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THE MHD STABILITY OF INERTIA-TIED Z-PINCHES WITH APPLICATION TO SOLAR CORONAL LOOPS
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Dissertation
THE MHD STABILITY OF INERTIA-TIED Z-PINCHES WITH APPLICATION TO SOLAR CORONAL LOOPS
1982
Overview
Solar coronal loops are observed to be amazingly stable structures. To be able to understand why, we need to know something about their magnetic fields, their pressure profiles and their special boundary conditions at the surface of the sun. In this dissertation, theoretical models are constructed to fit the observational data collected from various sources and then the stability of the loops is analyzed by using the laws of plasma physics. First a reasonable equilibrium field/pressure model is chosen, which can provide some stability effect. However, the photospheric inertia-tying boundary conditions, due to the anchoring of the feet of the loops at the surface of the sun, are the major stability factor. The energy principle is used extensively on the above magnetohydrodynamic system. The results of such applications enable us to determine the critical parameter (the aspect ratio of the loop, for example) which specifies stability. To use the energy principle correctly, one needs to treat a loop as an isolated system in which energy is conserved; i.e., the inflow of energy must be equal to the outflow. In addition, one must use the most general perturbation consistent with the symmetry and boundary conditions. This is necessary because, in a stability test, we should apply perturbations which are arbitrary except for these restrictions. For this purpose, we express our function in a complete sine/cosine series. This set has the property that the perturbations perpendicular to the magnetic field vanish at the solar surface, because of the high mass inertia there. This new theory for applying the energy principle, which involves the minimization of the potential energy of the coronal loop system, can be expressed in a general analytical formalism. However, when numerical applications are considered, approximations must be made because of the complexity of the generalized series which makes the problem an infinite dimensional one. Examples are worked out with the help of mathematical theorems of the calculus of variations applicable to coupled functions. We thereby illustrate that this problem can be solved very generally. The final computational accuracy is limited by the availability of time and energy only.
Publisher
ProQuest Dissertations & Theses
Subject
ISBN
1392454417, 9781392454411
