General Magnetic Configurations Research Articles

An extended Hasegawa–Mima equation for nonlinear drift wave turbulence in general magnetic configurations

We propose an extended Hasegawa–Mima equation describing the evolution of nonlinear drift wave turbulence in general magnetic configurations. Such HMGM equation can be derived within the kinetic framework of guiding center motion or from a two-fluid model of an ion-electron plasma by application of a drift wave turbulence ordering that does not involve conditions on spatial derivatives of magnetic field and plasma density. The HMGM equation is therefore appropriate to describe the evolution of drift wave turbulence in strongly inhomogeneous magnetized plasmas, such as magnetospheric and stellarator plasmas, involving complex magnetic field geometries and non-uniform plasma density distributions. We find conservation laws (mass, energy, and generalized enstrophy) of the HMGM equation, study its algebraic (Hamiltonian) structure, and prove a nonlinear stability criterion for steady solutions through the energy-Casimir method. We then apply these results to describe drift waves and infer the existence of stable toroidal zonal flows with radial shear in dipole magnetic fields.

A Gyrokinetic simulation model for low frequency electromagnetic fluctuations in magnetized plasmas

We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations. This novel model (termed as GK-E&B) employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields. It, thus, not only includes kinetic effects, such as wave-particle interaction and microscopic (ion Larmor radius scale) physics; but also is computationally more efficient than the conventional formulation described in terms of potentials. As a benchmark, we perform linear as well as nonlinear simulations of the kinetic Alfvén wave; demonstrating physics in agreement with the analytical theories.

Linear Transformation of Electromagnetic Wave Beams of the Electron-Cyclotron Range in Toroidal Magnetic Configurations

The field structure of quasi-optical wave beams tunneled through the evanescence region in the vicinity of the plasma cutoff in a nonuniform magnetoactive plasma is analyzed. This problem is traditionally associated with the process of linear transformation of ordinary and extraordinary waves. An approximate analytical solution is constructed for a rather general magnetic configuration applicable to spherical tokamaks, optimized stellarators, and other magnetic confinement systems with a constant plasma density on magnetic surfaces. A general technique for calculating the transformation coefficient of a finite-aperture wave beam is proposed, and the physical conditions required for the most efficient transformation are analyzed.

Aspect ratio effects on limited scrape-off layer plasma turbulence

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio.

Spin Interactions in bcc and fcc Fe beyond the Heisenberg Model

Usually, the adiabatic magnetic exchange-energy hypersurface is parametrized in terms of the bilinear Heisenberg interactions in pairs of atoms. For general magnetic configurations, this model is not complete even if it includes pairs with up to infinite interatomic distances. In contrast, the modeling by an in principle infinite spin-cluster expansion is complete for all conceivable magnetic configurations. In the present Letter, it is shown for bcc and fcc iron that a very accurate representation can be reached with a finite expansion with 20 terms which include biquadratic or multispin non-Heisenberg interactions.

Ballooning filament growth in the intermediate nonlinear regime

A theory is developed for the description of ballooning instability in the intermediate nonlinear regime for general magnetic configurations including toroidal systems such as tokamaks. The evolution equations for the plasma filament growth induced by the ballooning instability are derived accounting for the dominant nonlinear effects in an ideal magnetohydrodynamic description. The intermediate nonlinear regime of ballooning modes is defined by the ordering that the plasma filament displacement across the magnetic surface is comparable to the linear mode width in the same direction. In the tokamak case, this regime could become particularly relevant for a transport barrier as the width of the barrier (or pedestal) region approaches the mode width of the dominant ballooning mode. A remarkable feature of the nonlinear ballooning equations is that solutions of the associated local linear ballooning mode equations continue to be valid solutions into the intermediate nonlinear regime. The filament growth equations for the intermediate nonlinear ballooning regime may be applicable to the precursor and precollapse phase of edge localized modes observed in both simulations and experiments.

3D Monte Carlo modelling of edge plasmas in fusion experiments

A three-dimensional model for the numerical simulation of transport in the edge plasma of modern fusion devices is developed. The model is based on the Braginskii set of equations which are solved with the help of a Monte Carlo method by three-dimensional plasma transport code E3D. The multiple coordinate system approach and interpolated cell mapping technique used in E3D allow us to avoid artificial numerical cross-field transport due to a high anisotropy of Braginskii equations in the case of general magnetic configurations including ergodic regions. The complete self-consistent set of fluid equations (equations for the density, parallel momentum, ion and electron temperatures) has been successfully implemented in E3D. A stabilization method for iterating coupled momentum and density equations is discussed.

Extensions of the 3‐Dimensional Plasma Transport Code E3D

AbstractOne important aspect of modern fusion research is plasma edge physics. Fluid transport codes extending beyond the standard 2‐D code packages like B2‐Eirene or UEDGE are under development. A 3‐dimensional plasma fluid code, E3D, based upon the Multiple Coordinate System Approach and a Monte Carlo integration procedure has been developed for general magnetic configurations including ergodic regions. These local magnetic coordinates lead to a full metric tensor which accurately accounts for all transport terms in the equations. Here, we discuss new computational aspects of the realization of the algorithm.The main limitation to the Monte Carlo code efficiency comes from the restriction on the parallel jump of advancing test particles which must be small compared to the gradient length of the diffusion coefficient. In our problems, the parallel diffusion coefficient depends on both plasma and magnetic field parameters. Usually, the second dependence is much more critical. In order to allow long parallel jumps, this dependence can be eliminated in two steps: first, the longitudinal coordinate x3 of local magnetic coordinates is modified in such a way that in the new coordinate system the metric determinant and contra‐variant components of the magnetic field scale along the magnetic field with powers of the magnetic field module (like in Boozer flux coordinates). Second, specific weights of the test particles are introduced. As a result of increased parallel jump length, the efficiency of the code is about two orders of magnitude better. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Adiabatic Invariant and Evaluation of Particle Loss in Helical Torus

Analytic expression for the longitudinal adiabatic invariant is derived for general magnetic configuration. The orbit loss is evaluated to determine the outermost loss-free surface. Geometrical factor of the neoclassical transport coefficients in 1/ν regime in helical torus is calculated by using the longitudinal adiabatic invariant. The dependence of the particle confinement upon the geometrical parameter is investigated; and the improvement by the inward shift of the plasma is quantitatively clarified.

The homologous flare sites and the general solar activity

The homologous flares observed in the same region of a spotgroup testify the existence and the duration of a permanent instability. However, they also attest that the general magnetic configuration is not destroyed by these flares and that it changes slowly up to the death of the site. The study of every flaring sites where more than ten flares occur has been performed in Meudon for the 1974–1980 period. One hundred and sixty-six sites have been analysed from the rotation where the A.R. is observed up to five rotations ahead. The basis of the study are the “Synoptic Maps”. A relation is found between the presence of crossing of “filament-phantom” corridors and the location of the homologous flare sites. ∗ ∗ The specific analysis concerning every active regions observed in 1980 and selected for the “homologous flares” study, i.e. A.R. nr. 2363; 2372; 2478; 2466-69-79; 2490; 2507; 2516-17; 2522; 2570; 2629; 2646; were grouped into a composite figure which was presented and explained during the Symposium.