7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Richtmyer-Meshkov Instability in Magnetized Plasmas
Takayoshi Sano
Institute of Laser Engineering, Osaka University
e-mail (speaker): sano.takayoshi.ile@osaka-u.ac.jp

Interfacial instabilities are of great importance invarious plasma phenomena in the universe andlaboratory experiments. The Richtmyer-Meshkov
instability (RMI) is one of such instabilities that occurs
when a planar shock hits a corrugated surface of thecontact discontinuity. Turbulent mixing excited by theRMI often plays a crucial role associated with plasma
explosions in astrophysical objects and the implosion
in inertial confinement fusion. Interaction ofsupernova shocks and inhomogeneous interstellar
matters is one of the promising sites of the RMI, which
could contribute to the origin of the interstellar
turbulence as well as the amplification of magnetic
fields. The RMI is recognized as one of the severe
obstacles to prevent the ideal implosion in laser fusion
plasmas. Drastic symmetry reduction results ininadequate energy gain at the end of the process.
Therefore, the mitigation mechanisms of the RMI are
paid attention intensely in this field.
There are several effects proposed to stabilize theRMI. A strong magnetic field can suppress the growthof the RMI when the Alfven (Mach) number, which is
the ratio of the linear growth velocity to the Alfven
speed, is less than unity [1,2]. However, if thedirection of the magnetic field is parallel to theinterface but perpendicular to the wavevector of thesurface modulation, the Lorentz force hardly works on
the RMI. Then, the suppression by the magnetic fieldin three-dimensional geometry would be difficult so as
in the case of the Rayleigh-Taylor instability. Thevorticity deposited at the interface just after theincident shock refraction is the driving source of theRMI growth, while the vorticity left in the bulk of thefluids has been proved to be a physical agent that
decreases the growth of the contact surface ripple.
However, the effect of the bulk vorticity becomessignificant only when the shock is sufficiently strong,or the compression is high enough.
It is well known that the smooth density structure of
the interface affects the unstable growth of surface
fluctuations. For example, the density stratification at
the shear layer of the velocity stabilizes theKelvin-Helmholtz instability. The stability condition isgiven by the Richardson number, which is a functionof the density gradient. The Rayleigh-Taylor
instability is also affected by the density stratification.
The growth rate of the instability decreases
dramatically if the scale length of the density structure
is longer than the wavelength of the Rayleigh-Taylor
mode. As for the RMI, the transition-layer effects havenot been much investigated because of the difficulty of
the analytical approach.
We have investigated the effects of a smoothtransition layer at the contact discontinuity on thegrowth of the RMI by hydrodynamic numericalsimulations (see Fig. 1), and we derived an empiricalcondition for the suppression of the instability [3]. The
transition layer has little influence on the RMI when
the thickness L is narrower than the wavelength of aninterface modulation. However, if the transition layer
becomes broader than the wavelength, the perturbed
velocity associated with the RMI is reduced
considerably. The suppression condition is interpreted
as the cases in which the shock transit time throughthe transition layer is longer than the sound crossing
time of the modulation wavelength. This feature isfound to be quite universal and appeared in a wide
range of shock-interface interactions.
References[1] T. Sano, et al., Phys. Rev. Lett., 111, 205001 (2013)[2] T. Sano, Astrophys. J., 920, 29 (2021)[3] T. Sano, et al., Phys. Rev. E., 102, 013203 (2020)

Figure 1: Spacial distribution of the density (contourlines) and the tangential velocity (color) at thenonlinear regime of the RMI growth for the cases of(a) sharp and (b) shallow density gradient.