Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations
type: Item
instance of: scholarly article
title: Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations
zbMATH Open document ID: 1412.65081
author: Guillaume Latu
author: Michel Mehrenberger
author: Y. Güçlü
author: Maurizio Ottaviani
author: Eric Sonnendrücker
published in: Journal of Scientific Computing
publication date: 2018-04-13T00:00:00Z
review text: The authors study the numerical solution of the gyrokinetic Vlasov equation by means of a semi-Lagrangian method using field aligned interpolation. The equation under consideration is \[ \Big (\frac{\partial}{\partial t} +\mathbf{u}(t,\mathbf{x},v_{\parallel},\mu) \cdot \nabla + a_{\parallel}(t,\mathbf{x},v_{\parallel},\mu) \frac{\partial}{\partial v_{\parallel}} \Big )f(t,\mathbf{x},v_{\parallel},\mu) = 0.\tag{1} \] Here, \(f\) is the gyro-center distribution function for a single ion species which is immersed in a static magnetic field \(\mathbf{B}(\mathbf{x})\). The phase space coordinates are \((\mathbf{x},v_{\parallel},\mu)\) in which \(\mathbf{x}\) is the gyro-center position, \(v_{\parallel}\) is velocity parallel to \(\mathbf{B}\), and \(\mu\) is the modified magnetic moment. The fields \(\mathbf{u}\) and \(a_{\parallel}\) are given in terms of \(\mathbf{B}\) and the gyro-center Hamiltonian \(H(t,\mathbf{x},v_{\parallel},\mu) = \frac12 mv_{\parallel}^2 + \mu \mathbf{B}(\mathbf{x}) + q\langle \phi \rangle_{\alpha} (t,\mathbf{x})\) in which \(\phi(t,\mathbf{x})\) is the electrostatic potential, and \(\langle \cdot \rangle_{\alpha}\) the gyro-average operator. The function \(\phi(t,\mathbf{x})\) is obtained as the solution to \[ -\Big (\nabla_{\perp} \cdot \frac{\rho_{th,i}^2}{\lambda_{D,i}^2} \nabla_{\perp} \Big ) \phi + \frac{1}{\lambda_{D,e}^2}(\phi - \langle \phi \rangle_f) = \frac{q_i}{\epsilon_0}(n_i - n_0). \tag{2} \] In (2), \(\nabla_{\perp}\) is a gradient operator perpendicular to the magnetic field, \(\langle \cdot \rangle_f\) an averaging operator, \(\rho_{th,i}(\mathbf{x})\) is the thermal ion Larmor radius, \(\lambda_{D,i}(\mathbf{x}),\; \lambda_{D,e} (\mathbf{x})\) Debye lengths for ions and electrons, \(n_i(t,\mathbf{x})\) is the instantaneous ion number density, \(n_0(\mathbf{x})\) is the equilibrium ion density, \(q_i\) the ion charge, and \(\epsilon_0\) the vacuum permittivity. In the paper, the authors consider two model problems. The first …
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35Q83
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 82D10
Mathematics Subject Classification ID: 82D75
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 76M20
zbMATH DE Number: 6859537
zbMATH Keywords: plasma physics
zbMATH Keywords: gyrokinetics
zbMATH Keywords: semi-Lagrangian
zbMATH Keywords: tokamak plasma
Wikidata QID: Q59528333
reviewed by: Stephen Wollman
describes a project that uses: GYSELA
describes a project that uses: QUALIMUWABA
describes a project that uses: CYLGYR
MaRDI profile type: Publication
full work available at URL: s10915-017-0509-5
OpenAlex ID: W2407525779
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DOI: 10.1007/S10915-017-0509-5
description: scientific article; zbMATH DE number 6859537