Energy gain by an electron during its motion in the field of a fundamental ${\rm TE}_{10}$ mode excited by a microwave in a rectangular waveguide is analysed. Expressions have been obtained for the fields of the mode, angle of deflection and the acceleration gradient of the electron, when it is injected along the direction of mode propagation. A 25 keV electron gains an energy of 120.44 keV when a microwave of intensity $10^{10}$\,W\,m$^{-2}$ at frequency 6 GHz is employed to excite the mode in a waveguide of width 0.03 m and height 0.02 m. The effect of the microwave frequency and width of the waveguide is to decrease the electron energy gain for a fixed microwave intensity. However, higher acceleration gradients are obtained when the electron is injected with a larger energy.

The initial processes excited directly by high-frequency (HF) heating waves include parametric decay instabilities, which decay the HF heating wave to a frequency-downshifted Langmuir/upper hybrid sideband together with an ion acoustic/lower hybrid wave as the decay mode, and oscillating two stream instabilities, which decay the HF heating wave to two oppositely propagating Langmuir/upper hybrid sidebands and purely growing mode/field-aligned density irregularities. These instabilities provide effective channels to convert heating waves to electrostatic plasma waves in the F region of the ionosphere. The following-up parametric instabilities include the cascades of Langmuir pump waves into Langmuir sidebands and ion acoustic waves/lower hybrid waves, and the decay of upper hybrid waves to Langmuir sidebands and ion decay modes, as well as the filamentation of those HF electrostatic waves to generate field-aligned density irregularities. The instability thresholds, growth rates, angular distribution and regions of excitation are determined.

Compression of plasmas with laser pulses in the 10-kJ range produced densities in the range of 1000 times that of the solid state, where however the temperatures within a few hundred eV were rather low. This induced the fast ignitor scheme for central or peripheral deposition of some 10-kJ ps laser pulses on conventional $n_{\rm s}$-precompressed DT plasma of 3000 times solid-state density. We present results where the ps ignition is avoided and only a single-event conventional compression is used. Following our computations of volume ignition and the excellent agreement with measured highest fusion gains of volume compression, we found conditions where compression to 5000 times that of the solid state and by using laser pulses of 10 MJ produce volume ignition with temperatures between 400 and 800 eV only for high-gain volume ignition.

A generalized, but simplified, kinetic equation for the distribution $F$ of a dust component in a plasma is derived in the seven-dimensional phase space $({\bf{r}},{\bf{v}},Q)$, where $Q$ is the dust particle charge. The equation for $F({\bf{r}},{\bf{v}},Q,t)$ takes into account charging, charge spread, collisions and an electric field. The charge $Q$ is considered to vary continuously. From the equation we find an analytic solution for the evolution of dust in the seven-dimensional phase space that shows collisionless diffusion owing to the combined effects of charging, charge spread and a constant electric field. We also derive a ‘vector kinetic equation’ of dust and subsequently a set of macroscopic equations, and show that the equations lead to a generalized classical diffusion of dust particles owing to fields and non-uniformities, collisions and charging, including charge spread, and to plasma wave effects including damping caused by charging and charge spread in the collisionless case.

As is known, the minimum magnetic energy state for a frozen plasma, subject to the infinite topological constraints, corresponds to a nonlinear force-free field. The magnetic flux invariance in ideal magnetohydrodynamics is possible in important astrophysical applications. We develop a method for explicitly obtaining a minimum energy state starting from an arbitrary initial state. This method does not require the explicit use of the invariance of the differential magnetic helicities. It is particularly useful when the minimum magnetic energy state for the given topological structure is unique. We show examples of the application of the method for this kind of system.

The equations of ideal magnetohydrodynamics (MHD) form a non-strict hyperbolic system with a non-convex flux function and admit non-regular, so-called intermediate shocks. The presence of non-regular waves in the MHD system causes the Riemann problem to be not unique in some cases. This paper investigates the uniqueness of Riemann solutions of ideal MHD. To determine uniqueness conditions we discuss the correspondence of non-regular solutions and non-uniqueness. Additionally the structure of the Hugoniot curves and its non-regular behaviour are demonstrated. It follows that the degree of freedom for solving a Riemann problem is reduced in the case of a non-regular solution. From this, we can deduce uniqueness conditions depending on the initial conditions of an MHD Riemann problem. The results also allow one to construct non-unique solutions. We give an example for the case of non-planar initial conditions.

We study interaction potentials in unmagnetized as well as magnetized dusty plasmas composed of electrons, ions, and elongated charged dust rods. By using appropriate dielectric constants for coupled dipole oscillons and dust acoustic waves and the test particle approach, we determine the Debye–Hückel and dynamical oscillatory wake potentials. The relevance of our investigation to the alignment of dust rods in laboratory dusty plasmas is pointed out.

The evolution of a magnetic field line in two dimensions near a neutral sheet is analysed. It is found that the general features of this evolution are rather independent of any particular model, provided that the magnetic field is small and the current density does not vanish. The time of arrival of a field line to the neutral sheet as well as its breaking and reconnection are proved to be finite and to satisfy a simple formula whose main parameter is the resistivity, which may be a spatial function. The shape of the evolving field lines satisfies a differential equation whose solution in some simple cases is shown to agree with certain classical reconnection configurations. Hyperresistivity is found to be more often a hindrance than a positive contribution to the reconnection process.

The momentum balance equation and the balance equation for the pressure tensor of a collision-free one-species magnetoplasma are linearized and Fourier-transformed, together with Maxwell's curl equations. They are combined in an algebraic dispersion system for the average perturbation velocity of the plasma particles. To do this a set of five fourth-order projectors is introduced, constructed with the aid of a commutative ‘ring product’ of two second-order projectors. It is shown that the trace-free part of the anisotropic perturbation pressure tensor, usually ignored for the sake of simplicity in such analyses, is of the same order of magnitude as the trace of this tensor. The vanishing determinant of the dispersion system is the dispersion equation of fifth degree in the square of the refractive index.

Taylor and Cargill (2001) presented a general theory of expansion waves in MHD flows. On page 243 we defined the magnetic field in the $r$-$\theta$ plane as ${\bf B}=(B_{r}(\theta), B_{\theta}(\theta), B_{z}(\theta))$, and ${\bf V}=(V_{r}(\theta), V_{\theta}(\theta), 0)$. It has been pointed out to us that this assumption is in general inconsistent with the z-component of the momentum equation.

Low-frequency dusty plasma waves with frequencies much smaller than the frequency of charging collisions of plasma particles with dust particles are considered, taking into account elastic and charging collisions of plasma particles with dust and with neutrals. The usual dust sound waves with an upper frequency equal to the dust plasma frequency are found to be present only for wavelengths much smaller than the plasma particle effective mean free path due to the effective collision frequency. The effective collision frequency is found to be inversely proportional to the square root of the product of the charging frequency and the frequency of particle momentum losses, involving processes due to elastic plasma particle–dust collisions, and collisions with neutrals. It is shown that when the wavelength of the wave is much larger than the mean free path for effective collisions the properties of the waves are different from those previously considered. A negative mass instability is found in this domain of frequencies when the effective mean free path of ions is larger than the effective mean free path of electrons. In the absence of neutrals this appears to be possible only if the temperature of ions exceeds the electron temperature. This can occur in laboratory experiments and space plasmas but not in plasma-etching experiments. In the absence of instability a new dust oscillation, a dust charging mode, is found the frequency of which is almost constant over a certain range of wavenumbers. It is inversely proportional to the dust mass and charging frequency of the dust. A new dust electron sound wave is found for frequencies less than the frequency of the dust charging mode. The velocity of the dust electron sound wave is determined by the electron temperature but not the ion temperatures, as for the usual dust sound waves, with the electron temperature exceeding the ion temperature substantially.

The motivation of this paper is to study the formation of a sheath in plasma contaminated with additional negative ions. Sheath formation has been analysed through the solution of the Sagdeev potential equation derived in a plasma by using the pseudopotential method. Because of the negative ions, it has been shown that the sheath formation, in contrast to that in a simple plasma, faces difficulties. A potential barrier from which modes are reflected is introduced and the potential variation beyond it is complex which, in turn, shows new findings. It is also revealed that the potential variation should be estimated in the plasma sheath in the presence of low as well as high negative-ion concentrations. The levitation of a dust grain into the sheath and its characteristic behaviour have also been investigated. Furthermore, the dust size in the ideal plasma sheath along with the causes of formation of the dust atmosphere have been studied.

This paper deals with the linear response of a plasma in a one-dimensional bounded geometry under the action of a time-periodic electric field. The nonlinear Vlasov equation is solved by following the characteristic curves until they reach the boundary of the domain, where the distribution function of the incoming particles is supposed to be known and independent of time. Then, a first-order Taylor expansion in the velocity variable is performed, thanks to an approximation of the exact characteristics by the unperturbed ones. The resulting first-order correction to the distribution function is finally integrated over velocities to yield the dielectric function. The special case of a plane wave for the electric field is examined and the results are compared with the more usual unbounded case: the integral does not present any singularity in the vicinity of resonant particles and the dielectric function depends on the distance to the boundary and tends to the usual infinite-geometry value when this distance tends to infinity, with a rate of convergence proportional to its inverse square root. Numerical examples are provided for illustration.