Corrugation Instability Research Articles

Growth of Massive Molecular Cloud Filament by Accretion Flows. I. Slow-shock Instability versus Ambipolar Diffusion

The Herschel Gould Belt Survey showed that stars form in dense filaments in nearby molecular clouds. Recent studies suggest that massive filaments are bound by the slow shocks caused by accretion flows onto the filaments. The slow shocks are known to be unstable to corrugation deformation of the shock front. Corrugation instability could convert the accretion flow's ram pressure into turbulent pressure that influences the width of the filament, which, according to theory, determines the self-gravitational fragmentation scale and core mass. In spite of its importance, the effect of slow-shock instability on star-forming filaments has not been investigated. In addition, the linear dispersion relation obtained from ideal magnetohydrodynamics (MHD) analysis shows that the most unstable wavelength of shock corrugation is infinitesimally small. In the scale of dense filaments, the effect of ambipolar diffusion can suppress the instability at small scales. This study investigates the influence of ambipolar diffusion on the instability of the slow shock. We perform two-dimensional MHD simulations to examine the linear growth of the slow-shock instability, considering the effect of ambipolar diffusion. The results demonstrate that the most unstable scale of slow-shock instability is approximately 5 times the length scale of ambipolar diffusion ℓ AD calculated using post-shock variables, where ℓ AD corresponds to the scale where the magnetic Reynolds number for ambipolar diffusivity is unity.

Stability of two-fluid partially ionized slow-mode shock fronts

ABSTRACT A magnetohydrodynamic (MHD) shock front can be unstable to the corrugation instability, which causes a perturbed shock front to become increasingly corrugated with time. An ideal MHD parallel shock (where the velocity and magnetic fields are aligned) is unconditionally unstable to the corrugation instability, whereas the ideal hydrodynamic (HD) counterpart is unconditionally stable. For a partially ionized medium (for example, the solar chromosphere), both HD and MHD species coexist and the stability of the system has not been studied. In this paper, we perform numerical simulations of the corrugation instability in two-fluid partially ionized shock fronts to investigate the stability conditions, and compare the results to HD and MHD simulations. Our simulations consist of an initially steady two-dimensional parallel shock encountering a localized upstream density perturbation. In MHD, this perturbation results in an unstable shock front and the corrugation grows with time. We find that for the two-fluid simulation, the neutral species can act to stabilize the shock front. A parameter study is performed to analyse the conditions under which the shock front is stable and unstable. We find that for very weakly coupled or very strongly coupled partially ionized system the shock front is unstable, as the system tends towards MHD. However, for a finite coupling, we find that the neutrals can stabilize the shock front, and produce new features including shock channels in the neutral species. We derive an equation that relates the stable wavelength range to the ion-neutral and neutral-ion coupling frequencies and the Mach number. Applying this relation to umbral flashes gives an estimated range of stable wavelengths between 0.6 and 56 km.

Corrugation Instability of Rarefaction Shock Waves and Filament Generation in Plasma Focus

Corrugation instability of rarefaction shock waves (RSWs) is studied in the simple plasma model with London current. Filament generation in the plasma focus (PF) due to the RSW corrugation instability is considered. To achieve an optimum structure of filaments in the PF current sheath, it is proposed to use special metal inserts near an insulator.

Combined action of corrugation and Weibel instabilities from electron-beam interaction with laser-irradiated plasma

The combined action of corrugation and Weibel instabilities was experimentally observed in the interaction between energetic electrons and a laser-irradiated insulated target. The energetic electron beam, driven by an ultrashort laser pulse, splits into filaments with a diameter of ∼10 μm while traversing an insulated target, owing to the corrugation instability. The filaments continued to split into thinner filaments owing to the Weibel instability if a preplasma was induced by a heating beam on the rear side of the target. When the time delay between the heating beam and electron beam was larger than 1 ps, a merging of the current filaments was observed. The characteristic filamentary structures disappeared when the time delay between the two beams was larger than 3 ps. A simplified model was developed to analyze this process; the obtained results were in good agreement with the experiment. Two-dimensional particle-in-cell simulations supported our analysis and reproduced the filamentation of the electron beam inside the plasma.

Corrugation Instability of a Coronal Arcade

We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed.

Blast Dynamics in a Dissipative Gas.

The blast caused by an intense explosion has been extensively studied in conservative fluids, where the Taylor-von Neumann-Sedov hydrodynamic solution is a prototypical example of self-similarity driven by conservation laws. In dissipative media, however, energy conservation is violated, yet a distinctive self-similar solution appears. It hinges on the decoupling of random and coherent motion permitted by a broad class of dissipative mechanisms. This enforces a peculiar layered structure in the shock, for which we derive the full hydrodynamic solution, validated by a microscopic approach based on molecular dynamics simulations. We predict and evidence a succession of temporal regimes, as well as a long-time corrugation instability, also self-similar, which disrupts the blast boundary. These generic results may apply from astrophysical systems to granular gases, and invite further cross-fertilization between microscopic and hydrodynamic approaches of shock waves.

Theory of the corrugation instability of a piston-driven shock wave.

We analyze the two-dimensional stability of a shock wave driven by a steadily moving corrugated piston in an inviscid fluid with an arbitrary equation of state. For h≤-1 or h>h(c), where h is the D'yakov parameter and h(c) is the Kontorovich limit, we find that small perturbations on the shock front are unstable and grow--at first quadratically and later linearly--with time. Such instabilities are associated with nonequilibrium fluid states and imply a nonunique solution to the hydrodynamic equations. The above criteria are consistent with instability limits observed in shock-tube experiments involving ionizing and dissociating gases and may have important implications for driven shocks in laser-fusion, astrophysical, and/or detonation studies.

Generation of Ultrahigh-Velocity Ionizing Shocks with Petawatt-Class Laser Pulses

Ultrahigh-velocity shock waves (approximately 10,000 km/s or 0.03c) are generated by focusing a 350-TW laser pulse into low-density helium gas. The collisionless ultrahigh-Mach-number electrostatic shock propagates from the plasma into the surrounding gas, ionizing gas as it becomes collisional. The shock undergoes a corrugation instability due to propagation of the ionizing shock within the gas (the Dyakov-Kontorovich instability). This system may be relevant to the study of very high-Mach-number ionizing shocks in astrophysical situations.

On the Stability of Accelerating Relativistic Shock Waves

We consider the corrugation instability of the self-similar flow with an accelerating shock in the highly relativistic regime. We derive the correct dispersion relation for the proper modes in the self-similar regime, and conclude that this solution is unstable.

Intense electron beam propagation through insulators: Ionization front structure and stability

The structure and stability of the ionization front, which occurs as a high intensity electron beam propagates through an insulator, are considered. It is found that, due to the electric field ionization, the velocity of the front, Vf, has a nonmonotonic dependence on the beam density, nb, and in some particular beam density range Vf increases with increasing nb. Two instabilities of the ionization front associated with the electric field ionization process of the insulator are found: a long wavelength (⪞fewμ) and relatively slow (∼1013s−1) corrugation instability and a short wavelength (∼subμ) and relatively fast (∼few×1013s−1) electric field ionization instability.

Corrugation Flux Front Instability in Type-II Superconductors

The dynamics of vortex flux entering a superconductor containing immovable flux of the opposite sign (antivortices) is considered. We obtain a solution for a flat moving interface separating the positive and negative flux areas. When the velocity of the positive flux exceeds some critical value, a corrugation instability of the interface develops.

Corrugation instability of radiative shock waves in a relativistically hot plasma

The corrugation instability of magnetic shock waves in a relativistically hot plasma with photon gas has been investigated. Conditions under which spontaneous amplification of surface corrugations on the discontinuity occurs are obtained. The corrugation instability may cause the condensation of the plasma number density, as well as the magnetic field behind the shock wave.

Analyse de l'�quation caract�ristique de D'yakov dans la th�orie de la stabilit� de l'onde de choc

Two questions which are concerned with investigation [1] of corrugation instability of shock waves have been considered in the present paper. In the first place, the selection condition [1] for acoustic perturbations generated by the shock front has been analysed. Its equivalence to the conditions usually applied in the wave theory for determination of linear waves direction has been proved. Secondly, the causes of divergence of previous results for region (1) of values of parameterh which was introduced by D'yakov [2] have been analysed.

The Corrugation Instability in Slow Magnetosonic Shock Waves

The Corrugation Instability in Slow Magnetosonic Shock Waves

Spontaneous acoustic emission from strong ionizing shocks

Dyakov (1954) and Kontorovich (1957) formulated the conditions for corrugation instability of shock waves as well as for spontaneous emission of sound and entropy-vortex waves from them. For the first time since then, it is shown here that physical circumstances do exist under which shocks in gases spontaneously emit sound waves. Such circumstances are provided by strong ionizing shocks. In order to see that, the coefficient of reflection of an acoustic wave from a shock is derived as a function of the wave's frequency and the ionization degree. Spontaneous emission of sound occurs when the reflection coefficient becomes infinitely large. It is shown that the relevant frequency range for the occurrence of spontaneous emission is that for which the electrons are not in local thermodynamic equilibrium with the heavy particles. The special properties of acoustic perturbations behind the ionizing shock are considered for this frequency range and the sound velocity in a partially ionized gas is derived. In addition, the condition for spontaneous emission of sound is modified in order to take into account the difference between the electrons and heavy-particle perturbed temperatures. It is shown, by numerical calculations, that the criterion for spontaneous emission is satisfied behind ionizing shocks in argon. In particular, for an initial pressure of 5 Torr, the threshold for the occurrence of the spontaneous emission is found to be M1 = 15. This critical value of the shock Mach number, as well as other calculated physical features, agree very well with those obtained experimentally by Glass & Liu (1978) who observed the occurrence of instability behind shocks in argon.

Corrugation instability in MHD shock waves

Corrugation instability in MHD shock waves

Corrugation instability of a strong parallel slow shock wave. I. Numerical calculations for the case of a radiative shock

Corrugation instability of a strong parallel slow shock wave. I. Numerical calculations for the case of a radiative shock

Corrugation instability of a strong slow parallel shock wave. II. Approximate analytic investigation

Corrugation instability of a strong slow parallel shock wave. II. Approximate analytic investigation