In this review article the famous 'jet equation' in a Minkowski magnetosphere around the compact objects will be fully derived for the pedagogical purposes.

The magnetosphere is often perturbed by impulsive input such as interplanetary shocks and solar wind discontinuities. We study how these initial perturbations are propagating within the magnetosphere over various latitude regions by adopting a three-dimensional numerical dipole model. We examine the wave propagation on a meridional plane in a time-dependent manner and compare the numerical results with multi-satellite and ground observations. The dipole model is used to represent the plasmasphere and magnetosphere with a realistic Alfven speed profile. It is found that the effects of refraction, which result from magnetic field curvature and inhomogeneous Alfven speed, are' found to become important near the plasmapause. Our results show that, when the disturbances are assumed at the subsolar point of the dayside magnetosphere, the travel time becomes smaller to the polar ionosphere compared to the equatorial ionosphere.

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. Based on those papers we analyze the axisymmetric, nonstationary force-free black hole magnetosphere and the motion of the plasma. We concentrate on deriving the relations between the velocity components of the plasma and those of the accreting magnetic field lines. We conclude that the former are given by the sum of the latter and the magnetic field terms.

The response of the earth's magnetosphere to the variation of the solar wind parameters and Interplanetary magnetic field (IMF) has been stud}ed by using a high-resolution, three-dimension magnetohydrodynamic (MHD) simulation when the WIND data of velocity Vx, plasma density, dynamic pressure, By and Bz every 1 minute were used as input. Large electrojet and magnetic storm which occurred on October 21 and 22 are reproduced in the simulation (fig. 1). We have studied the energy transfer and tail reconnect ion in association with geomagnetic storms.

A magnetic cataclysmic variable has a rotating magnetic white dwarf which accretes matter from its late type companion. Kim & Beuermann (1995) presented a phenomenological model of the accretion from its surrounding structure e.g., a disk into the magnetosphere of the white dwarf, and presented results for the spin modulated X-ray spectrum and light curves. Using this model, we calculate the optical continuum and line emission which result from reprocessing of X-rays in the accretion stream within the magnetosphere. Penning (1985) suggested the observed spin-modulated radial-velocity variations might result from reprocession of X-rays in the disk. We, however, find the radiation can be originated from the magnetosphere accretion stream. We use the same geometrical model to calculate the optical and the X-ray behaviour. The results from the two wavelength bands are internally consistent. We conclude that this approach will increase the diagnostic accuracies of the results.

Since Goldreich and Julian's pioneering work in 1969, the pulsar magnetosphere theory has been dramatically developed for theorists to possess an elegant axisymmetric, stationary model. Based on this development the black hole magnetosphere theory has also been established in the last 30 years. Such theoretical developments will be reviewd equation by equation in this paper.

In the earlier papers we analyzed the axisymmetric, nonstationary electrodynamics of the central black hole and a surrounding thin accretion disk in an active galactic nucleus. In this paper we analyze the axisymmetric, nonstationary electrodynamics of the black hole magnetosphere in a similar way. In the earlier papers we employed the poloidal component of the plasma velocity which is confined only to the radial direction of the cylindrical coordinate system. In this paper we employ a more general poloidal velocity and get the Grad-Shafranov equation of the force-free magnetosphere of a Kerr black hole. The equation is consistent with the previous ones and is more general in many aspects as it should be. We also show in more general approaches that the angular velocity of the magnetic field lines anchored on the accreting matter tends to become close to that of the black hole at the equatorial zone of the hole.

We derive the Grad-Shafranov equation in the Macdonald-Thorne magnetosphere of the super-massive black hole in an active galactic nucleus. Our major assumption is that the plasma velocity is not only toroidal but also poloidal. As a result, we get the correction terms which are related to the poloidal motion of plasma like electrodynamic jets.

During their respective missions, the spacecraft Voyager and Cassini measured several Saturn magnetosphere parameters at different radial distances. As a result of information gathered throughout the journey, Voyager 1 discovered hot and cold electron distribution components, number density, and energy in the 6–18 Rs range. Observations made by Voyager of intensity fluctuations in the 20–30 keV range show electrons are situated in the resonance spectrum’s high energy tail. Plasma waves in the magnetosphere can be used to locate Saturn’s inner magnetosphere’s plasma clusters, which are controlled by Saturn’s spin. Electromagnetic electron cyclotron (EMEC) wave ring distribution function has been investigated. Kinetic and linear approaches have been used to study electromagnetic cyclotron (EMEC) wave propagation. EMEC waves’ stability can be assessed by analyzing the dispersion relation’s effect on the ring distribution function. The primary goal of this study is to determine the impact of the magnetosphere parameters which is observed by Cassini. The magnetosphere of Saturn has also been observed. When the plasma parameters are increased as the distribution index, the growth/damping rate increases until the magnetic field model affects the magnetic field at equator, as can be seen in the graphs. We discuss the outputs of our model in the context of measurements made in situ by the Cassini spacecraft.

The Earth’s outer radiation belt has long received considerable attention mainly because the MeV electron flux in the belt varies often dramatically and at various time scales. It is now widely accepted that the wave-particle interaction is one of the major mechanisms responsible for such flux variations. The wave-particle interaction can accelerate electrons to MeV energies, explaining the observed flux increase events, and can also scatter the electrons’ motion into the loss cone, resulting in atmospheric precipitation and thus contributing to flux dropouts. In this paper, we provide a review of the current state of research on relativistic electron scattering and precipitation due to the interaction with electromagnetic ion cyclotron (EMIC) waves in the inner magnetosphere. The review is intended to cover progress made over the last ~15 years in the theory and simulations of various issues, including quasilinear resonance diffusion, nonlinear interactions, nonresonant interactions, effects of finite normal angle on pitch angle scattering, effects due to rising tone emission, and ways to scatter near-equatorial pitch angle electrons. The review concludes with suggestions of a few promising topics for future research.

By adopting a 2D time-dependent wave code, we investigate how mode-converted waves at the Ion-Ion Hybrid (IIH) resonance and compressional waves propagate in 2D density structures with a wide range of field-aligned wavenumbers to background magnetic fields. The simulation results show that the mode-converted waves have continuous bands across the field line consistent with previous numerical studies. These waves also have harmonic structures in frequency domain and are localized in the field-aligned heavy ion density well. Our results thus emphasize the importance of a field-aligned heavy ion density structure for ultra-low frequency wave propagation, and suggest that IIH waves can be localized in different locations along the field line.

Earth’s magnetopause separating the fast and often turbulent magnetosheath and the relatively stagnant magnetosphere provides various forms of free energy that generate low-frequency surface waves. The source mechanism of this energy includes current-driven kinetic physical processes such as magnetic reconnection on the dayside magnetopause and flux transfer events drifting along the magnetopause, and velocity shear-driven (Kelvin-Helmholtz instability) or density/ pressure gradient-driven (Rayleigh-Taylor instability) magnetohydro-dynamics (MHD) instabilities. The solar wind external perturbations (impulsive transient pressure pulses or quasi-periodic dynamic pressure variations) act as seed fluctuations for the magnetopause waves and trigger ULF pulsations inside the magnetosphere via global modes or mode conversion at the magnetopause. The magnetopause waves thus play an important role in the solar wind-magnetosphere coupling, which is the key to space weather. This paper presents recent findings regarding the generation of surface waves (e.g., Kelvin- Helmholtz waves) at the Earth’s magnetopause and analytic and observational studies accountable for the linking of the magnetopause waves and inner magnetospheric ULF pulsations, and the impacts of magnetopause waves on the dynamics of the magnetopause and on the inner magnetosphere.