arXiv subjects

Ralf Kleiber

Publications and source records attributed to Ralf Kleiber.

6 recordsLinked to original sources

arXiv2026

Electromagnetic pressure-gradient-driven instabilities with moderate high mode numbers in tokamak plasmas

Pressure gradient-driven instabilities are investigated in tokamak plasmas using the global gyrokinetic code EUTERPE emphasizing the role of moderate high mode numbers. As the normalized plasma pressure $\beta$ is increased, there is a well-known, sudden transition from ion-temperature-gradient (ITG) instabilities to kinetic ballooning modes (KBM), if the magnetohydrodynamic (MHD) geometry is held fixed. However, if the equilibrium field is recomputed for each value of $\beta$, so that the equilibrium is consistent with the stability calculation, the transition can disappear. In a number of cases, we are only able to find an ITG-KBM transition if inconsistent equilibria are used. In the MHD unstable regime, gyrokinetic simulations and MHD stability calculations show good agreement for moderate ratios of ion temperature gradient to density gradient and small values of the ion gyro-radius. Otherwise, non-MHD contributions are important, such as the diamagnetic stabilization and ion wave--particle resonant effects.

physics.plasm-ph↗

arXiv2026

Smooth Polar B-Splines with High-Order Regularity at the Origin

We introduce a smooth B-spline discretization in polar coordinates on the unit disc that corrects the loss of regularity present at the origin caused by the coordinate singularity in standard tensor-product B-spline formulations. The method constructs "smooth polar splines" via a Galerkin projection of harmonic polar functions $S_l^{-m}(r,\theta) := r^l \sin(m\theta)$ and $S_l^{m}(r,\theta) := r^l \cos(m\theta)$, derived from the polar representation of Cartesian monomials, onto the central tensor-product B-spline basis in the innermost radial region. The radial component reproduces $r^l$ exactly for $0 \le l \leq p$, where $p$ is the B-spline degree, satisfying the near-origin regularity condition. However, exact compatibility with $C^\infty$-regularity at the origin is recovered only in the limit $\Delta\theta \to 0$, when the angular component resolves all angular harmonics accurately. The smooth polar splines are linear combinations of standard tensor-product B-splines and lie in the same function space, enabling mapping between the $C^\infty$-regular subspace and the original discretization space via an exact prolongation operator and a corresponding restriction operator acting on the discrete variables. They match standard tensor-product B-splines away from the origin, preserve orthogonality among the newly constructed origin-centered basis functions, and maintain local support and sparse matrices. This smoothness and locality improve the conditioning of mass and stiffness matrices, conserve charge, and reduce statistical errors in particle-in-cell simulations near the origin, while eliminating spurious eigenvalues in eigenvalue problems. The approach provides a robust, high-order, and efficient adaptation of tensor-product B-splines for polar coordinates in physics simulations.

physics.comp-ph↗

arXiv2021

Numerics and computation in gyrokinetic simulations of electromagnetic turbulence with global particle-in-cell codes

Electromagnetic turbulence is addressed in tokamak and stellarator plasmas with the global gyrokinetic particle-in-cell codes ORB5 [E. Lanti et al, Comp. Phys. Comm, vol. 251, 107072 (2020)] and EUTERPE [V. Kornilov et al, Phys. Plasmas, vol. 11, 3196 (2004)]. The large-aspect-ratio tokamak, down-scaled ITER, and Wendelstein 7-X geometries are considered. The main goal is to increase the plasma beta, the machine size, the ion-to-electron mass ratio, as well as to include realistic-geometry features in such simulations. The associated numerical requirements and the computational cost for the cases on computer systems with massive GPU deployments are investigated. These are necessary steps to enable electromagnetic turbulence simulations in future reactor plasmas.

physics.plasm-ph↗

arXiv2018

Pullback scheme implementation in ORB5

The pullback scheme is implemented in the global gyrokinetic particle-in-cell code ORB5 [S. Jolliet et al, Comp. Phys. Comm., 177, 409 (2007)] to mitigate the cancellation problem in electromagnetic simulations. The equations and the discretisation used by the code are described. Numerical simulations of the Toroidal Alfven Eigenmodes are performed in linear and nonlinear regimes to verify the scheme. A considerable improvement in the code efficiency is observed. For the internal kink mode, it is shown that the pullback mitigation efficiently cures a numerical instability which would make the simulation more costly otherwise.

physics.plasm-ph↗

arXiv2017

Semianalytical calculation of the zonal-flow oscillation frequency in stellarators

Due to their capability to reduce turbulent transport in magnetized plasmas, understanding the dynamics of zonal flows is an important problem in the fusion programme. Since the pioneering work by Rosenbluth and Hinton in axisymmetric tokamaks, it is known that studying the linear and collisionless relaxation of zonal flow perturbations gives valuable information and physical insight. Recently, the problem has been investigated in stellarators and it has been found that in these devices the relaxation process exhibits a characteristic feature: a damped oscillation. The frequency of this oscillation might be a relevant parameter in the regulation of turbulent transport, and therefore its efficient and accurate calculation is important. Although an analytical expression can be derived for the frequency, its numerical evaluation is not simple and has not been exploited systematically so far. Here, a numerical method for its evaluation is considered, and the results are compared with those obtained by calculating the frequency from gyrokinetic simulations. This "semianalytical" approach for the determination of the zonal-flow frequency reveals accurate and faster than the one based on gyrokinetic simulations.

physics.plasm-ph↗

arXiv2014

Pullback transformation in gyrokinetic electromagnetic simulations

It is shown that a considerable improvement in the global gyrokinetic electromagnetic simulations can be achieved by a slight modification of the simulation scheme. The new scheme is verified, simulating a Toroidal Alfvén Eigenmode in tokamak geometry at low perpendicular mode numbers, the so-called "MHD limit". Also, an electromagnetic drift mode has been successfully simulated in a stellarator.

physics.plasm-ph↗