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Exact solutions have been obtained for the equations of an electron subjected to a transverse rotating magnetic field superimposed on a homogeneous axial magnetic field. The solutions show that complete transfer of the axial energy into transverse energy is possible for a range of values of the injection velocity and the transverse magnetic field.
Synchrotron spectra were computed for a hypothetical Saturn radiation belt. A monoenergetic distribution of relativistic electrons was assumed to exist in a toroidal volume in a dipole magnetic field aligned with the rotation axis. When synchrotron emission is added to the thermal component implied by observations at wavelengths shorter than 50 cm, the upturn in the total emission spectrum may be gradual to sharp, depending on the critical wavelength and the number density of radiating electrons. With the constraint of the pressure balance equation, the ranges of magnetic field intensity, and electron energy, and density were tabulated and nomographically illustrated. For several estimates of the magnetic field loading factor, the minimum surface magnetic field intensity and minimum electron number density were computed.
Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative transfer equation according to the expected physical conditions of the systems under study. Aims. We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system pi using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth pi produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions. The algorithm has been implemented in the XPEC package for X-ray fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (approx > 10(exp 12) G). This latter case is expected to be of typical accreting systems such as X-ray pulsars and supergiant fast X ray transients.
Large scale flows within the solar convection zone are the primary drivers of the Sun s magnetic activity cycle. Differential rotation can amplify the magnetic field and convert poloidal fields into toroidal fields. Poleward meridional flow near the surface can carry magnetic flux that reverses the magnetic poles and can convert toroidal fields into poloidal fields. The deeper, equatorward meridional flow can carry magnetic flux toward the equator where it can reconnect with oppositely directed fields in the other hemisphere. These axisymmetric flows are themselves driven by large scale convective motions. The effects of the Sun s rotation on convection produce velocity correlations that can maintain the differential rotation and meridional circulation. These convective motions can influence solar activity themselves by shaping the large-scale magnetic field pattern. While considerable theoretical advances have been made toward understanding these large scale flows, outstanding problems in matching theory to observations still remain.
Motion equation of charged particle in static magnetic field
After the corotation resonance with an exterior satellite proved inapplicable to the Neptune ring arc confinement, a search for other mechanisms settled on the possible influence of Neptune's magnetic field. The areas of greater optical depth around the ring are much dustier than the low optical depth regions. These particles reside in a plasma; therefore, they must carry some charge. The components of Neptune's magnetic field on the equator at the radius of the ring arcs as a function of Neptunian longitude are shown. The components are those of an offset tilted dipole model. Although the dipole model is probably not a good approximation so close to the planet, the magnitude of the field that is given is probably close to the actual value. The possible importance of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic field on the smallest particles in the ring is indicated by the ratio of the magnetic force to the central gravitation attraction with the field strength of B = 0.01 gauss at the ring distance. A preferred position in the orbit for magnetically perturbed particles seems to require a commensurability between the rotation of the planet and the motion of the particle in the orbit. The period of rotation is assumed to be that of the radio bursts at 16.11 hours. However, without a model for the radio emission, one cannot be absolutely sure. Jupiter's decametric radiation depends on Io's orbital position as well as the rotation, so a synodic periodicity might be appropriate. But the latter radiation is highly directed, whereas Neptune's was seen all along the spacecraft trajectory on the 16.11 hour schedule, i.e., with no shifts in phase relative to a fixed longitude on the planet. The ring orbital period is 10.536 hours which is not commensurate with the rotation period. If the 16.11 hours is interpreted as a synodic period between the rotation and a satellite motion, the closest rotation periods to 16 hours are 15.9 hours if the satellite is 1989N4 and 18.2 hours if the satellite is Triton. The former is near a 3:2 resonance with the ring particle motion. The problem deserves some more thought before a possible herding of small particles by the magnetic field is abandoned.
The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the magnetic field in both the near- and far-field regions. However, in that work the downstream domain was constrained to a channel of constant cross-sectional area. In the present work we seek to address this issue by modeling the downstream region with a domain that permits free expansion of the plasma, permitting a better evaluation of the downstream effects the applied field has on the plasma. The inlet boundary conditions and applied magnetic field values will also be varied to determine the effect the initial plasma energy content and applied magnetic field energy density have on the near- and far-field plasma properties on the MHD code. This will determine the effect of inlet boundary conditions on the results downstream and address issues related to the restrictive numerical domain previously used.
Numerical simulations of the damping of magnetosonic waves via magnetic pumping in the presence of electromagnetic fluctuations that can pitch-angle scatter the plasma particles are presented. From the first simulation it is found that the magnetosonic-wave energy is transferred to high-energy particles. In the second type of simulation, magnetosonic waves produce a hot surface layer on the plasma that is ablated by the wave energy. Solution of a Fokker-Planck equation for the magnetic-pumping process is found to adequately represent magnetic pumping by small-amplitude magnetosonic waves.
The uniqueness and accuracy of the equations which describe the transport of charged particles diffusing in a random magnetic field parallel to a relatively large guiding field is examined. With regard to uniqueness, it is found that the same coefficient of diffusion is obtained by three methods that have apparently led to discrepancies in previous work. With regard to accuracy, it is found that two corrections must be added to Fick's law in which the diffusive flux is proportional to the gradient of the density. Explicit expressions are given for a characteristic time and a characteristic length which describe the corrections.
This paper discusses the phenomenological and formal similarities between the merging of aircraft vortex trails and the merging of magnetic field lines in a plasma. High-resolution photographs are shown of smoke trails from the wing tips of an airplane. These photographs show that the two vortex trails merge together downstream of the aircraft in a way similar to the merging of oppositely directed magnetic field lines in a plasma. Although there are some differences, this correspondence is apparently related to the fact that the vorticity equation in a fluid has the same mathematical form as the magnetic field equation in an MHD plasma. In both cases the merging proceeds at a rate considerably faster than would be predicted from classical estimates of the viscosity and resistivity. The enhanced merging rate in the fluid case appears to result from turbulence that increases the diffusion rate in the merging region.
A diffusion equation is derived which describes the evolution of a magnetic field in a plasma of arbitrary beta and resistivity. The equation is valid for a one-dimensional slab geometry, assumes the plasma remains in quasi-equilibrium throughout its evolution and does not include thermal transport. Scaling laws governing the rate of change of the magnetic energy, particle drift energy, and magnetic flux are calculated. It is found that the magnetic free energy can be substantially larger than the particle drift energy and can be an important energy reservoir in driving plasma instabilities (e.g., the lower-hybrid-drift instability). In addition, the effect of a spatially varying resistivity on the evolution of a reversed-field plasma is studied. The resistivity model used is based upon the anomalous transport properties associated with the nonlocal mode structure of the lower-hybrid-drift instability. The relevance of this research to laboratory plasmas (e.g., theta pinches, reversed-field theta pinches) and space plasmas (e.g., the earth's magnetotail) is discussed.
Analysis of global magnetic anomaly maps derived from satellite data is facilitated by inversion to the equivalent magnetization in a constant thickness magnetic crust or, equivalently, by reduction to the pole. Previous inversions have proven unstable near the geomagnetic equator. The instability results from magnetic moment distributions which are admissible in the inversion solution but which make only small contribution to the computed values of anomaly field. Their admissibility in the solution could result from noisy or incomplete data or from small poorly resolved anomalies. The resulting magnetic moments are unrealistically large and oscillatory. Application of the method of principal components (e.g. eigenvalue decomposition and selective elimination of less significant eigenvectors) is proposed as a way of overcoming the instability and the method is demonstrated by applying it to the region around the Bangui anomaly in Central Africa.
Cyclotron maser and plasma wave growth which results from electrons accelerated in magnetic loops are studied. The evolution of the accelerated electron distribution is determined by solving the kinetic equation including Coulomb collisions and magnetic convergence. It is found that for modest values of the column depth of the loop the growth rates of instabilities are significantly reduced and that the reduction is much larger for the cyclotron modes than for the plasma wave modes. The large decrease in the growth rate with column depth suggests that solar coronal densities must be much lower than commonly accepted in order for the cyclotron maser to operate. The density depletion has to be similar to that which occurs during auroral kilometric radiation events in the magnetosphere. The resulting distributions are much more complicated than the idealized distributions used in many theoretical studies, but the fastest growing mode can still simply be determined by the ratio of electron plasma to gyrofrequency, U=omega(sub p)/Omega(sub e). However, the dominant modes are different than for the idealized situations with growth of the z-mode largest for U approximately less than 0.5, and second harmonic x-mode (s=2) or fundamental o-mode (s=1) the dominant modes for 0.5 approximately less than U approximately less than 1. The electron distributions typically contain more than one inverted feature which could give rise to wave growth. It is shown that this can result in simultaneous amplification of more than one mode with each mode driven by a different feature and can be observed, for example, by differences in the rise times of the right and left circularly polarized components of the associated spike bursts.
Four equations for the origin and propagation of nonrelativistic jets and winds are derived from the basic conservation laws of ideal MHD. The axial current density is negative in the vicinity of the axis and positive at larger radii; there is no net current because this is energetically favored. The magnetic field is essential for the jet solutions in that the zz-component of the magnetic stress acts, in opposition to gravity, to drive matter through the slow magnetosonic critical point. For a representative self-consistent disk/jet solution relevant to a protostellar system, the reaction of the accreted mass expelled in the jets is 0.1, the ratio of the power carried by the jets to the disk luminosity is 0.66, and the ratio of the boundary layer to disk luminosities is less than about 0.13. The star's rotation rate decreases with time even for rotation rates much less than the breakup rate.
The recent emergence of a new class of accretion-powered, transient, millisecond X-ray pulsars presents some difficulties for the conventional picture of accretion onto rapidly rotating magnetized neutron stars and their spin behavior during outbursts. In particular, it is not clear that the standard paradigm can accommodate the wide range in M(i.e., approx. greater than a factor of 50) over which these systems manage to accrete and the high rate of spindown that the neutron stars exhibit in at least a number of cases. When the accretion rate drops sufficiently, the X-ray pulsar is said to become a "fast rotator," and in the conventional view, this is accompanied by a transition from accretion to "propellering," in which accretion ceases and the matter is ejected from the system. On the theoretical side, we note that this scenario for the onset of propellering cannot be entirely correct because it is not energetically self-consistent. We show that, instead, the transition is likely to take place through disks that combine accretion with spindown and terminate at the corotation radius. We demonstrate the existence of such disk solutions by modifying the Shakura-Sunyaev equations with a simple magnetic torque prescription. The solutions are completely analytic and have the same dependence on M and a (the viscosity parameter) as the original Shakura-Sunyaev solutions, but the radial profiles can be considerably modified, depending on the degree of fastness. We apply these results to compute the torques expected during the outbursts of the transient millisecond pulsars and find that we can explain the large spin-down rates that are observed for quite plausible surface magnetic fields of approx. 10(exp 90 G.
Cosmic ray (CR) propagation in a turbulent medium is usually considered in the diffusion approximation. Here, the diffusion equation is obtained for strongly magnetized particles in the general form. The influence of a large-scale random magnetic field on CR propagation in interstellar medium is discussed. Cosmic rays are assumed to propagate in a medium with a regular field H and an ensemble of random MHD waves. The energy density of waves on scales smaller than the free path 1 of CR particles is small. The collision integral of the general form which describes interaction between relativistic particles and waves in the quasilinear approximation is used.
The resistive-MHD equations are numerically solved in two-dimensions for an initial-boundary-value problem which models the emergence of magnetic flux from the photosphere into the corona. As the emergence begins a current sheet forms around the emerging region which separates the emerging region from the overlying coronal magnetic field. This current sheet is the source of the free-magnetic energy in the system, and in the limit of zero resistivity it is a simple tangential discontinuity. However, when the resistivity is finite, reconnection between the magnetic field in the emerging region and the overlying coronal magnetic field ensures, and the subsequent evolution of the enveloping current sheet becomes complex. The overall time history of the current evolution is suggestive of the expected current evolution for the pre-flare, impulsive, and main phases of flares.
Magnetic field effects on collisionless plasma sheath near planar electrode, solving electric and magnetic potentials nonlinear differential equations by numerical scheme