We study the normal and leaky kink oscillations of a thin magnetic tube embedded in a surrounding magnetized plasma. We adopt the cold plasma (zero plasma $\beta$) approximation, appropriate for typical solar coronal conditions. Using the Laplace transform, we solve the initial value problem to determine the motions of the flux tube. The asymptotic description of this motion is determined by the properties of a dispersion function $D(\omega)$, an infinitely valued function of the complex frequency $\omega$. Two cases arise. When the plasma density $\rho_{\rm i}$ inside the tube exceeds the density $\rho_{\rm e}$ of the surrounding plasma, the asymptotic behaviour is given by the normal mode that is associated with two zeros of $D(\omega)$. These zeros are real and symmetric with respect to the imaginary axis, and are situated on the principal sheet of the Riemann surface of $D(\omega)$. The asymptotics given by the normal mode is valid for times much longer than the period of tube oscillation, and is homogeneous with respect to the radial distance $r$. In the second case, where $\rho_{\rm i} < \rho_{\rm e}$, there are no zeros of $D(\omega)$ on the principal sheet. The asymptotics of the solution of the initial value problem is then given by a leaky mode of the tube kink oscillations. This mode is associated with two zeros of $D(\omega)$ on two different, non-principal, sheets of the Riemann surface of $D(\omega)$ attached to the principal sheet. The asymptotics given by the leaky mode is intermediate, i.e. valid for times much longer than the period of oscillations but smaller than (or of the order of) the damping time due to energy leakage. The asymptotics given by the leaky mode is inhomogeneous with respect to $r$. We also consider other solutions associated with the zeros of $D(\omega)$ on non-principal sheets, and argue that in the coronal loop case where $\rho_{\rm i} > \rho_{\rm e}$ these solutions have no physical meaning. In the opposite case, where $\rho_{\rm i} < \rho_{\rm e}$, only the two solutions associated with the two zeros of $D(\omega)$ lying on two different non-principal sheets attached to the principal sheet are physically meaningful; they determine the leaky mode. All other solutions of this type are devoid of physical meaning. On the basis of our results, we conclude that there is no radial wave energy leakage from a dense coronal loop oscillating in the kink mode; other mechanisms must be sought to explain the observed oscillation damping.

We review our recent numerical simulations of star formation. First, we show a simulation of magnetic turbulence in a plate-shaped self-gravitating stratified cloud. We find that the cloud is lifted up by the pressure of magnetic turbulence and reaches a steady-state characterized by oscillations about a new time-averaged equilibrium state. Next, we present a numerical simulation of gravitational fragmentation of the plate-shaped magnetized cloud. For strong magnetic field cases, we confirm that the gravitational instability develops gradually on a time scale characteristic of ambipolar diffusion. Finally, a numerical simulation of jet formation is shown. The important factors of jet formation are the magnetic field and rotation of a disk around a star.

The resonant interaction between three waves in a uniform magnetized plasma is considered. Using the somewhat inaccessible result of the general theory, we deduce the explicit expressions for the coupling coefficients of a cold magnetized two-component plasma.

We study the dispersion properties of low-frequency (in comparison with the electron/positron gyrofrequency) shear electromagnetic waves in an ultra-cold quantum magnetoplasma composed of electrons and positrons. By using the electron and positron fluid velocities deduced from the quantum momentum equations, together with the continuity equations and Ampère's law, we derive the governing equation for the shear waves. This equation is then Fourier transformed to obtain the dispersion relation, and to show the modification of the electromagnetic wave dispersions due to the electron and positron quantum effects. The latter can play a significant role in magnetic reconnection and in the formation of localized electromagnetic wave structures at quantum scales in ultra-cold quantum magnetoplasmas.

Nonlinear oscillations within a plasma slab are analyzed. Two types of solutions are found, depending on the initial value of the electron density. The first represents regular oscillations within the plasma slab, while the second gives rise to explosive growth at the slab centre or at the edges. The results are discussed.

The Hall effects are suggested to be responsible for the decoupling of electrons and ions of magnetic plasma in the process of magnetic reconnection. However, the process that ultimately causes the electrons to diffuse from the magnetic field in the very small diffusion region remains one of the main unsolved problems in magnetic reconnection theory. In this paper, the structure of the Hall electric field in the diffusion region is studied theoretically in the coordinate system located on the magnetic line. A numerical simulation result for this problem is also given. The new discovery is that electrons can be generated in the diffusion region due to the Hall effects. Therefore the role of the Hall effects in the decoupling of electrons and ions of a magnetic plasma can be clarified in the structure of the Hall electric field.

The dominant roles of pressure tensors in collisionless magnetic reconnection are demonstrated during a steady state of two-dimensional collisionless driven reconnection without any guide field by means of full-particle simulations. The pressure tensors in the momentum equations of ions and of electrons play two crucial roles in the collisionless magnetic reconnection. One role is the gyroviscous cancellation which suppresses the violation of frozen-in condition due to the inertia term. This cancellation causes ions to be tied to the magnetic field within the ion skin depth. The gyroviscous cancellation of electrons is also observed. The other role is a strong violation of the frozen-in condition due to non-gyrotropic pressure. The strong violation of the ion frozen-in condition forms the ion-dissipation region where the collisionless magnetic reconnection occurs. The strong violation of the electron frozen-in condition generates the reconnection electric field at the reconnection point.

The nonlinear dynamics of the ion temperature gradient (ITG) mode is investigated in a dusty plasma assuming the dust grains to be tiny and highly charged. The electrostatic drift waves cannot be ignored in the linear dispersion relation if polarization drifts of ions and dust are taken into account. The dipolar vortices are predicted to be formed in the nonlinear regime. The relevance of this study to space and astrophysical plasmas is pointed out.

The nonlinear interaction between a large-amplitude whistler pump and the modified ion-cyclotron perturbations is studied. A nonlinear dispersion relation for the modulation/filamentation interaction is derived and solved numerically to investigate the instability properties. We discuss the relevance of the present study with regard to recent laboratory experiments where the modulation/filamentation of a whistler pump by the modified ion-cyclotron waves has been observed.

Until recently, the calculation of field-line resonance (FLR) frequencies from magnetic field data, generated by magnetospheric models such as BATSRUS and Tsyganenko (T01), was restricted to orthogonal coordinate systems. With this restriction, only dipolar and axisymmetric configurations are admissible. The matter of addressing more general configurations such as non-axisymmetric stretched and twisted magnetic field topologies requires the use of a non-orthogonal coordinate system. This coordinate system can be constrained by defining the magnetic field as the product of Euler potentials, ${\bf B} = \nabla \alpha_i \times \nabla \alpha _j$, and imposing the condition, $\nabla \cdot {\bf B} = 0$, everywhere. As a consequence, the coordinates, $\alpha_i$, must satisfy the partial differential equation, ${\bf B}\cdot \nabla \alpha_i = 0$. In other words, $\alpha_i$ must be constant along magnetic field lines. Upon solving this differential equation implicitly using known magnetic field intensities, the metric tensor for the resulting basis can be computed. The elements of this tensor can be substituted directly into the eigenvalue problem for general coordinate systems written in covariant notation. The equation for FLR modes has been developed for arbitrary incompressible magnetospheric conditions and has been specialized to the case where spatial variations are constrained along the magnetic field. The result is a fourth-order system of ordinary differential equations, which can be evaluated numerically, provided that the variation of the metric coefficients as a function of the distance along field lines is sufficiently smooth. The eigenvalue problem is solved at several latitudes for a broad range of magnetospheric conditions.

The role of magnetic shear for zonal flow generation by ion temperature gradient and trapped electron (TE) mode turbulence is studied analytically using fluid descriptions. The scaling of the zonal flow (ZF) growth rate with magnetic shear is examined and compared with linear growth rates for typical tokamak parameter values. The results indicate that large levels of ZF are obtained in regions of negative magnetic shear, especially for ZF driven by TE mode turbulence. The strong magnetic shear scaling obtained for TE-mode-driven ZFs originates from the bounce average of the electron magnetic drifts.

The resonant interaction of a narrow electron beam spiraling in a cold homogeneous magnetized plasma with electromagnetic cylindrical waves is considered. The conclusions derived in recent papers about the formation, in the presence of effective electromagnetic energy dissipation out of the radially bounded beam, of dynamically stable and longtime living bunches of resonant electrons in the developed stage of their nonlinear interaction with the waves are discussed in this paper for more general physical cases and for wider ranges of characteristic parameters. General analytical formulas for the excited electromagnetic fields, the radiated electromagnetic power flux and the linear growth rate as well as relevant numerical simulations results are presented.

Analytical solutions for the minimum Ohmic dissipation states satisfying helicity balance in a cylindrical vessel with circular electrodes on the plane surfaces are presented. The solutions show the basic features of flux core spheromaks and are given in terms of Fourier–Bessel series. The total plasma current and magnetic field profiles are determined for different values of resistivity, elongation and electrode radius.

Fast ignition is an epoch-making scheme for inertial fusion energy. In this scheme, the formation of high-density core plasma is one of the key issues which must be solved, because the implosion dynamics of the fast ignition target, which is non-spherical with a conical target, is quite different from that of the conventional central ignition target. Some previous works showed the possibility of formation of a high-density core. However, the effects of hydrodynamic instability were not discussed in those works. In this paper, we simulate the whole implosion dynamics of a perturbed non-spherical target, and the effect of radiation transport instability is estimated using the two-dimensional integrated implosion (radiation hydrodynamics) code PINOCO. In the result, we have found that the hydrodynamic instabily has less of an effect on the formation of high-density core plasma in the cone-guided implosion, in comparision with the spherical implosion.

In the parameter regime where the ion/electron–dust collisions dominate with respect to the plasma binary collisions, the presence of plasma fluxes to the dust surfaces and dust charge fluctuations can significantly modify the dusty plasma response to low-frequency perturbations, with respect to the multi-component response (no charging collisions, fixed dust charge). Here the response found from the kinetic theory which consistently takes into account collisions and charge fluctuations is examined, analytic expressions are given and the parameter regime where significant differences with respect to the multi-component approach arise is determined. The streaming instability is considered as a particular example and it is shown that both the real and imaginary parts of the frequency can be significantly changed with respect to the multi-component results.

In a recent study [1] the effect of ionization and losses on the propagation of ion acoustic solitary waves is investigated. For that purpose the corresponding source and sink terms of the form $$\begin{equation} Q_{\rm i}- \nu_{\rm L}n_{\rm i}, \label{ss}\end{equation}$$ are included in the right-hand side of the ion continuity equation. The related contribution of the source–sink effects in the ion momentum equation is then given as the above source–sink term multiplied by the ion velocity, so that the ion momentum equation used in [1]becomes $$\begin{equation}n_{\rm i} \biggl(\frac{\partial v_{\rm i}}{\partial t} + v_{\rm i}\frac{\partial v_{\rm i}}{\partial x}\biggr)= - n_{\rm i}\frac{\partial \phi}{\partial x} - \sigma_{\rm i} \frac{\partial n_{\rm i}}{\partial x} - \nu_{\rm i} n_{\rm i} v_{\rm i} - (Q_{\rm i}- \nu_{\rm L} n_{\rm i}) v_{\rm i}.\end{equation}$$ The objective of this Comment is to show that the last term in (2) cancels out exactly, as will be shown in the further text, so that any effect originating from this term is spurious. In addition, this term implies that the velocity of the neutrals that become ions, before the impact ionization (or whatever the cause of its ionization may be), is equal to the velocity of ions that become neutrals, since this source–sink term is multiplied by the same velocity. A similar improper model has been used previously in the literature (see the references cited in [1]). It is remarked that the proper inclusion of the source–sink effects has been described in the literature before, although it seems to remain unnoticed. Therefore, it is timely to address this issue in order to provide a formally correct model for future studies.

The relativistic modified formula for the energy loss of the relativistic electron beam due to binary electron–electron collisions is obtained. Another important energy loss mechanism, the excitation of Langmuir collective plasma oscillation, is also treated within the relativistic framework. Then the relevant physics parameters in the fast-ignitor scenario, including the continuous winded range, the maximum penetration depth and the stopping time, have been calculated. The results obtained are much better than those from non-relativistic cases and even partially relativistic modified theories. Thus, we re-examine theoretically the possibility of igniting hot spots in a super-compressed deuterium–tritium plasma.

The existence of arbitrary amplitude nonlinear electrostatic waves is investigated for a plasma with positively charged dust in the presence of two-temperature electron species. It is shown that such a plasma supports both soliton and double layer structures.

Broadband coherent emission around the electron plasma frequency can be produced from a laser wakefield by linear mode conversion in inhomogeneous plasmas. In addition to its potential use as a powerful terahertz source, it can be used as diagnostics of the wakefield produced for particle acceleration. In this paper, some simulation results are presented on the wake emission when the wakefield is driven in the wavebreaking regime and driven inside a plasma channel.

The main objective of the Comment made by J. Vranjes et al. is that the source–sink approach in studying physical phenomena, such as the ionization instability, is suspect. Also the term $(Q_{\rm i}-\nu_{\rm L} n_{\rm i})v_{\rm i}$ in the ion momentum conservation equation of the source–sink model used by [1] is improper.