Rapid Generation of Angular Momentum in Bounded Magnetized Plasma

Abstract

Direct numerical simulations of two-dimensional decaying MHD turbulence in bounded domains show the rapid generation of angular momentum in non-axisymmetric geometries. It is found that magnetic fluctuations enhance this mechanism. On a larger timescale, the generation of a magnetic angular momentum, or angular field, is observed. For axi-symmetric geometries, the generation of angular momentum is absent, nevertheless a weak angular field can be observed. The derived evolution equations for both angular momentum and angular field yield possible explanations for the observed behaviour.PACS numbers: 52.30. Cv, 52.65.Kj, The generation of large coherent structures of the size of the flow domain is a generic feature of two-dimensional (2D) turbulence. Indeed, due to the inverse energy cascade, 2D flows show a tendency to create space filling structures. The nature of these structures and the way they are produced vary from flow to flow. In the context of Navier-Stokes turbulence the generation of a largescale domain-filling structure was predicted by Kraichnan [1] and observed in the case of forced turbulence in a periodic domain in which energy condenses at the smallest possible wave number modes [2,3]. In forced wallbounded flows this was reproduced numerically [4] and experimentally [5], and it was shown that a large scale rotating structure emerges, which dramatically reduces the level of the turbulent fluctuations [6].A similar observation can be made in fusion plasmas, in which the dynamics share many features with 2D flows due to the imposed magnetic field. It is often assumed that in these plasmas large scale poloidal structures, called zonal flows, are beneficial for the confinement as they suppress turbulence and shear apart radially extended structures, which are largely responsible for anomalous transport [7][8][9]. The hereby created transport barriers might play a key role in the transition to an improved confinement state (H-mode) [10]. In the case of MHD turbulence the role of rotation was shown to have a similar effect on the flow, reducing the velocity fluctuations and hereby stabilizing the magnetic field [11]. In the present work we will continue the investigation of wall bounded non-ideal MHD. The generation of zonal flows through the absence of charge neutrality will not be addressed (charge neutrality being implied by the onefield MHD approximation). However, MHD allows for an affordable global description of non-uniform magnetoplasmas [12]. The present work could be related to the L-H transition through the beneficial effects of large scale poloidal rotation (which is observed in the present work) on the confinement of the plasma. The present study is also motivated by the observation that MHD-equilibria in toroidal geometry imply finite flow-fields due to the finite viscosity and resistivity [12][13][14]. In these works non-ideal MHD steady states were investigated in both the limit of small and large viscosity. In each case it was shown that the steady state contains non-vanishing velocity ...

Universal statistics of point vortex turbulence

“…Additionally, however, condensation is observed in numerical simulations (e.g. Chertkov et al 2007) and experiments (Paret & Tabeling 1998;Shats et al 2005) of both forced and unforced 2D turbulence in fluids, as well as in bounded magnetized plasmas (Bos et al 2008), where its occurrence has been argued to be of importance for plasma confinement in tokomak experiments. One particularly interesting example of condensation occurs in numerical simulations of decaying two-dimensional Navier-Stokes turbulence in a square domain (Clercx et al 1998(Clercx et al , 2001.…”

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

“…The strength of the combination of a pseudo-spectral Navier-Stokes solver with the penalization method is the compromise between accuracy and ease of implementation while retaining a great flexibility in the choice of the geometry of the boundaries. We have already used this method to study two-dimensional MHD [18,19,20] which allowed to compare square, circular and periodic boundaries using the same Cartesian grid and numerical method. In the present paper we will present a detailed validation of the method for two and three-dimensional confined HD and MHD flows.…”

Magnetohydrodynamically generated velocities in confined plasma

“…Results for two-dimensional viscoresistive MHD can be found in Ref. [6,4]. The method is presented in detail for three-dimensional viscoresistive MHD equations in [7].…”

“…A steep gradient between the two regions serves as an active visco-resistive boundary. The method has been used to considerable effect both for Navier-Stokes turbulence [5] and for magnetofluids in the recent past [6,7,4]. The Fourier pseudo-spectral codes used for the dynamical advancement of the field quantities are of a well-studied type.…”