The Kelvin-Helmholtz (KH) instability is studied in a two dimensional strongly coupled dusty plasma medium using a fluid approach as well as through a molecular dynamic (MD) simulation. For the fluid description the generalized hydrodynamic (GH) model which treats the strongly coupled dusty plasma as a visco-elastic fluid is adopted. For the MD studies the ensemble of particles are assumed to interact through a Yukawa potential. Both the approaches predict a stabilization of the KH growth rate with an increase in the strong coupling parameter. The present study also delineates the temporal evolution and the interaction of transverse shear waves with the collective dynamics of the dusty plasma medium within the framework of both these approaches.

Error field penetration processes in magnetic island mode locking with the time-varying and fixed boundary perturbations are investigated numerically by using a two-dimensional resistive magnetohydrodynamic model in slab geometry. The evolution of various poloidal torques on the rational surface in the processes is analyzed in detail. In particular, three different states with the fixed boundary perturbations, viz. below the threshold (nearly locked regime), on the threshold (just locked regime), and above the threshold (strongly locked regime), are discussed and compared with the physical processes of the Rutherford regime.

Numerical and theoretical investigations are carried out for the stability of the dust acoustic waves (DAWs) under the transverse perturbation in a two-ion temperature magnetized and collisionless dusty plasma. The Zakharov-Kuznetsov (ZK) equation, modified ZK equation, and Extended ZK (EZK) equation of the DAWs are given by using the reductive perturbation technique. The cut-off frequency is obtained by applying higher-order transverse perturbations to the soliton solution of the EZK equation. The propagation velocity of solitary waves, the real cut-off frequency, as well as the growth rate of the higher-order perturbation to the solitary wave are obtained.

The head-on collision of dust magnetoacoustic solitary waves (DMASWs) is studied in magnetized electron–ion–dust plasma. The extended Poincaré–Lighthill–Kuo perturbation method is used to derive the Korteweg de Vries equations for DMASWs in this three-component plasma. The effects of the magnetic field intensity B0, the number of electrons residing on dust surface Zd, the ratio of electron to dust number density δ, the ratio of electron to ion temperature σ, and the ratio of dust acoustic velocity to dust Alfvén velocity β on the phase shift are investigated. It is found that these parameters can significantly influence the phase shifts of colliding DMASWs. The present investigation may be beneficial to understand the interaction between two DMASWs that may occur in plasma with dust impurities situations.

Schamel's modified Korteweg-de Vries–Zakharov–Kuznetsov (S-ZK) equation, governing the behavior of long wavelength, weak nonlinear ion acoustic waves propagating obliquely to an external uniform static magnetic field in a plasma consisting of warm adiabatic ions and non-thermal electrons (due to the presence of fast energetic electrons) having vortex-like velocity distribution function (due to the presence of trapped electrons), immersed in a uniform (space-independent) and static (time-independent) magnetic field, admits solitary wave solutions having a sech4 profile. The higher order stability of this solitary wave solution of the S-ZK equation has been analyzed with the help of multiple-scale perturbation expansion method of Allen and Rowlands (Allen, M. A. and Rowlands, G. 1993 J. Plasma Phys. 50, 413; 1995 J. Plasma Phys. 53, 63). The growth rate of instability is obtained correct to the order k2, where k is the wave number of a long wavelength plane wave perturbation. It is found that the lowest order (at the order k) instability condition is strongly sensitive to the angle of propagation (δ) of the solitary wave with the external uniform static magnetic field, whereas at the next order (at the order k2) the solitary wave solutions of the S-ZK equation are unstable irrespective of δ. It is also found that the growth rate of instability up to the order k2 for the electrons having Boltzmann distribution is higher than that of the non-thermal electrons having vortex-like distribution for any fixed δ.

The effects of gravitation on the permittivity tensor in the relativistic electron--positron or ions plasma in a frame of reformulated relativistic two-fluid equations by gravitational effects due to the event horizon using the 3 + 1 formalism of general relativity are investigated. The plasma is assumed to be freefalling in the radial direction toward the event horizon due to the strong gravitational field of a Schwarzschild black hole. The elements of the generalized permittivity tensor in this configuration are obtained. It is shown that the permittivity tensor could be written as a summation of two parts: Hermitian and non-Hermitian parts. Furthermore, the generalized dispersion relations are investigated for transverse and longitudinal modes. In the absence of gravitation effects, correctness of the obtained results is confirmed.

Using a fluid theory approach, this article provides a comparative study on the evolution of nonlinear waves in dusty plasmas, as well as other plasma environments, viz electron-ion, and electron-positron plasmas. Where applicable, relevance to satellite measurements is pointed out. A range of nonlinear waves from low frequency (ion acoustic and ion cyclotron waves), high frequency (electron acoustic and electron cyclotron waves) in electron-ion plasmas, ultra-low frequency (dust acoustic and dust cyclotron waves) in dusty plasmas and in electron-positron plasmas are discussed. Depending upon the plasma parameters, saw-tooth and bipolar structures are shown to evolve.

In this study, two-dimensional principal component analysis (2DPCA) was used to determine the reason for the ionospheric two-dimensional total electron content (TEC) anomaly after China's Lushan earthquake at 00:02:47 UT on April 20, 2013 (Mw = 6.6). TEC data from 00:00 to 00:15 (UT) on April 20, 2013 were examined. The TEC anomaly was very intense 00:05 to 00:10 (UT) after the earthquake. One potential cause of the TEC anomaly, which might have been a density variance, is a rising acoustic shock wave, with speed of at least 1127.82, ms−1, resulting from the mainshock. The duration of the TEC anomaly was at least 5 min.

An electron–positron pair plasma having dust impurity and density non-uniformity is studied for its unperturbed state and evolution of solitary structures under the effect of either positively charged or negatively charged dust grains. Zeroth-order equations are solved to examine the unperturbed state of the plasma via unperturbed potential φ0, drift velocities of the electrons and positrons (ve0 and vp0), and plasma (positron) density gradient np0η. It is observed that the dust distribution affects the gradient np0η significantly, which increases very sharply with a small increment in the dust density gradient nd0η. With relation to the solitary structures, a modified form of Korteweg–deVries equation (mKdV equation) is realized in the said plasma, which reveals that a tailing structure is associated with the soliton (sech2 structure). This tail is less prominent in the present pair plasma, contrary to the observation made in ordinary plasmas having only ions and electrons. The dust impurity is found to influence the solitary structure much significantly and its presence suppresses the rarefactive solitons, which are generally observed in multi-component species plasmas.

The formation of carbon nanoparticles in low pressure magnetized H2/CH4 and H2/C2H2 plasmas is investigated using infrared quantum cascade laser absorption, mass spectrometry, and electrostatic probe measurements. Results showed that dust formation is correlated to the presence of a significant amount of large positively charged hydrocarbon ions. Large negative ions or neutral hydrocarbon were not observed. These results, along with a qualitative comparison of diffusion and reaction characteristic, suggest that a positive ion may contribute to the growth of nanoparticles in hydrocarbon magnetized plasmas.

In this paper we analyze the motion of charged particles in a vacuum tube diode by solving linear differential equations. Our analysis is based on expressing the volume charge density as a function of the current density and coordinates only, i.e. ρ=ρ(J,z), while in the usual scheme the volume charge density is expressed as a function of the current density and electrostatic potential, i.e. ρ=ρ(J,V). We show that, in the case of slow varying charge density, the space-charge-limited current is reduced up to 50%. Our approach gives the well-known behavior of the classical current density proportional to the three-halves power of the bias potential and inversely proportional to the square of the gap distance between electrodes, and does not require the solution of the nonlinear differential equation normally associated with the Child–Langmuir formulation.

In this work the effects of Cold Biased Limiter (CBL) and Emissive Biased Limiter (EBL) have been individually investigated, in both positive and negative polarities, on the width and frequency of magnetic islands. The effects were examined using singular value decomposition and wavelet techniques on mirnov coil signals. The results show that the application of EBL with both positive and negative polarities has been more effective on plasma stability compared with CBL. Comparing different polarities of CBL and EBL revealed that the positive polarity was more effective on the width of magnetic islands than negative polarity. The greatest impact occurs during EBL with positive polarity, in which reduction is observed in both width of magnetic islands and emission of Hα radiation. Besides, intensity and frequency of magnetic islands are reduced from 50 to 25 kHz in around 1 ms after bias application. Meanwhile, the minimal effect on width and frequency of magnetic field occurs in CBL with negative polarity.

Theoretical and numerical works on dusty plasmas with cylindrical symmetry are presented. The main purpose has been to investigate behavior of dust particles in strongly coupled dusty plasmas which are expected to be realized in the planned experiments by PK-4 on the International Space Station and experiments by PK-4J, a similar apparatus constructed in Japan. The distribution of dust particles is analyzed on the basis of the drift-diffusion equations and, with the effect of discreteness taken into account, structure formations are numerically simulated.

It is pointed out that in the slow time scale perturbations the displacement current is ignored but it does not imply that the electron density fluctuations vanish. The dispersion relation of the low-frequency electromagnetic wave described within the framework of electron magnetohydrodynamics (EMHD) is modified by taking into account the longitudinal effects. This wave can couple with plasma lower hybrid oscillations if ion dynamics is also considered. The low-frequency wave discussed here can have many applications in plasma transport and plasma opening switches.

We have built a code to obtain the exact solutions of Riemann problems in ideal magnetohydrodynamics (MHD) for an arbitrary initial condition. The code can handle not only regular waves but also switch-on/off rarefactions and all types of non-regular shocks: intermediate shocks and switch-on/off shocks. Furthermore, the initial conditions with vanishing normal or transverse magnetic fields can be handled, although the code is partly based on the algorithm proposed by Torrilhon (2002) (Torrilhon, M. 2002 Exact solver and uniqueness condition for Riemann problems of ideal magnetohydrodynamics. Research report 2002-06, Seminar for Applied Mathematics, ETH, Zurich, Switzerland), which cannot deal with all types of non-regular waves nor the initial conditions without normal or transverse magnetic fields. Our solver can find all the solutions for a given Riemann problem, and hence, as demonstrated in this paper, one can investigate the structure of the solution space in detail. Therefore, the solver is a powerful instrument to solve the outstanding problem of existence and uniqueness of solutions of MHD Riemann problems. Moreover, the solver may be applied to numerical MHD schemes like the Godunov scheme in the future.

The theory for nonlinear three-wave interaction in magnetized plasmas is reconsidered using quantum hydrodynamics. The general coupling coefficients are calculated for the generalized Bohm de Broglie term. It is found that the Manley–Rowe relations are fulfilled only if the form of the particle dispersive term coincides with the standard expression. The implications of our results are discussed.

There is a typographical error in our recently published paper (Kourakis et al. 2014), namely, in the algebraic expression for the quantity C210 provided in the Appendix.

The correct expression for C210 should read:

${C}_{2_1}^0=\frac{c_1\left(\frac{c_1+k^2}{b}\right)^2\left(\frac{2v_g\omega}{k}+\frac{\omega^2}{k^2}\right)-2ac_2}{c_1v_g^2-ab} \, .\$

The modification is limited to the presentation of the algebraic calculation, hence the plots presented in the paper are not affected by the typographical error.