Gian Luca Delzanno

Electron acceleration during guide field magnetic reconnection

Particle-in-cell simulations of the guide field intermittent magnetic reconnection are performed to study electron acceleration and pitch angle distributions. During the growing stage of reconnection, the power-law distribution function for the high-energy electrons and the pitch angle distributions of the low-energy electrons are obtained and compare favorably with observations by the Wind spacecraft. Direct evidence is found for the secondary acceleration during the later reconnection stage. A correlation between the generation of energetic electrons and the induced reconnection electric field is found. Energetic electrons are accelerated first around the X line, and then in the region outside the diffusion region, when the reconnection electric field has a bipolar structure. The physical mechanisms of these accelerations are discussed. The in-plane electrostatic field that traps the low-energy electrons and causes the anisotropic pitch angle distributions has been observed.

Orbital-motion-limited theory of dust charging and plasma response

The foundational theory for dusty plasmas is the dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma. The most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, which predicts the dust potential and heat collection accurately for a variety of applications, but was previously found to be incapable of evaluating the dust charge and plasma response in any situation. Here, we report a revised OML formulation that is able to predict the plasma response and hence the dust charge. Numerical solutions of the new OML model show that the widely used Whipple approximation of dust charge-potential relationship agrees with OML theory in the limit of small dust radius compared with plasma Debye length, but incurs large (order-unity) deviation from the OML prediction when the dust size becomes comparable with or larger than plasma Debye length. This latter case is expected for the important application of dust particles in a tokamak plasma.

Robust, multidimensional mesh-motion based on Monge-Kantorovich equidistribution

Mesh-motion (r-refinement) grid adaptivity schemes are attractive due to their potential to minimize the numerical error for a prescribed number of degrees of freedom. However, a key roadblock to a widespread deployment of this class of techniques has been the formulation of robust, reliable mesh-motion governing principles, which (1) guarantee a solution in multiple dimensions (2D and 3D), (2) avoid grid tangling (or folding of the mesh, whereby edges of a grid cell cross somewhere in the domain), and (3) can be solved effectively and efficiently. In this study, we formulate such a mesh-motion governing principle, based on volume equidistribution via Monge-Kantorovich optimization (MK). In earlier publications [1,2], the advantages of this approach with regard to these points have been demonstrated for the time-independent case. In this study, we demonstrate that Monge-Kantorovich equidistribution can in fact be used effectively in a time-stepping context, and delivers an elegant solution to the otherwise pervasive problem of grid tangling in mesh-motion approaches, without resorting to ad hoc time-dependent terms (as in moving-mesh PDEs, or MMPDEs [3,4]). We explore two distinct r-refinement implementations of MK: the direct method, where the current mesh relates to an initial, unchanging mesh, and the sequential method, where the current mesh is related to the previous one in time. We demonstrate that the direct approach is superior with regard to mesh distortion and robustness. The properties of the approach are illustrated with a hyperbolic PDE, the advection of a passive scalar, in 2D and 3D. Velocity flow fields with and without flow shear are considered. Three-dimensional grid, time-step, and nonlinear tolerance convergence studies are presented which demonstrate the optimality of the approach.

Kink instability of flux ropes anchored at one end and free at the other

The kink instability of a magnetized plasma column (flux rope) is a fundamental process observed in laboratory and in natural plasmas. Previous theoretical, experimental, and observational work has focused either on the case of periodic (infinite) ropes (relevant to toroidal systems) or on finite ropes with both ends tied to a specified boundary (relevant to coronal ropes tied at the photosphere). However, in the Suns corona and in astrophysical systems there is an abundant presence of finite flux ropes tied at one end but free at the other. Motivated by recent experiments conducted on the RSX device (Furno et al., 2006) and by recent theoretical work (Ryutov et al., 2006), the present paper investigates by simulation the linear and nonlinear evolution of free-ended flux ropes. The approach is based on comparing the classic case of a periodic flux rope with the case of a rope tied at one end and free at the other. In the linear phase, periodic and free ropes behave radically differently. A simulation analysis of the linear phase confirms the experimental and phenomenological findings relative to an increased instability of a free rope: the new stability limit is shown to be just half of the classic limit for periodic ropes. In the nonlinear phase, reconnection is observed to be a fundamental enabler to reach the eventual steady state. The mechanism for saturation of a flux rope is investigated and compared with the classic theory (the so-called bubble state model) by Rosenbluth et al. (1976). A remarkable agreement is found for the classic periodic case. The case of a free rope is again very different. The saturated state is observed to present a outwardly spiraling configuration with the displacement of the plasma column increasing progressively and monotonically from the tied end to the free end. The maximum displacement is observed at the free end where it is consistent with the displacement observed in a periodic rope. The key distinction is that in a periodic rope the same displacement is observed throughout the whole rope to form a helix with constant radius.

Grid Generation and Adaptation by Monge-Kantorovich Optimization in Two and Three Dimensions

The derivation of the Monge-Ampere (MA) equation, as it results from a variational principle involving grid displacement, is outlined in two dimensions (2D). This equation, a major element of Monge-Kantorovich (MK) optimization, is discussed both in the context of grid generation and grid adaptation. It is shown that grids which are generated by the MA equation also satisfy equations of an alternate variational principle minimizing grid distortion. Numerical results are shown, indicating robustness to grid tangling. Comparison is made with the deformation method [G. Liao and D. Anderson, Appl. Analysis 44, 285 (1992)], the existing method of equidistribution. A formulation is given for more general physical domains, including those with curved boundary segments. The Monge-Ampere equation is also derived in three dimensions (3D). Several numerical examples, both with more general 2D domains and in 3D, are given.

A new method for analyzing line-tied kink modes in cylindrical geometry

A new method for studying linear stability of the m=1 (kink) mode in a cylinder with line-tied boundary conditions is presented. The method is applicable to both resistive and ideal MHD. It is based on expansion in one-dimensional eigenfunctions depending on the radius, satisfying boundary conditions on the cylindrical axis and radial wall. The boundary conditions at the end plates are satisfied by a sum of such radial eigenfunctions. The spectrum of possibly complex axial eigenvalues k is studied and is shown to consist of a continuum part and a discrete part in ideal MHD. Only the discrete part is used to give an approximation to the complete two-dimensional eigenfunction. The method is applied to a special equilibrium magnetic field with constant field line pitch. The role of the individual radial eigenfunctions is explained. It is shown that our method reproduces previously found values of the critical pitch (at marginal stability) for a plasma column in vacuum. The method also suggests important diff...

On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier–Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

Plasma dragged microparticles as a method to measure plasma flows

The physics of microparticle motion in flowing plasmas is studied in detail for plasmas with electron and ion densities ne,i∼1019m−3, electron and ion temperatures of no more than 15eV, and plasma flows on the order of the ion thermal speed, vf∼vti. The equations of motion due to Coulomb interactions and direct impact with ions and electrons, of charge variation, as well as of heat exchange with the plasma, are solved numerically for isolated particles (or dust grains) of micron sizes. It is predicted that microparticles can survive in plasma long enough, and can be dragged in the direction of the local ion flow. Based on the theoretical analysis, we describe a new plasma flow measurement technique called microparticle tracer velocimetry (mPTV), which tracks microparticle motion in a plasma with a high-speed camera. The mPTV can reveal the directions of the plasma flow vectors at multiple locations simultaneously and at submillimeter scales, which is hard to achieve by most other techniques. Thus, mPTV ca...

The effect of line-tying on tearing modes

Cylindrical magnetohydrodynamic (MHD) constant-ψ or nonconstant-ψ tearing modes that are linearly unstable with periodic axial boundary conditions are studied in a line-tied cylinder. Examples of these two respective classes of modes, with m=1 and m=2 (m being the azimuthal mode number), are studied. With a suitable MHD equilibrium, the former modes are marginally stable in ideal MHD for periodic axial boundary conditions, and occur as fast tearing modes (resistive kinks) in the presence of resistivity η. The latter modes are stable in ideal MHD for periodic axial boundary conditions, and with resistivity occur as constant-ψ tearing modes, unstable in a range of parameters. In both cases, the results for the line-tied modes show the expected tearing scaling with η for very long plasmas, but the scaling becomes γ∝η for smaller cylinder lengths L. These results are consistent with the following interpretation: For L→∞, the modes have a tearing width characteristic of tearing, leading to characteristic teari...

Multi-dimensional, fully-implicit, spectral method for the Vlasov-Maxwell equations with exact conservation laws in discrete form

A spectral method for the numerical solution of the multi-dimensional Vlasov-Maxwell equations is presented. The plasma distribution function is expanded in Fourier (for the spatial part) and Hermite (for the velocity part) basis functions, leading to a truncated system of ordinary differential equations for the expansion coefficients (moments) that is discretized with an implicit, second order accurate Crank-Nicolson time discretization. The discrete non-linear system is solved with a preconditioned Jacobian-Free Newton-Krylov method.It is shown analytically that the Fourier-Hermite method features exact conservation laws for total mass, momentum and energy in discrete form. Standard tests involving plasma waves and the whistler instability confirm the validity of the conservation laws numerically. The whistler instability test also shows that we can step over the fastest time scale in the system without incurring in numerical instabilities. Some preconditioning strategies are presented, showing that the number of linear iterations of the Krylov solver can be drastically reduced and a significant gain in performance can be obtained.