Planar and Nonplanar Shock Waves in a Degenerate Quantum Plasma

The nonlinear propagation of modified electron‐acoustic (mEA) shock waves in an unmagnetized, collisionless, relativistic, degenerate quantum plasma (containing non‐relativistic degenerate inertial cold electrons, both nonrelativistic and ultra‐relativistic degenerate hot electron and inertial positron fluids, and positively charged static ions) has been investigated theoretically. The well‐known Burgers type equation has been derived for both planar and nonplanar geometry by employing the reductive perturbation method. The shock wave solution has also been obtained and numerically analyzed. It has been observed that the mEA shock waves are significantly modified due to the effects of degenerate pressure and other plasma parameters arised in this investigation. The properties of planar Burgers shocks are quite different from those of nonplanar Burgers shocks. The basic features and the underlying physics of shock waves, which are relevant to some astrophysical compact objects (viz. non‐rotating white dwarfs, neutron stars, etc.), are briefly discussed. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonplanar Shock Structures in a Relativistic Degenerate Multi-Species Plasma

A nonlinear propagation of cylindrical and spherical modified ion-acoustic (mIA) waves in an unmagnetized, collisionless, relativistic, degenerate multi-species plasma has been investigated theoretically. This plasma system is assumed to contain non-relativistic degenerate light ions, both non-relativistic and ultra-relativistic degenerate electron and positron fluids, and arbitrarily charged static heavy ions. The restoring force is provided by the degenerate pressures of the electrons and positrons, whereas the inertia is provided by the mass of ions. The arbitrarily charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The modified Burgers (mB) equation is derived by using reductive perturbation technique and numerically analyzed to identify the basic features of mIA shock structures. The basic characteristics of mIA shock waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge state of heavy ions. The implications of our results to dense plasmas in astrophysical compact objects (e.g., non-rotating white dwarfs, neutron stars, etc.) are briefly discussed.     

Cylindrical and Spherical Ion-Acoustic Shock Waves in a Relativistic Degenerate Multi-Ion Plasma

A rigorous theoretical investigation has been made to study the existence and basic features of the ion-acoustic (IA) shock structures in an unmagnetized, collisionless multi-ion plasma system (containing degenerate electron fluids, inertial positively as well as negatively charged ions, and arbitrarily charged static heavy ions). This investigation is valid for both non-relativistic and ultra-relativistic limits. The reductive perturbation technique has been employed to derive the modified Burgers equation. The solution of this equation has been numerically examined to study the basic properties of shock structures. The basic features (speed, amplitude, width, etc.) of these electrostatic shock structures have been briefly discussed. The basic properties of the IA shock waves are found to be significantly modified by the effects of arbitrarily charged static heavy ions and the plasma particle number densities. The implications of our results in space and interstellar compact objects like white dwarfs, neutron stars, black holes, and so on have been briefly discussed.     

Dust-electron-acoustic shock waves due to dust charge fluctuation

The nonlinear propagation of the dust-electron-acoustic waves in a dusty plasma consisting of cold and hot electrons, stationary and streaming ions, and charge fluctuating stationary dust has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation, and is responsible for the formation of the dust-electron-acoustic shock waves in such a dusty plasma. The basic features of such dust-electron-acoustic shock waves have been identified. It has been proposed to design a new laboratory experiment which will be able to identify the basic features of the dust-electron-acoustic shock waves predicted in this theoretical investigation.     

Heavy-and light-nuclei acoustic dressed shock waves in white dwarfs

In this investigation, the evolution of heavy-and light-nuclei acoustic (HLNA) dressed shock waves (DSWs) due to the contribution of higher order of nonlinearity and dissipation effects has been examined in a degenerate quantum plasma composed of inertial heavy as well as light nuclei and inertia-less ultra-relativistic degenerate electrons. By employing the reductive perturbation method, the nonlinear Burgers equation is derived. Further, an inhomogeneous Burgers-type equation accounting for the higher order contributions of nonlinearity and dissipation is also derived. With the insertion of higher order effects, a new humped type or dressed shock structures are evolved. The influence of different plasma parameters on the dynamical evolution of the HLNA-DSWs is examined. It is observed that these plasma parameters play significant role on the characteristics of HLNA-DSWs and their corresponding electric fields. The findings of present investigation may be applicable to provide a new insight to understand the evolution of HLNA-DSWs in different dense astrophysical regions such as white dwarfs.     

Dust-ion-acoustic shock waves due to dust charge fluctuation

A dusty plasma system containing Boltzmann electrons, mobile ions and charge fluctuating stationary dust has been considered. The nonlinear propagation of the dust-ion-acoustic waves in such a dusty plasma has been investigated by employing the reductive perturbation method. It has been shown that the dust charge fluctuation is a source of dissipation and is responsible for the formation of the dust-ion-acoustic shock waves. The basic features of such dust-ion-acoustic shock waves have been identified. The implications of our results in space and laboratory dusty plasmas are discussed.     

Shock Wave Propagation in Gases and Low Temperature Plasma Under Subatmospheric Pressure

Results of investigation of the shock wave dynamics under subatmospheric pressure in neutral gases and weakly ionized low temperature plasma are presented. The characteristics of spherical and plane configuration shock wave excitation and propagation in gases in the pressure region 1 Torr < p <100 Torr are studied. The same is done for the plane configuration shock wave in weakly ionized plasma in the pressure region 1 Torr < p <10 Torr. It is shown that when p = 3 Torr it is still possible to fix successfully the shock wave appearance and propagation in various neutral gases. The pressure dependence of the shock wave propagation velocity and amplitude is determined experimentally. It is shown that when the pressure decreases the shock wave amplitude decrease and the increase of the Mach number take place. In the case of plane shock wave Mach number reaches the value M = 5.2 under the pressure p = 3 Torr. As for shock wave propagation in low temperature plasma, our experiments showed a significant decrease of wave amplitude and simultaneous increase of its velocities up to 35 wave velocity is related to the heating of neutral gases in plasma.     

Magnetosonic Shocks in Ultra-Relativistic Dissipative Degenerate Plasmas

Magnetosonic shock structures in dissipative magnetized degenerate electron ion plasma are studied.The two fluid quantum magnetohydrodynamic equations for non-degenerate ions and ultra-relativistic degenerate electron fluids with the Maxwell equations are presented.Using the reductive perturbation technique the Korteweg de Vries Burgers(KdVB)equation is derived and its solution is presented with the tanh method.Astrophysical plasma parameters are used to study the effects of variation of plasma density,magnetic held intensity and kinematic viscosity on the propagation characteristics of nonlinear shock structures in such plasma systems.     

Ion-Acoustic Shock Waves in Nonextensive Multi-Ion Plasmas

The nonlinear propagation of ion-acoustic (IA) shock waves (SHWs) in a nonextensive multi-ion plasma system (consisting of inertial positive light ions as well as negative heavy ions, noninertial nonextensive electrons and positrons) has been studied. The reductive perturbation technique has been employed to derive the Burgers equation. The basic properties (polarity, amplitude, width, etc.) of the IA SHWs are found to be significantly modified by the effects of nonextensivity of electrons and positrons, ion kinematic viscosity, temperature ratio of electrons and positrons, etc. It has been observed that SHWs with positive and negative potential are formed depending on the plasma parameters. The findings of our results obtained from this theoretical investigation may be useful in understanding the characteristics of IA SHWs both in laboratory and space plasmas.     

Ion-Acoustic Shock Waves in Nonextensive Multi-Ion Plasmas

The nonlinear propagation of ion-acoustic(IA) shock waves(SHWs) in a nonextensive multi-ion plasma system(consisting of inertial positive light ions as well as negative heavy ions, noninertial nonextensive electrons and positrons) has been studied. The reductive perturbation technique has been employed to derive the Burgers equation.The basic properties(polarity, amplitude, width, etc.) of the IA SHWs are found to be significantly modified by the effects of nonextensivity of electrons and positrons, ion kinematic viscosity, temperature ratio of electrons and positrons, etc.It has been observed that SHWs with positive and negative potential are formed depending on the plasma parameters.The findings of our results obtained from this theoretical investigation may be useful in understanding the characteristics of IA SHWs both in laboratory and space plasmas.     

Effect of Bohm quantum potential in the propagation of ion–acoustic waves in degenerate plasmas

A theoretical investigation has been carried out on the propagation of the ion–acoustic(IA) waves in a relativistic degenerate plasma containing relativistic degenerate electron and positron fluids in the presence of inertial non-relativistic light ion fluid. The Korteweg-de Vries(K-dV), modified K-dV(m K-dV), and mixed m K-dV(mm K-dV) equations are derived by adopting the reductive perturbation method. In order to analyze the basic features(phase speed, amplitude, width,etc.) of the IA solitary waves(SWs), the SWs solutions of the K-dV, m K-dV, and mm K-d V are numerically analyzed. It is found that the degenerate pressure, inclusion of the new phenomena like the Fermi temperatures and quantum mechanical effects(arising due to the quantum diffraction) of both electrons and positrons, number densities, etc., of the plasma species remarkably change the basic characteristics of the IA SWs which are found to be formed either with positive or negative potential. The implication of our results in explaining different nonlinear phenomena in astrophysical compact objects, e.g.,white dwarfs, neutron stars, etc., and laboratory plasmas like intense laser–solid matter interaction experiments, etc., are mentioned.     

Two‐dimensional magnetosonic shock wave propagation in dense electron–positron–ion plasmas

Two‐dimensional (2D) magnetosonic wave propagation in magnetized quantum dissipative plasmas is studied. The plasma system is comprised of inertial ions, inertia‐less electrons, and positrons. The multi‐fluid quantum hydrodynamic model is used, in which quantum statistical and quantum tunnelling effects of electrons and positrons are included. Reductive perturbation analysis is performed to derive the Zabolotskaya–Khokhlov equation for the 2D propagation of a magnetosonic shock wave in a magnetized qauntum plasma. The effects of varying the different plasma parameters such as positron density and magnetic field intensity on the propagation characteristics of magnetosonic shock waves are discussed with non‐relativistic degenerate plasma parameters in astrophysical plasma situations.     

Nonlinear propagation of ion-acoustic waves in a degenerate dense plasma

Nonlinear propagation of ion-acoustic (IA) waves in a degenerate dense plasma (with all the constituents being degenerate, for both the non-relativistic or ultrarelativistic cases) have been investigated by the reductive perturbation method. The linear dispersion relation and Korteweg–de Vries (KdV) equation have been derived, and the numerical solutions of KdV equation have been analysed to identify the basic features of electrostatic solitary structures that may form in such a degenerate dense plasma. The implications of our results in compact astrophysical objects, particularly, in white dwarfs and neutron stars, have been briefly discussed.     

Modified Ion-Acoustic Shock Waves and Double Layers in a Degenerate Electron-Positron-Ion Plasma in Presence of Heavy Negative Ions

A general theory for nonlinear propagation of one dimensional modified ion-acoustic waves in an unmagnetized electron-positron-ion (e-p-i) degenerate plasma is investigated. This plasma system is assumed to contain relativistic electron and positron fluids, non-degenerate viscous positive ions, and negatively charged static heavy ions. The modified Burgers and Gardner equations have been derived by employing the reductive perturbation method and analyzed in order to identify the basic features (polarity, width, speed, etc.) of shock and double layer (DL) structures. It is observed that the basic features of these shock and DL structures obtained from this analysis are significantly different from those obtained from the analysis of standard Gardner or Burgers equations. The implications of these results in space and interstellar compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are also briefly mentioned.     

Obliquely propagating ion-acoustic solitary and shock waves in magnetized quantum degenerate multi-ions plasma in the presence of trapped electrons

The properties of obliquely propagating ion-acoustic waves have been investigated in multi-ions magnetized plasma comprising of inertial, positively and negatively charged ion fluids, trapped electrons, and negatively charged stationary heavy ions. The propagation of the waves is oblique to the ambient magnetic field which is along the z-direction. Only fast type of modes exists in the linear regime. The reductive perturbation method was adopted to derive the Korteweg– de Vries (KdV) and Burger equations, as well as the solitary and shock wave solutions of the evolved equations, have been used to analyze the properties of the small but finite amplitude waves. The effects of the constituent plasma parameters, namely, the trapping effect of electrons, the electron degenerate temperature and the viscosity coefficient on the dynamics of the small amplitude solitary and shock waves have been examined. The influence of the magnetic field and the obliquity parameter on the propagation characteristics of ion-acoustic waves are discussed.     

Effect of viscosity on dust–ion acoustic shock wave in dusty plasma with negative ions

The properties of dust–ion acoustic (DIA) shock wave in a dusty plasma containing positive and negative ions is investigated. The reductive perturbation method has been used to derive the Korteweg–de Vries–Burgers equation for dust acoustic shock waves in a homogeneous, unmagnetized and collisionless plasma whose constituents are Boltzmann distributed electrons, singly charged positive ions, singly charged negative ions and cold static dust particles. The KdV–Burgers equation is derived and its stationary analytical solution is numerically analyzed where the effect of viscosity on the DIA shock wave propagation is taken into account. It is found that the viscosity in the dusty plasma plays as a key role in dissipation for the propagation of DIA shock.     

Reversed current structure in a Z-pinch plasma

The current profile of a Z-pinch plasma is investigated using a one-dimensional magnetohydrodynamic code. Simulation results reveal the formation of a reversed current profile, its propagation, and an ejection of plasma at boundary region, which have been observed in previous experiments. A new physical mechanism is proposed to account for such phenomena. The physical mechanism involves the propagation of a shock wave. It is found that a reversed current profile appears when a shock wave reflected at axis expands in a compressing plasma column.     

Electrostatic Solitary Structures in a Relativistic Degenerate Multispecies Plasma

The nonlinear propagation of cylindrical and spherical modified ion-acoustic (mIA) waves in an unmagnetized, collisionless, relativistic, degenerate multispecies plasma has been investigated theoretically. This plasma system is assumed to contain both relativistic degenerate electron and positron fluids, nonrelativistic degenerate positive and negative ions, and positively charged static heavy ions. The restoring force is provided by the degenerate pressures of the electrons and positrons, whereas the inertia is provided by the mass of positive and negative ions. The positively charged static heavy ions participate only in maintaining the quasi-neutrality condition at equilibrium. The nonplanar K-dV and mK-dV equations are derived by using reductive perturbation technique and numerically analyzed to identify the basic features (speed, amplitude, width, etc.) of mIA solitary structures. The basic characteristics of mIA solitary waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge states of heavy ions. The implications of our results to dense plasmas in astrophysical compact objects (e.g., nonrotating white dwarfs, neutron stars, etc.) are briefly mentioned.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

液体中激光等离子体冲击波波前传播特性研究及测试

将空气中球对称冲击波衰减波前传播公式推广到非完全中心对称情况，根据对光学阴影法对激光等离子体冲击波波前测试数据的计算分析，提出液体中点源激光等离子体冲击波旋转椭球面波前传播公式.并且用声学方法对水中和酒精中的激光等离子体冲击波波前进行实验测试，结果表明测试结果与计算公式相吻合. 关键词： 激光 等离子体冲击波 旋转椭球面