General connected and reconnected fields in plasmas
TL;DR: In this paper, the connection theorem for two-fluid dynamics was established for the case where the magnetic field is no longer connected to the fluid lines; it is replaced by more general fields (one for each plasma specie) that are weighted combination of the electromagnetic and the thermal-vortical fields.
Abstract: For plasma dynamics, more encompassing than the magnetohydrodynamical (MHD) approximation, the foundational concepts of “magnetic reconnection” may require deep revisions because, in the larger dynamics, magnetic field is no longer connected to the fluid lines; it is replaced by more general fields (one for each plasma specie) that are weighted combination of the electromagnetic and the thermal-vortical fields. We study the two-fluid plasma dynamics plasma expressed in two different sets of variables: the two-fluid (2F) description in terms of individual fluid velocities, and the one-fluid (1F) variables comprising the plasma bulk motion and plasma current. In the 2F description, a Connection Theorem is readily established; we show that, for each specie, there exists a Generalized (Magnetofluid/Electro-Vortic) field that is frozen-in the fluid and consequently remains, forever, connected to the flow. This field is an expression of the unification of the electromagnetic, and fluid forces (kinematic and the...
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TL;DR: In this article, the dynamical evolution of a generalized vorticity (a combination of the magnetic and kinematic parts) in a cosmological context was studied in a general covariant electrovortic formalism for relativistic plasmas.
Abstract: Using a generally covariant electrovortic (magnetofluid) formalism for relativistic plasmas, the dynamical evolution of a generalized vorticity (a combination of the magnetic and kinematic parts) is studied in a cosmological context. We derive macroscopic vorticity and magnetic field structures that can emerge in spatial equilibrium configurations of the relativistic plasma. These fields, however, evolve in time. These magnetic and velocity fields, self-consistently sustained in a plasma with arbitrary thermodynamics, constitute a diamagnetic state in the expanding universe. In particular, we explore a special class of magnetic and velocity field structures supported by a plasma in which the generalized vorticity vanishes. We derive a highly interesting characteristic of such "superconductor-like" fields in a cosmological plasmas in the radiation era in the early universe. In that case, the fields grow proportional to the scale factor, establishing a deep connection between the expanding universe and the primordial magnetic fields.
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TL;DR: In this article, a generalized, intuitive two-fluid picture of 2D non-driven collisionless magnetic reconnection is described using results from a full-3D numerical simulation.
Abstract: A generalized, intuitive two-fluid picture of 2D non-driven collisionless magnetic reconnection is described using results from a full-3D numerical simulation. The relevant two-fluid equations simplify to the condition that the flux associated with canonical circulation Q=m_e ∇ × u_e + q_e B is perfectly frozen into the electron fluid. In the reconnection geometry, flux tubes defined by Q are convected with the central electron current, effectively stretching the tubes and increasing the magnitude of Q exponentially. This, coupled with the fact that Q is a sum of two quantities, explains how the magnetic fields in the reconnection region reconnect and give rise to strong electron acceleration. The Q motion provides an interpretation for other phenomena as well, such as spiked central electron current filaments. The simulated reconnection rate was found to agree with a previous analytical calculation having the same geometry. Energy analysis shows that the magnetic energy is converted and propagated mainly in the form of the Poynting flux, and helicity analysis shows that the canonical helicity ∫P·Q dV as a whole must be considered when analyzing reconnection. A mechanism for whistler wave generation and propagation is also described, with comparisons to recent spacecraft observations.
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TL;DR: This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD), and particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD.
Abstract: This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results obtained with different numerical SRHD methods are compared, and two astrophysical applications of SRHD flows are discussed. An evaluation of the various numerical methods is given and future developments are analyzed.
376 citations
TL;DR: In this article, the basic properties of relativistic magnetohydrodynamics, as a hyperbolic system of quasi-linear conservation laws, are discussed and a multidimensional Godunov-type numerical scheme that enforces the magnetic flux conservation is developed.
Abstract: The basic properties of relativistic magnetohydrodynamics, as a hyperbolic system of quasi-linear conservation laws, are discussed. These are then used to develop a multidimensional Godunov-type numerical scheme that enforces the magnetic flux conservation. This scheme is based on linear Riemann solvers and has second-order accuracy in smooth regions. The results of thorough test calculations demonstrate that the scheme is robust and can cope with truly ultrarelativistic problems.
266 citations
TL;DR: In this article, it was shown that a line of force in a magnetic field can be assumed to move with a certain velocity v(r, t) if and only if the flux through a closed curve moving with velocity v is constant.
232 citations
01 Jan 1955
TL;DR: In this paper, it was shown that a line of force in a magnetic field can be assumed to move with a certain velocity v(r, t) if and only if the flux through a closed curve moving with velocity v is constant.
Abstract: It is often said that magnetic lines of force in a conducting fluid move with the fluid. In the case of a plasma, this means that the lines of force move with the particle drift velocity1 v p = ( E × H ) H 2 . Such statements are not directly verifiable, since the velocity of a line of force is not a measurable quantity. However, the statement that the lines of force move with a certain velocity v(r, t) does have verifiable consequences, such as: (1) The flux through a closed curve moving with velocity v is constant. (2) A line, moving with velocity v, which is initially a line of force, remains a line of force in the course of its motion. Statement (2), as well as all other verifiable consequences of the original hypothesis, follows from statement (1). A velocity is said to be flux-preserving if it satisfies (1), line-preserving if it satisfies (2). It is permissible to ascribe a velocity v to the lines of force if and only if ∇ × (E + v × H) vanishes identically. It is always possible to choose a v satisfying this relation, although it is not generally possible to do this uniquely. To say that a certain velocity v is permissible means that all the verifiable consequences of ascribing this velocity to the lines of force are valid, i.e., that v is flux-preserving. In the case of the particle drift velocity the condition for flux-preservation reduces to ∇ × [ H(E·H) H 2 ] = 0 . Even if vp is not flux-preserving, there may be some closed curves moving with velocity vp which have constant flux. A semiexhaustive enumeration of such curves is given for a general electromagnetic field. Among these curves are those which lie in a surface everywhere perpendicular to H, if this surface is independent of time. A family of such surfaces will exist if and only if H·∇ × H and H × Ḣ both vanish identically. A velocity may be line-preserving without being flux-preserving, but not vice versa. The necessary and sufficient condition for line-preservation is that H × [∇ × (E + v × H)] should vanish identically. The motion of the lines of force in a plasma is related only to the transverse motion of the charged particles. The latter is separable from the longitudinal motion if and only if vp is line-preserving. A necessary and sufficient condition is also given for the separability of only one component of the transverse motion. The concept of a line of force is not relativistically covariant, because each point of a line of force has the same time coordinate. A curve in space-time which appears as a line of force in one frame of reference will therefore not be a line of force in another frame of reference. However, a moving line of force will trace out a two-dimensional surface in space-time, and it may be that this surface will intersect every space-like hyperplane in a line of force. In that case the surface will appear as the path of a moving line of force in every frame of reference, thus defining a moving line of force as a covariant concept. It is shown that a family of such surfaces exists if and only if E·H vanishes identically, in which case they will be generated by lines of force moving with the particle drift velocity vp.
182 citations
TL;DR: In this article, collisionless magnetic reconnection in a two-dimensional plasma is analyzed, using a twofluid model where electron mass and pressure effects are important, and numerical simulations show the formation of current and vorticity layers along two branches crossing at the stagnation point of the plasma flow.
Abstract: Collisionless magnetic reconnection in a two dimensional plasma is analyzed, using a two-fluid model where electron mass and pressure effects are important. Numerical simulations show the formation of current and vorticity layers along two branches crossing at the stagnation point of the plasma flow. These structures are interpreted on the basis of the Hamiltonian Casimirs (conserved fields) of the fluid plasma model.
133 citations