 Plasma Phys. Control. Fusion
It is argued that fusion chain reactions in the D-D system is feasible with
supra-thermal deuterons in the MeV regime, with new generations of deuterons being
generated either via neutron-deuteron or proton-deuteron collisions. The propagation of
supra-thermal deuterons in an infinite, hot, dense deuterium target was studied using a
Monte Carlo method that includes multiple nuclear reactions, electron and ion stopping,
along with neutron and proton knock-ons. Over a wide range of densities we observed
significant, albeit sub-critical chain reactions in the multi-keV temperature regime. At very
high densities (over 1000 gcm −3 ) and temperatures (over 40keV) we observed chain reactions
that reached criticality. These results suggest that there is a case to re-assess the potential
of ICF based on deuterium-heavy targets.
Qian Xia et al 2024 Plasma Phys. Control. Fusion
Tokamak edge turbulence is crucial for the cross-field transport of particles and energy away from the separatrix. A better understanding of what affects the turbulence helps to control the heat flux to the divertor targets and the wall. One potentially important factor is the ion particle source in the divertor, as the neutral pathways and the ionisation source distributions are different depending on the divertor geometry, e.g., vertical- and horizontal-target configurations. Numerically, how to represent the sources and mimic the effects on the SOL in the simulations is still an open question. In this paper, we use a 3D turbulence code STORM, based on drift-reduced Braginskii equations, to study the effects of the divertor particle source distribution on turbulence in a simplified 3D slab geometry. The results show that it requires a large amount of divertor particle source to be peaked near the separatrix to alter the heat flux deposited on the target in attached conditions. This large non-uniform particle source can locally enhance the turbulence in the divertor volume, which redistributes the energy flux to the target and reduces the maximum amplitude. Meanwhile, the plasma profiles evaluated at the outboard midplane, such as the amplitudes and fluctuations of the density and temperature, are marginally changed. Another consequence of our results is that the prediction of the temperature difference between the outboard midplane and the target would be underestimated, if the calculation only considers the conductive heat flux and ignores this enhanced cross-field transport in the divertor.
Yuqiang Tao et al 2024 Plasma Phys. Control. Fusion
Low-frequency drift-wave instabilities play an important role in the radial transport of present tokamaks, and trapped electron collisions can significantly influence the instabilities. In this paper, the effects of trapped electron collisions on these instabilities are investigated based on linear gyro-kinetic simulation. The basic numerical techniques including dispersion relation integral method and orthogonal basis function expansion are presented in detail with necessary benchmark work. The results show that in medium gradients, the increase of trapped electron proportion promotes the growth rate and radial heat transport largely for quasi-linear TEMs and ITG modes, and trapped electron collisions have strong stabilizing effects, especially for the TEMs driven by electron temperature gradient. Two distinctive branches, named as Mode \#1 and \#2, are investigated in steep gradients. Both behave varied instability nature during different range of normalized wave vector $\hat{k}_{\theta}$. Mode \#1 mainly induces radial heat transport during $\hat{k}_{\theta}<0.5$, and is significantly suppressed by the collisions. Mode \#2 mainly induces the radial heat transport during 0.4<$\hat{k}_{\theta}<0.8$, and is largely enhanced by the collisions. When the collisionality is large enough, Mode \#2 has stronger transport capacity than the other. Mode \#2 at medium wave vector, known as DTEM, may be the mechanism of the ECM observed in EAST H-mode plasmas, in which the collisionality plays an important role in the mode excitation.
O Février et al 2024 Plasma Phys. Control. Fusion 66 065005
In recent years, negative triangularity (NT) has emerged as a potential high-confinement L-mode reactor solution. In this work, detachment is investigated using core density ramps in lower single null Ohmic L-mode plasmas across a wide range of upper, lower, and average triangularity (the mean of upper and lower triangularity: δ) in the TCV tokamak. It is universally found that detachment is more difficult to access for NT shaping. The outer divertor leg of discharges with could not be cooled to below through core density ramps alone. The behavior of the upstream plasma and geometrical divertor effects (e.g. a reduced connection length with negative lower triangularity) do not fully explain the challenges in detaching NT plasmas. Langmuir probe measurements of the target heat flux widths (λq) were constant to within 30% across an upper triangularity scan, while the spreading factor S was lower by up to 50% for NT, indicating a generally lower integral scrape-off layer width, λint. The line-averaged core density was typically higher for NT discharges for a given fuelling rate, possibly linked to higher particle confinement in NT. Conversely, the divertor neutral pressure and integrated particle fluxes to the targets were typically lower for the same line-averaged density, indicating that NT configurations may be closer to the sheath-limited regime than their PT counterparts, which may explain why NT is more challenging to detach.
Dimitrios A Kaltsas et al 2024 Plasma Phys. Control. Fusion
We derive axisymmetric equilibrium equations in the context of the hybrid Vlasov model with kinetic ions and massless fluid electrons, assuming isothermal electrons and deformed Maxwellian distribution functions for the kinetic ions. The equilibrium system comprises a Grad-Shafranov partial differential equation and an integral equation. These equations can be utilized to calculate the equilibrium magnetic field and ion distribution function, respectively, for given particle density or given ion and electron toroidal current density profiles. The resulting solutions describe states characterized by toroidal plasma rotation and toroidal electric current density. Additionally, due to the presence of fluid electrons, these equilibria also exhibit a poloidal current density component. This is in contrast to the fully kinetic Vlasov model, where axisymmetric Jeans equilibria can only accommodate toroidal currents and flows, given the absence of a third integral of the microscopic motion.