Active and passive fields face to face

This paper is concerned with a physical understanding of the main features of interstellar plasma turbulence. Our observational knowledge of this turbulence is provided by radio-wave propagation observations, generically referred to as interstellar scintillations. Distinctive features of the observations are the nearly omnipresent anisotropy of scattering, revealed by elliptical rather than circular scattering disks, drastic differences in the magnitude of scattering between closely spaced lines of sight through the interstellar medium, evidence from Faraday rotation observations that the interstellar vector magnetic field changes markedly on small spatial scales, and the existence of a power-law spectrum of density irregularities over a wide range of spatial scales. This power-law density spectrum strongly suggests the existence of similar spatial power spectra for the other magnetohydrodynamic (MHD) variables such as flow velocity and magnetic field. In this paper, it is pointed out that the aforementioned features arise or may naturally be explained by an approximate theory of magnetohydrodynamic turbulence, two-dimensional magnetohydrodynamics. In this theory, the plasma turbulence is described by two scalar functions (a velocity stream function and one component of the magnetic vector potential) that are coupled by nonlinear partial differential equations. These equations are physically transparent, possess some relevant analytic results, and are easily solved numerically. Arguments for the relevance of this reduced plasma description are presented. Although obviously an incomplete description of the interstellar plasma, these equations provide plausible explanations for the observational features described above. Anisotropy of scattering arises as an obvious consequence of the conditions for validity of the two-dimensional MHD description, i.e., that spatial gradients along a large-scale magnetic field are much smaller than those perpendicular to the field. The equations of two-dimensional MHD predict the formation of intense electrical current and vorticity sheets from broad classes of initial conditions. It is highly plausible that these sheets are the loci of elevated turbulence, which could explain the variations of radio-wave scattering and provide a physical explanation for intermittency in interstellar turbulence. The strong current sheets would also produce localized reversals in the turbulent component of the interstellar magnetic field. Finally, the equations of two-dimensional MHD produce spectral flattening of initial conditions with steep spatial power spectra. The calculations presented here, as well as elsewhere in the literature, indicate that the equilibrium magnetic field and velocity spectra may be power laws with indices close to those observed for the density fluctuations. In summary, the equations of two-dimensional magnetohydrodynamics are proposed as a simplified theoretical tool for use in understanding interstellar plasma turbulence.

The non blow-up of the 3D ideal incompressible magnetohydrodynamics (MHD) equations is proved for a class of three-dimensional initial data characterized by uniformly large vorticity and magnetic field in bounded cylindrical domains. There are no conditional assumptions on properties of solutions at later times, nor are the global solutions close to some 2D manifold. The approach of proving regularity is based on investigation of fast, singular, oscillating limits and nonlinear averaging methods in the context of almost periodic functions. We establish the global regularity of the 3D limit resonant MHD equations without any restrictions on the size of the 3D initial data. After establishing the strong convergence to the limit resonant equations, we bootstrap this into the regularity on arbitrarily large time intervals for solutions of the 3D MHD equations with weakly-aligned uniformly large vorticity and magnetic field at t = 0. Bibliography: 36 titles.

Annular linear induction pumps (ALIPs) are one of the electromagnetic (EM) pumps, which drive liquid metal using EM force, for fast reactors and have been developed in many countries. An ALIP mainly consists of multiple coils, iron cores and an annular flow channel. We have calculated the developed pressure of ALIPs using a two-dimensional magnetohydrodynamics (MHD) code. There are some reports in which pressure drop and fluctuation were observed in EM pump operations near the top of the pressure and flow rate relation (P–Q) curve. For fear of this phenomenon, the EM pump design is sometimes too conservative. To simulate the pressure drop and fluctuation occurrence conditions, we have developed a new three-dimensional (3D) MHD code. Clarification of this condition and its phenomena in the sodium flow will enable design of a new structure or determination of operation conditions that preclude this pressure drop and fluctuation and, thereby, achieve high efficiency. In this paper, the model of our new 3D MHD code, the accuracy of the code, simulation results focusing on pressure drop and fluctuation by radial and circumferential vortices are reported.

We study the fundamental physics of cascades and spectra in 2D Cahn-Hilliard-Navier-Stokes (CHNS) turbulence, and compare and contrast this system with 2D MagnetoHydroDynamic (MHD) turbulence. The important similarities include basic equations, ideal quadratic invariants, cascades and the role of linear elastic waves. Surface tension induces elasticity, and the balance between surface tension energy and turbulent kinetic energy determines a length scale (Hinze scale) of the system. The Hinze scale may be thought of as the scale of emergent critical balance between fluid straining and elastic restoring forces. The scales between the Hinze scale and dissipation scale constitute the elastic range of the 2D CHNS system. By direct numerical simulation, we find that in the elastic range, the mean square concentration spectrum $H^\psi_k$ of the 2D CHNS system exhibits the same power law ($-7/3$) as the mean square magnetic potential spectrum $H^A_k$ in the inverse cascade regime of 2D MHD. This power law is consistent with an inverse cascade of $H^\psi$, which is observed. The kinetic energy spectrum of the 2D CHNS system is $E^K_k\sim k^{-3}$ if forced at large scale, suggestive of the direct enstrophy cascade power law of 2D Navier-Stokes (NS) turbulence. The difference from the energy spectra of 2D MHD turbulence implies that the back reaction of the concentration field to fluid motion is limited. We suggest this is because the surface tension back reaction is significant only in the interfacial regions. The interfacial regions fill only a small portion of the 2D CHNS system, and their interface packing fraction is much smaller than that for 2D MHD.

The investigation of liquid metal (LM) magnetohydrodynamic (MHD) flows through multiple electrically coupling ducts with U-turn bends is of crucial importance for accurately predicting the thermal-hydraulic performance of LM blankets in fusion reactors. Moreover, this duct configuration is often adopted in liquid blanket designs. Here, the combination effects of the MHD coupling, 3D MHD and inclined external magnetic fields on LM MHD flows through the multiple coupling ducts with different aspect ratios and wall conductance ratios are systematically investigated by numerical simulations. The results indicate that the MHD pressure gradient caused by MHD coupling effect decreases but the 3D MHD pressure gradient increases firstly and then decreases as the inclined angles of external magnetic fields increase. In addition, the results also indicate that the normalized pressure gradient can be reduced by increasing the wall conductance ratio ( Cw ) through the increase of the wall thickness. Furthermore, an important finding is that the pressure gradients caused by the MHD coupling decrease with the increases of aspect ratios (b/a) of ducts, while the 3D MHD pressure gradient when b/a = 16 increases to an excessive large degree about 40 times of the pressure gradient in a single conductive duct. The related investigation results will provide a theoretical support for the liquid blanket designs in fusion reactors and deepen our understanding on the LM MHD effects.

The kinetic and extended magnetohydrodynamic (MHD) simulation methods are discussed in the context of their ability to simulate macroscopic plasma evolution on an MHD evolution time scale with microturbulence in toroidal magnetized plasmas. To properly model the evolution of neoclassical equilibrium, it is important to use full-f gyrokinetic calculation with sufficient accuracy for perpendicular viscosity. Similarly in MHD problems, a good accuracy in constructing the closures, in particular for the viscosity stress elements, is required. Although evidence of spontaneous reduction of transport with the consequent rapid steepening of the pressure gradient is found in simulations with full-f 5D gyrokinetic and 3D Braginskii fluid equations, no simulation of the transport barrier formation in agreement with experimental observations has yet been presented. For a comprehensive description of edge plasma dynamics, including L–H transition, pedestal formation, and ELM oscillation problems, full-f 5D gyrokinetic simulation is a necessity, at least in hybrid with 3D MHD. With present-day computers, the global transport time scale can be reached with full-f gyrokinetic simulations in small tokamaks (ρ* ≤ 50–100), while fluid simulation has to be used for MHD evolution time scale in medium-sized tokamaks.

Core-collapse supernovae (CCSNe) are among the most energetic explosions in the universe, liberating the prodigious amount of ~ 1053 erg, the binding energy of their compact remnants, neutron stars or stellar mass black holes. While 99% of this energy is emitted in neutrinos, 1% goes into the internal and asymptotic kinetic energy of the ejecta, and it is reasonable to assume that a tiny fraction is radiated in gravitational waves (GWs). Ever since the first experimental efforts to detect GWs, CCSNe have been considered prime sources of gravitational waves for interferometric detectors. Besides neutrinos, which have already been observed in the context of stellar core collapse of SN1987A, GWs could provide us access to the electromagnetically hidden compact inner core of some such cataclysmic events, supplying us for example with valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. However, GW astronomy strongly depends on the extensive data processing of the detector output on the basis of reliable GW estimates, which only recently have become feasible with the emerging power of supercomputers. The work presented in this thesis is concerned with numerical CCSN models and their imprints in GWs. I performed an extensive series of more than 30 three-dimensional magnetohydrodynamical (MHD) core-collapse simulations. My models are based on a 15M [...] progenitor stemming from stellar evolution calculations, an effective general relativistic potential and either the Lattimer-Swesty (with three possible compressibilities) or the Shen equation of state (EoS) for hot, dense matter. Furthermore, the neutrino transport is tracked by computationally efficient algorithms for the radiative transfer of massless fermions. I systematically investigated the effects of the microphysical finite-temperature nuclear EoS, the initial rotation rate, both the toroidal and the poloidal magnetic fields, and multidimensional gravitational potentials on the GW signature. Based on the results of these calculations, I obtained the largest – and also one of the most realistic – catalogue of GW signatures from 3D MHD stellar core collapse simulations at present. I stress the importance of including postbounce neutrino physics, since it quantitatively alters the GW signature. Non- and slowly-rotating models show GW emission caused by prompt and protoneutron star (PNS) convection. Moreover, the signal stemming from prompt convection allows for the distinction between the two different nuclear EoS indirectly by different properties of the fluid instabilities. For simulations with moderate or even fast rotation rates, I only find the axisymmetric type I wave signature at core bounce. In line with recent results, I could confirm that the maximum GW amplitude scales roughly linearly with the ratio of rotational to gravitational energy (T/|W|) at core bounce below a threshold value of about 10%. Furthermore, I point out that PNS can become dynamically unstable to rotational instabilities at T/|W| values as low as ~ 2% at core bounce. Apart from these two points, I show that it is generally very difficult to discern the effects of the individual features of the input physics in a GW signal from a rotating CCSN that can be attributed unambiguously to a specific model. Weak magnetic fields do not notably influence the dynamical evolution of the core and thus the GW emission. However, for strong initial poloidal magnetic fields ≥ 1012G, the combined action of flux-freezing and field winding leads to conditions where the ratio of magnetic field pressure to matter pressure reaches about unity which leads to the onset of a jet-like supernova explosion. The collimated bipolar out-stream of matter is then reflected in the emission of a type IV GW signal. In contradiction to axisymmetric simulations, I find evidence that nonaxisymmetric fluid modes can counteract or even suppress jet formation for models with strong initial toroidal magnetic fields. I emphasize the importance of including multidimensional gravitational potentials in rapidly rotating 3D CCSN simulations: taking them into account can alter the resulting GW amplitudes up to a factor of 2 compared to simulations which encounter gravity only by a monopolar approximation. Moreover, I show that the postbounce dynamics occuring in the outer layers (at radii R ≥ 200km) of models run with 3D gravity deviates vastly from the ones run with a 1D or 2D gravitational potential. The latter finding implies that both spherically symmetric and axisymmetric treatments of gravity are too restrictive for a quantitative description of the overall postbounce evolution of rapidly rotating CCSN models. The results of models with continued neutrino emission show that including deleptonization during the postbounce phase is an indispensable issue for the quantitative prediction of GWs from core-collapse supernovae, because it can alter the GW amplitude up to a factor of 10 compared to a pure hydrodynamical treatment. My collapse simulations indicate that corresponding events in our Galaxy would be detectable either by LIGO, if the source is rotating, or at least by the advanced LIGO detector, if it is not or only slowly rotating.

The determination of the chemical composition of interplanetary coronal mass ejection (ICME) plasma is an open issue. More specifically, it is not yet fully understood how remote sensing observations of the solar corona plasma during solar disturbances evolve into plasma properties measured in situ away from the Sun. The ambient conditions of the background interplanetary plasma are important for space weather because they influence the evolutions, arrival times, and geo-effectiveness of the disturbances. The Reverse In situ and MHD APproach (RIMAP) is a technique to reconstruct the heliosphere on the ecliptic plane (including the magnetic Parker spiral) directly from in situ measurements acquired at 1 AU. It combines analytical and numerical approaches, preserving the small-scale longitudinal variability of the wind flow lines. In this work, we use RIMAP to test the interaction of an ICME with the interplanetary medium. We model the propagation of a homogeneous non-magnetised (i.e. with no internal flux rope) cloud starting at 800 km s−1at 0.1 AU out to 1.1 AU. Our 3D magnetohydrodynamics (MHD) simulation made with the PLUTO MHD code shows the formation of a compression front ahead of the ICME, continuously driven by the cloud expansion. Using a passive tracer, we find that the initial ICME material does not fragment behind the front during its propagation, and we quantify the mixing of the propagating plasma cloud with the ambient solar wind plasma, which can be detected at 1 AU.

The response of the Earth's magnetosphere to changing solar wind conditions are studied with a 3D Magnetohydrodynamic (MHD) model. One full year (155 Cluster orbits) of the Earth's magnetosphere is simulated using Grand Unified Magnetosphere Ionosphere Coupling simulation (GUMICS-4) magnetohydrodynamic code. Real solar wind measurements are given to the code as input to create the longest lasting global magnetohydrodynamics simulation to date. The applicability of the results of the simulation depends critically on the input parameters used in the model. Therefore, the validity and the variance of the OMNIWeb data is first investigated thoroughly using Cluster measurement close to the bow shock. The OMNIWeb and the Cluster data were found to correlate very well before the bow shock. The solar wind magnetic field and plasma parameters are not changed significantly from the $L_1$ Lagrange point to the foreshock, therefore the OMNIWeb data is appropriate input to the GUMICS-4. The Cluster SC3 footprints are determined by magnetic field mapping from the simulation results and the Tsyganenko (T96) model in order to compare two methods. The determined footprints are in rather good agreement with the T96. However, it was found that the footprints agree better in the northern hemisphere than the southern one during quiet conditions. If the By is not zero, the agreement of the GUMICS-4 and T96 footprint is worse in longitude in the southern hemisphere. Overall, the study implies that a 3D MHD model can increase our insight of the response of the magnetosphere to solar wind conditions.

We study the small scale magnetic reconnection above the radiative inefficient accretion flow around massive black hole via 2D magnetohydrodynamics (MHD) numerical simulation, in order to model the blob formation and ejection from the accretion flow around Sgr A*. The connection of both the newly emerging magnetic field and the pre-existing magnetic field is investigated to check whether blobs could be driven in the environment of black hole accretion disc. After the magnetic connection, both the velocity and temperature of the plasma can be comparable to the inferred physical properties at the base of the observed blob ejection. For illustration, three small boxes which are located within 40 Schwarzschild radii from the central black hole are chosen as our simulation areas. At the beginning of the reconnections, the fluid is pulled toward the central black hole due to the gravitational attraction and the current sheet produced by the reconnection is also pulled toward the same direction, consequently, the resulting outflows move both upwards and towards the symmetry axis of the central black hole. Eventually, huge blobs appear, which supports the catastrophe model of episodic jets (Yuan et al. 2009a). It is also found that the closer to the black hole the magnetic connection happens, the higher the converting efficiency of the magnetic energy into the heat and kinetic energy. For these inner blobs, they have vortex structure due to the Kelvin–Helmholtz instability, which happens along the current sheet separating the fluids with different speed.

In this paper, we give some new global regularity criteria for three-dimensional incompressible magnetohydrodynamics (MHD) equations. More precisely, we provide some sufficient conditions in terms of the derivatives of the velocity or pressure, for the global regularity of strong solutions to 3D incompressible MHD equations in the whole space, as well as for periodic boundary conditions. Moreover, the regularity criterion involving three of the nine components of the velocity gradient tensor is also obtained. The main results generalize the recent work by Cao and Wu (2010 Two regularity criteria for the 3D MHD equations J. Diff. Eqns 248 2263–74) and the analysis in part is based on the works by Cao C and Titi E (2008 Regularity criteria for the three-dimensional Navier–Stokes equations Indiana Univ. Math. J. 57 2643–61; 2011 Gobal regularity criterion for the 3D Navier–Stokes equations involving one entry of the velocity gradient tensor Arch. Rational Mech. Anal. 202 919–32) for 3D incompressible Navier–Stokes equations.

High-resolution spectroscopy is the most accurate tool for measuring the properties of the solar corona. However, interpreting measured line intensities and line profiles emitted by the optically thin solar corona is complicated by line-of-sight (LOS) integration, which leads to measuring weighted averages of the plasma properties along the LOS. LOS integration effects can be removed by combining CHIANTI spectral emissivities with a 3D global model of the solar corona to calculate the contribution of all structures along the LOS to the measured intensities. In this paper, we describe SPECTRUM, a postprocessing tool that can calculate the emission from the optically thin solar corona by combining 3D magnetohydrodynamic (MHD) space plasma simulation results with the CHIANTI database. Doppler-shifted, nonthermal line broadening due to low-frequency Alfvén waves and anisotropic proton and isotropic electron temperatures can be individually taken into account during calculations. Synthetic spectral calculations can then be used for model validation, for interpretation of solar observations, and for forward modeling purposes. SPECTRUM is implemented within the Space Weather Modeling Framework (SWMF) and is therefore publicly available. In this paper, we describe the SPECTRUM module and show its applications by comparing synthetic spectra using simulation data by the 3D MHD Alfvén Wave Solar Model with observations done by the Hinode/Extreme-ultraviolet Imaging Spectrometer during Carrington rotations 2063 and 2082.

The purpose of this paper is to present a two-phase 3D magnetohydrodynamics (MHD) flow model that combines the volume of fluid (VOF) method with the technique derived from induced-magnetic-field equations for liquid metal free surface MHD-jet-flow. Analogy between the induced-magnetic-filed equation and the conventional computational fluid dynamics (CFD) equation is made, so that the equation can be conveniently accounted for by CFD. A penalty factor numerical method is introduced in order to force the local divergence-free condition of the magnetic fields and an extension of the void insulating calculation domain is applied to ensure that the induced-magnetic field at its boundaries is null. These simulation results for lithium liquid metal jets under magnetic field configurations of Magnetic Torus (Mtor) and National Spherical Torus Experiment (NSTX) outboard divertor have shown that three dimensional jet can not be annihilated by magnetic braking and its cross-section will deform in such a way that the momentum flux of the jet is conserved. 3D MHD effects from a magnetic field gradient cause return currents to interact with applied magnetic fields and produce unfavorable Lorentz forces. Under 3D applied non-uniform magnetic fields of the divertor, unfavorable Lorentz forces lead to a substantial change in flow pattern and a reduction in flow velocity, with the jet cross-section moving to one side of the jet space. These critical phenomena can not be revealed by 2D models.

Context.Type II radio bursts are evidence of shocks in the solar atmosphere and inner heliosphere that emit radio waves ranging from sub-meter to kilometer lengths. These shocks may be associated with coronal mass ejections (CMEs) and reach speeds higher than the local magnetosonic speed. Radio imaging of decameter wavelengths (20–90 MHz) is now possible with the Low Frequency Array (LOFAR), opening a new radio window in which to study coronal shocks that leave the inner solar corona and enter the interplanetary medium and to understand their association with CMEs.Aims.To this end, we study a coronal shock associated with a CME and type II radio burst to determine the locations at which the radio emission is generated, and we investigate the origin of the band-splitting phenomenon.Methods.Thetype II shock source-positions and spectra were obtained using 91 simultaneous tied-array beams of LOFAR, and the CME was observed by the Large Angle and Spectrometric Coronagraph (LASCO) on board the Solar and Heliospheric Observatory (SOHO) and by the COR2A coronagraph of the SECCHI instruments on board the Solar Terrestrial Relation Observatory(STEREO). The 3D structure was inferred using triangulation of the coronographic observations. Coronal magnetic fields were obtained from a 3D magnetohydrodynamics (MHD) polytropic model using the photospheric fields measured by the Heliospheric Imager (HMI) on board the Solar Dynamic Observatory (SDO) as lower boundary.Results.The type II radio source of the coronal shock observed between 50 and 70 MHz was found to be located at the expanding flank of the CME, where the shock geometry is quasi-perpendicular withθBn~ 70°. The type II radio burst showed first and second harmonic emission; the second harmonic source was cospatial with the first harmonic source to within the observational uncertainty. This suggests that radio wave propagation does not alter the apparent location of the harmonic source. The sources of the two split bands were also found to be cospatial within the observational uncertainty, in agreement with the interpretation that split bands are simultaneous radio emission from upstream and downstream of the shock front. The fast magnetosonic Mach number derived from this interpretation was found to lie in the range 1.3–1.5. The fast magnetosonic Mach numbers derived from modelling the CME and the coronal magnetic field around the type II source were found to lie in the range 1.4–1.6.

We propose a complete relaxation magnetohydrodynamic (MHD) model for the simulation of electromagnetically driven high energy density (HED) systems. The full relaxation MHD model is composed of relaxation electromagnetic wave, relaxation heat transport, P1/3 approximate radiation transport and certainly the indispensable hydrodynamics (HD). The electromagnetic part transitions from electromagnetic propagation in vacuum to magnetic diffusion in plasma in a natural way. The phase and group velocities are finite for this relaxation system. Therefore, the relaxation MHD can degenerate to resistive MHD and is convenient for explicit parallel computations. The FOI-PERFECT code is developed, based on the relaxation MHD. The key numerical techniques and various applications are given.