The theory of inoizing shock waves in a magnetic field. Part 1. Skew and oblique shock waves, boundary conditions and ionization stability

1981 ◽  
Vol 26 (1) ◽  
pp. 29-53 ◽  
Author(s):  
M. A. Liberman ◽  
A. L. Velikovich
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Shock Waves ◽  
Electric Field ◽  
Boundary Conditions ◽  
Wave Front ◽  
Shock Wave Front ◽  
Neutral Gas ◽  
Supersonic Shock ◽  
Photo Ionization

The general theory of ionizing shock waves in a magnetic field has been constructed. The theory takes into account precursor ionization of a neutral gas ahead of the shock wave front, caused by photo-ionization, as well as by the impact ionization with electrons accelerated by a transverse electric field induced by the shock front in the incident flow of a neutral gas. The concept of shock wave ionization stability, being basic in the theory of ionizing shock waves in a magnetic field, is introduced. An additional equation for the electric field in the shock wave is obtained. This equation, together with the investigation of the singular point in the downstream flow behind the shock wave front, provides all the information required for solving the problem. For example, this provides two additional boundary conditions for the shock waves of type 2, determining the value and direction of the electric field in the incident flow. One additional boundary condition determines a relation between the value and direction of the electric field for supersonic shock waves of type 3. There are no additional boundary conditions for supersonic shock waves of type 4. The electric field ahead of the shock front has two degrees of freedom. As well as for shocks of other types, its value is less than that of the transverse electric field at which an ionization wave could be emitted by the shock wave front (the ionization stability condition). The additional relationship for supersonic waves of type 4 determines the onset of an isomagnetic (viscous) jump in the structure of the shock wave front. The boundary conditions and ionizing shock wave structures, considered earlier by the authors of the present paper in the ‘limit of electrostatic breakdown’, as well as the structural determination of the electric field, considered earlier by Leonard, are limiting cases in the theory developed here. The ionizing shock wave structures are shown to transform from the GD regime at a low shock velocity to the MHD regime at an enhanced intensity of the shock wave. The abruptness of such a transition (e.g. the transition width on the Mach number scale) is determined by precursor photo-ionization.

Dynamics Evolution of Shock Waves in Laser-Material Interaction

2008 ◽  
Author(s):  
Sobieslaw Gacek ◽  
Xinwei Wang
Keyword(s):  
Shock Wave ◽  
Wave Front ◽  
Shock Wave Front ◽  
Structural Evolution ◽  
Md Simulations ◽  
Background Gas ◽  
Supersonic Shock ◽  
Kinetics Of ◽  
Material Interaction ◽  
Insight Into

In this work, the dynamics of the shock wave in laser-ablated argon plume with its evolution through the background gas is explored at the atomic level. Molecular Dynamics (MD) simulations have been conducted which give the insight into atomistic scale interaction and correlation effects of the propagating shock wave in the background medium. The supersonic shock wave front carries inherent sharp increase in density, temperature, and pressure. These thermodynamic parameters of the expanding shock wave are evaluated with emphasis on the kinetics of the shock wave front. The position of the shock wave front has been defined and determined over nanoseconds. Extensive research is elaborated upon to study the inside structural evolution of the shock wave and the effect of optical absorption depth.

The theory of ionizing shock waves in a magnetic field. Part 2. Transverse, normal and switch-off shock waves and the piston problem

1981 ◽  
Vol 26 (1) ◽  
pp. 55-81 ◽  
Author(s):  
M. A. Liberman ◽  
A. L. Velikovich
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Electric Field ◽  
Shock Velocity ◽  
Shock Structure ◽  
Piston Problem ◽  
Flow Parameters ◽  
Basic Relationship ◽  
Type 3 ◽  
Photo Ionization

Solutions for transverse, normal and switch-off ionizing shock waves have been obtained on the basis of the general theory of ionizing shock waves in a magnetic field presented in part 1. Some details of the shock structure were considered at Pm → 0. In particular, the transition from the gasdynamic to the magnetohydrodynamic regime, while increasing the shock velocity, is traced in detail. The additional relationship, obtained in part 1, determines the value of a transverse electric field ahead of the front for the case of a transverse shock wave and for normal and switch-off shock waves, if the latter are shock waves of type 3. In the case of normal and switch-off shock waves of type 4, basic relationship obtained in part 1 is not a boundary condition, but determines the position of a viscous isomagnetic jump in the shock structure. The transition of ionizing shock waves from the GD to the MHD regime, while increasing the shock velocity, was considered. The width of such a transition on shock velocity scale depends significantly on the intensity of precursor photo-ionization. In particular, this transition occurs slowly at zero precursor photo-ionization: the electric field ahead of the front tends to zero as l/vxo when vxo increases. The problem of formation of ionizing shock waves ahead of a magnetic piston and a conducting piston with a magnetic field directed along the normal to the piston surface has been solved. We indicate the set of flow parameters, for which Chapman-Jouguet's model of ionizing front motion ahead of the piston is inapplicable. A transition from the Chapman-Jouguet regime to the MHD one is considered.

The generation of interpenetrating plasma flows in an expanding discharge

1976 ◽  
Vol 15 (2) ◽  
pp. 293-307 ◽  
Author(s):  
H. A. Davis ◽  
M. A. Mahdavi ◽  
R. H. Lovberg
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Shock Waves ◽  
Electric Field ◽  
Electric Fields ◽  
Magnetic Disturbance ◽  
Collisionless Shock ◽  
Driving Field ◽  
Piston Speed ◽  
Electron Density And Temperature

We report on an experiment designed to study collisionless shock waves in an inverse pinch discharge using argon. A magnetic disturbance was generated which propagated ahead of the driving field at twice the piston speed. Measurements of the magnetic and electric field structures, electron density and temperature, as well as ion velocities revealed that the disturbance was produced by a beam of plasma moving through the ionized ambient plasma rather than by a true shock wave. Calculations of ion trajectories using measured electric fields demonstrated that the beam originated at small radii and early times, and was not the result of a steady specular reflexion from the piston field. It is concluded that the ions comprising this stream, which were collisionless relative to the ambient ions, did not couple to the background plasma even though a strong magnetic field was applied.

Numerical Simulation of Air Flow in the State of Thermal and Chemical Nonequilibrium behind a Shock Wave Front

2021 ◽  
pp. 94-111
Author(s):  
A.I. Bryzgalov
Keyword(s):  
Shock Wave ◽  
Shock Front ◽  
Wave Front ◽  
Shock Wave Front ◽  
Reaction Rate ◽  
Vibrational Temperature ◽  
Pure Oxygen ◽  
Published Data ◽  
Calculation Results ◽  
Temperature Nonequilibrium

We used the model of a five-component air mixture flow behind the front of a one-dimensional shock wave to compute the flow parameters for shock front temperatures of up to 7000 K, taking into account the variable composition, translational and vibrational temperatures and pressure in the relaxation zone. Vibrational level population in oxygen and nitrogen obeys the Boltzmann distribution with one common vibrational temperature. We consider the effect that temperature nonequilibrium has on the chemical reaction rate by introducing a nonequilibrium factor to the reaction rate constant, said factor depending on the vibrational and translational temperatures. We compared our calculation results for dissociation behind the shock front to the published data concerning temperature nonequilibrium in a pure oxygen flow behind a shock wave front for two different intensities of the latter. The comparison shows a good agreement between the vibrational temperature, experimental data and calculations based on the experimental values of vibrational temperature and molality. We computed the parameters of thermodynamically nonequilibrium dissociation in the air behind the shock wave front, comparing them to those of equilibrium dissociation and calculation results previously published by others. The study demonstrates that the molality values computed converge gradually with those found in published data as the distance from the shock front increases. We list the reasons for the discrepancy between our calculation results and previously published data

The thermal wave before a shock wave front in metals

1975 ◽  
Vol 9 (3) ◽  
pp. 378-380 ◽  
Author(s):  
V. F. Nesterenko ◽  
A. M. Staver ◽  
B. K. Styron
Keyword(s):  
Shock Wave ◽  
Wave Front ◽  
Shock Wave Front ◽  
Thermal Wave

Effects of geometric similarity ratio on the disturbance amplitude of shock-wave front in viscosity measurement

2021 ◽  
pp. 2150330
Author(s):  
Kai Yang ◽  
Quan-Yu Xu ◽  
Xiao Wu ◽  
Xiao-Juan Ma
Keyword(s):  
Shock Wave ◽  
Phase Shift ◽  
Wave Front ◽  
Shock Wave Front ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Viscosity Measurement ◽  
Geometric Similarity ◽  
Similarity Ratio ◽  
Simulation Results

Geometric similarity ratio is one of the important factors that affects the disturbance amplitude of shock-wave front in viscosity measurement. In this paper, the Euler difference scheme of two-dimensional (2D) equations of viscous fluid mechanics is used to simulate the disturbance amplitude damping curves under different geometric similarity ratios, and the corresponding numerical solutions are shown. The samples of aluminum shocked to 80 GPa are taken as an example. The simulation results show that the initial conditions, material viscosity, wavelength, and sample geometric similarity ratio affect the evolution of the shock front sine wave disturbance. For flyer-impact flow field, the phase shift increases from 0 to a certain value with the viscosity coefficient for sample with wavelength [Formula: see text] mm and geometric similarity ratio [Formula: see text], 0.1. So, the geometric similarity method can be used to measure the viscosity of material. But it is found that the phase shift is sensitive to the geometric similarity ratio, which should be considered in Zaidel’s equation. So, some flyer-impact experiments will be carried out to determine the simulation results, and find the quantity relation of phase shift and viscosity of material in the future investigation.

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