The concept of magnetic connections is extended to non-ideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall and current-inertia effects, we derive a new covariant connection equation showing the existence of generalized magnetofluid connections that are preserved during the dissipationless plasma dynamics. These connections are intimately linked to a general antisymmetric tensor that unifies the electromagnetic and fluid fields, allowing the extension of the magnetic connection notion to a much broader concept.
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, t…
We extend the magnetic connection theorem of ideal magnetohydrodynamics to nonideal relativistic pair plasmas. Adopting a generalized Ohm's law, we prove the existence of generalized magnetofluid connections that are preserved by the plasma dynamics. We show that these connections are related to a general antisymmetric tensor that unifies the electromagnetic and fluid fields. The generalized magnetofluid connections set important constraints on the plasma dynamics by forbidding transitions between configurations with different magnetofluid connectivity. An approximated solution is explicitly s…
Resistive steady states in toroidal magnetohydrodynamics (MHD), where Ohm's law must be taken into account, differ considerably from ideal ones. Only for special (and probably unphysical) resistivity profiles can the Lorentz force, in the static force-balance equation, be expressed as the gradient of a scalar and thus cancel the gradient of a scalar pressure. In general, the Lorentz force has a curl directed so as to generate toroidal vorticity. Here, we calculate, for a collisional, highly viscous magnetofluid, the flows that are required for an axisymmetric toroidal steady state, assuming un…
The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is extended to non-ideal relativistic plasmas in curved spacetime. The existence of generalized magnetofluid connections that are preserved by the plasma dynamics is formalized by means of a covariant connection equation that includes different non-ideal effects. These generalized connections are constituted by 2-dimensional hypersurfaces, which are linked to an antisymmetric tensor field that unifies the electromagnetic and fluid fields. They can be interpreted in terms of generalized…
In analogy with the load and the metage in hydrodynamics, we define magnetohydrodynamic load and magnetohydrodynamic metage in the case of magnetofluids. They can be used to write the magnetic field in MHD in Clebsch's form. We show how these two concepts can be utilised to derive the magnetic analogue of the Ertel's theorem and also, how in the presence of non-trivial topology of the magnetic field in the magnetofluid one may associate the linking number of the magnetic field lines with the invariant MHD loads. The paper illustrates that the symmetry translation of the MHD metage in the corre…
A higher-order multiscale analysis of spatial anisotropy in inertial range magnetohydrodynamic turbulence is presented using measurements from the STEREO spacecraft in fast ambient solar wind. We show for the first time that, when measuring parallel to the local magnetic field direction, the full statistical signature of the magnetic and Elsässer field fluctuations is that of a non-Gaussian globally scale-invariant process. This is distinct from the classic multi-exponent statistics observed when the local magnetic field is perpendicular to the flow direction. These observations are interprete…
Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is in particular the case when flows are present. These differences are explored explicitly by working out in detail two magnetohydrodynamic examples: convection against gravity in a stratified fluid and translationally invariant perturbations of a rotating magnetized plasma pinch. In this second example we show in explicit form how to perform the time-depende…
Certain unresolved ambiguities surround pressure determinations for incompressible flows, both Navier-Stokes and magnetohydrodynamic. For uniform-density fluids with standard Newtonian viscous terms, taking the divergence of the equation of motion leaves a Poisson equation for the pressure to be solved. But Poisson equations require boundary conditions. For the case of rectangular periodic boundary conditions, pressures determined in this way are unambiguous. But in the presence of "no-slip" rigid walls, the equation of motion can be used to infer both Dirichlet and Neumann boundary conditions…
This study shows that a relativistic Hall effect significantly changes the properties of wave propagation by deriving a linear dispersion relation for relativistic Hall magnetohydrodynamics (HMHD). Whereas, in non- relativistic HMHD, the phase and group velocities of fast magnetosonic wave become anisotropic with an increasing Hall effect, the relativistic Hall effect brings upper bounds to the anisotropies. The Alfveén wave group velocity with strong Hall effect also becomes less anisotropic than non-relativistic case. Moreover, the group velocity surfaces of Alfvén and fast waves coalesce in…
When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfvénic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). …
Magnetic reconnection with a 0.1 rate: Effective resistivity in general relativistic magnetohydrodynamics
Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；Department of Physics, University of Toronto（多伦多大学物理系）；David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto（多伦多大学大卫·邓拉普天文与天体物理系）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Department of Astronomy, Columbia University（哥伦比亚大学天文学系）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）；Department of Physics, University of Maryland（马里兰大学物理系）；Princeton Center for Theoretical Science and Department of Astrophysical Sciences, Princeton University（普林斯顿大学理论科学中心和天体物理科学系）；Anton Pannekoek Institute（安东·潘内克研究所）
By taking into account the radiation reaction force, we derive a set of one-fluid relativistic magnetohydrody-namics (RMHD) equations with the Landau-Lifshitz radiation reaction force based on a relativistic two-fluid plasma. These equations could be used to situations where spatiotemporal scales of plasma's motion are suffi-ciently large.
We show that large-amplitude, non-planar, Alfvén wave (AW) packets are exact nonlinear solutions of the relativistic MHD equations when the total magnetic-field strength in the local fluid rest frame ($b$) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant-$b$ AWs propagate without distortion at the relativistic Alfvén velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant-$b$ AWs in the solar wind suggest that such waves may be present in …
We construct and analyze a model of the relativistic steady-state magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already p…
Using the generally covariant magnetofluid formalism for a hot plasma, a new curvature (of space time) driven mechanism for generating seed vorticity/magnetic field is presented. The "battery" owes its origin to the interaction between gravity (epitomized in the spatial variation of the metric tensor) and the inhomogeneous plasma thermodynamics. The general relativistic drive for the seed field is evaluated in a simplified model of a hot plasma accreting around a Schwarzschild black hole. Some astrophysical applications are suggested.
In this Letter, we report compressible mode effects on relativistic magnetohydrodynamic (RMHD) turbulence in Poynting-dominated plasmas using 3-dimensional numerical simulations. We decomposed fluctuations in the turbulence into 3 MHD modes (fast, slow, and Alfvén) following the procedure mode decomposition in (Cho & Lazarian 2002), and analyzed their energy spectra and structure functions separately. We also analyzed the ratio of compressible mode to Alfvén mode energy with respect to its Mach number. We found the ratio of compressible mode increases not only with the Alfvén Mach number but w…
We present high resolution 2D and 3D simulations of magnetized decaying turbulence in relativistic resistive magneto-hydrodynamics. The simulations show dynamic formation of large scale intermittent long-lived current sheets being disrupted by the tearing instability into plasmoid chains. These current sheets are locations of enhanced magnetic field dissipation and heating of the plasma. We find magnetic energy spectra $\propto k^{-3/2}$, together with strongly pronounced dynamic alignment of Elsasser fields and of velocity and magnetic fields, for strong guide-field turbulence, whereas we ret…
The magnetic connection theorem of ideal Magnetohydrodynamics by Newcomb [Newcomb W.A., Ann. Phys., 3, 347 (1958)] and its covariant formulation are rederived and reinterpreted in terms of a "time resetting" projection that accounts for the loss of simultaneity in different reference frames between spatially separated events.
The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differential equation. This note provides an analytical solution of the 2D isentropic vortex problem with explicit algebraic expressions in the special relativistic hydrodynamics and magnetohydrodynamics and extends it to the 3D case.
We derive a number of solution for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. …
This study investigates the properties of waves in relativistic extended magnetohydrodynamics (RXMHD), which includes Hall and electron thermal inertia effects. We focus on the case when the electron temperature is ultrarelativistic, and thus, the electron thermal inertia becomes finite at near the proton inertial scale. We derive the linear dispersion relation of RXMHD and find that the Hall and electron thermal inertia effects couple with the displacement current, giving rise to three superluminous waves in addition to the slow, fast, and Alfvén waves. We also show that the phase- and group-…
Iharm3D: Vectorized General Relativistic Magnetohydrodynamics
University of Illinois at Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）；Illinois Center for Advanced Studies of the Universe（伊利诺伊高级宇宙研究中心）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）
Exact solutions of the self-consistent relativistic magnetohydrodynamics equations for an anisotropic magnetized plasma on the background of Bondi-Pirani-Robinson's vacuum plane gravitational wave (PGW) metric with an arbitrary polarization are obtained, which generalize the results obtained earlier by one of the authors for the transverse polarization of a gravitational wave. Based on the reformulated energobalance equation it is shown that in the linear approximation by gravitational wave amplitude only the transverse polarization of PGW interacts with magnetized plasma.
We investigate the propagation of electromagnetic waves in resistive pair plasmas using a onefluid theory derived from the relativistic two-fluid equations. When the resistivity normalized by the electron/positron inertia variable exceeds a critical value, the dispersion relation for electromagnetic waves shows that the group velocity is larger than the light speed in vacuum. However, in such a case, it also is found that the plasma parameter is less than unity: that is, the electron-positron pair medium no longer can be treated as plasma. Thus the simple two-fluid approximation is invalid. Th…
Relativistic magnetohydrodynamics (RMHD) provides an extremely useful description of the low-energy long-wavelength phenomena in a variety of physical systems from quark-gluon plasma in heavy-ion collisions to matters in supernovas, compact stars, and early universe. We review the recent theoretical progresses of RMHD, such as a formulation of RMHD from the perspective of magnetic flux conservation using the entropy-current analysis, the nonequilibrium statistical operator approach applied to quantum electrodynamics, and the relativistic kinetic theory. We discuss how the transport coefficient…
Relativistic Six-Fluid Rotating-Plasma Force-Balance Equilibria for p-11B Fusion Conditions in Spherical Tori
Beijing ENN Fusion Energy Science and Technology Co., Ltd.（北京恩诺聚变能源科学与技术有限公司）；Beijing Key Laboratory of High Magnetic Field Spherical Torus Fusion Energy（北京市高磁场球环聚变能重点实验室）；Hebei Key Laboratory of Compact Fusion（河北省紧凑型聚变重点实验室）
Using the generally covariant magnetofluid formalism for a hot plasma, a new spacetime curvature driven mechanism for generating seed vorticity/magnetic field is presented. The ``battery'' owes its origin to the interaction between gravity and the inhomogeneous plasma thermodynamics. The general relativistic drive is evaluated for two simple cases: seed formation in a simplified model of a hot plasma accreting in stable orbits around a Schwarzschild black hole, and for particles in free fall near the horizon. Some astrophysical applications are suggested.
Based on a 14-moment closure for non-resistive (general-) relativistic viscous plasmas, we describe a new numerical scheme that is able to handle all first-order dissipative effects (heat conduction, bulk and shear viscosities), as well the anisotropies induced by the presence of magnetic fields. The latter is parameterized in terms of a thermal gyrofrequency or, equivalently, a thermal Larmor radius and allows to correctly capture the thermal Hall effect. By solving an extended Israel-Stewart-like system for the dissipative quantities that enforces algebraic constraints via stiff-relaxation, …
We derive the relativistic non-resistive, viscous second-order magnetohydrodynamic equations for the dissipative quantities using the relaxation time approximation. The Boltzmann equation is solved for a system of particles and antiparticles using Chapman-Enskog like gradient expansion of the single-particle distribution function truncated at second order. In the first order, the transport coefficients are independent of the magnetic field. In the second-order, new transport coefficients that couple magnetic field and the dissipative quantities appear which are different from those obtained in…
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection dri…
Recent advances in black hole astrophysics, particularly the first visual evidence of a supermassive black hole at the center of the galaxy M87 by the Event Horizon Telescope (EHT), and the detection of an orbiting "hot spot" nearby the event horizon of Sgr A* in the Galactic center by the Gravity Collaboration, require the development of novel numerical methods to understand the underlying plasma microphysics. Non-thermal emission related to such hot spots is conjectured to originate from plasmoids that form due to magnetic reconnection in thin current layers in the innermost accretion zone. …
