Seminar

Synopsis:

Synopsis:

Synopsis:

In this talk I will introduce an extended magnetohydrodynamical model (XMHD)
and discuss the importance of correctly including the dynamics of the low-density
plasma that can be orders of magnitude lower in density than the target or load
material in high-energy density (HED) experiments. Including the low-density
plasma component in these experiments requires the Hall term in the Generalized
Ohm’s Law, if one is to correctly model the physics. However, the Hall term is
notoriously difficult to include in the MHD range of frequencies due to the strong
dispersive (stiff) and nonlinear character. We have developed a method that handles
the stiff nature of the equations that we call a hyperbolic relaxation method, which
is local in the spatial discretization. The basic idea is that a specific semi-implicit
time stepping algorithm applied to the full GOL (including electron inertia) and

Maxwell-Ampere law (including displacement current) is shown to relax to the Hall-
MHD Ohm’s law (without electron inertia) and Ampere’s law (without displacement

current) in the limit of large time steps. The method naturally includes standard
resistive MHD when the density is sufficiently high, without the need for a global
implicit solve of the resistive diffusion equation. Most importantly, inclusion of the
Hall term allows for a much more physical transition to the vacuum that is
problematic for resistive MHD. We will present the relaxation method, the
implementation in the PERSEUS code, and simulation results of HED experiments
that highlight the importance of low-density plasma dynamics and the necessity of
the Hall term.

Synopsis:

Symmetries are a powerful tool for extracting qualitative information from reduced models. In particular, an asymptotically consistent reduced model must contain all of the symmetries of the first principles description, but the converse is not true: reduced models can have additional symmetries which are an artifact of the simplification achieved by the asymptotic reduction. These emergent symmetries can signal the existence of (approximately) conserved quantitites. In this talk, I will present symmetries of the KREHM model derived by A. Zocco and A. A. Schekochihin. This model, which is formally obtained by considering gyrokinetics in the limit of small beta, possesses many emergent symmetries which are not obvious from physical considerations. We will also discuss how the formal techniques of symmetry analysis are applied to equations with integral relations, which are a ubiquitous feature of reduced kinetic models. Finally, we will show how these symmetries can be used to study the behavior of three dimensional reconnecting systems.

Synopsis:

In this talk, I present a systematic derivation of a wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and inhomogeneous. Primarily based on the Weyl phase-space representation, the derivation makes use of the well-known ordering assumptions of geometrical optics and of a statistical closure based on the quasinormal approximation. The resulting wave kinetic equation describes the wave dynamics in the ray phase space. It captures linear effects, such as refraction, linear damping, and external sources, as well as nonlinear wave scattering. This general formalism could potentially serve as a stepping stone for future studies of weak wave turbulence interacting with mean fields in nonstationary and inhomogeneous media. In particular, I demonstrate how the general formalism can be applied to the study of interacting drift-wave turbulence and zonal flows in plasmas.

Synopsis:

The breaking of magnetic field line connections is of fundamental importance in essentially all applications of plasma physics: laboratory to astrophysics.  For sixty years the theory of magnetic reconnection has been focused on two-coordinate models.  When dissipative time scales far exceed natural evolution times, such models are not realistic for ordinary three dimensional space.  The ideal (dissipationless) evolution of a magnetic field is shown to in general lead to a state in which the magnetic field lines change their connections on an Alfvénic (inertial), not resistive, time scale.  Only a finite mass of the lightest current carrier, the electron, is required.  During the reconnection, the gradient in j_||/B relaxes while conserving magnetic helicity in the reconnecting region.  This implies a definite amount of energy is released from the magnetic field and transferred to shear Alfvén waves, which in turn transfer their energy to the plasma.  When there is a strong non-reconnecting component of the magnetic field, called a guide field,  j_||/B obeys the same evolution equation as that of an impurity being mixed into a fluid by stirring.  Although the enhancement of mixing by stirring has been recognized by every cook for many millennia, the analogous effect in magnetic reconnection is not generally recognized.  An interesting mathematical difference is a three-coordinate model is required for the enhancement of magnetic reconnection while only two coordinates are required in fluid mixing.  The issue is the number of spatial coordinates required to obtain an exponential spatial separation of magnetic field lines versus streamlines of a fluid flow.