Two-dimensional magnetohydrodynamic equilibria with flow and studies of equilibria fluctuations

Technical Report · Tue Aug 01 00:00:00 EDT 1989

DOI:https://doi.org/10.2172/6896738· OSTI ID:6896738

Agim, Y Z

A set of reduced ideal MHD equations is derived to investigate equilibria of plasmas with mass flow in general two-dimensional geometry. These equations provide a means of investigating the effects of flow on self-consistent equilibria in a number of new two-dimensional configurations such as helically symmetric configurations with helical axis, which are relevant to stellarators, as well as axisymmetric configurations. It is found that as in the axisymmetric case, general two-dimensional flow equilibria are governed by a second-order quasi-linear partial differential equation for a magnetic flux function, which is coupled to a Bernoulli-type equation for the density. The equation for the magnetic flux function becomes hyperbolic at certain critical flow speeds which follow from its characteristic equation. When the equation is hyperbolic, shock phenomena may exist. As a particular example, unidirectional flow along the lines of symmetry is considered. In this case, the equation mentioned above is always elliptic. An exact solution for the case of helically symmetric unidirectional flow is found and studied to determine flow effects on the magnetic topology. In second part of this thesis, magnetic fluctuations due to the thermally excited MHD waves are investigated using fluid and kinetic models to describe stable, uniform, compressible plasma in the range above the drift wave frequency and below the ion cyclotron frequency. It is shown that the fluid model with resistivity yields spectral densities which are roughly Lorentzian, exhibit equipartition with no apparent cutoff in wavenumber space and a Bohm-type diffusion coefficient. Under certain conditions, the ensuing transport may be comparable to classical values. For a phenomenological cutoff imposed on the spectrum, the typical fluctuating-to-equilibrium magnetic field ratio is found to be of the order of 10 {sup {minus}10}.

• Research Organization: Wisconsin Univ., Madison, WI (USA)
• Sponsoring Organization: DOE/ER; National Science Foundation (NSF)
• DOE Contract Number: FG02-85ER53212
• OSTI ID: 6896738
• Report Number(s): DOE/ER/53212-151; ON: DE90011789; TRN: 90-018604
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
MAGNETIC CONFINEMENT
MHD EQUILIBRIUM
ALFVEN WAVES
EQUATIONS OF STATE
FLUCTUATIONS
INCOMPRESSIBLE FLOW
MAGNETIC FIELDS
MAGNETIC SURFACES
PARTIAL DIFFERENTIAL EQUATIONS
SPECTRAL DENSITY
STELLARATORS
TENSORS
TWO-DIMENSIONAL CALCULATIONS
CLOSED PLASMA DEVICES
CONFINEMENT
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUILIBRIUM
FLUID FLOW
FUNCTIONS
HYDROMAGNETIC WAVES
MAGNETIC FIELD CONFIGURATIONS
PLASMA CONFINEMENT
SPECTRAL FUNCTIONS
THERMONUCLEAR DEVICES
VARIATIONS
700103* - Fusion Energy- Plasma Research- Kinetics