31 research outputs found
A high resolution wave propagation scheme for ideal two-fluid plasma equations
Abstract Algorithms for the solution of the five-moment ideal Two-Fluid equations are presented. The ideal Two-Fluid model is more general than the often used magnetohydrodynamic (MHD) model. The model takes into account electron inertia effects, charge separation and the full electromagnetic field equations and allows for separate electron and ion motion. The algorithm presented is the high resolution wave propagation method. The wave propagation method is based on solutions to the Riemann problem at cell interfaces. Operator splitting is used to incorporate the Lorentz and electromagnetic source terms. To preserve the divergence constraints on the electric and magnetic fields two different approaches are used. In the first approach Maxwell equations are rewritten in their mixed-potential form. In the second approach the so-called perfectly hyperbolic form of Maxwell equations are used which explicitly incorporate the divergence equations into the time stepping scheme. The algorithm is applied to a one-dimensional Riemann problem, ion-acoustic soliton propagation and magnetic reconnection. In each case Two-Fluid physics described by the ideal Two-Fluid model is highlighted
Evolution of Plasma Flow Shear and Stability in the ZaP Flow Z-Pinch
Abstract. The stabilizing effect of an axial flow on the m = 1 kink instability in Z-pinches has been studied numerically with a linearized ideal MHD model to reveal that a sheared axial flow stabilizes the kink mode when the shear exceeds a threshold. The sheared flow stabilizing effect is investigated with the ZaP Flow Zpinch experiment. An azimuthal array of surface mounted magnetic probes measures the fluctuation levels of the azimuthal modes m = 1, 2, and 3. After pinch assembly a quiescent period is found where the mode activity is significantly reduced. The quiescent period lasts for over 2000 times the expected instability growth time in a static Z-pinch. Optical images from a fast framing camera, a two-chord HeNe interferometer, and a ruby holographic interferometer indicate a stable, discrete pinch plasma during this time. Multichord Doppler shift measurements of impurity lines show a large, sheared flow during the quiescent period and low, uniform flow profiles during periods of high mode activity. The value of the velocity shear satisfies the theoretical threshold for stability during the quiescent period and does not satisfy the threshold during the high mode activity. Experiments are conducted with varying amounts of injected neutral gas to gain an understanding of the Z-pinch formation and lifetime
Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations
Two-fluid ideal plasma equations are a generalized form of the ideal MHD
equations in which electrons and ions are considered as separate species. The
design of efficient numerical schemes for the these equations is complicated on
account of their non-linear nature and the presence of stiff source terms,
especially for high charge to mass ratios and for low Larmor radii. In this
article, we design entropy stable finite difference schemes for the two-fluid
equations by combining entropy conservative fluxes and suitable numerical
diffusion operators. Furthermore, to overcome the time step restrictions
imposed by the stiff source terms, we devise time-stepping routines based on
implicit-explicit (IMEX)-Runge Kutta (RK) schemes. The special structure of the
two-fluid plasma equations is exploited by us to design IMEX schemes in which
only local (in each cell) linear equations need to be solved at each time step.
Benchmark numerical experiments are presented to illustrate the robustness and
accuracy of these schemes.Comment: Accepted in Journal of Scientific Computin
Sheared Flow As A Stabilizing Mechanism In Astrophysical Jets
It has been hypothesized that the sustained narrowness observed in the
asymptotic cylindrical region of bipolar outflows from Young Stellar Objects
(YSO) indicates that these jets are magnetically collimated. The j cross B
force observed in z-pinch plasmas is a possible explanation for these
observations. However, z-pinch plasmas are subject to current driven
instabilities (CDI). The interest in using z-pinches for controlled nuclear
fusion has lead to an extensive theory of the stability of magnetically
confined plasmas. Analytical, numerical, and experimental evidence from this
field suggest that sheared flow in magnetized plasmas can reduce the growth
rates of the sausage and kink instabilities. Here we propose the hypothesis
that sheared helical flow can exert a similar stabilizing influence on CDI in
YSO jets.Comment: 13 pages, 2 figure
Numerical approximation of the Euler-Poisson-Boltzmann model in the quasineutral limit
This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB)
model of plasma physics. This model consists of the pressureless gas dynamics
equations coupled with the Poisson equation and where the Boltzmann relation
relates the potential to the electron density. If the quasi-neutral assumption
is made, the Poisson equation is replaced by the constraint of zero local
charge and the model reduces to the Isothermal Compressible Euler (ICE) model.
We compare a numerical strategy based on the EPB model to a strategy using a
reformulation (called REPB formulation). The REPB scheme captures the
quasi-neutral limit more accurately
Pressure-driven instabilities in astrophysical jets
Astrophysical jets are widely believed to be self-collimated by the
hoop-stress due to the azimuthal component of their magnetic field. However
this implies that the magnetic field is largely dominated by its azimuthal
component in the outer jet region. In the fusion context, it is well-known that
such configurations are highly unstable in static columns, leading to plasma
disruption. It has long been pointed out that a similar outcome may follow for
MHD jets, and the reasons preventing disruption are still not elucidated,
although some progress has been accomplished in the recent years.
In these notes, I review the present status of this open problem for
pressure-driven instabilities, one of the two major sources of ideal MHD
instability in static columns (the other one being current-driven
instabilities).
I first discuss in a heuristic way the origin of these instabilities.
Magnetic resonances and magnetic shear are introduced, and their role in
pressure-driven instabilities discussed in relation to Suydam's criterion. A
dispersion relation is derived for pressure-driven modes in the limit of large
azimuthal magnetic fields, which gives back the two criteria derived by
Kadomtsev for this instability. The growth rates of these instabilities are
expected to be short in comparison with the jet propagation time.
What is known about the potential stabilizing role of the axial velocity of
jets is then reviewed. In particular, a nonlinear stabilization mechanism
recently identified in the fusion literature is discussed.
Key words: Ideal MHD: stability, pressure-driven modes; Jets: stabilityComment: 20 pages, 3 figures. Lecture given at the JETSET European school
"Numerical MHD and Instabilities". To be published by Springer in the
"Lectures notes in physics" serie
A general nonlinear fluid model for reacting plasma-neutral mixtures
A generalized, computationally tractable fluid model for capturing the effects of neutral particles in plasmas is derived. The model derivation begins with Boltzmann equations for singly charged ions, electrons, and a single neutral species. Electron-impact ionization, radiative recombination, and resonant charge exchange reactions are included. Moments of the reaction collision terms are detailed. Moments of the Boltzmann equations for electron, ion, and neutral species are combined to yield a two-component plasma-neutral fluid model. Separate density, momentum, and energy equations, each including reaction transfer terms, are produced for the plasma and neutral equations. The required closures for the plasma-neutral model are discussed
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A General Nonlinear Fluid Model for Reacting Plasma-Neutral Mixtures
A generalized, computationally tractable fluid model for capturing the effects of neutral particles in plasmas is derived. The model derivation begins with Boltzmann equations for singly charged ions, electrons, and a single neutral species. Electron-impact ionization, radiative recombination, and resonant charge exchange reactions are included. Moments of the reaction collision terms are detailed. Moments of the Boltzmann equations for electron, ion, and neutral species are combined to yield a two-component plasma-neutral fluid model. Separate density, momentum, and energy equations, each including reaction transfer terms, are produced for the plasma and neutral equations. The required closures for the plasma-neutral model are discussed