In the above entitled recent publication by Giovanni Lapenta [Phys. Rev. Lett. Vol 90, 135005 (2003) ] it is claimed construction of a new class of solitonlike solutions for the Grad-Shafranov equation in plane geometry. It is proved here that, because of the mathematically erroneous choice \nabla p= |Ψ|^2 Ψ\nabla Ψfor an analytic continuation of the poloidal magnetic flux-function Ψin the complex plane (p is the pressure), the cubic Schrödinger equation considered by the author is irrelevant to the equilibrium problem and the Grad-Shafranov equation.
Solution to the Grad-Shafranov Boundary Value Problem for a Thermonuclear Plasma contained in a Toroidal Vase With a Conducting Wall under the Assumption of Constant Sources to the Equilibrium in Flux Space
A mimetic spectral element solver for the Grad-Shafranov equation
在这项工作中，我们提出了一个强大的和准确的任意阶求解器的固定边界等离子体平衡环轴对称几何形状。为了实现这一点，我们将[56]中提出的模拟谱元素公式应用于Grad-Shafranov方程的求解。这种方法结合了有限体积离散与混合有限元法。这样，离散微分算子（$\nabla$，$\nabla\times$，$\nabla\cdot$）就可以精确地表示出来，并且所有的近似误差都存在于本构关系中。这种提法的结果是一个任意阶的方法，即使在高度弯曲的网格。另外，\reviewerone{toroidal current $J_ϕ$}的积分正好等于极向场在等离子体边界上的边界积分。这个属性可以在平衡和传输求解器之间的耦合中发挥重要作用。所提出的求解器进行了测试的等离子体横截面（光滑和X点），也为广泛的压力和\reviewertwo{toroidal magnetic flux profiles}。平衡精确到机器精度。最佳的代数收敛速度的顺序$(p+1)$和几何收敛速度所示的Soloviev解决方案（包括高Shafranov位移），场反转配置（FRC）的解决方案和spheromak解析解。该方法的鲁棒性证明了非线性测试用例，特别是在平衡解决方案与压力基座。
An Inverse Grad-Shafranov Neural Network Approach to Tokamak Magnetic Control
MIT Plasma Science and Fusion Center（麻省理工学院等离子体科学与聚变中心）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；Google DeepMind（谷歌DeepMind）；Fusionality SA；Commonwealth Fusion Systems（联邦聚变系统）
VEQ: a fast parametric Grad--Shafranov solver for fixed-boundary tokamak equilibria with flexible source profiles
Dalian University of Technology（大连理工大学）；Beijing VeloAlpha Technology Co., Ltd.（北京维奥阿尔法科技有限公司）；ENN Science and Technology Development Co., Ltd.（新奥科技开发有限公司）；Tianjin University of Technology and Education（天津职业技术师范大学）；Nankai University（南开大学）
A fast, high-order solver for the Grad-Shafranov equation
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Plasma Science and Fusion Center, Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）
Accurate Derivative Evaluation for any Grad-Shafranov Solver
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Plasma Science and Fusion Center, Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）
Grad-Shafranov equilibria via data-free physics informed neural networks
Institute for Research in Electronics and Applied Physics, University of Maryland（马里兰大学电子与应用物理研究所）；Courant Institute, New York University（纽约大学柯朗数学科学研究所）；Princeton University（普林斯顿大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）
Towards Data-Efficient Cross-Device Generalization of Grad-Shafranov Equilibria via Transfer Learning Neural Operator
Grainger College of Engineering, Nuclear, Plasma & Radiological Engineering Department, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院核、等离子体与放射工程系）；Fusion Energy Division, Oak Ridge National Lab（橡树岭国家实验室聚变能源部）；National Center for Supercomputing Applications（国家超级计算应用中心）；Department of Applied Mechanics, Indian Institute of Technology Delhi（印度理工学院德里分校应用力学系）；Yardi School of Artificial Intelligence, Indian Institute of Technology Delhi（印度理工学院德里分校亚迪人工智能学院）
What Is the Minimum Number of Parameters Required to Represent Solutions of the Grad-Shafranov Equation?
Hebei Key Laboratory of Compact Fusion（河北紧凑型聚变重点实验室）；ENN Science and Technology Development Co., Ltd.（新奥科技发展有限公司）；School of Science, Tianjin University of Technology and Education（天津职业技术师范大学理学院）
Physics-informed Neural Operator Learning for Nonlinear Grad-Shafranov Equation
ENN Science and Technology Development Co., Ltd.（新奥科技发展有限公司）；Hebei Key Laboratory of Compact Fusion（河北省紧凑型聚变重点实验室）；Xi’an University of Science and Technology（西安科技大学）；Xi’an Jiaotong University（西安交通大学）；Dalian University of Technology（大连理工大学）
Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad-Shafranov equation by extension from polygonal subdomains
New York University, Courant Institute of Mathematical Sciences（纽约大学 库朗数学科学研究所）；Universidad de Concepción, Department of Mathematical Engineering（康塞普西翁大学 数学工程系）；Universidad de Concepción, Center for Research in Mathematical Engineering（康塞普西翁大学 数学工程研究中心）
