Force-free Region Research Articles

Observation of the scalar Aharonov-Bohm effect by neutron interferometry.

A phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space is known as the scalar Aharonov-Bohm (AB) effect. Unlike the more familiar AB effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. We have performed an analogous interferometric experiment with thermal neutrons subject to pulsed magnetic fields. The observations were carried out at the University of Missouri Research Reactor using a skew-symmetric perfect-silicon-crystal neutron interferometer. The expected phase shifts have been observed to a high degree of accuracy. A detailed description of the experiment and its interpretation is given in this paper.

Scalar Aharonov-Bohm experiment with neutrons.

The scalar version of the Aharonov-Bohm effect predicts a phase shift for de Broglie waves due to the action of a scalar potential in an otherwise field-free (i.e., force-free) region of space. Unlike the more familiar effect due to the magnetic vector potential, the scalar effect has hitherto remained unverified due, presumably, to technical difficulties in electron interferometry. Rather than using electrons acted on by electrostatic potentials, we have performed an analogous interferometry experiment with thermal neutorns subject to pulsed magnetic fields. The expected phase shifts have been observed to a high degree of accuracy.

Question of the nonlocality of the Aharonov-Casher effect

The Aharanov-Casher effect is manifested in a (2+1)-dimensional model that screens the electromagnetic fields, in order to demonstrate that the effect is essentially nonlocal in its nature. The question of nonlocality is discussed by means of a nonrelativistic model for a superconductor. It is demonstrated that although the superconductor screens the electric field generated by an external charge it does not screen the modular electric field which is a constant of motion of the system. Consequently, a magnetic fluxon will accumulate the same phase as if the electric field were unscreened and the Aharonov-Casher effect will exist even in a force-free region.

Equilibrium Configuration of a High-Beta Screw Pinch

The magnetohydrodynamic equilibrium of a moderately elongated screw pinch is considered. From comparisons of experimental and calculated data on the elongation factor and radial shift of the plasma column, the configuration is described by a two-region flat-current tokamak model. The inner high-beta plasma is surrounded by a force-free current region.

An efficient procedure for calculating the evolution of the wave function by fast Fourier transform methods for systems with spatially extended wave function and localized potential

Various methods using fast Fourier transform algorithms or other ‘‘grid’’ methods for solving the time-dependent Schrödinger equation are very efficient if the wave function remains spatially localized throughout its evolution. Here we present and test an extension of these methods which is efficient even if the wave function spreads out, provided that the potential remains localized. The idea is to split the wave function at various times during the propagation into two parts, one localized in the interaction region and the other in the force free region; the first is propagated by a fast Fourier transform method on a grid whose size barely exceeds the interaction region, and the latter by a single application of a free particle propagator. This splitting is performed whenever the interaction region wave function comes close to the end of the grid. The total asymptotic wave function at a given time t is reconstructed by adding coherently all the asymptotic wave function pieces which were split at earlier times, after they have been propagated to the common time t. The method is tested by studying the wave function of a diatomic molecule dissociated by a strong laser field. We compute the rate of energy absorption and dissociation and the momentum distribution of the fragments.

Turbulent relaxation to a force-free field-reversed state.

The evolution of nonequilibrium initial conditions of an incompressible magnetohydrodynamic $Z$ pinch is described by a three-dimensional, pseudospectral numerical code. Magnetohydrodynamic turbulence develops in the resistive, nonviscous magnetofluid, resulting in the selective decay of the energy relative to the magnetic helicity, at Lundquist numbers of only a few hundred. An interior force-free region grows with time and achieves spontaneous reversal of the toroidal magnetic field at the wall, without the necessity of an external electric field.

Black-hole electrodynamics: an absolute-space/universal-time formulation*

This paper reformulates and extends the Blandford–Znajek theory of a stationary, axisymmetric magnetosphere anchored in a black hole and in its accretion disc. Such a magnetosphere should transfer much of the rotational energy of the hole and orbital energy of the disc into an intense flux of electromagnetic energy – which in turn might be the energizer for quasars and active galactic nuclei. Our reformulation of the theory attempts to make it accessible to plasma astrophysicists who have little experience with general relativity. This is done by replacing the relativist's ‘unified spacetime’ viewpoint with an equivalent Galilean-type ‘absolute-space-plus-universal-time’ viewpoint, and by replacing the electromagnetic field tensor |$F_{\mu\nu}$| with electric and magnetic fields E and B that reside in the absolute space outside the black hole. The resulting formalism resembles the theory of axisymmetric pulsar magnetospheres; it will, we hope, permit a fairly easy transfer of physical intuition and results from the pulsar problem to the black-hole problem. The Blandford–Znajek theory focused primarily on force-free regions of the magnetosphere. This paper, in addition to recasting the force-free theory in new language, extends it to encompass regions that are degenerate (E · B = 0) but not force-free, and regions that are neither degenerate nor force-free. Blandford & Znajek showed that the magnetospheric structure in the force-free region is determined by a general relativistic ‘stream differential equation’. This paper presents an action principle for the stream equation, it elucidates the boundary conditions that one must pose on the stream function ψ, and it shows that ψ and the poloidal magnetic field distribute themselves over the hole's horizon in such a manner as to extremize the horizon's electromagnetic surface energy. This paper also constructs a general relativistic version of DC electronic circuit theory and uses it to elucidate the flows of electric current and of electromagnetic power in the magnetosphere. The circuit-theory analysis, and independently a torque-balance analysis, suggests that those magnetic field lines which thread the hole will be dragged into rotation with roughly half the angular velocity of the hole – and, consequently, that the hole will deliver to the magnetosphere the maximum electromagnetic power permitted by the horizon strengths of the magnetic fields.

Experimental verification of an Aharonov-Bohm effect in rotating reference frames

A thought experiment is reviewed which shows two things. First, in a region of a rotating frame that is not simply connected, the inertial forces can be canceled without completely canceling the inertial vector potential (whose curl determines the Coriolis force); second, the presence of this uncanceled potential can be detected in a quantum interference experiment. It is then argued that the thought experiment was realized in an earlier experiment involving a rotating superconductor, and that the experimental results confirm the theoretical prediction. In this way, the first experimental verification of a physical effect due to a nonelectromagnetic potential in a force-free region is established. An analogous experiment for the gravitational vector potential is also discussed. Finally, it is pointed out that the close connection between electromagnetic and inertial vector potentials provides an intuitive way to make predictions about rotating superconductors.

On charge neutrality and dissipative effects in pulsar systems

In the search for the state of minimum energy dissipation in aligned pulsars, force-free (rho/sub q/E x B = O) states are considered which have no net charge to the star plus its atmosphere (neutral system). All attempts to obtain finite, force-free atmospheres for neutral systems have failed to date, and some necessary complexities of such systems (if they exist) are discussed. Neutral systems with infinite atmospheres are then considered, such systems (if they exist) are discussed. Neutral systems with infinite atmospheres are then considered, such that their magnetic field, B = del x (A (r,THETA)epsilon/sub phi/), has a dipole componet as r..-->..infinity. It is proved that such force-free atmospheres must have an angular velocity ..cap omega..(psi), where psiequivalentrA sin theta/B/sub o/R/sup 2/, which tends to zero as psi..-->..0, corresponding to the magneitc surfaces eminating from the polar region. It is also proved that the charge density goes to zero everywhere on the axis, rho/sub q/ = 0 as THETA..-->..0. A decreasing angular velocity implies that either there is slippage between the atmosphere and the crust near the poles, or else the infinite portion of the atmosphere is detached from the star by a non-- force-free region (''gap''). Specific modelsmore » of the former type are presented, which have no slippage at the stellar equator, and a maximum slippage of a few percent of the equatorial velocity, confined to a ring which is (at most) a few degrees off axis. These models explicitly demonstrate how a small modification of the Pacini and Goldreich-Julian boundary condition (only in the region of the poles) can strongly influence the atmosphere in most of space, due to the ''inversion mapping'' generated by the magnetic field. Several dissipative mechanisms in the atmosphere are discussed and contrasted with the dissipation in the crust.« less

Magnetohydrodynamic stability of high-beta tokamak equilibria with force-free currents

The growth rates and eigenfunctions of the leading internal modes are calculated for some high-beta tokamak equilibria with force-free currents for beta values ranging from 5 to 20%. The force-free currents flowing between the main plasma and the conducting wall stabilize the internal hydromagnetic instabilities including the ballooning modes. Modes with low toroidal mode numbers (n ⩽ 3) are stabilized at a plasma beta of about 10% when the current density in the force-free region is comparable to that in the main column.

A new pulsar atmospheric model. I - Aligned magnetic and rotational axes

A model is proposed for the plasma atmosphere about a rotating magnetized neutron star with aligned magnetic and rotational axes. The model is generated with the aid of a gedanken experiment in which the rotational velocity ..cap omega.. of the star is adiabatically increased. By this device it is established that the star will acquire a charge sufficient to stop the charge loss to the nebula, but not the local surface emission. The resulting monopole electric field causes plasma to flow across magnetic surfaces at large distances from the star, where it dominates the dipole magnetic field, thereby forming a current loop from the polar caps to polar annuli. This same electric flow region can also establilsh current loops to the nebula, provided electron-positron pairs are produced. The vacuum electric field has a surface where ExB=0, which is a dome over the polar cap. For larger ..cap omega.., radiation losses cause beam particles to be trapped around this surface, forming a relatively stationary, possibly turbulent component of the atmosphere. It is shown that this plasma dome is more stable than the force-free atmosphere, and is therefore presumably maintained by a balance between the radiative capture and diffusion of particles backmore » to the star. A small toroidal, nearly force-free region consisting of opposite charges also exists near the equator and is attached to an equatorial disk, maintained by diffusion. The limited atmospheric extent and toroidal drift velocity suggest that all the magnetic surfaces are closed (near-dipolar). (AIP)« less

On the dynamic accessibility of toroidal belt pinch equilibria

Topological constraints on the motion of finite toroidal systems are employed to show that most force-field configurations in a belt pinch geometry are not dynamically accessible via an adiabatic compression of force-free fields. This result is independent of any stability considerations. The leading asymptotic term (in the ratio column width/column height), for equilibria which are accessible via a radial motion, is determined by requiring that poloidal flux surfaces must also be poloidal current surfaces. As an application, it is shown that if the belt pinch column is a uniform, beta=1, column, surrounded by a force-free field region, then near the interface the magnitude of the poloidal magnetic field is a decreasing function of the poloidal flux, and toroidal currents in the sheath and neighboring force-free field region are opposed.

Quantum-related reference frames and the local physical significance of potentials

In a sequel to our previous paper we discuss two thought experiments which show that potentials in force-free regions have not only a nonlocal physically measurable significance (via, e.g., ∮A ·dl), but, in singly connected portions of that region, also have a necessary local significance (via their quantum spread ΔA, which cannot be neglected). We then show, in continuation to the foregoing paper, how suchA arise “geometrically” as kinematic quantities associated with the transformation between “quantum-related” reference frames, e.g., when the relative frame velocities areq-numbers possessing a quantum spread.

Stabilization of magnetohydrodynamic instabilities by force-free magnetic fields: II. Linear pinch

The marginal-stability analysis, developed in a previous paper 1), is applied to the stability problem of a linear pinch with a distributed current. Complete stability criteria are derived from the marginal equation of motion and it is shown that this method is equivalent to the application of the energy principle. For a sharp-pinch model of a dense plasma surrounded by a force-free magnetic field of constant α kinks, unstable modes of the surface-layer, and of the force-free region are shown to be absent if α is properly chosen. Explicit expressions for the growth rates of unstable configurations are derived. An appendix is devoted to the stability with respect to resistive tearing modes.

THE CHANNELING OF ENERGETIC ATOMS IN CRYSTAL LATTICES

Preliminary studies showed that approximates - 1% of 10-kev Cu atoms, starting from lattice sites and slowing down according to the Bohr potential, made very long flights, predominantly in (110) directions. These channeled particies did not move in force-free regions but experienced very many glancing collisions with atoms of the lattice, which steered them into (110) directions. This phenomenon of channeling so dominates the Bohr potential calculations for particles normally incident upon the low index planes of Cu that no reliable statistical inferences about range distributions can be drawn. The probability of channeling increases rapidly with increasing energy for particles incident upon (110) and (100) from energies below 1 kev and for particles incident upon (111) from about 3 kev. In each case, the preferred channel is normal to the crystal surface. In the isotropic case, the probability of channeling remains roughiy constant at about 1% between 1 and 10 kev, the (110) channels being strongly preferred. Channeling is not restricted to fcc crystals. Calculations for diamond and bcc structures al4o show extensive channeling. The existence of channeling may have significant implications for radiation damage theory, since the channeled particies lose their energy in very small increments, thus producing farmore » fewer displacements than would be expected on the basis of conventional cascade theory. (C.E.S.) The hamiltonian of a system of charged particles interacting with the electromagnetic field is investigated. For an arbitrary system the multipole expansion of the interaction between the system and the field is derived by means of a suitable canonical transformation. The transformed hamiltonian is obtained from the hamiltonian of the system by replacing the momenta by the transformed kinetic momenta and by addirg to the hamiltonian a term representing the interaction of the system with the eiectric component of the field. By expanding this interaction term, as weli as the transformed momenta, in powers of the dimension of the system over the wavelength, the multipole expansion of the hamiltonian is obtained. For a system interacting with a classical field the muitipole form of the hamiltonian is exactly equivalent to the originai hamiltonian. For a quantized field this is not true, and the multipole form of the transformed hamiltonian is shown to be equivalent to the original hamiitonian oniy for first-order radiation processes. (auth)« less