# Posts Tagged magnetohydrodynamic

## Recent Postings from magnetohydrodynamic

### On the Alfven wave cut-off in partly ionized collisional plasmas [Cross-Listing]

The cut-off of the Alfven wave, caused by plasma collisions with neutrals in multi-component partially ionized plasmas, is discussed. Full multi-component theory is used, and similarities and differences regarding the classic magnetohydrodynamic theory are presented. It is shown that the cut-off in partially ionized plasma in principle may remain the same as predicted in classic magnetohydrodynamic works, although multi-component theory also yields some essential differences. Due to electric field, the ion motion is intrinsically two-dimensional and this results in additional forced oscillations of neutrals. One new small parameter, containing the ion inertial length, appears in the multi-component theory. This new small parameter is missing in the magnetohydrodynamic description, and it turns out that for some parameters it may be greater than the ions-to-neutrals density ratio which is the only small parameter in the magnetohydrodynamic description. Due to this the Alfven wave behavior can become much different as compared to classic magnetohydrodynamic results. It is shown also that in plasmas with unmagnetized ions, Alfv}n waves cannot be excited. This by all means applies to the solar photosphere where the ion collision frequency may be far above the ion gyro-frequency.

### Search for Stable Magnetohydrodynamic Equilibria in Barotropic Stars

It is now believed that magnetohydrodynamic equilibria can exist in stably stratified stars due to the seminal works of Braithwaite & Spruit (2004) and Braithwaite & Nordlund (2006). What is still not known is whether magnetohydrodynamic equilibria can exist in a barotropic star, in which stable stratification is not present. It has been conjectured by Reisenegger (2009) that there will likely not exist any magnetohydrodynamical equilibria in barotropic stars. We aim to test this claim by presenting preliminary MHD simulations of barotropic stars using the three dimensional stagger code of Nordlund & Galsgaard (1995).

### Simulation of homologous and cannibalistic CMEs produced by the emergence of a twisted flux rope into the Corona

We report the first results of a magnetohydrodynamic (MHD) simulation of the development of a homologous sequence of three coronal mass ejections (CMEs) and demonstrate the so-called cannibalistic behavior. These CMEs originate from the repeated formations and partial eruptions of kink unstable flux ropes as a result of continued emergence of a twisted flux rope across the lower boundary into a pre-existing coronal potential arcade field. The simulation shows that a CME erupting into the open magnetic field created by a preceding CME has a higher speed. The second of the three successive CMEs simulated is cannibalistic catching up and merging with the first into a single fast CME before exiting the domain. All the CMEs including the leading merged CME, attained speeds of about 1000 km/s as they exit the domain. The reformation of a twisted flux rope after each CME eruption during the sustained flux emergence can naturally explain the X-ray observations of repeated reformations of sigmoids and "sigmoid-under-cusp" configurations at a low-coronal source of homologous CMEs.

### A new equilibrium torus solution and GRMHD initial conditions

General relativistic magnetohydrodynamic (GRMHD) simulations are providing influential models for black hole spin measurements, gamma ray bursts, and supermassive black hole feedback. Many of these simulations use the same initial condition: a rotating torus of fluid in hydrostatic equilibrium. A persistent concern is that simulation results sometimes depend on arbitrary features of the initial torus. For example, the Bernoulli parameter (which is related to outflows), appears to be controlled by the Bernoulli parameter of the initial torus. In this paper, we give a new equilibrium torus solution and describe two applications for the future. First, it can be used as a more physical initial condition for GRMHD simulations than earlier torus solutions. Second, it can be used in conjunction with earlier torus solutions to isolate the simulation results that depend on initial conditions. We assume axisymmetry, an ideal gas equation of state, constant entropy, and ignore self-gravity. We fix an angular momentum distribution and solve the relativistic Euler equations in the Kerr metric. The Bernoulli parameter, rotation rate, and geometrical thickness of the torus can be adjusted independently. Our torus tends to be more bound and have a larger radial extent than earlier torus solutions. While this paper was in preparation, several GRMHD simulations appeared based on our equilibrium torus. We believe it will continue to provide a more realistic starting point for future simulations.

### Magnetohydrodynamics dynamical relaxation of coronal magnetic fields. IV. 3D tilted nulls

In this paper we study current accumulations in 3D "tilted" nulls formed by a folding of the spine and fan. A non-zero component of current parallel to the fan is required such that the null’s fan plane and spine are not perpendicular. Our aims are to provide valid magnetohydrostatic equilibria and to describe the current accumulations in various cases involving finite plasma pressure.To create our equilibrium current structures we use a full, non-resistive, magnetohydrodynamic (MHD) code so that no reconnection is allowed. A series of experiments are performed in which a perturbed 3D tilted null relaxes towards an equilibrium via real, viscous damping forces. Changes to the initial plasma pressure and to magnetic parameters are investigated systematically.An initially tilted fan is associated with a non-zero Lorentz force that drives the fan and spine to collapse towards each other, in a similar manner to the collapse of a 2D X-point. In the final equilibrium state for an initially radial null with only the current perpendicular to the spine, the current concentrates along the tilt axis of the fan and in a layer about the null point with a sharp peak at the null itself. The continued growth of this peak indicates that the system is in an asymptotic regime involving an infinite time singularity at the null. When the initial tilt disturbance (current perpendicular to the spine) is combined with a spiral-type disturbance (current parallel to the spine), the final current density concentrates in three regions: one on the fan along its tilt axis and two around the spine, above and below the fan. The increased area of current accumulation leads to a weakening of the singularity formed at the null. The 3D spine-fan collapse with generic current studied here provides the ideal setup for non-steady reconnection studies.

### Global hydromagnetic simulations of a planet embedded in a dead zone: gap opening, gas accretion and formation of a protoplanetary jet

(Abridged) We present the results of 3D global hydrodynamic and magnetohydrodynamic (MHD) simulations of accreting planets embedded in protoplanetary disks (PPDs). The MHD calculation includes an Ohmic resistivity depending on the density, temperature and overlying mass column, leading to a layered disk that has turbulent surface layers and an inert dead zone near the midplane. [...] The main results can be summarized as follows: (i) In agreement with previous studies we find that the accretion flow in the planet Hill sphere is intrinsically three dimensional for both laminar and turbulent models. Net inflow toward the planet is dominated by flows that originate from high latitudes. Midplane regions of the quasi-Keplerian circumplanetary disks (CPDs) that form display outflow away from the planet, with a spatial distribution that varies between the models. (ii) Gap opening ignites the dead zone into a turbulent state due to increased ionization in the low density gas. The accreting planet is then embedded in a turbulent environment, leading to stochastic accretion and a quasi-turbulent flow within the Hill sphere. (iii) Advection of gas and magnetic field into the Hill sphere, where it joins the rotating CPD, generates helical fields that launch magnetocentrifugally driven outflows. During one particular time interval we observe that a highly-collimated, one-sided protoplanetary jet is launched from the circumplanetary disk. (iv) The surface density of the CPD is found to be ~ 30g/cm^2, small enough to allow significant ionization and magnetized turbulence to develop. (v) The accretion rate onto the planet in the MHD simulation reaches a steady value of approximately 0.008 earth masses per year. [...] Our simulations suggest that gas accretion onto a forming giant planet within a magnetized PPD with dead zone allows rapid growth from Saturnian to Jovian masses and above. [...]

### Simulations of Emerging Magnetic Flux. I: The Formation of Stable Coronal Flux Ropes

We present results from 3D visco-resistive magnetohydrodynamic (MHD) simulations of the emergence of a convection zone magnetic flux tube into a solar atmosphere containing a pre-existing dipole coronal field, which is orientated to minimize reconnection with the emerging field. We observe that the emergence process is capable of producing a coronal flux rope by the transfer of twist from the convection zone as found in previous simulations. We find that this flux rope is stable, with no evidence of a fast rise, and that its ultimate height in the corona is determined by the strength of the pre-existing dipole field. We also find that although the electric currents in the initial convection zone flux tube are almost perfectly neutralized, the resultant coronal flux rope carries a significant net current. These results suggest that flux tube emergence is capable of creating non-current-neutralized stable flux ropes in the corona, tethered by overlying potential fields, a magnetic configuration that is believed to be the source of coronal mass ejections.

### Direct Numerical Simulations of Reflection-Driven, Reduced MHD Turbulence from the Sun to the Alfven Critical Point

We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfv\’en critical point. These are the first such simulations that take into account the solar-wind outflow velocity and the radial inhomogeneity of the background solar wind without approximating the nonlinear terms in the governing equations. RMHD turbulence is driven by outward-propagating Alfv\’en waves ($z^+$ fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfv\’en waves ($z^-$ fluctuations). We present ten simulations with different values of the correlation time $\tau_{\rm c\,\sun}^+$ and perpendicular correlation length $L_{\perp \sun}$ of outward-propagating Alfv\’en waves (AWs) at the coronal base. We find that between 15\% and 33\% of the $z^+$ energy launched into the corona dissipates between the coronal base and Alfv\’en critical point. Between 33\% and 40\% of this input energy goes into work on the solar-wind outflow, and between 22\% and 36\% escapes as $z^+$ fluctuations through the simulation boundary at $r=r_{\rm A}$. The $z^\pm$ power spectra scale like $k_\perp^{-\alpha^\pm}$, where $k_\perp$ is the wavenumber in the plane perpendicular to $\vec{B}_0$. In our simulation with the smallest value of $\tau_{\rm c\,\sun}^+$ ($\sim 2 \mbox{ min}$) and largest value of $L_{\perp \sun}$ ($2\times 10^4 \mbox{ km}$), we find that $\alpha^+$ decreases approximately linearly with increasing $\ln(r)$, reaching a value of 1.3 at $r=11.1 R_{\sun}$. Our simulations with larger values of $\tau_{\rm c\,\sun}^+$ exhibit alignment between the contours of constant $\phi^+$, $\phi^-$, $\Omega_0^+$, and $\Omega_0^-$, where $\phi^\pm$ are the Els\"asser potentials and $\Omega_0^\pm$ are the outer-scale parallel Els\"asser vorticities.

### Direct Numerical Simulations of Reflection-Driven, Reduced MHD Turbulence from the Sun to the Alfven Critical Point [Replacement]

We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfv\’en critical point. These are the first such simulations that take into account the solar-wind outflow velocity and the radial inhomogeneity of the background solar wind without approximating the nonlinear terms in the governing equations. RMHD turbulence is driven by outward-propagating Alfv\’en waves ($z^+$ fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfv\’en waves ($z^-$ fluctuations). We present ten simulations with different values of the correlation time $\tau_{\rm c\,\sun}^+$ and perpendicular correlation length $L_{\perp \sun}$ of outward-propagating Alfv\’en waves (AWs) at the coronal base. We find that between 15% and 33% of the $z^+$ energy launched into the corona dissipates between the coronal base and Alfv\’en critical point. Between 33% and 40% of this input energy goes into work on the solar-wind outflow, and between 22% and 36% escapes as $z^+$ fluctuations through the simulation boundary at $r=r_{\rm A}$. The $z^\pm$ power spectra scale like $k_\perp^{-\alpha^\pm}$, where $k_\perp$ is the wavenumber in the plane perpendicular to $\vec{B}_0$. In our simulation with the smallest value of $\tau_{\rm c\,\sun}^+$ ($\sim 2 \mbox{min}$) and largest value of $L_{\perp \sun}$ ($2\times 10^4 \mbox{km}$), we find that $\alpha^+$ decreases approximately linearly with increasing $\ln(r)$, reaching a value of 1.3 at $r=11.1 R_{\sun}$. Our simulations with larger values of $\tau_{\rm c\,\sun}^+$ exhibit alignment between the contours of constant $\phi^+$, $\phi^-$, $\Omega_0^+$, and $\Omega_0^-$, where $\phi^\pm$ are the Els\"asser potentials and $\Omega_0^\pm$ are the outer-scale parallel Els\"asser vorticities.

### Explosive reconnection of double tearing modes in relativistic plasmas: application to the Crab flares

Magnetic reconnection associated to the double tearing mode (DTM) is investigated by means of resistive relativistic magnetohydrodynamic (RRMHD) simulations. A linearly unstable double current sheet system in two dimensional cartesian geometry is considered. For initial perturbations of large enough longitudinal wavelengths, a fast reconnection event is triggered by a secondary instability that is structurally driven by the nonlinear evolution of the magnetic islands. The latter reconnection phase and time scale appear to weakly depend on the plasma resistivity and magnetization parameter. We discuss the possible role of such explosive reconnection dynamics to explain the MeV flares observed in the Crab pulsar nebula. Indeed the time scale and the critical minimum wavelength give constraints on the Lorentz factor of the striped wind and on the location of the emission region respectively.

### Cosmic Ray Parallel and Perpendicular Transport in Turbulent Magnetic Fields

A correct description of cosmic ray (CR) diffusion in turbulent plasma is essential for many astrophysical and heliospheric problems. This paper aims at presenting physical diffusion behavior of CRs in actual turbulent magnetic fields, model of which has been numerically tested. We perform test particle simulations in compressible magnetohydrodynamic (MHD) turbulence. We obtain scattering and spatial diffusion coefficients by tracing particle trajectories. We find no resonance gap for pitch-angle scattering at 90$^\circ$. Our result confirms the dominance of mirror interaction with compressible modes for most pitch angles as revealed by the nonlinear theory. For cross field transport, our results are consistent with normal diffusion predicted earlier for large scales. The diffusion behavior strongly depends on the Alfvenic Mach number and particle’s parallel mean free path. We for the first time numerically derive the dependence of M_A^4 for perpendicular diffusion coefficient with respect to the mean magnetic field. We conclude that CR diffusion coefficients are anisotropic in sub-Alfvenic turbulence and spatially correlated to the local turbulence properties. On scales smaller than the injection scale, we find that CRs are superdiffusive. We emphasize the importance of our results in a wide range of astrophysical processes, including magnetic reconnection.

### Cosmic Ray Parallel and Perpendicular Transport in Turbulent Magnetic Fields [Replacement]

A correct description of cosmic ray (CR) diffusion in turbulent plasma is essential for many astrophysical and heliospheric problems. This paper aims at presenting physical diffusion behavior of CRs in actual turbulent magnetic fields, model of which has been numerically tested. We perform test particle simulations in compressible magnetohydrodynamic (MHD) turbulence. We obtain scattering and spatial diffusion coefficients by tracing particle trajectories. We find no resonance gap for pitch-angle scattering at 90$^\circ$. Our result confirms the dominance of mirror interaction with compressible modes for most pitch angles as revealed by the nonlinear theory. For cross field transport, our results are consistent with normal diffusion predicted earlier for large scales. The diffusion behavior strongly depends on the Alfvenic Mach number and particle’s parallel mean free path. We for the first time numerically derive the dependence of M_A^4 for perpendicular diffusion coefficient with respect to the mean magnetic field. We conclude that CR diffusion coefficients are anisotropic in sub-Alfvenic turbulence and spatially correlated to the local turbulence properties. On scales smaller than the injection scale, we find that CRs are superdiffusive. We emphasize the importance of our results in a wide range of astrophysical processes, including magnetic reconnection.

### The Collisionless Magnetothermal Instability

It is likely that nearly all central galactic massive and supermassive black holes are nonradiative: their accretion luminosities are orders of magnitude below what can be explained by efficient black hole accretion within their ambient environments. These objects, of which Sagittarius A* is the best-known example, are also dilute (mildly collisional to highly collisionless) and optically thin. In order for accretion to occur, magnetohydrodynamic instabilities must develop that not only transport angular momentum, but also gravitational energy generated through matter infall, outwards. A class of new magnetohydrodynamical fluid instabilities — the magnetoviscous-thermal instability (MVTI) (Islam12) — was found to transport angular momentum and energy along magnetic field lines through large (fluid) viscosities and thermal conductivities. This paper describes the collisionless and mildly collisional analogue to the MVTI, the collisional magnetothermal instability (CMTI), that similarly transports energy and angular momentum outwards, expected to be important in describing the flow properties of hot, dilute, and radiatively inefficient accretion flows around black holes. In this paper we derive a form of the collisionless drift-kinetic equation appropriate for accretion physics. We construct a local equilibrium for MHD stability analysis in this differentially rotating disk. We then find and characterize specific instabilities expected to be important in describing the flow properties of hot, dilute, and radiatively inefficient accretion flows around black holes, and show their qualitative similarities to instabilities derived using a fluid formalism (Islam12). We conclude with further work needed in modeling this class of accretion flow.

### Magnetic self-organisation in Hall-dominated magnetorotational turbulence

The magnetorotational instability (MRI) is the most promising mechanism by which angular momentum is efficiently transported outwards in astrophysical discs. However, its application to protoplanetary discs remains problematic. These discs are so poorly ionised that they may not support magnetorotational turbulence in regions referred to as `dead zones’. It has recently been suggested that the Hall effect, a non-ideal magnetohydrodynamic (MHD) effect, could revive these dead zones by enhancing the magnetically active column density by an order of magnitude or more. We investigate this idea by performing local, three-dimensional, resistive Hall-MHD simulations of the MRI in situations where the Hall effect dominates over Ohmic dissipation. As expected from linear stability analysis, we find an exponentially growing instability in regimes otherwise linearly stable in resistive MHD. However, instead of vigorous and sustained magnetorotational turbulence, we find that the MRI saturates by producing large-scale, long-lived, axisymmetric structures in the magnetic and velocity fields. We refer to these structures as zonal fields and zonal flows, respectively. Their emergence causes a steep reduction in turbulent transport by at least two orders of magnitude from extrapolations based upon resistive MHD, a result that calls into question contemporary models of layered accretion. We construct a rigorous mean-field theory to explain this new behaviour and to predict when it should occur. Implications for protoplanetary disc structure and evolution, as well as for theories of planet formation, are briefly discussed.

### Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, nonlinear magnetohydrodynamic process whose study is relevant to the understanding of accretion and magnetic field generation in astrophysics. Transition to this form of dynamo is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. This suggests that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in various astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.

### MHD Simulation of a Sigmoid Eruption of Active Region 11283

Current magnetohydrodynamic (MHD) simulations of the initiation of solar eruptions are still commonly carried out with idealized magnetic field models, whereas the realistic coronal field prior to eruptions can possibly be reconstructed from the observable photospheric field. Using a nonlinear force-free field extrapolation prior to a sigmoid eruption in AR 11283 as the initial condition in a MHD model, we successfully simulate the realistic initiation process of the eruption event, as is confirmed by a remarkable resemblance to the SDO/AIA observations. Analysis of the pre-eruption field reveals that the envelope flux of the sigmoidal core contains a coronal null and furthermore the flux rope is prone to a torus instability. Observations suggest that reconnection at the null cuts overlying tethers and likely triggers the torus instability of the flux rope, which results in the eruption. This kind of simulation demonstrates the capability of modeling the realistic solar eruptions to provide the initiation process.

### A discontinuous Galerkin method for solving the fluid and MHD equations in astrophysical simulations [Cross-Listing]

A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite volume (FV) approach. We demonstrate that the DG technique offers distinct advantages over FV formulations on both static and moving meshes. The DG method is also easily generalized to higher than second-order accuracy without requiring the use of extended stencils to estimate derivatives (thereby making the scheme highly parallelizable). We implement the technique in the AREPO code for solving the fluid and the magnetohydrodynamic (MHD) equations. By examining various test problems, we show that our new formulation provides improved accuracy over FV approaches of the same order, and reduces post-shock oscillations and artificial diffusion of angular momentum. In addition, the DG method makes it possible to represent magnetic fields in a locally divergence-free way, improving the stability of MHD simulations and moderating global divergence errors, and is a viable alternative for solving the MHD equations on meshes where Constrained-Transport (CT) cannot be applied. We find that the DG procedure on a moving mesh is more sensitive to the choice of slope limiter than is its FV method counterpart. Therefore, future work to improve the performance of the DG scheme even further will likely involve the design of optimal slope limiters. As presently constructed, our technique offers the potential of improved accuracy in astrophysical simulations using the moving mesh AREPO code as well as those employing adaptive mesh refinement (AMR).

### A discontinuous Galerkin method for solving the fluid and MHD equations in astrophysical simulations [Replacement]

A discontinuous Galerkin (DG) method suitable for large-scale astrophysical simulations on Cartesian meshes as well as arbitrary static and moving Voronoi meshes is presented. Most major astrophysical fluid dynamics codes use a finite volume (FV) approach. We demonstrate that the DG technique offers distinct advantages over FV formulations on both static and moving meshes. The DG method is also easily generalized to higher than second-order accuracy without requiring the use of extended stencils to estimate derivatives (thereby making the scheme highly parallelizable). We implement the technique in the AREPO code for solving the fluid and the magnetohydrodynamic (MHD) equations. By examining various test problems, we show that our new formulation provides improved accuracy over FV approaches of the same order, and reduces post-shock oscillations and artificial diffusion of angular momentum. In addition, the DG method makes it possible to represent magnetic fields in a locally divergence-free way, improving the stability of MHD simulations and moderating global divergence errors, and is a viable alternative for solving the MHD equations on meshes where Constrained-Transport (CT) cannot be applied. We find that the DG procedure on a moving mesh is more sensitive to the choice of slope limiter than is its FV method counterpart. Therefore, future work to improve the performance of the DG scheme even further will likely involve the design of optimal slope limiters. As presently constructed, our technique offers the potential of improved accuracy in astrophysical simulations using the moving mesh AREPO code as well as those employing adaptive mesh refinement (AMR).

### The influence of numerical resolution on coronal density in hydrodynamic models of impulsive heating

The effect of the numerical spatial resolution in models of the solar corona and corona / chromosphere interface is examined for impulsive heating over a range of magnitudes using one dimensional hydrodynamic simulations. It is demonstrated that the principle effect of inadequate resolution is on the coronal density. An underresolved loop typically has a peak density of at least a factor of two lower than a resolved loop subject to the same heating, with larger discrepencies in the decay phase. The temperature for under-resolved loops is also lower indicating that lack of resolution does not "bottle up" the heat flux in the corona. Energy is conserved in the models to under 1% in all cases, indicating that this is not responsible for the low density. Instead, we argue that in under-resolved loops the heat flux "jumps across" the transition region to the dense chromosphere from which it is radiated rather than heating and ablating transition region plasma. This emphasises the point that the interaction between corona and chromosphere occurs only through the medium of the transition region. Implications for three dimensional magnetohydrodynamic coronal models are discussed.

### Role of magnetic field strength and numerical resolution in simulations of the heat-flux driven buoyancy instability

The role played by magnetic fields in the intracluster medium (ICM) of galaxy clusters is complex. The weakly collisional nature of the ICM leads to thermal conduction that is channelled along field lines. This anisotropic heat conduction profoundly changes the stability of the ICM atmosphere, with convective stabilities being driven by temperature gradients of either sign. Here, we employ the Athena magnetohydrodynamic code to investigate the local non-linear behavior of the heat-flux driven buoyancy instability (HBI), relevant in the cores of cooling-core clusters where the temperature increases with radius. We study a grid of 2-d simulations that span a large range of initial magnetic field strengths and numerical resolutions. For very weak initial fields, we recover the previously known result that the HBI wraps the field in the horizontal direction thereby shutting off the heat flux. However, we find that simulations which begin with intermediate initial field strengths have a qualitatively different behavior, forming HBI-stable filaments that resist field-line wrapping and enable sustained vertical conductive heat flux at a level of 10–25% of the Spitzer value. While astrophysical conclusions regarding the role of conduction in cooling cores require detailed global models, our local study proves that systems dominated by HBI do not necessarily quench the conductive heat flux.

### A Dynamical Systems Approach to a Bianchi Type I Viscous Magnetohydrodynamic Model [Replacement]

We use the expansion-normalized variables approach to study the dynamics of a non-tilted Bianchi Type I cosmological model with both a homogeneous magnetic field and a viscous fluid. In our model the perfect magnetohydrodynamic approximation is made, and both bulk and shear viscous effects are retained. The dynamical system is studied in detail through a fixed-point analysis which determines the local sink and source behavior of the system. We show that the fixed points may be associated with Kasner-type solutions, a flat universe FLRW solution, and interestingly, a new solution to the Einstein Field equations involving non-zero magnetic fields, and non-zero viscous coefficients. It is further shown that for certain values of the bulk and shear viscosity and equation of state parameters, the model isotropizes at late times.

### Residual Energy Spectrum of Solar Wind Turbulence [Cross-Listing]

It has long been known that the energy in velocity and magnetic field fluctuations in the solar wind is not in equipartition. In this paper, we present an analysis of 5 years of Wind data at 1 AU to investigate the reason for this. The residual energy (difference between energy in velocity and magnetic field fluctuations) was calculated using both the standard magnetohydrodynamic (MHD) normalization for the magnetic field and a kinetic version, which includes temperature anisotropies and drifts between particle species. It was found that with the kinetic normalization, the fluctuations are closer to equipartition, with a mean normalized residual energy of sigma_r = -0.19 and mean Alfven ratio of r_A = 0.71. The spectrum of residual energy, in the kinetic normalization, was found to be steeper than both the velocity and magnetic field spectra, consistent with some recent MHD turbulence predictions and numerical simulations, having a spectral index close to -1.9. The local properties of residual energy and cross helicity were also investigated, showing that globally balanced intervals with small residual energy contain local patches of larger imbalance and larger residual energy at all scales, as expected for non-linear turbulent interactions.

### Determination of Transverse Density Structuring from Propagating MHD Waves in the Solar Atmosphere

We present a Bayesian seismology inversion technique for propagating magnetohydrodynamic (MHD) transverse waves observed in coronal waveguides. The technique uses theoretical predictions for the spatial damping of propagating kink waves in transversely inhomogeneous coronal waveguides. It combines wave amplitude damping length scales along the waveguide with theoretical results for resonantly damped propagating kink waves to infer the plasma density variation across the oscillating structures. Provided the spatial dependence of the velocity amplitude along the propagation direction is measured and the existence of two different damping regimes is identified, the technique would enable us to fully constrain the transverse density structuring, providing estimates for the density contrast and its transverse inhomogeneity length scale.

### Plasmoid solutions of the Hahm--Kulsrud--Taylor equilibrium model [Cross-Listing]

The Hahm–Kulsrud (HK) [T. S. Hahm and R. M. Kulsrud, Phys. Fluids {\bf 28}, 2412 (1985)] solutions for a magnetically sheared plasma slab driven by a resonant periodic boundary perturbation illustrate fully shielded (current sheet) and fully reconnected (magnetic island) responses. On the global scale, reconnection involves solving a magnetohydrodynamic (MHD) equilibrium problem. In systems with a continuous symmetry such MHD equilibria are typically found by solving the Grad–Shafranov equation, and in slab geometry the elliptic operator in this equation is the 2-D Laplacian. Thus, assuming appropriate pressure and poloidal current profiles, a conformal mapping method can be used to transform one solution into another with different boundary conditions, giving a continuous sequence of solutions in the form of partially reconnected magnetic islands (plasmoids) separated by Syrovatsky current sheets. The two HK solutions appear as special cases.

### Current Status of Simulations

As the title suggests, the purpose of this chapter is to review the current status of numerical simulations of black hole accretion disks. This chapter focuses exclusively on global simulations of the accretion process within a few tens of gravitational radii of the black hole. Most of the simulations discussed are performed using general relativistic magnetohydrodynamic (MHD) schemes, although some mention is made of Newtonian radiation MHD simulations and smoothed particle hydrodynamics. The goal is to convey some of the exciting work that has been going on in the past few years and provide some speculation on future directions.

### Influence of initial conditions on large scale dynamo growth rate [Replacement]

To investigate the effect of energy and helicity on the growth of magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as initial conditions. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. It is already known that the helical component of small scale magnetic field(i.e., current helicity $\langle {\bf j}\cdot {\bf b}\rangle$) quenches the growth of large scale magnetic field. However, $\langle {\bf j}\cdot {\bf b}\rangle$ can also boost the growth of large scale magnetic field by changing its sign and magnitude. In addition, simulation shows the nonhelical magnetic field can suppress the velocity field through Lorentz force. Comparison of the profiles of evolving magnetic and kinetic energy indicates that kinetic energy migrates backward when the external energy flows into the three dimensional MHD system, which means the velocity field may play a preceding role in the very early MHD dynamo stage.

### Influence of initial conditions on large scale dynamo growth rate

To investigate the effect of energy and helicity on the growth of large scale magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as an initial condition. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. Comparison of the profiles of evolving magnetic and kinetic energy implies that the large scale kinetic energy plays a preceding role in the MHD dynamo in the early time regime. Kinetic energy was observed to migrate backward when the external energy flew into the three dimensional MHD system. The data were analyzed and interpreted using the equations from quasi normal approximation and two scale mean field method.

### Influence of initial conditions on the large-scale dynamo growth rate [Replacement]

To investigate the effect of energy and helicity on the growth of magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as initial conditions. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. It is already known that the helical component of small scale magnetic field(i.e., current helicity $<{\bf j}\cdot {\bf b}>$) quenches the growth of large scale magnetic field. However, $<{\bf j}\cdot {\bf b}>$ can also boost the growth of large scale magnetic field by changing its sign and magnitude. In addition, simulation shows the nonhelical magnetic field can suppress the velocity field through Lorentz force. Comparison of the profiles of evolving magnetic and kinetic energy indicates that kinetic energy migrates backward when the external energy flows into the three dimensional MHD system, which means the velocity field may play a preceding role in the very early MHD dynamo stage.

### Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests [Replacement]

We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part independent homogeneous Riemann problems for the two fluids are solved using Godunov’s method. In the other equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (i) MHD wave packets ranging over orders of magnitude in length and time scales; (ii) early evolution of mulitfluid shocks caused by two colliding clouds; and (iii) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to a MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

### Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests [Replacement]

We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part independent homogeneous Riemann problems for the two fluids are solved using Godunov’s method. In the other equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (i) MHD wave packets ranging over orders of magnitude in length and time scales; (ii) early evolution of mulitfluid shocks caused by two colliding clouds; and (iii) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to a MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

### Molecular Line Emission from Multifluid Shock Waves. I. Numerical Methods and Benchmark Tests

We describe a numerical scheme for studying time-dependent, multifluid, magnetohydrodynamic shock waves in weakly ionized interstellar clouds and cores. Shocks are modeled as propagating perpendicular to the magnetic field and consist of a neutral molecular fluid plus a fluid of ions and electrons. The scheme is based on operator splitting, wherein time integration of the governing equations is split into separate parts. In one part independent homogeneous Riemann problems for the two fluids are solved using Godunov’s method. In the other equations containing the source terms for transfer of mass, momentum, and energy between the fluids are integrated using standard numerical techniques. We show that, for the frequent case where the thermal pressures of the ions and electrons are << magnetic pressure, the Riemann problems for the neutral and ion-electron fluids have a similar mathematical structure which facilitates numerical coding. Implementation of the scheme is discussed and several benchmark tests confirming its accuracy are presented, including (i) MHD wave packets ranging over orders of magnitude in length and time scales; (ii) early evolution of mulitfluid shocks caused by two colliding clouds; and (iii) a multifluid shock with mass transfer between the fluids by cosmic-ray ionization and ion-electron recombination, demonstrating the effect of ion mass loading on magnetic precursors of MHD shocks. An exact solution to a MHD Riemann problem forming the basis for an approximate numerical solver used in the homogeneous part of our scheme is presented, along with derivations of the analytic benchmark solutions and tests showing the convergence of the numerical algorithm.

### On the Support of Solar Prominence Material by the Dips of a Coronal Flux Tube

The dense prominence material is believed to be supported against gravity through the magnetic tension of dipped coronal magnetic field. For quiescent prominences, which exhibit many gravity-driven flows, hydrodynamic forces are likely to play an important role in the determination of both the large and small scale magnetic field distributions. In this study, we present the first steps toward creating three-dimensional magneto-hydrostatic prominence model where the prominence is formed in the dips of a coronal flux tube. Here 2.5D equilibria are created by adding mass to an initially force-free magnetic field, then performing a secondary magnetohydrodynamic relaxation. Two inverse polarity magnetic field configurations are studied in detail, a simple o-point configuration with a ratio of the horizontal field (B_x) to the axial field (B_y) of 1:2 and a more complex model that also has an x-point with a ratio of 1:11. The models show that support against gravity is either by total pressure or tension, with only tension support resembling observed quiescent prominences. The o-point of the coronal flux tube was pulled down by the prominence material, leading to compression of the magnetic field at the base of the prominence. Therefore tension support comes from the small curvature of the compressed magnetic field at the bottom and the larger curvature of the stretched magnetic field at the top of the prominence. It was found that this method does not guarantee convergence to a prominence-like equilibrium in the case where an x-point exists below the prominence flux tube. The results imply that a plasma beta of ~ 0.1 is necessary to support prominences through magnetic tension.

### Hot Electromagnetic Outflows I: Acceleration and Spectra

The theory of cold, relativistic, magnetohydrodynamic outflows is generalized by the inclusion of an intense radiation source. In some contexts, such the breakout of a gamma-ray burst jet from a star, the outflow is heated to a high temperature at a large optical depth. Eventually it becomes transparent and is pushed to a higher Lorentz factor by a combination of the Lorentz force and radiation pressure. We obtain its profile, both inside and outside the fast magnetosonic critical point, when the poloidal magnetic field is radial and monopolar. Most of the energy flux is carried by the radiation field and the toroidal magnetic field that is wound up close to the rapidly rotating engine. Although the entrained matter carries little energy, it couples the radiation field to the magnetic field. Then the fast critical point is pushed inward from infinity and, above a critical radiation intensity, the outflow is accelerated mainly by radiation pressure. We identify a distinct observational signature of this hybrid outflow: a hardening of the radiation spectrum above the peak of the seed photon distribution, driven by bulk Compton scattering. The non-thermal spectrum — obtained by a Monte Carlo method — is most extended when the Lorentz force dominates the acceleration, and the seed photon beam is wider than the Lorentz cone of the MHD fluid. This effect is a generic feature of hot, magnetized outflows interacting with slower relativistic material. It may explain why some GRB spectra appear to peak at photon energies above the original Amati et al. scaling. A companion paper addresses the case of jet breakout, where diverging magnetic flux surfaces yield strong MHD acceleration over a wider range of Lorentz factor.

### Numerical Simulations of Solar Chromospheric Jets Associated with Emerging Flux

We studied the acceleration mechanisms of chromospheric jets associated with emerging flux using a two dimensional magnetohydrodynamic (MHD) simulation. We found that slow mode shock waves generated by magnetic reconnection in the chromosphere and the photosphere play key roles in the acceleration mechanisms of chromospheric jets. An important parameter is the height of magnetic reconnection. When magnetic reconnection takes place near the photosphere, the reconnection out- flow collides with the region where the plasma beta is much larger than unity. Then the plasma moves along a magnetic field. This motion generates a slow mode wave. The slow mode wave develops to a strong slow shock as it propagates upward. When the slow shock crosses the transition region, the transition region is lifted up. As a result, we obtain a chromospheric jet as the lifted transition region. When magnetic reconnection takes place in the upper chromosphere, the chromospheric plasma is accelerated due to the combination of the Lorentz force and the whip-like motion of magnetic field. We found that the chromospheric plasma is further accelerated through the interaction between the transition region (steep density gradient) and a slow shock emanating from the reconnection point. This is an MHD effect which has not been discussed before.

### Protostellar Disk Formation Enabled by Weak, Misaligned Magnetic Fields

The gas from which stars form is magnetized, and strong magnetic fields can efficiently transport angular momentum. Most theoretical models of this phenomenon find that it should prevent formation of large (>100 AU), rotationally-supported disks around most protostars, even when non-ideal magnetohydrodynamic (MHD) effects that allow the field and gas to decouple are taken into account. Using recent observations of magnetic field strengths and orientations in protostellar cores, we show that this conclusion is incorrect. The distribution of magnetic field strengths is very broad, and alignments between fields and angular momentum vectors within protostellar cores are essentially random. By combining the field strength and misalignment data with MHD simulations showing that disk formation is expected for both weak and misaligned fields, we show that these observations imply that we should expect disk fractions of ~10 – 50% even when protostars are still deeply embedded in their parent cores, and even if the gas is governed by ideal MHD.

### Mineral Processing by Short Circuits in Protoplanetary Disks [Replacement]

Meteoritic chondrules were formed in the early solar system by brief heating of silicate dust to melting temperatures. Some highly refractory grains (Type B calcium-aluminum-rich inclusions, CAIs) also show signs of transient heating. A similar process may occur in other protoplanetary disks, as evidenced by observations of spectra characteristic of crystalline silicates. One possible environment for this process is the turbulent magnetohydrodynamic flow thought to drive accretion in these disks. Such flows generally form thin current sheets, which are sites of magnetic reconnection, and dissipate the magnetic fields amplified by a disk dynamo. We suggest that it is possible to heat precursor grains for chondrules and other high-temperature minerals in current sheets that have been concentrated by our recently described short-circuit instability. We extend our work on this process by including the effects of radiative cooling, taking into account the temperature dependence of the opacity; and by examining current sheet geometry in three-dimensional, global models of magnetorotational instability. We find that temperatures above 1600 K can be reached for favorable parameters that match the ideal global models. This mechanism could provide an efficient means of tapping the gravitational potential energy of the protoplanetary disk to heat grains strongly enough to form high-temperature minerals. The volume-filling nature of turbulent magnetic reconnection is compatible with constraints from chondrule-matrix complementarity, chondrule-chondrule complementarity, the occurrence of igneous rims, and compound chondrules. The same short-circuit mechanism may perform other high-temperature mineral processing in protoplanetary disks such as the production of crystalline silicates and CAIs.

### Mineral Processing by Short Circuits in Protoplanetary Disks

Meteoritic chondrules were formed in the early Solar System by brief heating of silicate dust to melting temperatures. Some highly refractory grains (Type B calcium-aluminum rich inclusions, CAIs) also show signs of transient heating. A similar process may occur in other protoplanetary disks, as evidenced by observations of spectra characteristic of crystalline silicates. One possible environment for this process is the turbulent magnetohydrodynamic flow thought to drive accretion in these disks. Such flows quite generally form thin current sheets, which are sites of magnetic reconnection and dissipate the magnetic fields amplified by a disk dynamo. We suggest that it is possible to heat precursor grains for chondrules and other high-temperature minerals in current sheets that have been concentrated by our recently described short-circuit instability. We extend our work on this process by including the effects of radiative cooling, taking into account the temperature dependence of the opacity; and by examining current sheet geometry in three dimensional, global models of magnetorotational instability. We find that temperatures above 1600 K can be reached for favorable parameters that match the ideal global models. This mechanism could provide an efficient means of tapping the gravitational potential energy of the protoplanetary disk to heat grains strongly enough to form high-temperature minerals. The volume-filling nature of turbulent magnetic reconnection is compatible with constraints from chondrule-matrix complementarity, chondrule-chondrule complementarity, the occurrence of igneous rims, and compound chondrules. The same short-circuit mechanism may perform other high-temperature mineral processing in protoplanetary disks such as the production of crystalline silicates and CAIs.

### Well-posedness of some initial-boundary-value problems for dynamo-generated poloidal magnetic fields

Given a bounded domain $G \subset \R^d$, $d\geq 3$, we study smooth solutions of a linear parabolic equation with non-constant coefficients in $G$, which at the boundary have to $C^1$-match with some harmonic function in $\R^d \setminus \ov{G}$ vanishing at spatial infinity. This problem arises in the framework of magnetohydrodynamics if certain dynamo-generated magnetic fields are considered: For example, in the case of axisymmetry or for non-radial flow fields, the poloidal scalar of the magnetic field solves the above problem. We first investigate the Poisson problem in $G$ with the above described boundary condition as well as the associated eigenvalue problem and prove the existence of smooth solutions. As a by-product we obtain the completeness of the well-known poloidal "free decay modes" in $\R^3$ if $G$ is a ball. Smooth solutions of the evolution problem are then obtained by Galerkin approximation based on these eigenfunctions.

### Equilibrium disks, MRI mode excitation, and steady state turbulence in global accretion disk simulations

Global three dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when non-linear motions – perhaps triggered by the onset of turbulence – upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once the disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with previous works. In particular, the globally averaged stress normalized to the gas pressure, <\alpha_{\rm P}> = 0.034, with notably higher values achieved for simulations with higher azimuthal resolution. Supplementary tests are performed using different numerical algorithms and resolutions. Convergence with resolution during the initial linear MRI growth phase is found for 23-35 cells per scaleheight (in the vertical direction).

### Variation rate of sunspot area

The emergence of the magnetic field through the photosphere has multiple manifestations and sunspots are the most prominent examples of this. One of the most relevant sunspot properties, to study both its structure and evolution, is the sunspot area: either total, umbra or penumbra area. Recently Schlichenmaier et al. (2010) studied the evolution of the active region (AR) NOAA 11024 concluding that during the penumbra formation the umbra area remains constant and that the increase of the total sunspot area is caused exclusively by the penumbra growth. In this presentation the Schlichenmaier’s conclusion is firstly tested, investigating the evolution of four different ARs. Hundreds of Intensitygram images from the Helioseismic and Magnetic Imager (HMI) images are used, obtained by the Solar Dynamics Observatory, in order to describe the area evolution of the above ARs and estimate the increase and decrease rates for umbra and penumbra areas, separately. A simple magnetohydrodynamic model is then tentatively used in a first approximation to explain the observed results.

### MHD Turbulence in Accretion Disk Boundary Layers

The physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations and suggests that the detailed structure of turbulent MHD boundary layers could differ appreciably from those derived within the standard framework of turbulent shear viscosity.

### Self-heating in kinematically complex magnetohydrodynamic flows

The non-modal self-heating mechanism driven by the velocity shear in kinematically complex magnetohydrodynamic (MHD) plasma flows is considered. The study is based on the full set of MHD equations including dissipative terms. The equations are linearized and unstable modes in the flow are looked for. Two different cases are specified and studied: (a) the instability related to an exponential evolution of the wave vector; and (b) the parametric instability, which takes place when the components of the wave vector evolve in time periodically. By examining the dissipative terms, it is shown that the self-heating rate provided by viscous damping is of the same order of magnitude as that due to the magnetic resistivity. It is found that the heating efficiency of the exponential instability is higher than that of the parametric instability.

### Coronal heating by the partial relaxation of twisted loops [Replacement]

Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. Methods: A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity conserving relaxation theory. Results: For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions: The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops.

### Coronal heating by the partial relaxation of twisted loops

Context: Relaxation theory offers a straightforward method for estimating the energy that is released when a magnetic field becomes unstable, as a result of continual convective driving. Aims: We present new results obtained from nonlinear magnetohydrodynamic (MHD) simulations of idealised coronal loops. The purpose of this work is to determine whether or not the simulation results agree with Taylor relaxation, which will require a modified version of relaxation theory applicable to unbounded field configurations. Methods: A three-dimensional (3D) MHD Lagrangian-remap code is used to simulate the evolution of a line-tied cylindrical coronal loop model. This model comprises three concentric layers surrounded by a potential envelope; hence, being twisted locally, each loop configuration is distinguished by a piecewise-constant current profile. Initially, all configurations carry zero-net-current fields and are in ideally unstable equilibrium. The simulation results are compared with the predictions of helicity conserving relaxation theory. Results: For all simulations, the change in helicity is no more than 2% of the initial value; also, the numerical helicities match the analytically-determined values. Magnetic energy dissipation predominantly occurs via shock heating associated with magnetic reconnection in distributed current sheets. The energy release and final field profiles produced by the numerical simulations are in agreement with the predictions given by a new model of partial relaxation theory: the relaxed field is close to a linear force free state; however, the extent of the relaxation region is limited, while the loop undergoes some radial expansion. Conclusions: The results presented here support the use of partial relaxation theory, specifically, when calculating the heating-event distributions produced by ensembles of kink-unstable loops.

### Magnetic Wreaths and Cycles in Convective Dynamos

Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global 3D magnetohydrodynamic (MHD) simulations with the anelastic spherical harmonic (ASH) code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3$\Omega_\odot$), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed.

### The Column Density Variance in Turbulent Interstellar Media: A Fractal Model Approach

Fractional Brownian motion (fBm) structures are used to investigate the dependency of column density variance ({\sigma}_{\ln N}^2) in the turbulent interstellar medium on the variance of three-dimensional density ({\sigma}_{\ln\rho}^2) and the power-law slope of the density power spectrum. We provide quantitative expressions to infer the three-dimensional density variance, which is not directly observable, from the observable column density variance and spectral slope. We also investigate the relationship between the column density variance and sonic Mach number (Ms) in the hydrodynamic (HD) regime by assuming the spectral slope and density variance as functions of sonic Mach number, as obtained from the HD turbulence simulations. They are related by the expression {\sigma}_{\ln N}^2 = A{\sigma}_{\ln\rho}^2 = Aln(1+b^2M^2), suggested by Burkhart & Lazarian for the magnetohydrodynamic (MHD) case. The proportional constant A varies from ~ 0.2 to ~ 0.4 in the HD regime as the turbulence forcing parameter b increases from 1/3 (purely solenoidal forcing) to 1 (purely compressive forcing). It is also discussed that the parameter A is lowered in the presence of a magnetic field.

### Time Dependent Radiative Transfer for Multi-Level Atoms using Accelerated Lambda Iteration

We present a general formalism for computing self-consistent, numerical solutions to the time-dependent radiative transfer equation in low velocity, multi-level ions undergoing radiative interactions. Recent studies of time-dependent radiative transfer have focused on radiation hydrodynamic and magnetohydrodynamic effects without lines, or have solved time-independent equations for the radiation field simultaneously with time-dependent equations for the state of the medium. In this paper, we provide a fully time-dependent numerical solution to the radiative transfer and atomic rate equations for a medium irradiated by an external source of photons. We use Accelerated Lambda Iteration to achieve convergence of the radiation field and atomic states. We perform calculations for a three-level atomic model that illustrates important time-dependent effects. We demonstrate that our method provides an efficient, accurate solution to the time-dependent radiative transfer problem. Finally, we characterize astrophysical scenarios in which we expect our solutions to be important.

### Turbulence, Magnetic Reconnection in Turbulent Fluids and Energetic Particle Acceleration

Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD) turbulence, in particular its decomposition into Alfv\’en, slow and fast modes, discuss the density structure of turbulent subsonic and supersonic media, as well as other relevant regimes of astrophysical turbulence. All this information is essential for understanding the energetic particle acceleration that we discuss further in the review. For instance, we show how fast and slow modes accelerate energetic particles through the second order Fermi acceleration, while density fluctuations generate magnetic fields in pre-shock regions enabling the first order Fermi acceleration of high energy cosmic rays. Very importantly, however, the first order Fermi cosmic ray acceleration is also possible in sites of magnetic reconnection. In the presence of turbulence this reconnection gets fast and we present numerical evidence supporting the predictions of the Lazarian & Vishniac (1999) model of fast reconnection. The efficiency of this process suggests that magnetic reconnection can release substantial amounts of energy in short periods of time. As the particle tracing numerical simulations show that the particles can be efficiently accelerated during the reconnection, we argue that the process of magnetic reconnection may be much more important for particle acceleration than it is currently accepted. In particular, we discuss the acceleration arising from reconnection as a possible origin of the anomalous cosmic rays measured by Voyagers as well as the origin cosmic ray excess in the direction of Heliotail.

### Transverse kink oscillations in the presence of twist

Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases. The goal of this work is to study the fingerprints of magnetic twist on stable transverse kink oscillations. We numerically calculated the eigenmodes of propagating and standing MHD waves for a model of a loop with magnetic twist. The azimuthal component of the magnetic field was assumed to be small in comparison to the longitudinal component. We did not consider resonantly damped modes or kink instabilities in our analysis. For a nonconstant twist the frequencies of the MHD wave modes are split, which has important consequences for standing waves. This is different from the degenerated situation for equilibrium models with constant twist, which are characterised by an azimuthal component of the magnetic field that linearly increases with the radial coordinate. In the presence of twist standing kink solutions are characterised by a change in polarisation of the transverse displacement along the tube. For weak twist, and in the thin tube approximation, the frequency of standing modes is unaltered and the tube oscillates at the kink speed of the corresponding straight tube. The change in polarisation is linearly proportional to the degree of twist. This has implications with regard to observations of kink modes, since the detection of this variation in polarisation can be used as an indirect method to estimate the twist in oscillating loops.

### Regular and non-regular solutions of the Riemann problem in ideal magnetohydrodynamics

We have built a code to numerically solve the Riemann problem in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition to investigate a variety of solutions more thoroughly. The code can handle not only regular solutions, in which no intermediate shocks are involved, but also all types of non-regular solutions if any. As a first application, we explored the neighborhood of the initial condition that was first picked up by Brio & Wu (1988) and has been frequently employed in the literature as a standard problem to validate numerical codes. Contrary to the conventional wisdom that there will always be a regular solution, we found an initial condition, for which there is no regular solution but a non-regular one. The latter solution has only regular solutions in its neighborhood and actually sits on the boundary of regular solutions. This implies that the regular solutions are not sufficient to solve the ideal MHD Riemann problem and suggests that at least some types of non-regular solutions are physical. We also demonstrate that the non-regular solutions are not unique. In fact, we found for the Brio & Wu initial condition that there are uncountably many non-regular solutions. This poses an intriguing question: why a particular non-regular solution is always obtained in numerical simulations? This has important ramifications to the discussion of which intermediate shocks are really admissible.