H. Tasso, G. N. Throumoulopoulos
A previous proof of non existence of tokamak equilibria with purely poloidal flow within macroscopic theory [Throumoulopoulos, Weitzner, Tasso, Physics of Plasmas Vol. 13, 122501 (2006)] motivated this microscopic analysis near magnetic axis for toroidal and "straight" tokamak plasmas. Despite the new exact solutions of Vlasov's equation found here, the structure of macroscopic flows remains elusive.
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Vlasov equilibria of axisymmetric plasmas with vacuum toroidal magnetic field can be reduced, up to a selection of ions and electrons distributions functions, to a Grad-Shafranov-like equation. Quasineutrality narrow the choice of the distributions functions. In contrast to two-dimensional translationally symmetric equilibria whose electron distribution function consists of a displaced Maxwellian, the toroidal equilibria need deformed Maxwellians. In order to be able to carry through the calculations, this deformation is produced by means of either a Heaviside step function or an exponential f…
By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution func…
Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas
本文推导了包含动能离子和无质量流体电子的混合 Vlasov 模型轴对称平衡方程，该系统由 Grad-Shafranov 方程和积分方程组成，可用于计算 tokamak 等离子体的平衡磁场和离子分布，并揭示了流体电子带来的极向电流分量。
Modeling of plasma transport during edge-localized mode in tokamak using a kinetic Vlasov-Poisson code
本文开发了基于有限体积法的动理学代码KOBRA，采用自适应网格细化（AMR）模拟托卡马克ELM输运，在保持精度的同时减少30-40%内存并加速至两倍。
High frequency non-gyrokinetic turbulence at tokamak edge parameter
本文首次通过6D-Vlasov模拟托卡马克边缘参数下的高频离子伯恩斯坦波湍流，发现其输运与回旋动理学湍流相当，表明回旋动理学近似的限制主要源于计算成本而非物理本质。
We analyze an axisymmetric equilibrium of a plasma endowed with toroidal and poloidal velocity fields, with the aim to characterize the influence of the global motion on the morphology of the magnetic confinement. We construct our configuration assuming that the poloidal velocity field is aligned with the poloidal magnetic field lines and, furthermore, we require that the plasma mass density depend on the magnetic flux function (or equivalently, that the plasma fluid be incompressible). We then derive a sort of Grad-Shafranov equation for such an equilibrium and implement it to tokamak relevan…
Non-axisymmetric stationary magnetic perturbations lead to the formation of homoclinic tangles near the divertor magnetic saddle in tokamak discharges. These tangles intersect the divertor plates in static helical structures that delimit the regions reached by open magnetic field lines reaching the plasma column and leading the charged particles to the strike surfaces by parallel transport. In this article we introduce a non-axisymmetric rotating magnetic perturbation to model the time development of the three-dimensional magnetic field of a single-null DIII-D tokamak discharge developing a ro…
MHD stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators
本文基于近轴描述研究环形磁场构型的MHD稳定性，发现正三角性可稳定托卡马克，但在准对称仿星器中正豆形截面并不提升稳定性，且有限$β$在无磁剪切时仍能改善稳定性。
A largely unsolved theoretical issue in controlled fusion research is the consistent \textit{kinetic} treatment of slowly-time varying plasma states occurring in collisionless and magnetized axisymmetric plasmas. The phenomenology may include finite pressure anisotropies as well as strong toroidal and poloidal differential rotation, characteristic of Tokamak plasmas. Despite the fact that physical phenomena occurring in fusion plasmas depend fundamentally on the microscopic particle phase-space dynamics, their consistent kinetic treatment remains still essentially unchalleged to date. The goal…
Trapped ion modes (TIM) belong to the family of ion temperature gradient (ITG) modes, which are one of the important ingredients in heat turbulent transport at the ion scale in tokamak plasmas. It is essential to properly estimate their linear growth rate to understand their influence on ion-scale turbulent transport. A global linear analysis of a reduced gyro-bounce kinetic model for trapped particle modes is performed, and a spectral method is proposed to solve the dispersion relation. Importantly, the radial profile of the particle drift velocity is taken into account in the linear analysis…
Plasma Position Constrained Free-Boundary MHD Equilibrium in Tokamaks using pyIPREQ
本研究开发了基于有限差分与格林函数法的托卡马克自由边界MHD平衡程序pyIPREQ，在PEST、IPREQ框架基础上新增多项功能，经基准验证后可用于多托卡马克装置的平衡计算与场景预测。
Trapped-particle precession and modes in quasi-symmetric stellarators and tokamaks: a near-axis perspective
本文基于近轴框架解析计算了轴对称与准对称磁场中捕获粒子的弹跳平均漂移，揭示了其对磁场几何与稳定性的依赖，并证明捕获电子可用能量与MHD稳定性密切相关。
A new constant of motion for helically symmetric equilibria in the vicinity of the magnetic axis is obtained in the framework of Vlasov theory. In view of this constant of motion the Vlasov theory is compared with drift kinetic and gyrokinetic theories near axis. It turns out that as in the case of axisymmetric equilibria [H. Tasso and G. N. Throumoulopoulos, Phys. Plasmas 18, 064507 (2011)] the Vlasov current density thereon can differ appreciably from the drift kinetic and gyrokinetic current densities. This indicates some limitation on the implications of reduced kinetic theories, in partic…
Control of the bootstrap current in approximately quasi-axisymmetric magnetic fields
本文提出了一种基于近准轴对称磁场和分段无源扰动的新策略，旨在实现简单线圈几何、托卡马克式约束性能及通过调节反向电流与岛型分流器的兼容性。
A kinetic consideration of an axisymmetric equilibrium with vanishing electric field near the magnetic axis shows that del f should not vanish on axis within the framework of Vlasov theory while it can either vanish or not in the framework of both a drift kinetic and a gyrokinetic theories (f is either the pertinent particle or the guiding center distribution function). This different behavior, relating to the reduction of phase space which leads to the loss of a Vlasov constant of motion, may result in the construction of different currents in the reduced phase space than the Vlasov ones. Thi…
Collisionless plasmas, such as those encountered in tokamaks, exhibit a rich variety of instabilities. The physical origin, triggering mechanisms and fundamental understanding of many plasma instabilities, however, are still open problems. We investigate the stability properties of a collisionless Vlasov plasma in a stationary homogeneous magnetic field. We narrow the scope of our investigation to the case of Maxwellian plasma. For the first time using a fully kinetic approach we show the emergence of the local instability, a transient growth, followed by classical Landau damping in a stable m…
A local magnetic equilibrium solution is sought around the magnetic axis in order to identify the key parameters defining the magnetic-surface's up-down asymmetry in the core of tokamak plasmas. The asymmetry is found to be determined essentially by the ratio of the toroidal current density flowing on axis to the fraction of the external field's odd perturbation that manages to propagate from the plasma boundary into the core. The predictions are tested and illustrated first with an analytical Solovev equilibrium and then using experimentally relevant numerical equilibria. Hollow current-densi…
A hybrid model of the Vlasov equation in multiple spatial dimension $D>1$ [H. A. Rose and W. Daughton, Physics of Plasmas v. 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the $z$ direction, and $N$ flows. At each $z$ these flows are in the plane perpendicular to the $z$ axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show convergence of the VMD Langmuir wave dispersion r…
Characterizing Flux-Surface Shapes in Tokamaks and Quasi-Symmetric Stellarators
本文提出了一种计算托卡马克和恒星仪磁通面形状的方法，通过傅里叶分析揭示准对称性与形状复杂度和旋转之间的共振关系。
It is shown that small externally applied magnetic perturbations can significantly alter important geometric properties of magnetic flux surfaces in tokamaks. Through 3D shaping, experimentally relevant perturbation levels are large enough to influence turbulent transport and MHD stability in the pedestal region. It is shown that the dominant pitch-resonant flux surface deformations are primarily induced by non-resonant 3D fields, particularly in the presence of significant axisymmetric shaping. The spectral content of the applied 3D field can be used to control these effects.
We present various techniques that make orbit-following Monte Carlo simulations faster and more reliable when assessing collisionless fast particle losses due to magnetic field perturbations. These techniques are based on identifying various loss channels in constants of motion space using the so-called loss maps. We demonstrate that this allows one to attribute losses quantitatively to different transport mechanisms, increase signal-to-noise ratio when estimating FILD signal and peak power loads, and connect magnetic field structure directly to fast particle losses. Furthermore, we show that …
Axisymmetric free-boundary equilibrium reconstructions of tokamak plasmas in the Lithium Tokamak eXperiment (LTX) are performed using the PSI-Tri equilibrium code. Reconstructions in LTX are complicated by the presence of long-lived non-axisymmetric eddy currents generated by vacuum vessel and first wall structures. To account for this effect, reconstructions are performed with additional toroidal current sources in these conducting regions. The source distributions are fixed poloidally, but their scale is adjusted as part of the full reconstruction. Eddy distributions are computed by toroidal…
Shaping of magnetic flux surfaces is found to have a strong impact on turbulence and transport in tokamak edge plasmas. A series of axisymmetric equilibria with varying elongation and triangularity, and a divertor configuration are implemented into a computational gyrofluid turbulence model. The mechanisms of shaping effects on turbulence and flows are identified. Transport is mainly reduced by local magnetic shearing and an enhancement of zonal shear flows induced by elongation and X-point shaping.
SPARC Tokamak Error Field Expectations and Physics-Based Correction Coil Design
SPARC环形磁体通过基于物理的校正线圈设计，实现高效误差场校正和抑制边缘局域模，确保高场运行稳定性。
Collisionless geodesic acoustic modes in tokamaks being supersonic for large "safety factor" q, the CGL (G. Chew, M. Goldberger, F. Low, 1956)1 double-adiabatic fluid closure is applied to formulate a theory for these modes. The basic linear normal mode is obtained. External means to drive these modes at resonance, as has been proposed earlier, are explored. The external drivers considered include external magnetic forces to effect flux surface displacements, as well as non-axisymmetric ion heating. Finally, the damping of these modes from collisional magnetic pumping is investigated using a m…
Recent tokamak experiments employing off-axis, non-inductive current drive have found that a large central current hole can be produced. The current density is measured to be approximately zero in this region, though in principle there was sufficient current drive power for the central current density to have gone significantly negative. Recent papers have used a large aspect-ratio expansion to show that normal MHD equilibria (with axisymmetric nested flux surfaces, non-singular fields, and monotonic peaked pressure profiles) can not exist with negative central current. We extend that proof he…
On the Effects of Tokamak Plasma Edge Symmetries on Turbulence Relaxation
本文构建简化的3D Hasegawa-Wakatani模型研究托卡马克边缘湍流弛豫，发现X点对称性因背景与极向扰动共振改变湍流输运特性，且微扰法求解电势动力学不总可行。
Isotope Effects on TEM-driven Turbulence and Zonal Flows in Helical and Tokamak Plasmas
研究同位素质量对磁镜和托卡马克等离子体中TEM驱动湍流和区流的影响，发现同位素效应导致输运减少，与传统标度相反。
Species dependence of the impurity injection induced poloidal flow and magnetic island rotation in a tokamak
本文通过电阻MHD模拟研究了托卡马克中杂质注入引起的极向流和磁岛旋转的物种依赖性，发现局部等离子体团形成决定杂质极向流，电磁转矩驱动磁岛同步旋转。
Nonlinear edge localized modes in a tokamak are examined using global three-dimensional resistive magnetohydrodynamics simulations. Coherent current-carrying filament (ribbon-like) structures wrapped around the torus are nonlinearly formed due to nonaxisymmetric reconnecting current sheet instabilities, the so called peeling-like edge localized modes. These fast growing modes saturate by breaking axisymmetric current layers isolated near the plasma edge and go through repetitive relaxation cycles by expelling current radially outward and relaxing it back. The local bi-directional fluctuation-i…
A geometrical correction to the E x B drift causes an outward flux of cocurrent momentum whenever electrostatic potential energy is transferred to ion parallel flows. The robust symmetry breaking follows from the free energy flow in phase space and does not depend on any assumed linear eigenmode structure, acting both for axisymmetric fluctuations (such as geodesic acoustic modes) as well as more general nonaxisymmetric fluctuations. The resulting rotation peaking is countercurrent and scales as electron temperature over plasma current. This peaking mechanism can only act when fluctuations are…
Constructing Field Aligned Coordinate Systems for Gyrokinetic Simulations of Tokamaks in X-point Geometries
提出一种避免磁X点奇点的算法，用于在标准磁场对齐坐标系中计算几何量，实现托卡马克核心区与刮削层的2D轴对称模拟，并通过STEP示例验证有效性。
Uncertainties and errors in magnetic equilibrium reconstructions are a wide-spread problem in interpreting experimental data measured in the tokamak edge. This study demonstrates errors in EFIT++ reconstructions performed on the COMPASS tokamak by comparing the outer midplane separatrix position to the Velocity Shear Layer (VSL) position. The VSL is detected as the plasma potential peak measured by a reciprocating ball-pen probe. A subsequent statistical analysis of nearly 400 discharges shows a strong systematic trend in the reconstructed separatrix position relative to the VSL, where the pri…
Design of Passive and Structural Conductors for Tokamaks Using Thin-Wall Eddy Current Modeling
本文基于PSI-Tet开发三维薄壁涡流建模工具ThinCurr，为SPARC和DIII-D建立导电结构模型，并用于优化无源REMC设计以缓解破裂中的逃逸电子。
FEQIS: A free-boundary equilibrium solver for integrated modeling of tokamak plasmas
本文介绍了一种名为FEQIS的新型轴对称自由边界平衡求解器，用于托卡马克等离子体集成建模，其特点是电路连接灵活，并采用多层简化数值方案求解Grad-Shafranov方程。
Simulation of ion temperature gradient driven modes with 6D kinetic Vlasov code
本文利用优化的6D动力学Vlasov半拉格朗日求解器模拟离子温度梯度模式，超越回旋动力学限制，首次展示完整垂直能量通量及非线性饱和阶段的高频波激发。
Here diffusion and Ware pinch are analyzed as opposed effects for plasma confinement, when instabilities are not considered. In this work it is studied the equilibrium inductive electric field where both effects annul each other in the sense that the average normal velocity is zero, that is, marginal velocity confinement is reached. The critical electric field defined in that way is studied for different values of elliptic elongation, Shafranov shift and triangularity. A short complementary analysis is also performed of the variation of the poloidal magnetic field along a magnetic line. Magnet…
GSPD: An algorithm for time-dependent tokamak equilibria design
提出GSPD算法，用于设计时变托卡马克平衡，同时满足力平衡和导体电路动力学，代码开源。
Radio frequency waves are routinely used in tokamak fusion plasmas for plasma heating, current control, and as well as in diagnostics. These waves are excited by antenna structures placed near the tokamak's wall and they have to propagate through a turbulent layer known as scrape-off layer, before reaching the core plasma (which is their target). This layer exhibits coherent density fluctuations in the form of blobs and filaments. The scattering processes of RF plane waves by single blob is studied, with the assumption that the blob has cylindrical shape and infinite length. The axis of the bl…
Ray tracing codes are useful to study the electromagnetic wave propagation and absorption in the geometrical optics approximation. In magnetized fusion plasma community, most ray tracing codes assume the plasma density and temperature be functions of the magnetic flux and study waves only inside the last closed flux surface, which are sufficient for the present day tokamak. However, they are difficult to be used for configurations with open magnetic field line plasmas, such as mirror machine and field-reversed-configuration (FRC). We develop a ray tracing code in cylindrical coordinates $(r,ϕ,…
In the presence of energetic particles (EPs) from auxiliary heating and burning plasmas, fishbone instability and Alfvén modes can be excited and their transition can take place in certain overlapping regimes. Using the hybrid kinetic-magnetohydrodynamic model in the NIMROD code, we have identified such a transition between the fishbone instability and the $β$-induced Alfvén Eigenmode (BAE) for the NBI heated plasmas on HL-2A. When the safety factor at magnetic axis is well below one, typical kink-fishbone transition occurs as the EP fraction increases. When $q_0$ is raised to approaching one,…
A new representation of electromagnetic gyrokinetic Vlasov-Maxwell theory is presented in which the gyrocenter equations of motion are expressed solely in terms of the perturbed electric and magnetic fields. In this representation, the gyrocenter symplectic (Poisson-bracket) structure and the gyrocenter Jacobian contain electric and magnetic perturbation terms associated with the standard first-order gyrocenter polarization and magnetization terms that traditionally appear in the gyrokinetic Maxwell equations. In addition, the gyrocenter polarization drift (which includes perturbed magnetic-fi…
In magnetically confined plasmas used in Tokamak, turbulence is responsible for specific transport that limits the performance of this kind of reactors. Gyrokinetic simulations are able to capture ion and electron turbulence that give rise to heat losses, but require also state-of-the-art HPC techniques to handle computation costs. Such simulations are a major tool to establish good operating regime in Tokamak such as ITER, which is currently being built. Some of the key issues to address more realistic gyrokinetic simulations are: efficient and robust numerical schemes, accurate geometric des…
Externally applied non-axisymmetric magnetic fields such as error field and resonant magnetic perturbation (RMP) are known to influence the plasma momentum transport and flow evolution through plasma response in a tokamak, whereas the evolution of plasma response itself strongly depends on the plasma flow as well. The nonlinear interaction between the two have been captured in the conventional error field theory with a ``no-slip'' condition, which has been recently extended to allow the ``free-slip'' condition. For comparison with simulations, we solve for the nonlinear plasma response and flo…
We analyze a Hamiltonian model with five wire loops that delineates the magnetic surfaces of the tokamak ITER, including a similar safety factor profile and the X-point related to the presence of a poloidal divertor. Non-axisymmetric magnetic perturbations are added by external coils, similar to the correction coils installed at the tokamak DIII-D and those that will be installed at ITER. To show the influence of magnetic perturbations on the field line escape, we integrate numerically the field line differential equations and obtain the footprints and deposition patterns on the divertor plate…
The potential formation of multi-mega-ampere beams of relativistic "runaway" electrons (REs) during sudden terminations of tokamak plasmas poses a significant challenge to the tokamak's development as a fusion energy source. Here, we use state-of-the-art modeling of disruption magnetohydrodynamics coupled with a self-consistent evolution of RE generation and transport to show that a non-axisymmetric in-vessel coil will passively prevent RE beam formation during disruptions in the SPARC tokamak, a compact, high-field, high-current device capable of achieving a fusion gain Q > 2 in deuterium-tri…
New axisymmetric equilibria with flow from an expansion about the generalized Solov'ev solution
本研究通过线性化假设与广义Solov'ev解展开，得到含环向和极向流动的广义Grad-Shafranov方程解析解，分析自由参数对平衡位形的影响，构建了多种适用于托卡马克、球形托卡马克和球马克的平衡态。
Topological Arrest of Ballooning Modes in Non-Axisymmetric Plasmas
研究非轴对称稳态器为何能避免受约束磁体中反气球崩溃的现象，通过三维几何诱导安德森局部化，将全球不稳定性转化为吉恩兹-兰道网络中的孤立波包网络，提出临界阈值作为非线性稳定性指标用于反应堆优化。
Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant NTV regimes including superbanana plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbation…
In this work, we have formulated and implemented a mixed unstructured mesh-based finite element (FE)-Fourier decomposition scheme for gyrokinetic simulations in realistic tokamak geometry. An efficient particle positioning (particle-triangle mapping) scheme for the charge deposition and field scattering using an intermediate grid as the search index for triangles has been implemented and a significant speed-up by a factor of $\sim30$ is observed as compared with the brute force scheme for a medium-size simulation. The TRIMEG (TRIangular MEsh based Gyrokinetic) code has been developed. As an ap…
The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal Magnetohydrodynamics (MHD) theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the Mirror-induced Alfvén Eigenmode (MAE) gap and the Helicity-induced Alfvén Eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside Toroidal Alfvén Eigenmode (TAE) gap into t…
Ion orbit loss is considered important for generating the radially inward electric field $E_r$ in a tokamak edge plasma. In particular, this effect is emphasized in diverted tokamaks with a magnetic X point. In neoclassical equilibria, Coulomb collisions can scatter ions onto loss orbits and generate a radially outward current, which in steady state is balanced by the radially inward current from viscosity. To quantitatively measure this loss-orbit current in an edge pedestal, an ion-orbit-flux diagnostic has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code…
The application of non-axisymmetric resonant magnetic perturbations (RMPs) to low current plasmas in the Mega Amp Spherical Tokamak (MAST) was found to be correlated with substantial drops in neutron production, suggesting a significant degradation of fast ion confinement. The effects of such perturbations on fast ions in MAST have been modelled using a revised version of a non-steady-state orbit-following Monte-Carlo code (NSS OFMC), in which the parametrization of fusion reaction rates has been updated and neutron rates have been recalculated. Losses of fast ions via charge-exchange (CX) wit…
Fundamental Lagrangian, frozen-in and topological invariants can be useful to explain systematic connections between plasma parameters. At high plasma temperature the dissipation is small and the robust invariances are manifested. We invoke a frozen-in invariant which is an extension of the Ertel's theorem and connects the vorticity of the large scale motions with the profile of the safety factor and of particle density. Assuming ergodicity of the small scale turbulence we consider the approximative preservation of the invariant for changes of the vorticity in an annular region of finite radia…
In this Master thesis we investigate the influence of pressure anisotropy and incompressible flow of arbitrary direction on the equilibrium properties of magnetically confined, axisymmetric toroidal plasmas. The main novel contribution is the derivation of a pertinent generalised Grad-Shafranov equation. This equation includes six free surface functions and recovers known Grad-Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets…
An international experiment, ITER is proposed as the next essential and critical step on the path to demonstrating the scientific and technological feasibility of fusion energy. ITER would give unique opportunities to explore, in reactor relevant conditions, the physics of α-particle heating, plasma turbulence and turbulent transport, stability limits to the plasma pressure and exhaust of power and particles. Improved understanding of the physical processes occurring in tokamak plasmas give enhanced confidence in ITER achieving its goals. In particular, progress has been made in research …
A 3D numerical model for the ablation of pellets and shattered pellet injection (SPI) fragments in tokamaks in the plasma disruption mitigation and fueling parameter space has been developed based on the Lagrangian particle code [R. Samulyak, X. Wang, H.-S. Chen, Lagrangian Particle Method for Compressible Fluid Dynamics, J. Comput. Phys., 362 (2018), 1-19]. The pellet code implements the low magnetic Reynolds number MHD equations, kinetic models for the electronic heating, a pellet surface ablation model, an equation of state that supports multiple ionization states, radiation, and a model fo…
Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field terms. Equations for the fields are given by functional derivatives. The symmetry through the Hamiltonian with time and toroidal angle invariance of the geometry lead to energy and toroidal momentum conservation. In various levels of ordering against fluctuation amplitude, energetic consistency is exact. The role of this in underpinning of conservation laws…
Synthetic measurements of runaway electron synchrotron emission in the SPARC tokamak
针对SPARC托卡马克中多MA级失控电子（REs）的潜在风险，本文利用SOFT合成诊断工具，对电流上升、稳态平顶及破裂三种场景下RE同步辐射的图像与光谱进行建模，评估了所需时间分辨率、空间覆盖和光谱范围。
Symmetries of the Electromagnetic Turbulence in a Tokamak Edge
本文构建托卡马克边界等离子体湍流的低频简化模型，证明可由单一电势方程描述，并揭示二维湍流对非轴对称涨落具有吸引性的特定傅里叶分支及其两种物理状态。
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