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We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfv\'en eigenmodes and energetic particle transport in tokamak plasmas. In order to resolve the Alfv\'en eigenmodes with high toroidal numbers effectively, the field-aligned coordinates and meshes are adopted. The extended MHD equations are solved with five-points finite difference method and fourth order Runge-Kutta method. The gyrokinetic equations are solved by particle-in-cell (PIC) method for the perturbed energetic particle pressures that are coupled into the MHD equations. Up to now, a simplified version of the hybrid code has been completed with several successful verifications including linear simulations of toroidal Alfv\'en eigenmodes and reversed shear Alfv\'en eigenmodes., Comment: 11 pages, 17 figures

A machine learning based surrogate model for fishbone linear instability in tokamaks is constructed. Hybrid simulations with the kinetic-magnetohydrodynamic (MHD) code M3D-K is used to generate the database of fishbone linear instability, through scanning the four key parameters which are thought to determine the fishbone physics. The four key parameters include (1) central total beta of both thermal plasma and fast ions, (2) the fast ion pressure fraction, (3) central value of safety factor $q$ and (4) the radius of $q=1$ surface. Four machine learning methods including linear regression, support vector machines (SVM) with linear kernel, SVM with nonlinear kernel and multi-layer perceptron are used to predict the fishbone instability, growth rate and real frequency, mode structure respectively. Among the four methods, SVM with nonlinear kernel performs very well to predict the linear instability with accuracy $\approx$95%, growth rate and real frequency with $R^2\approx$98%, mode structure with $R^2\approx$98%., Comment: 28 pages,19 figures

A new magnetohydrodynamics (MHD) code based on initial value approach, GMEC_I, has been developed for simulating various MHD physics in tokamak plasmas, as the MHD foundation of the gyrokinetic-MHD energetic particle simulation code (GMEC) family. GMEC_I solves multi-level reduced-MHD models that form a hierarchy of physics complexity, which provide conveniences for the cross-code verification and the identification of key physics effect in tokamak geometry. The field-aligned coordinates are used to represent mode structure efficiently. High-order finite difference methods are used for spatial discretization. The shifted metric methods are used for numerical stability. The discrete expansion forms of physics equations in the code are generated symbolically using the compile-time symbolic solver (CSS), which is specifically developed to reduce the complexity of the high-order finite difference form of the MHD equations. Advanced computational techniques have been implemented for optimizing memory access and code parallelization that show a good efficiency using both Thread Building Block (TBB) and Message Passing Interface (MPI). Benchmarks between GMEC_I and the eigenvalue code MAS are presented for ballooning modes without and with diamagnetic drift effects, and tearing modes, which show excellent agreements., Comment: 17 pages, 38 figures