Generalized flux conservation for plasmas

When particle inertia causes the magnetohydrodynamic flux-freezing condition to fail, a fluxvorticity conservation theorem can be valid: for relativistically streaming, multifluid. pressure-free plasmas, each species has a 'fluxoid' that is frozen-in to its motion. Here, fluxoid dynamics is treated with particular reference to the effects of scalar partial pressure gradients corresponding to nonrelativistic thermal speeds. Several forms or the theorem are given, including explicitly covariantones valid in general relativity. The circumstances under which the separate contributions to the fluxoid law have significant effects on fluxoid dynamics are made clear by order-or-magnitude analysis. The case of steadily rotating systems is developed and used to investigate the applicability or the fluxoid theorem to pulsar magnetospheres.

“…is the fluxoid through c. When V x/vanishes, equation 11reduces to the theorem obtained by Buckingham et al (1972Buckingham et al ( , 1973.…”

Section: Ds) (10)supporting

confidence: 54%

Section: The Fluxoid Theoremmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fluxoid Dynamics in Relativistically Streaming Plasmas

Burman¹

1980

“…In the nonrelativistic limit, the mechanical terms in equation (2) are proportional to !vf -Qmvk<p, as in the Jacobi-type integral derived by Freeman and Mestel (1966) for a standard two-fluid plasma, and applied by them to galactic gas streaming. For multi-species cold relativistic plasmas, the flux conservation theorem of magnetohydrodynamics can be generalized to a 'fluxoid' conservation theorem, in order to incorporate the effects of particle inertia (Buckingham et al 1972(Buckingham et al , 1973: the quantity \1 x (Pk +ekA/c), where h == Ykmk vk, is 'frozen in' to the motion of species k. The steady-rotation condition a/at = -Q 0/00/ (Mestel 1971;Endean 1972a) is valid for, in particular, cylindrical polar components of vectors. Using this condition, we have previously shown (Burman and Mestel 1978) how to simplify considerably the equations of motion; in particular, fJ\ is found to be constant on lines of the vector Uk' defined by…”

Section: Equations Of Motion In Dissipation-free Domainsmentioning

confidence: 99%

A Cylindrical Pulsar Magnetosphere Model with Particle Inertia

Burman¹,

Mestel²

1979

An investigation is made of the equations to a steadily rotating nonaxisymmetric pulsar magnetosphere model, with the effects of particle inertia fully incorporated but with no dissipative forces. As an illustrative example the basic theory is applied to a 'cylindrical pulsar' model, in which quantities do not vary parallel to the rotation axis. It is shown that Endean's Bernoulli-type integral imposes severe constraints on particle motion, indicating that, in a realistic model, dissipation (e.g. by radiation damping) may play an essential role.

“…For multi species relativistic plasmas, the flux conservation theorem of magnetohydrodynamics can be generalized to a fluxoid conservation theorem, in order to incorporate the effects of particle inertia (Buckingham et al 1972(Buckingham et al , 1973. A differential form of the fluxoid theorem is obtained (Buckingham et al 1973) by using equation (3) in the equation of motion for each species, and then taking the curl and eliminating E by use of Faraday's law: the quantity V x (Pk + e k A/ c) is 'frozen-in' to species k. Using the steady-rotation condition a/at = -Q %cp (MesteI1971;Endean 1972a) which is valid for, in particular, cylindrical polar components of vectors, equation (3) becomes…”

mentioning

confidence: 99%

Equations for Pulsar Magnetospheres with Particle Inertia

Burman¹,

Mestel²

1978

This note deals with steadily rotating nonaxisymmetric pulsar magnetospheres, with the effects of particle inertia fully incorporated. It is pointed out that the equations of motion for the component species of a relativistically streaming nondissipative plasma can be considerably simplified by using the steady-rotation constraint together with a fluxoid conservation law and Endean's Bernoulli-type integral..The canoniCal pulsar model consists of a rotating magnetized neutron star with its magnetic axis inclined to the rotation axis, but a self-consistent model of the pulsar magnetosphere is still lacking. Both the vacuum model, in which the particles are regarded as test charges in the vacuum field, and the zero-inertia model are unacceptable: the plasma is not only a source of the electromagnetic field, but also carries energy and angular momentum.For the axisymmetric vacuum model, Goldreich and Julian (1969) pointed out that the component Ell of the electric field E parallel to the magnetic field B is sufficiently powerful near the star to pull charges out of it, so creating a charged magnetosphere. The solution for the nonaxisymmetric vacuum model with a dipolar magnetic field on. the stellar surface was obtained by Deutsch (1955), in the context of the theory of normal magnetic stars: This enabled Mestel (1971) and Cohen and Toton (1971) to extend the argument of Goldreich and Julian to the oblique rotator model, in which the magnetic and rotation axes are not aligned or anti parallel. Subsequent investigations of the physics of neutron star surfaces have suggested that, for most pulsars, the Goldreich-Julian mechanism might not be sufficiently powerful to extract positive ions (Ruderman 1971).The -argument of Goldreich and Julian (1969) poses the problem of studying magneto spheres that are sufficiently dense near the star to make Ell R! 0 there. Various authors have investigated charge-separated plasmas with inertial and other non-electromagnetic terms neglected, so that the equation of motion is justwhere c and v are the vacuum speed of light and the plasma's fluid velocity. But in the last few years it has become clear that inertial effects are crucial in pulsar magnetospheres: the need for the fields to be nonsingular at the light cylinder leads to difficulties when inertial effects are neglected.