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We give theoretical analyses of the Magneto-Rayleigh-Taylor instability driven by a rotating magnetic field. Both slab and liner configurations with finite thicknesses are dealt with in the WKB and the non-WKB approximations. Results show that instabilities for all modes (combinations of wave vectors) are alleviated. We further discuss the potential application of the alternant/nested configurations of a theta and a Z pinch to the Theta-Z Liner Inertia Fusion (Theta-Z-LIF) concept., in Chinese

Current-driven resistive tearing instability is verified using the newly developed global first-principles particle-in-cell code called VirtEx, which was coded from scratch in conformity with the C++'11 specifications. The tearing instability is first verified in the fluid limit in a cylinder geometry by ignoring the gyrokinetic effect of ions, and the numerical results agree well with the analytical predictions of the resistive tearing theory. Then, the effect of toroidicity on resistive tearing instability is investigated.

Using the quantum hydrodynamic (QHD) equations with magnetic field on the Wigner–Maxwell system, the general dielectric tensor and dispersion equation for quantum plasmas were derived. Dispersion relations of one-, two-stream and beam-plasma instabilities in uniform quantum magnetized plasmas are investigated through the new dielectric tensor. The magnetic field which is parallel to the fluid velocity does not work on stream instabilities. The quantum and thermal effects have remarkable impact on two-stream instability. The critical wave number for beam-plasma instability with quantum effects correction is given too.

A new mechanism for geodesic acoustic mode (GAM) excitation by a not fully slowed down energetic particle (EP) beam is analyzed to explain experimental observations in Large Helical Device. It is shown that the positive velocity space gradient near the lower-energy end of the EP distribution function can strongly drive the GAM unstable. The new features of this EP-induced GAM (EGAM) are: (1) no instability threshold in the pitch angle; (2) the EGAM frequency can be higher than the local GAM frequency; and (3) the instability growth rate is much larger than that driven by a fully slowed down EP beam. © 2015 AIP Publishing LLC.

In contrast with the stability effects of trapped energetic ions on tearing modes, the effects of circulating energetic ions (CEI) on tearing modes depend on the toroidal circulating direction, and are closely related to the momentum of energetic ions. CEI provide an additional source or sink of momentum to affect tearing modes. For co-CEI, tearing modes can be stabilized if the momentum of energetic ions is large enough. On the other hand, the growth of tearing modes can be enhanced by counter-CEI. Further, a possibility to suppress the island growth of neoclassical tearing modes by co-CEI is pointed out.

The magnetorotational instability of dusty plasmas is investigated using the multi-fluid model and the general dispersion relation is derived based on local approximation. The dust grains are found to play an important role in the dispersion relation in the low-frequency mode and exhibit destabilizing effects on the plasma. Both the instability criterion and growth rate are affected significantly by the dust and when the dust is heavy enough to be unperturbed, the reduced dispersion relations are obtained. The instability criteria show that the dust grains have stabilizing effects on the instability when the rotation frequency decreases outwards and conversely lead to destabilizing effects when the rotation frequency increases outwards. The results are relevant to accession and protoplanetary disks.

We use a multi-fluid model to describe the dynamic behavior of electrons, ions, and neutrals in a weakly ionized three-component plasma and investigate the differentially rotational instability. Charged species and neutrals are supposed to have the same angular velocity to eliminate the equilibrium current and collisions in the unperturbed state. By taking into account collisions between electrons/ions and neutrals, we derive the analytical expression of the general local dispersion relation and examine the collision effect on the rotational instability in different limiting cases. Collisions on neutrals are neglected in the first case to obtain a simplified dispersion, in which collisions play an important role in the instability criteria. In the low-frequency region, the previous result in the magnetohydrodynamic model is reproduced. The collision effect in the high-frequency case for non-magnetized electrons is found to be similar to the low-frequency region, but can induce instability for both the negative and positive radial derivative of rotational frequency.

The linear stability of a differential rotating magnetized plasma is analyzed in the collisionless approximation along with heat flux vector. The dispersion relation is derived and simplified cases are discussed with instability criteria presented. Anisotropic pressures are shown to not only alter the classical instability criterion but also induce new unstable regions. The shear rotating instability in a collisional magnetized plasma with a scalar kinetic pressure in the presence of self-gravitational effect is then considered. Three cases are discussed specifically according to the general dispersion relation. The effects of Jeans term and compressibility on the local shear instability induced by differential rotation are examined and the analytic instability criteria are presented.

The magnetorotational instability (MRI) is investigated using a two-fluid model. Electrons and singly charged ions are supposed to have the same angular velocity to eliminate the equilibrium current. The linear dispersion relation governing local MRI is derived. The instability criteria in the non-magnetized and weakly magnetized cases differ remarkably from those predicted by the one-fluid model. Based on the general magnetized case, we present the critical conditions for the occurrence of instability. Gyroeffects significantly alter the instability criterion and introduce four unstable regions, one of which is reduced to the magnetohydrodynamic result when the angular frequency is much less than the ion gyrofrequency. When the angular frequency is much less than the electron gyrofrequency, the ion gyroeffect contributes to the instability criterion and induces the Hall term.

Thermal convective instability is investigated in a thermally stratified plasma in the presence of shear flow, which is known to give rise to the Kelvin–Helmholtz (KH) instability. We examine how the KH instability and magnetothermal instability (MTI) affect each other. Based on the sharp boundary model, the KH instability coupled with the MTI is studied. We present the growth rate and instability criteria. The shear flow is shown to significantly alter the critical condition for the occurrence of thermal convective instability.

The effects of the equilibrium density gradient on non-axisymmetric magnetorotational instability are investigated in a pure axial magnetic field for ideal incompressible plasmas. A second-order ordinary differential equation is employed to determine the magnetic field perturbation and the full dispersion relationship regarding the non-axisymmetric magnetohydrodynamic instability in the presence of gravitation and density gradient effects. By means of local linear analysis, the reduced dispersion relationship is derived with a small azimuthal wavenumber. Spatial variations in the radial field perturbation magnitude cannot be neglected in the calculation since this term has the same order of magnitude as LD, which is the scale length of radial density gradient. The analytical expression of the instability growth rate is presented. Our analysis shows that the instability criterion is modified by the density gradient which has a stabilizing effect when increasing outwards and conversely a destabilizing effect when decreasing outwards. The growth rate increases with LD when LD is small. For a sufficiently large LD, the growth rate decreases with increasing LD. The magnetic field exerts a similar effect on the growth rate and can totally quench the instability. The non-axisymmetric effect introduces a frequency shift and increases the growth rate but does not affect the instability criterion.

The Jeans instability in dense quantum plasmas is investigated by taking into account the Hall term and resistivity in the presence of two-dimensional magnetic fields. The general dispersion relation is presented. The presence of the Hall term introduces a new wave mode which does not exist in the ideal magnetohydrodynamic framework. Two limiting cases with respect to the Hall effect are discussed. The Hall effect is shown to induce a frequency shift but does not change the instability criterion. The resistivity exhibits damping or destabilizing effects on the plasma system under different circumstances. The analytical expressions of the growth/damping rate of Jeans instability are obtained for both the finite and remarkable resistivity cases in the absence of the Hall term.

The linear buoyancy instability in magnetized plasmas is investigated in the presence of anisotropic resistivity and viscosity. The magnetic field is assumed to be horizontal and the background heat flux is not taken into account. That is, the magnetic field lines are initially isothermal. The heat is assumed to be primarily transported along the magnetic force lines. The general dispersion relationship of the thermal convective instability in the presence of anisotropic resistive and viscous dissipative effects is derived and discussed in detail in weak magnetic field limit. Our results show that the perturbation is damped when the temperature decreases in the direction of gravity due to the resistive or viscous effect while this situation results in pure oscillation modes in the ideal MHD case. The resistive and viscous effects are shown to reduce the growth rate of the magnetothermal instability when the temperature increases in the direction of gravity.

The magnetorotational instability (MRI) in differential rotating dusty plasmas with dissipative effects is investigated by using local linear analysis. We assume that the dust grains are heavy enough to be immobile so that the dust effects are contained in our model only by introducing an electric field term in the one-fluid equation of plasma motion. The general local dispersion relation is derived and two limiting cases are discussed with respect to the dust-induced effect. The instability criterions in the different limiting cases are presented and the growth rate of local MRI in the last case is demonstrated.

The linear buoyancy instability in a magnetized plasma, generally referred to as magnetothermal instability (MTI), is investigated by considering anisotropic heat conduction. The external magnetic field is assumed to be horizontal and background heat flux is not taken into account. The general dispersion relationship of the convective instability is derived. The growth rate of the MTI in fixed boundary condition is presented and discussed. The effect of density spacial gradient on the MTI is investigated. The magnetic field is shown to suppress the MTI and even quench the instability when the magnetic field is strong enough. Under the standard Wentzel–Kramaers–Brillouin approximation, our results could be simplified to a brief form reported by one previous paper [E. Quataert, Astrophys. J. 673, 758 (2008)].

Electrostatic drift waves (EDWs) are investigated in nonuniform quantum magnetized dusty plasmas by taking into account dust gravitational effects with the help of the quantum hydrodynamic model. Ions and electrons are viewed as low-temperature Fermi gases, whereas quantum effects are neglected for the dust grains. The analytical dispersion relationship of the quantum EDWs is derived. Quantum effects are shown to affect the dispersion of EDW significantly. The Jeans terms induce a driftlike instability, which does not exist with the absence of gravitational effects. The criteria and growth rate of the kind of instability are presented. Our results are relevant to dense astrophysical objects such as the interiors of astrophysical compact objects (e.g., white dwarfs and neutron stars).

The Jeans instability in dense quantum plasmas is investigated in the presence of two dimensional magnetic fields and resistive effects. The resistive effects are shown to introduce instability whether the perturbation is stable or not in the ideal magnetohydrodynamic model. The analytical expressions of the growth rate of Jeans instability are obtained for both the finite and remarkable resistive effects cases. The results are relevant to dense astrophysical objects, e.g., neutron stars and the interior of white dwarfs, as well as low-temperature laboratory plasmas.

In the present work, the Richtmyer–Meshkov instability is examined in an N-layer stratified fluid which is impulsively accelerated and immersed in a homogeneous transverse magnetic field. By solving the initial value problem and the second-order linear differential perturbation equation, the expressions of interface amplitudes are analytically obtained. Two special cases N=2 and N=3 are discussed, and it is found that the Richtmyer–Meshkov instability is suppressed by the transverse magnetic field. It is also shown for the N=3 case, when a transverse magnetic field is present, that the interfaces oscillate with a high frequency and the oscillations repeat themselves periodically with a low frequency.

The effects of transverse magnetic field and viscosity on the Richtmyer–Meshkov instability are considered under the framework of two semi-infinite fluids with densities ρ+ and ρ−, magnetic fields B+ and B−, and viscosities μ+ and μ−, respectively. The amplitude of the perturbations is analytically obtained. It is found that the magnetic field provides oscillation and damping, and viscosity provides damping. When both are present, the perturbations of the interface undergo damped oscillation provided that the magnetic field is strong enough; otherwise the perturbations will damp from the beginning.

The effects of the quantum mechanism and magnetic field on Rayleigh–Taylor (RT) instability in an ideal incompressible plasma are investigated. The explicit expression of the linear growth rate is obtained in the presence of fixed boundary conditions. It is shown that the magnetic field has a stabilizing effect on RT instability similar to the behavior in classical plasmas and RT instability is affected significantly by quantum effects. Quantum effects are also shown to suppress RT instability with the appropriate physical quantities. Some astrophysical parameters are discussed as an example to investigate the new effects.