Nicolas Besse

A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation

A new code is presented here, named Gyrokinetic SEmi-LAgragian (GYSELA) code, which solves 4D drift-kinetic equations for ion temperature gradient driven turbulence in a cylinder (r,θ,z). The code validation is performed with the slab ITG mode that only depends on the parallel velocity. This code uses a semi-Lagrangian numerical scheme, which exhibits good properties of energy conservation in non-linear regime as well as an accurate description of fine spatial scales. The code has been validated in the linear and non-linear regimes. The GYSELA code is found to be stable over long simulation times (more than 20 times the linear growth rate of the most unstable mode), including for cases with a high resolution mesh (δr ∼ 0.1 Larmor radius, δz ∼ 10 Larmor radius).

Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space

A new scheme for solving the Vlasov equation using an unstructured mesh for the phase space is proposed. The algorithm is based on the semi-Lagrangian method which exploits the fact that the distribution function is constant along the characteristic curves. We use different local interpolation operators to reconstruct the distribution function f, some of which need the knowledge of the gradient of f. We can use limiter coefficients to maintain the positivity and the L∞ bound of f and optimize these coefficients to ensure the conservation of the L1 norm, that is to say the mass by solving a linear programming problem. Several numerical results are presented in two and three (axisymmetric case) dimensional phase space. The local interpolation technique is well suited for parallel computation.

Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov-Poisson system

Abstract: In this paper we present some classes of high-order semi-Lagran- gian schemes for solving the periodic one-dimensional Vlasov-Poisson system in phase-space on uniform grids. We prove that the distribution function

A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system

f(t,x,v)

Gyrokinetic modeling: A multi-water-bag approach

and the electric field

Validity of quasilinear theory: refutations and new numerical confirmation

E(t,x)

Gyro-water-bag approach in nonlinear gyrokinetic turbulence

converge in the

Gyrokinetic-water-bag modeling of low-frequency instabilities in a laboratory magnetized plasma column

L^2

Self-induced transparency scenario revisited via beat-wave heating induced by Doppler shift in overdense plasma layer

norm with a rate of

Beyond scale separation in gyrokinetic turbulence

\displaystyle \mathcal{O}\left(\Delta t^2 +h^{m+1}+ \frac{h^{m+1}}{\Delta t}\right),