Stationary collisionless shock waves in an initial plasma with high ion temperature

Stationary collisonless shock waves propagating perpendicularly to an initial magnetic field are produced by the fast-rising magnetic field \((\dot B = 7 \cdot 10^{10} G/sec)\) of a theta pinch (coil diameter 16 cm, coil length 60 cm). The initial plasma is produced by a fast theta pinch discharge (810 kHz). At filling pressures between 5 and 15 mtorr H₂ or D₂ the degree of ionization is about 50%. By choosing the filling pressure properly it is possible to trap a homogeneous magnetic field. The ions of this plasma have a temperature of a few 10 eV. This value is much higher than the electron temperature and results in a local plasmaβ between 0.3 and 5. In this initial plasma stationary collisionless shock waves with Mach numbers between 1.5 and 5 are observed. The snow-plough model is used to derive conditions for the stationary state, attainable Mach number, and velocity of the front which relate the external magnetic field and the parameters of the initial plasma. Strong collisionless dissipation can be demonstrated by measuring the profiles of magnetic field, density, and electron temperature of the shock waves. For the electrons this dissipation mechanism can be described by an effective collison frequency. This phenomenologically introduced frequency determines the width of the shock front at least for subcritical shock waves. It exceeds the classical electron-ion collision frequency by 1–2 orders of magnitude and is roughly equal to one-third of the ion plasma frequency. The ion temperature can be estimated from the steady state conservation relations. The ions are heated in the two degrees of freedom perpendicular to the magnetic field. For shock waves with Mach numbers below the critical one the ions seem to be heated merely adiabatically. In strong shock waves this heating is considerably exceeded, and for high Mach numbers it yields ion temperatures up to about 500 eV. Finally, semi-empirical formulas are derived to estimate the possible temperatures of electrons and ions behind the shock front.     

Observation of collisionless plasma heating by strong shock waves

The heating of a plasma by collisionless shock waves is investigated by measuring the variation of magnetic field (with magnetic probes), density and electron temperature (from Thomson scattering of laser light) in the shock waves. The compression waves are produced in a tube of 14 cm diameter by the fast rising magnetic field (12 kG in 0.5Μsec) of a theta pinch. For shocks with Mach numbers between 2 and 3 propagating into a hydrogen or deuterium plasma with a localΒ of about 1 (Β=ratio of particle pressure to magnetic pressure) the measured jump in density and magnetic field across the front is 2 to 4, and the electron temperature increases in the front from 3 to 50 eV with a further rise to between 100 and 250 eV in the piston region. Only about 20% of the measured electron heating can be explained by adiabatic heating and resistive heating based on binary collisions, indicating a high turbulent plasma resistance. Both the observed electron heating and the width of the shock front, which is about 0.6 ·c/Ω _p, can be accounted for using an effective collision frequency close to the ion plasma frequencyΩ _p. The ion heating in the almost stationary shock fronts can be inferred indirectly from the steady state conservation relations. For shock waves with Mach numbersM<M _crit it seems to be consistent with an adiabatic heating process, whereas forM>M _crit the calculated ion temperatures exceed those one would except for a merely adiabatic heating.     

Reversible electron heating vs . Wave-particle interactions in quasi-perpendicular shocks

Summary The energy necessary to explain the electron heating in quasiperpendicular collisionless shocks can be derived either from the electron acceleration in the d.c. cross shock electric potential, or by the interactions between the electrons and the waves existing in the shock. A Monte Carlo simulation has been performed to study the electron distribution function evolution through the shock structure, with and without particle diffusion on waves. This simulation has allowed us to clarify the relative importance of the two possible energy sources; in particular it has been shown that the electron parallel temperature is determined by the d.c. electromagnetic field and not by any wave-particle-induced heating. Wave particle interactions are effective in smoothing out the large gradients in phase space produced by the ?reversible? motion of the electrons, thus producing a ?cooling? of the electrons. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

Solitary waves and rogue waves in a plasma with nonthermal electrons featuring Tsallis distribution

In this Letter, we discuss the electron acoustic (EA) waves in plasmas, which consist of nonthermal hot electrons featuring the Tsallis distribution, and obtain the corresponding governing equation, that is, a nonlinear Schrödinger (NLS) equation. By means of Modulation Instability (MI) analysis of the EA waves, it is found that both electron acoustic solitary wave and rogue wave can exist in such plasmas. Basing on the Darboux transformation method, we derive the analytical expressions of nonlinear solutions of NLS equations, such as single/double solitary wave solutions and single/double rogue wave solutions. The existential regions and amplitude of solitary wave solutions and the rogue wave solutions are influenced by the nonextensive parameter q and nonthermal parameter α. Moreover, the interaction of solitary wave and how to postpone the excitation of rogue wave are also studied.     

Gasdynamic design of a two-dimensional supersonic inlet with the increased flow rate factor

A two-dimensional inlet of external compression with the increased flow rate factor at high supersonic velocities is constructed by the method of gasdynamic design. Its feature is that a flow with the initial oblique shock wave and the subsequent centered isentropic compression wave is formed over the external compression ramp of the inlet. These waves interact with one another so that a resulting stronger oblique shock wave and a velocity discontinuity arise in front of the entrance to the inlet internal duct. An example of an inlet configuration with the design flow regime corresponding to the Mach number M_d = 7 is considered. The characteristics of this inlet were obtained in the range of the free-stream Mach numbers M = 4–7 with the use of a Navier—Stokes code for turbulent flow. They are compared with characteristics of an equivalent conventional shocked inlet. As computations have shown, the inlet with the isentropic compression wave has much higher values of flow rate factor φ at Mach numbers M < M_d. So, for example, at M = 4 the value φ ≈ 0.72 for it is by 33 % higher in comparison with φ ≈ 0.54 for the equivalent shocked inlet.     

Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media

The nonlinear analysis of the behavior of a shock wave on a Hugoniot curve fragment that allows for the ambiguous representation of shock wave discontinuity has been performed. The fragment under consideration includes a section where the condition L > 1 + 2M is satisfied, which is a linear criterion of the instability of the shock wave in media with an arbitrary equation of state. The calculations in the model of a viscous heat-conductive gas show that solutions with an instable shock wave are not implemented. In the one-dimensional model, the shock wave decays into two shock waves or a shock wave and a rarefaction wave, which propagate in opposite directions, or can remain in the initial state. The choice of the solution depends on the parameters of the shock wave (position on the Hugoniot curve), as well as on the form and intensity of its perturbation. In the two-dimensional and three-dimensional calculations with a periodic perturbation of the shock wave, a “cellular” structure is formed on the shock front with a finite amplitude of perturbations that does not decrease and increase in time. Such behavior of the shock wave is attributed to the appearance of the triple configurations in the inclined sections of the perturbed shock wave, which interact with each other in the process of propagation along its front.     

Numerical study of shock wave interaction in steady flows of a viscous heat-conducting gas with a low ratio of specific heats

Specific features of shock wave interaction in a viscous heat-conducting gas with a low ratio of specific heats are numerically studied. The case of the Mach reflection of shock waves with a negative angle of the reflected wave with respect to the free-stream velocity vector is considered, and the influence of viscosity on the flow structure is analyzed. Various issues of nonuniqueness of the shock wave configuration for different Reynolds numbers are discussed. Depending on the initial conditions and Reynolds numbers, two different shock wave configurations may exist: regular configuration interacting with an expansion fan and Mach configuration. In the dual solution domain, a possibility of the transition from regular to the Mach reflection of shock waves is considered.     

凝聚炸药爆轰波在高声速材料界面上的折射现象分析

凝聚炸药爆轰在边界高声速材料约束下传播时,爆轰波会在约束材料界面上产生复杂的折射现象.本文针对凝聚炸药爆轰波在高声速材料界面上的折射现象展开理论和数值模拟分析.首先通过建立在爆轰ZND模型上的改进爆轰波极曲线理论给出爆轰波折射类型,然后发展一种求解爆轰反应流动方程的基于特征理论的二阶单元中心型Lagrange计算方法来数值模拟典型的爆轰波折射过程.从改进爆轰波极曲线理论和二阶Lagrange方法数值模拟给出的结果看出,凝聚炸药爆轰波在高声速材料界面上的折射类型有四种:反射冲击波的正规折射、带束缚前驱波的非正规折射、带双Mach反射的非正规折射、带λ波结构的非正规折射.     

On the existence and formation of small amplitude electrostatic double-layer structure in nonthermal dusty plasma

In the present article, we studied the effect of nonthermal electrons on the formation and existence of double-layer structures in a three-species plasma consisting of positive ions, nonthermal electrons, and immobile negative dust-charged grains. Employing the reductive perturbations, a modified Korteweg–de Vries (mKdV) type equation is derived for the dust-ion-acoustic waves (DIAWs) bearing nonthermality. We found that both positive and negative polarity shock structures (double layer) can exist such that it switches polarity while changing the dust charge concentrations. However, strong nonthemality favours only rarefactive structures irrespective of the ion temperature. It is also found that increasing the nonthermal electron in the system the width of the double layer is increased; furthermore, the shock structure forms with small dust charge concentration. For small ionic temperature, increasing the nonthermal electrons in the system makes the double layer potential to increase; however, for σ = 1 reverse phenomena occurs. Our results are relevant to the shock observations in Q machine experiments and in the ionospheric regime of the earth.     

Theoretical analysis of planar and non‐planar electron ‐ acoustic shock waves in electron‐positron‐ion plasma

The propagation properties of planar and non‐planar electron acoustic shock waves composed of stationary ions, cold electrons, and q‐non‐extensive hot electrons and positrons are studied in unmagnetized electron‐positron‐ion plasma. In this model, the Korteweg‐de Vries Burgers equation is obtained in the planar and non‐planar coordinates. We have investigated the combined action of the dissipation, non‐extensivity, density ratio of hot to cold electrons, concentration of positrons, and temperature difference of cold electrons, hot electrons, and positrons. It was found that the amplitude of shock wave in e‐p‐i plasma increases when the positron concentration and temperature increase. The same effect is observed in the case of kinematic viscosity η. Furthermore, it is noticed that spherical wave moves faster in comparison to the shock waves in cylindrical geometry. This difference arises due to the presence of the geometry term m/2τ. It should be noted that the contribution of the geometry factor comes through the continuity equation. Results of our work may be helpful to illustrate the different properties of shock wave features in different astrophysical and space environments like supernova, polar regions, and in the vicinity of black holes.     

Nanodomain shock wave in near-field laser–material interaction

In this work, molecular dynamics simulation is conducted to explore the shock wave phenomena in a nanodomain in near-field laser–material interaction. A large system consisting of over 800,000 atoms is studied. The work focuses on the kinetic and physical properties of the disturbed gas compression driven by the high speed movement of the molten particulates ejected from the solid target in a nanodomain. The quick interaction between solid and gas atoms compresses the gas and forms a steep shock wave front, which moves at a supersonic speed. The fast compression of gas also induces a steep interface of density, temperature and pressure distribution, which is viewed as typical characteristics of nanoscale shock waves. Evolutions of shock wave front position, velocity and Mach number are also explored and show quick decay during wave propagation.     

激光引致激波演化数值研究

在高重复频率激光推进的研究中,激波的合并是发生在激波演化后期的,同时由于脉冲间隔短,脉冲宽度对流场演化的影响也需要详细研究。考虑了激光辐照过程对流场演化的影响,通过数值计算对激波演化特性进行了研究。结果表明,初期波阵面的椭球形状逐渐转化为一个球形,球心与击穿点的距离随时间逐渐减小并最终趋于稳定。基于激波合并的应用,当激波马赫数在1~2之间时,给出了激波波阵面半径随时间的变化规律,以及激波高压区长度和波峰压强随激波波阵面半径变化规律的经验公式。     

Effects of polarization force and nonthermal ions on dust-acoustic (DA) shock waves in a strongly coupled dusty plasma with positively charged dust

The nonlinear propagation of the dust-acoustic (DA) waves in a strongly coupled dusty plasma containing Maxwellian electrons, nonthermal ions, and positively charged dust is theoritically investigated by a Burgers equation. The effects of the polarization force (which arises due to the interaction between electrons and highly positively charged dust grains) and nonthermal ions are studied. DA shock waves are found to exist with positive potential only. It represents that the strong correlation among the charged dust grains is a source of dissipation, and is responsible for the formation of DA shock waves. The effects of polarization force and nonthermal ions significantly modified the basic features of DA shock waves in strongly coupled dusty plasma.     

Analysis of Plasmadynamic Nanosecond-Range Processes in the Formation of Shock Waves from Pulsed Discharges

We have studied the dynamics of the plasma glow of pulsed discharges (sliding surface discharge and combined volume discharge with plasma electrodes) in the nanosecond range (100–12 000 ns) in stationary air and in the flow behind the front of a plane shock wave with Mach numbers 1.7–5.0 in the shock tube channel. The temporal characteristics of the flow, the radiation spectra, and the discharge currents in air are compared in the pressure range 5–150 Torr, a pulsed voltage of 20–30 kV, and a current of about 1 kA. It is shown that the time of current under various conditions does not exceed 400 ns, and the duration of the glow can reach a few microseconds. It is shown that as a result of energy supply near the planar shock wave front, the decay of discontinuities occurs with the formation of shock waves and contact surfaces. The positions of the plasma glow regions are compared with the positions of discontinuity surfaces of numerically calculated gasdynamic parameters in the flow.     

场向传播的内磁层哨声波对辐射带高能电子的共振扩散

基于高斯分布的哨声波谱密度分布、偶极子背景磁场模型以及建立在卫星观测数据基础上的半经验电子密度纬度分布模型,对于等离子体层顶以外区域(4≤L≤7),计算了准线性当地及弹跳平均电子共振扩散系数,并估算了与磁层哨声波回旋共振导致的辐射带电子损失及加速时间尺度.结果表明,波粒共振相互作用区域取决于电子能量、波谱分布、电子赤道抛射角以及当地电子密度及背景磁场.哨声波共振频率除了与以上5个参量有关外,还与地磁纬度有关.赤道哨声波主要影响较低能量辐射带电子的加速,中高纬度哨声波主要作用于较高能量辐射带电 关键词： 共振波粒相互作用 地球辐射带 哨声波 回旋共振加速及散射沉降     

Passage of the discharge current through the plasma–electrode interface in the electromagnetic rail accelerator channel

We investigate the phenomena that accompany the acceleration of a free plasma piston (without a striker) in the electromagnetic rail accelerator channel filled with different gases (argon, helium). An intense glow appears in the shock-compressed layer (SCL) in the case of strong shock waves that produce a high electron concentration (~10¹⁷–10¹⁸ cm^–3) behind the front. We have proposed that explosive electron emission (EEE) ensures the high-intensity emission of electrons, the passage of a part of the discharge current through the SCL, and the glow of the SCL. The velocity of a shock wave for which the strong electric field in the Debye layer at the cathode causes EEE from its surface and the passage of the current in the SCL has been determined. It has been concluded that, for high velocities of the plasma, the EEE is a universal mechanism that ensure the passage of a strong current through the interface between the cold electrode and the plasma.     

Unlimited relativistic shock surfing acceleration

Nonrelativistic shock surfing acceleration at quasiperpendicular shocks is usually considered to be a preacceleration mechanism for slow pickup ions to initiate diffusive shock acceleration. In shock surfing, the particle accelerates along the shock front under the action of the convective electric field of the plasma flow. However, the particle also gains kinetic energy normal to the shock and eventually escapes downstream. We consider the case when ions are accelerated to relativistic velocities. In this case, the ions are likely to be trapped for infinitely long times, because the energy of bounce oscillations tends to decrease during acceleration. This suggests the possibility of unlimited acceleration by shock surfing.     

Dust-acoustic waves in a self-gravitating complex plasma with trapped electrons and nonisothermal ions

It is shown that the nonlinear equations governing the dynamics of the large amplitude waves in a self-gravitating unmagnetized collisionless dust-electron-ion plasma admit stationary dust-acoustic shock solutions. Owing to the adiabaticity of dust-charge variation, inclusion of self-gravitation, and to the departure from the so-called Botzmannian electrons and ions to the trapped electrons and nonthermal ions, the dynamics of the nonlinear wave is found to be governed by a new energy-like integral equation.     

About one analogy for the activation stage of a detonation process in condensed systems

The modern concepts of detonation processes in condensed systems are analyzed. A theoretical explanation of processes basic to nonthermal explosive solid-state transformations at a high pressure suggested earlier allows a deep analogy between these processes and processes at the activation detonation wave stage that occur inside its shock fore front and in its immediate vicinity to be established.