Physics
Scientific paper
Jul 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995jgr...10012307o&link_type=abstract
Journal of Geophysical Research (ISSN 0148-0227), vol. 100, no. A7, p. 12,307-12,318
Physics
34
Beta Particles, Gas Pressure, Magnetic Flux, Nonlinear Evolution Equations, Magnetic Fields, Magnetohydrodynamics, Mathematical Models, Oscillators, Plasma Potentials
Scientific paper
In this second paper on the evolution of magnetic flux ropes we study the effects of gas pressure. We assume that the energy transport is described by a polytropic relationship and reduce the set of ideal MHD equations to a single, second-order, nonlinear, ordinary differential equation for the evolution function. For this conservative system we obtain a first integral of motion. To analyze the possible motions, we use a mechanical analogue -- a one-dimensional, nonlinear oscillator. We find that the effective potential for such an oscillator depends on two parameters: the polytropic index gamma and a dimensionless quantity kappa the latter being a function of the plasma beta, the strength of the azimuthal magnetic field relative to the axial field of the flux rope, and gamma. Through a study of this effective potential we classify all possible modes of evolution of the system. In the main body of the paper, we focus on magnetic flux ropes whose field and gas pressure increase steadily towards the symmetry axis. In this case, for gamma greater than 1 and all values of kappa, only oscillations are possible. For gamma less than 1, however, both oscillations and expansion are allowed. For gamma less than 1 and kappa below a critical value, the energy of the nonlinear oscillator determines whether the flux rope will oscillate or expand to infinity. For gamma less than 1 and kappa above critical, however, only expansion occurs. Thus by increasing kappa while keeping gamma fixed (less than 1), a phase transition occurs at kappa = kappa(sub critical) and the oscillatory mode disappears. We illustrate the above theoretical considerations by the example of a flux rope of constant field line twist evolving self-similarly. For this example, we present the full numerical MHD solution. In an appendix to the paper we catalogue all possible evolutions when (1) either the magnetic field or (2) the gas pressure decreases monotonically toward the axis. We find that in these cases critical conditions can occur for gamma greater than 1. While in most cases the flux rope collapses, there are notable exceptions when, for certain ranges of kappa and gamma, collapse may be averted.
Burlaga Leonard Francis
Farrugia Charles J.
Osherovich Vladimir A.
No associations
LandOfFree
Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear evolution of magnetic flux ropes. 2: Finite beta plasma will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1173470