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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Physics Basis, Optimization, and Control for Integrated 3D Edge Long-pulse Tokamak Scenarios

The aim of this project with international collaborations (PI: J.-K. Park of Princeton Plasma Physics Laboratory) is to develop a unified physics basis and predictive capability for the control of edge-localized modes (ELMs) with optimized non-axisymmetric (3D) fields, by leveraging the unique research capabilities of international KSTAR tokamak in Korea. At the University of California, Irvine, we use a fusion simulation code GTC to study the effects of the 3D magnetic fields (including both magnetic islands and stochastic magnetic field lines) on microturbulence. We focus on the effects of 3D equilibrium on turbulent and neoclassical transport that leads to ELM suppression. During the project period, the UCI team of this collaboration has made significant progress in understanding turbulent transport in 3D geometry including both tokamaks with RMP and stellarators. Four UCI postdoctoral researchers, Drs. Javier Nicolau, Gyungjin Choi, Pengfei Liu, and Xishuo Wei were partially supported by this project and collaborating with the entire project team. We have published 4 journal papers and gave several invited talks. This project advance physics understand of 3D effects on microturbulence, specially effects of magnetic islands. It will contribute to the DOE SciDAC ISEP project in the area of GTC development for general 3D geometry capability, rigorous verification and validation, and readiness for the emerging exascale computing. Through collaborations with computational scientists, the project helps to advance high performance computing in the area of GPU acceleration, linear solver, and data management.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

THE MECHANISMS OF ELECTRON ACCELERATION DURING MULTIPLE X LINE MAGNETIC RECONNECTION WITH A GUIDE FIELD

The interactions between magnetic islands are considered to play an important role in electron acceleration during magnetic reconnection. In this paper, two-dimensional particle-in-cell simulations are performed to study electron acceleration during multiple X line reconnection with a guide field. Because the electrons remain almost magnetized, we can analyze the contributions of the parallel electric field, Fermi, and betatron mechanisms to electron acceleration during the evolution of magnetic reconnection through comparison with a guide-center theory. The results show that with the magnetic reconnection proceeding, two magnetic islands are formed in the simulation domain. Next, the electrons are accelerated by both the parallel electric field in the vicinity of the X lines and the Fermi mechanism due to the contraction of the two magnetic islands. Then, the two magnetic islands begin to merge into one, and, in such a process, the electrons can be accelerated by both the parallel electric field and betatron mechanisms. During the betatron acceleration, the electrons are locally accelerated in the regions where the magnetic field is piled up by the high-speed flow from the X line. At last, when the coalescence of the two islands into one big island finishes, the electrons can be further accelerated by the Fermi mechanism because of the contraction of the big island. With the increase of the guide field, the contributions of the Fermi and betatron mechanisms to electron acceleration become less and less important. When the guide field is sufficiently large, the contributions of the Fermi and betatron mechanisms are almost negligible.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Thermal island destabilization and the Greenwald limit

Magnetic reconnection is ubiquitous in the magnetosphere, the solar corona, and in toroidal fusion research discharges. A magnetic island saturates at a width which produces a minimum in the magnetic energy of the configuration is evident in a fusion device. At saturation, the modified current density profile, a function of the flux in the island, is essentially flat, the growth rate proportional to the difference in the current at the O-point and the X-point. Furthermore, modification of the current density profile in the island interior causes a change in the island stability and additional growth or contraction of the saturated island. Because field lines in an island are isolated from the outside plasma, an island can heat or cool preferentially depending on the balance of Ohmic heating and radiation loss in the interior, changing the resistivity and hence the current in the island. A simple model of island destabilization due to radiation cooling of the island is constructed, and the effect of modification of the current within an island is calculated. In addition destabilization effect is described, and it is shown that a small imbalance of heating can lead to exponential growth of the island. A destabilized magnetic island near the plasma edge can lead to plasma loss, and because the radiation is proportional to plasma density and charge, this effect can cause an impurity dependent density limit.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection. I. Macroscopic effects of the electron flows

In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (b{sub g}). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (β{sub i} = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (b{sub g} ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (b{sub g} ≳ 5). Kinetic PIC simulations using guide fields b{sub g} ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (β{sub i} = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (b{sub g} ≲ 3)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Two-stage crash process in resistive drift ballooning mode driven ELM crash

We report a two-stage crash process in edge localized mode (ELM) driven by resistive drift-ballooning modes (RDBMs) numerically simulated in a full annular torus domain with a scale-separated four-field reduced MHD (RMHD) model using the BOUT++ framework. In the early nonlinear phase, the small first crash is triggered by linearly unstable RDBMs, and m/n=2/1 magnetic islands are nonlinearly excited by nonlinear coupling of RDBMs as well as their higher harmonics. Here, m is the poloidal mode number, n is the toroidal mode number, the q = 2 rational surface exists near the pressure gradient peak, and q is the safety factor. Simultaneously, middle-n RDBM turbulence develops but is poloidally localized around X-points of the magnetic islands, leading to the small energy loss. The second large crash occurs in the late nonlinear phase. Higher harmonics of m/n=2/1 magnetic islands well develop around the q = 2 surface via nonlinear coupling and make the magnetic field stochastic by magnetic island overlapping. Turbulence heat transport develops at X-points of higher harmonics of m/n=2/1 magnetic islands, resulting in the turbulence spreading in the poloidal direction. The large second crash is triggered when the turbulence covers the whole poloidal region so that the magnetic island generation and magnetic field stochastization before the large crash can be interpreted as ELM precursors. It is concluded that the ELM trigger is attributed to the turbulent spreading in the poloidal direction in synchronization with the magnetic field stochastization and the crash is driven by E × B convection rather than the conventional Rechester–Rosenbluth anomalous electron heat transport.

Seto, H. (ORCID:0000000259278643)↗
DOE OSTI2016

Fast island phase identification for tearing mode feedback control on J-TEXT tokamak

A new method to control the tearing mode (TM) in tokamaks has been proposed [Q. Hu and Q. Yu, Nucl. Fusion 56, 034001 (5pp.) (2016)], according to which, the external resonant magnetic perturbation needs to be applied in certain magnetic island phase regions. Therefore, it is very important to identify the helical phase of magnetic islands in real time. The TM in tokamak plasmas is normally rotating and carries magnetic oscillations, which are known as Mirnov oscillations and can be detected by Mirnov probes. When the O-point or X-point of the magnetic island passes through the probe, the signal will experience a zero-crossing. A poloidal Mirnov probe array and a corresponding island phase identification method are presented. A field-programmable gate array is used to provide the magnetic island helical phase in real time by using multichannel zero crossing detection. This system has been developed on the J-TEXT tokamak and works well. This paper introduces the establishment of the fast magnetic island phase identifying system.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Blob Formation and Ejection in Coronal Jets due to the Plasmoid and Kelvin–Helmholtz Instabilities

We perform 2D resistive magnetohydrodynamic simulations of coronal jets driven by flux emergence along the lower boundary. The reconnection layers are susceptible to the formation of blobs that are ejected in the jet. Our simulation with low plasma β (Case I) shows that magnetic islands form easily and propagate upward in the jet. These islands are multithermal and thus are predicted to show up in hot channels (335 Å and 211 Å) and the cool channel (304 Å) in observations by the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory . The islands have maximum temperatures of 8 MK, lifetimes of 120 s, diameters of 6 Mm, and velocities of 200 km s{sup −1}. These parameters are similar to the properties of blobs observed in extreme-ultraviolet (EUV) jets by AIA. The Kelvin–Helmholtz instability develops in our simulation with moderately high plasma β (Case II) and leads to the formation of bright vortex-like blobs above the multiple high magnetosonic Mach number regions that appear along the jet. These vortex-like blobs can also be identified in the AIA channels. However, they eventually move downward and disappear after the high magnetosonic Mach number regions disappear. In the lower plasma β case, the lifetime for the jet is shorter, the jet and magnetic islands are formed with higher velocities and temperatures, the current-sheet fragments are more chaotic, and more magnetic islands are generated. Our results show that the plasmoid instability and Kelvin–Helmholtz instability along the jet are both possible causes of the formation of blobs observed at EUV wavelengths.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Effects of edge-localized electron cyclotron current drive on edge-localized mode suppression by resonant magnetic perturbations in DIII-D

Abstract According to recent DIII-D experiments (Logan et al 2024 Nucl. Fusion 64 014003), injecting edge localized electron cyclotron current drive (ECCD) in the counter-plasma-current (counter- I p ) direction reduces the n = 3 resonant magnetic perturbation (RMP) current threshold for edge-localized mode (ELM) suppression, while co- I p ECCD during the suppressed ELM phase causes a back transition to ELMing. This paper presents nonlinear two-fluid simulations on the ECCD manipulation of edge magnetic islands induced by RMP using the TM1 code. In the presence of a magnetic island chain at the pedestal-top, co- I p ECCD is found to decrease the island width and restore the initially degraded pedestal pressure when its radial deposition location is close to the rational surface of the island. With a sufficiently strong co- I p ECCD current, the RMP-driven magnetic island can be healed, and the pedestal pressure fully recovers to its initial ELMing state. On the contrary, counter- I p ECCD is found to increase the island width and further reduce the pedestal pressure to levels significantly below the peeling-ballooning-mode limited height, leading to even stationary ELM suppression. These simulations align with the results from DIII-D experiments. However, when multiple magnetic island chains are present at the pedestal-top, the ECCD current experiences substantial broadening, and its effects on the island width and pedestal pressure become negligible. Further simulations reveal that counter- I p ECCD enhances RMP penetration by lowering the penetration threshold, with the degree of reduction proportional to the amplitude of ECCD current. For the ∼1 MW ECCD in DIII-D, the predicted decrease in the RMP penetration threshold for ELM suppression is approximately 20%, consistent with experimental observations. These simulations indicate that edge-localized ECCD can be used to either facilitate RMP-driven ELM suppression or optimize the confinement degradation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Plasma response to rotating resonant magnetic perturbations with a locked mode in the J-TEXT tokamak

Disruption affected by locked modes (LMs) is one of the most critical issues to be solved for tokamak fusion reactors. This paper aimed to understand the plasma response to external rotating resonant magnetic perturbations (RMPs), which are applied at a few kilohertz for controlling the pre-existing LMs. In the J-TEXT tokamak, the plasma response to a rotating RMP showed a feature of travelling wave, if no tearing mode (TM) existed. With a LM, the application of a rotating RMP led to unique features of plasma responses, which could be roughly described by the formula δb θ (θ, t)=2Asin(mθ–mθ O )cos(2πf RRMP t), where δb θ , A, m, θ O and f RRMP are the perturbed poloidal magnetic field, the amplitude, the poloidal mode number, the poloidal location of the TM's O-point and the frequency of the rotating RMP. These features are analogous to that of a standing wave in the TM rest frame, with the nodes locating at the O-/X- points. The perturbations of electron temperature, T e , due to plasma responses were zero or minimal inside the magnetic island or outside the magnetic island but at the same poloidal positions as the O-/X- points. Both δb θ and the T e perturbations increased linearly with the rotating RMP. A phenomenological model is presented that the rotating RMP drives the phase oscillation of the TM by applying a periodical electromagnetic torque. Then the phase oscillation of TM, combined with the poloidal gradient of the plasma parameters, induces the plasma response measured experimentally. The nonlinear numerical modelling confirmed the forced phase oscillation of the TM, and qualitatively verified the amplitude and phase dependences among the plasma response, the phase oscillation of the TM and the rotating RMP, which have been predicted by the model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Model for current drive induced crash cycles in W7-X

In the Wendelstein 7-X (W7-X) stellarator, the vacuum rotational transform, ι, has a flat radial profile and does not cross any major rational resonance. Nevertheless, during plasma operation the ι–profile can be strongly modified by electron cyclotron current drive in such a way that the resulting ι-profile passes through low-order rational values, and this can trigger magnetohydrodynamic (MHD) events. Indeed, W7-X plasmas are sometimes subject to repetitive collapses of core confinement, which can be observed regardless of the direction in which the EC current is driven. Even though the origin of these MHD instabilities is under investigation, the crashes may be connected to the formation of magnetic islands and magnetic reconnection. In the present work, we try to shed light on the dynamics of different events happening during the course of sawtooth cycles in W7-X by proposing a model that combines a slow current diffusion with a recipe for fast relaxation that conserves the corresponding helical flux (Kadomtsev 1975 Fiz. Plazmy 1 710–15). We also propose a simple model based on Taylor relaxation (Taylor 1974 Phys. Rev. Lett. 33 1139), (Taylor 1986 Rev. Mod. Phys. 58 741) to predict the nonlinear redistribution of plasma current caused by the largest of the observed events.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Numerical simulation of runaway electrons: 3-D effects on synchrotron radiation and impurity-based runaway current dissipation

Numerical simulations of runaway electrons (REs) with a particular emphasis on orbit dependent effects in 3-D magnetic fields are presented. The simulations were performed using the recently developed Kinetic Orbit Runaway electron Code (KORC) that computes the full-orbit relativistic dynamics in prescribed electric and magnetic fields including radiation damping and collisions. The two main problems of interest are synchrotron radiation and impurity-based RE dissipation. Synchrotron radiation is studied in axisymmetric fields and in 3-D magnetic configurations exhibiting magnetic islands and stochasticity. For passing particles in axisymmetric fields, neglecting orbit effects might underestimate or overestimate the total radiation power depending on the direction of the radial shift of the drift orbits. For trapped particles, the spatial distribution of synchrotron radiation exhibits localized “hot” spots at the tips of the banana orbits. In general, the radiation power per particle for trapped particles is higher than the power emitted by passing particles. The spatial distribution of synchrotron radiation in stochastic magnetic fields, obtained using the MHD code NIMROD, is strongly influenced by the presence of magnetic islands. 3-D magnetic fields also introduce a toroidal dependence on the synchrotron spectra, and neglecting orbit effects underestimates the total radiation power. In the presence of magnetic islands, the radiation damping of trapped particles is larger than the radiation damping of passing particles. Results modeling synchrotron emission by RE in DIII-D quiescent plasmas are also presented. The computation uses EFIT reconstructed magnetic fields and RE energy distributions fitted to the experimental measurements. Qualitative agreement is observed between the numerical simulations and the experiments for simplified RE pitch angle distributions. However, it is noted that to achieve quantitative agreement, it is necessary to use pitch angle distributions that depart from simplified 2-D Fokker-Planck equilibria. Finally, using the guiding center orbit model (KORC-GC), a preliminary study of pellet mitigated discharges in DIII-D is presented. The dependence of RE energy decay and current dissipation on initial energy and ionization levels of neon impurities is studied. Furthermore, the computed decay rates are within the range of experimental observations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Runaway electron transport in stochastic toroidal magnetic fields

Here, we study the transport and confinement properties of runaway electrons (RE) in the presence of magnetic fields with perturbations producing different levels of stochasticity. We use Kinetic Orbit Runaway Electron Code (KORC) [Carbajal et al. , Phys. Plasmas 24, 042512 (2017) and del-Castillo-Negrete et al. , Phys. Plasmas 25, 056104 (2018)] for simulating the full-orbit (FO) and guiding-center (GC) dynamics of RE in perturbed magnetic fields that exhibit magnetic islands. We extend previous works on this problem [Wingen et al. , Nucl. Fusion 46, 941 (2006); Izzo et al. , Nucl. Fusion 51, 063032 (2011); Papp et al. , Nucl. Fusion 51, 043004 (2011); V. Izzo and P. Parks, Phys. Plasmas 24, 060705 (2017); and Sommariva et al. , Nucl. Fusion 58, 016043 (2018)] by studying in detail full-orbit effects on the RE dynamics. We quantify FO effects on RE transport by performing one-to-one comparisons between FO and GC simulations. It is found that, for the magnetic field configurations considered, GC simulations predict twice the RE losses of FO simulations for 1 MeV and four times the RE losses of FO simulations for 25 MeV. Similarly, we show how different GC and FO dynamics of RE moving around magnetic islands can be, especially in the scenario where the RE Larmor radius is on the order of the size of the magnetic island. We also study the role of rotation of the magnetic islands on RE confinement, and we find that low-frequency toroidal rotation has no observable effect on RE transport in the cases considered. These results shed some light into the potential of avoidance or mitigation mechanisms based on magnetic perturbations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Error field measurements with rotating RMP fields for DIII-D H-mode

3D magnetic sensors are employed to identify the amplitude and toroidal phase of error fields (EF) by analyzing the torque balance for magnetic islands entrained by rotating resonant magnetic perturbations (RMPs) in DIII-D H-mode plasmas. This technique of torque balance allows for efficient error field identification, offering a valuable tool for scenario-specific and optimized error field compensation (EFC) and requires only magnetic diagnostics. The torque balance used in this work includes the contribution from electromagnetic torque due to error fields, wall response, RMP fields, and viscous. Results show that viscous torque plays a crucial role, particularly during locked modes and H-mode plasmas, ensuring accurate data fits with lower residuals. The torque balance technique reveals that the L- and H-mode plasmas have distinct EF configurations, and consistent with a model-based EF analysis including MHD response in IPEC and the SURFMN EF simulation. This technique shows great robustness in measuring the intrinsic EF amplitude regardless of its amplitude or toroidal phase. Repeated discharges with EFC disparities exhibit consistent results of intrinsic error field within a reasonable range near the “standard” error field compensation. Additionally, the use of a rotating n = 1 resonant magnetic perturbation offers the advantage of reducing disruption risks by entraining saturated magnetic islands. These findings are instrumental for optimizing EF correction in fusion devices, thereby enhancing tearing mode suppression and overall plasma stability.

3D magnetic sensors↗
DOE OSTI2016

Non-perturbative measurement of cross-field thermal diffusivity reduction at the O-point of 2/1 neoclassical tearing mode islands in the DIII-D tokamak

Neoclassical tearing modes (NTMs) often lead to the decrease of plasma performance and can lead to disruptions, which makes them a major impediment in the development of operating scenarios in present toroidal fusion devices. Recent gyrokinetic simulations predict a decrease of plasma turbulence and cross-field transport at the O-point of the islands, which in turn affects the NTM dynamics. In this paper, a heat transport model of magnetic islands employing spatially non-uniform cross-field thermal diffusivity (χ{sub ⊥}) is presented. This model is used to derive χ{sub ⊥} at the O-point from electron temperature data measured across 2/1 NTM islands in DIII-D. It was found that χ{sub ⊥} at the O-point is 1 to 2 orders of magnitude smaller than the background plasma transport, in qualitative agreement with gyrokinetic predictions. As the anomalously large values of χ{sub ⊥} are often attributed to turbulence driven transport, the reduction of the O-point χ{sub ⊥} is consistent with turbulence reduction found in recent experiments. Finally, the implication of reduced χ{sub ⊥} at the O-point on NTM dynamics was investigated using the modified Rutherford equation that predicts a significant effect of reduced χ{sub ⊥} at the O-point on NTM saturation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Analytical model for quasi-linear flow response to resonant magnetic perturbation in resistive-inertial and viscous-resistive regimes

In this work, a quasi-linear model for plasma flow response to the resonant magnetic perturbation (RMP) in a tokamak has been rigorously developed in the resistive-inertial (RI) and viscousresistive (VR) regimes purely from the two-field reduced MHD model. Models for plasma response to RMP are commonly composed of equations for the resonant magnetic field response (i.e. the magnetic island) and the torque balance of plasma flow. However, in previous plasma response models, the magnetic island and the torque balance equations are often derived separately from reduced MHD and full MHD equations, respectively. By contrast, in this work we derive both the magnetic island response and the torque balance equations in a quasi-linear model for plasma flow response entirely from a set of two-field reduced MHD equations. Such a quasi-linear model can recover previous plasma flow response models within certain limits and approximations. Furthermore, the physical origins of quasi-linear forces and moments in the flow response equation are also accurately calculated and clarified self-consistently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Beta-induced Alfvén eigenmodes destabilized by resonant magnetic perturbations in the J-TEXT tokamak

Investigations of beta-induced Alfvén eigenmodes (BAEs) destabilized by resonant magnetic perturbations (RMPs) have been conducted on the J-TEXT tokamak. In the Ohmic discharges, with RMPs having finite perturbed amplitudes, two different types of Alfvén eigenmodes have been observed and identified. One is considered as m-BAE, due to the strong correlation with magnetic island in some noticeable aspects, for example, frequency characteristic, mode number and driving mechanism. Specifically, the standing wave nodes of m-BAE are located at the O point and X point of the magnetic island. Another one is discerned as the magnetic island-induced AE (labeled as the MIAE-like mode in this work), which is consistent with the prediction of theory (Biancalani et al 2010 Phys. Rev. Lett. 105 095002). The frequency of MIAE-like mode is found to be approximately proportional to the square of magnetic island width.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

An improved theory of the response of DIII-D H-mode discharges to static resonant magnetic perturbations and its implications for the suppression of edge localized modes

The plasma response to an externally generated, static, n = 2, resonant magnetic perturbation (RMP) in the pedestal region of DIII-D H-mode discharge #158115 is investigated using a toroidal generalization of the asymptotic matching model presented by Fitzpatrick [Phys. Plasmas 27, 042506 (2020)]. Just as in a recent paper [Q. M. Hu et al., Phys. Plasmas 26, 120702 (2019)], it is hypothesized that the density pump-out phenomenon is due to locked magnetic island chains induced at the bottom of the pedestal, whereas the suppression of edge localized modes is associated with a locked magnetic island chain induced at the top of the pedestal. Neutral penetration inside the last closed magnetic flux-surface is found to have a significant influence on locked magnetic island chain formation at the bottom of the pedestal. It is found that locked island formation at the top of the pedestal is only possible when q95 lies in certain narrow windows. Finally, it is inferred that, in order to successfully induce a locked island chain at the top of the pedestal, an external RMP field-coil system must generate a magnetic field that is simultaneously strongly amplified by the plasma (via the ideal kink response) and has a large resonant component at a rational surface that lies close to the top of the pedestal.

Fitzpatrick, R. (ORCID:0000000162379309)↗
DOE OSTI2024

Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalised kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ/L (ρ is the particle Larmor radius and L is the system size). Resolving finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, B $\vartheta$ /B, it generalises the drift kinetic theory of [Hazeltine Phys. Plasmas 15 (1973) 77] to the limit of B $\vartheta$ /B ~ 1 (e.g. to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalised gyrokinetic formalism of [Dudkovskaia et al. Plasma Phys. Control. Fusion 65 (2023) 045010], derived specifically to capture neoclassical equilibrium currents in gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of [Dudkovskaia et al. Nucl. Fusion 63 (2023) 016020] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. In conclusion, resolving ρ ~ ρ $\vartheta$ (or B $\vartheta$ ~ B), where ρ $\vartheta$ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗