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We present a new Particle-in-Cell method for plasma simulations. This is based on the original algorithm of FLIP-MHD, which uses a Lagrangian formulation of the macroscopic equations. A finite-difference approximation of the equations of motion is solved on a fixed (non-moving) grid, while convection of the quantities is modeled with the support of Lagrangian particles. Interpolation with first-order b-splines is used to project the conserved quantities from particles to the grid and back. In this work, we introduce two modifications of the original scheme. A particle volume evolution procedure is adopted to reduce the computational error, based on the formulation used in the Material Point Method for computational mechanics. The additional step introduces little to none computational diffusion and turns out to efficiently suppress the so-called ringing instability, allowing the use of explicit time differencing. Furthermore, we eliminate the need for a Poisson solver in the magnetic field computation with the use of a vector potential in place of the particles’ magnetic moment. The vector potential evolution is modeled with a moving grid and interpolated to the fixed grid points at each time step to obtain a solenoidal magnetic field. The method is tested with a number of standard hydrodynamic and magnetohydrodynamic tests to show the efficiency of the new approach. The results show good agreement with the reference solutions and rather fast time and space convergence.

We have developed a new magnetohydrodynamic (MHD) simulation code that automatically satisfies the solenoidal magnetic field ( B ) property ∇ ⋅ B = 0 . We use the vector potential ( A ) instead of the magnetic field itself in the magnetohydrodynamic equation. To solve the advection term, we adopt a Rational-CIP algorithm in the simulation code. The non-advection terms are solved by the 4th order Runge–Kutta method for time and 4th order central difference for space in a regular grid system. Code assessments are carried out to evaluate the properties of the developed code. A remarkable feature of the new code is the description of Alfven wave propagation with less numerical dispersion. After the code assessments, we apply the code to a global simulation of the planet Mercury's magnetosphere. Fundamental structures of the magnetosphere are successfully reproduced.

The formulation for solving numerically the two-dimensional Newcomb equation has been extended to calculate the vacuum energy integral by using a vector potential method. According to this extension, a stability code MARG2D has been adapted, and coded for parallel computing in order to reduce substantially the CPU time. The MARG2D code enables a fast stability analysis of ideal external MHD modes from low to high toroidal mode numbers on the basis of the single physical model, and then the code works as a powerful tool in an integrated simulation where it is combined with transport codes, and also in the analysis of tokamak edge plasma experiments.

The problem of the current-driven linear instability of a general force-free equilibrium has been formulated in terms of a variational problem with the vector potential as the trial function. The formalism allows A·B 0 ≠ 0 so that nonideal effects are modeled. The variational problem has been studied numerically for both infinite aspect ratio and finite aspect ratio tokamaks. Results of these numerical studies are presented.