Parametric decay of circularly polarized Alfvén waves: Multidimensional simulations in periodic and open domains

The nonlinear evolution of monochromatic large-amplitude circularly polarized Alfvén waves subject to the decay instability is studied via numerical simulations in one, two, and three spatial dimensions. The asymptotic value of the cross helicity depends strongly on the plasma beta: in the low beta case multiple decays are observed, with about half of the energy being transferred to waves propagating in the opposite direction at lower wave numbers, for each saturation step. Correspondingly, the other half of the total transverse energy (kinetic and magnetic) goes into energy carried by the daughter compressive waves and to the associated shock heating. In higher beta conditions we find instead that the cross helicity decreases monotonically with time towards zero, implying an asymptotic balance between inward and outward Alfvénic modes, a feature similar to the observed decrease with distance in the solar wind. Although the instability mainly takes place along the propagation direction, in the two and three-dimensional case a turbulent cascade occurs also transverse to the field. The asymptotic state of density fluctuations appears to be rather isotropic, whereas a slight preferential cascade in the transverse direction is seen in magnetic field spectra. Finally, parametric decay is shown to occur also in a non-periodic domain with open boundaries, when the mother wave is continuously injected from one side. In two and three dimensions a strong transverse filamentation is found at long times, reminiscent of density ray-like features observed in the extended solar corona and pressure-balanced structures found in solar wind data

Magnetic Effects Change Our View of the Heliosheath

There is currently a controversy as to whether Voyager 1 has already crossed the Termination Shock, the first boundary of the Heliosphere. The region between the Termination Shock and the Heliopause, the Helisheath, is one of the most unknown regions theoretically. In the Heliosheath magnetic effects are crucial, as the solar magnetic field is compressed at the Termination Shock by the slowing flow. Recently, our simulations showed that the Heliosheath presents remarkable dynamics, with turbulent flows and the presence of a jet flow at the current sheet that is unstable due to magnetohydrodynamic instabilities \cite{opher,opher1}. In this paper we review these recent results, and present an additional simulation with constant neutral atom background. In this case the jet is still present but with reduced intensity. Further study, e.g., including neutrals and the tilt of the solar rotation from the magnetic axis, is required before we can definitively address how the Heliosheath behaves. Already we can say that this region presents remarkable dynamics, with turbulent flows, indicating that the Heliosheath might be very different from what we previously thought.Comment: 6 pages, 5 figures, to appear in IGPP 3rd Annual International Astrophysics Conference, "PHYSICS OF THE OUTER HELIOSPHERE

An introductory guide to fluid models with anisotropic temperatures Part 1 -- CGL description and collisionless fluid hierarchy

We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modeling turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the CGL fluid model in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius (FLR) corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the 4th-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the "normal" closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the "normal" closure, and beyond the 4th-order moment, Landau fluid closures are required.Comment: Improved version, accepted to JPP Lecture Notes. Some parts were shortened and some parts were expanded. The text now contains Conclusion

Three-dimensional magnetic reconnection simulations using the Eulerian Conservative High Order (ECHO) code

Magnetic reconnection and shear driven instabilities are pervasive phenomena in the heliosphere and in astrophysical plasmas in general. Magnetic reconnection and Kelvin-Helmholtz-like instabilities require the use of high-order numerical approximations to study their linear and non-linear evolution. At the same time, in compressible MHD the dynamical activity following reconnection processes leads to formation of discontinuous modes which should be treated by shock-capturing numerical schemes. For this purpose we have designed an Eulerian Conservative High Order (ECHO) code in which, i) explicit diffusivity is taken into account, ii) high-order numerical approximations of flux derivatives are included and iii) shock-capturing algorithms are employed in managing flux discontinuities. This code has been applied successfully in studying the linear and non-linear 3D evolution of the tearing instability and in following the 3D evolution of a current sheet embedded in a sheared flow