Relaxation to magnetohydrodynamics equilibria via collision brackets

Metriplectic dynamics is applied to compute equilibria of fluid dynamical systems. The result is a relaxation method in which Hamiltonian dynamics (symplectic structure) is combined with dissipative mechanisms (metric structure) that relaxes the system to the desired equilibrium point. The specific metric operator, which is considered in this work, is formally analogous to the Landau collision operator. These ideas are illustrated by means of case studies. The considered physical models are the Euler equations in vorticity form, the Grad-Shafranov equation, and force-free MHD equilibria.Comment: Conference Proceeding (Theory of Fusions Plasmas, 2018), 9 pages, 8 figure

Incoherent Thomson scattering diagnostics in non-relativistic current-carrying plasmas

measurements of electron distribution functions to the case of the experimental setup proposed by Kantor [1] for the ASDEX Upgrade tokamak; these cal-culations have been used in the feasibility study by Tsalas et al. [2]. More specifically, we begin from the theory reported by Sheffield [3] for the scattered power, and we follow closely the analysis of Segre [4, 5]; then, we compute the signal to noise ratio (SNR) as in the work of Carretta et al. [6]. In our analysis, we assume that electrons are well described by the Spitzer and Härm distribution function [7]; such an assumption is common in the Thom-son scattering literature [5, 6], though it implies that trapping effects, due to the inhomogeneous magnetic field of a tokamak, as well as relativistic effects, are neglected. Moreover, strictly speaking, the use of the Spitzer-Härm electron distribution function is justified for an Ohmic current density only, i.e., a cur-rent density driven by an external electric field. A more precise analysis would require a detailed modeling of the electron distribution function, which could be obtained, e.g., by solving the Fokker-Planck equation in the drift approximation

Giant dipole resonance with exact treatment of thermal fluctuations

The shape fluctuations due to thermal effects in the giant dipole resonance (GDR) observables are calculated using the exact free energies evaluated at fixed spin and temperature. The results obtained are compared with Landau theory calculations done by parameterizing the free energy. The Landau theory is found to be insufficient when the shell effects are dominating.Comment: 5 pages, 2 figure

The wave energy flux of high frequency diffracting beams in complex geometrical optics

We consider the construction of asymptotic solutions of Maxwell's equations for a diffracting wave beam in the high frequency limit and address the description of the wave energy flux transported by the beam. With this aim, the complex eikonal method is applied. That is a generalization of the standard geometrical optics method in which the phase function is assumed to be complex valued, with the non-negative imaginary part accounting for the finite width of the beam cross section. In this framework, we propose an argument which simplifies significantly the analysis of the transport equation for the wave field amplitude and allows us to derive the wave energy flux. The theoretical analysis is illustrated numerically for the case of electron cyclotron beams in tokamak plasmas by using the GRAY code [D. Farina, Fusion Sci. Technol. 52, 154 (2007)], which is based upon the complex eikonal theory. The results are compared to those of the paraxial beam tracing code TORBEAM [E. Poli et al., Comput. Phys. Commun. 136, 90 (2001)], which provides an independent calculation of the energy flow