A Second-Order Unsplit Godunov Scheme for Cell-Centered MHD: the CTU-GLM scheme

We assess the validity of a single step Godunov scheme for the solution of the magneto-hydrodynamics equations in more than one dimension. The scheme is second-order accurate and the temporal discretization is based on the dimensionally unsplit Corner Transport Upwind (CTU) method of Colella. The proposed scheme employs a cell-centered representation of the primary fluid variables (including magnetic field) and conserves mass, momentum, magnetic induction and energy. A variant of the scheme, which breaks momentum and energy conservation, is also considered. Divergence errors are transported out of the domain and damped using the mixed hyperbolic/parabolic divergence cleaning technique by Dedner et al. (J. Comput. Phys., 175, 2002). The strength and accuracy of the scheme are verified by a direct comparison with the eight-wave formulation (also employing a cell-centered representation) and with the popular constrained transport method, where magnetic field components retain a staggered collocation inside the computational cell. Results obtained from two- and three-dimensional test problems indicate that the newly proposed scheme is robust, accurate and competitive with recent implementations of the constrained transport method while being considerably easier to implement in existing hydro codes.Comment: 31 Pages, 16 Figures Accepted for publication in Journal of Computational Physic

High-order conservative finite difference GLM-MHD schemes for cell-centered MHD

We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting family of schemes is robust, cost-effective and straightforward to implement. Compared to previous existing approaches, it completely avoids the CPU intensive workload associated with an elliptic divergence cleaning step and the additional complexities required by staggered mesh algorithms. Extensive numerical testing demonstrate the robustness and reliability of the proposed framework for computations involving both smooth and discontinuous features.Comment: 32 pages, 14 figure, submitted to Journal of Computational Physics (Aug 7 2009

Proton imaging of stochastic magnetic fields

Recent laser-plasma experiments report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for understanding the physical processes these experiments are attempting to investigate. In this paper, we show how a proton imaging diagnostic can be used to determine a range of relevant magnetic field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. We conclude that features of the beam's final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter - the contrast parameter - which quantifies the relative size of the correlation length of the stochastic field, proton displacements due to magnetic deflections, and the image magnification. For stochastic magnetic fields, we establish the existence of four contrast regimes - linear, nonlinear injective, caustic and diffusive - under which proton-flux images relate to their parent fields in a qualitatively distinct manner. As a consequence, it is demonstrated that in the linear or nonlinear injective regimes, the path-integrated magnetic field experienced by the beam can be extracted uniquely, as can the magnetic-energy spectrum under a further statistical assumption of isotropy. This is no longer the case in the caustic or diffusive regimes. We also discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, as well as limitations currently placed by experimental capabilities on extracting magnetic field statistics. The results presented in this paper provide a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of given proton-flux images.Comment: Main paper pp. 1-29; appendices pp. 30-84. 24 figures, 2 table

Parameter study in disk-jet systems: Magnetization

In this study we discuss the impact of the magnetic field’s strength onto the characteristics of solutions in models where both the collimated outflow and the accretion disk are treated consistently. We perform an analysis on the range of magnetic field by non-relativistic 2.5 dimension numerical simulations using the PLUTO code. The main results are that magnetic fields around equipartition with plasma pressure allow for steady super-fast-magnetosonic collimated jet solutions; magnetic fields below equipartition correspond to intermittent collimated outflows, whereas above equipartition cases lead to sub-alfvenic winds. This allows to conclude that the configuration proposed by Blandford and Payne to interpret supersonic jets is viable both for equipartition and weaker magnetic fields