Asymmetric structure of an isolated flux arch

This paper extends two-dimensional model of symmetric magnetostatic flux arches confined in stratified atmospheres (Zhang and Hu, 1992, 1993) to asymmetric models. Numerical results show that the flux structure is influenced greatly by the boundary condition of magnetic field, the force-free factor, the atmospheric pressure distribution and the position of footpoints (especially the width ratio of outlet to entrance, which differs from symmetric case).

Equilibrium of isolated magnetostatic flux structure

Two-dimensional magnetostatic models of flux structure confined in stratified atmosphere are discussed in the present paper. The magnetic field in the flux structure is assumed to be force-free at the first step. Numerical solutions for this nonlinear free boundary problem are obtained by finite element method. Results show clearly the relation between the inside fields and outside pressure, especially the influence of atmospheric pressure distribution on the flux structure.

Magnetostatic equilibrium of isolated magnetic-flux tube

In the present paper, an isolated axisymmetric flux tube is discussed for slender magnetic configuration. The magnetostatic model and the stratified atmospheric model are applied, respectively, to the regions inside and outside the flux tube. The problem is described mathematically by the nonlinear partial differential equations under the nonlinear boundary condition at the free boundary of flux tube. According to the approximation of a small expansive angle, the solutions of series expressions are obtained formally. The model of polytropic plasma is discussed in detail especially. The results show the distributions of thermodynamic quantities and magnetic field extending from the high β region to the low β region, and the flux tube may be either divergent or convergent according to the pressure difference outside and inside the flux tube.

A model of an isolated magnetic-flux tube in a stratified atmosphere

A two-dimensional model of a magnetic flux tube confined in a gravitational stratified atmosphere is discussed. The magnetic field in the flux tube is assumed to be force-free. By using the approximation of large scale height, the problem of a free boundary with nonlinear conditions may be reduced to one involving a fixed boundary. The two-dimensional features are obtained by applying the perturbation method and adopting the Luest-Schlueter model as the basic state. The results show that the configuration of a flux tube confined in a gravitational stratified atmosphere is divergent, and the more twisted the magnetic field, the more divergent is the flux tube.

A consistent model of isolated force-free magnetic arches

The magnetic flux tube concentrating strong magnetic field is the basic configuration of magneticfield in the solar atmosphere. In the present paper, the equilibrium of isolated magnetic flux tube inthe solar atmosphere is discussed. In the viewpoint of mathematics, the boundary condition is nonlinearand the position of boundary needs to be determined by the physical condition although the equation ofmagnetic potential is linear for the linear force-free field. Analytical solutions to the arches of bothuniform circular cross-section and non-uniform cross section have been obtained. The results show thatthe nonlinear problem may have or not have any solution according to different azimuthal components of the magnetic field; the number of solutions to the nonlinear problem is four at most, and two in some cases. In the present paper, the analytical solutions to the approximations of both fat and slender arches are given in detail, and the general features of magnetic arch structure are shown.

Valuing Flexibility: The case of an Integrated Gasification Combined Cycle Power Plant

In this paper we analyze the valuation of options stemming from the flexibility in an Integrated Gasification Combined Cycle (IGCC) Power Plant. First we use as a base case the opportunity to invest in a Natural Gas Combined Cycle (NGCC) Power Plant, deriving the optimal investment rule as a function of fuel price and the remaining life of the right to invest. Additionally, the analytical solution for a perpetual option is obtained. Second, the valuation of an operating IGCC Power Plant is studied, with switching costs between states and a choice of the best operation mode. The valuation of this plant serves as a base to obtain the value of the option to delay an investment of this type. Finally, we derive the value of an opportunity to invest either in a NGCC or IGCC Power Plant, that is, to choose between an inflexible and a flexible technology, respectively. Numerical computations involve the use of one- and two-dimensional binomial lattices that support a mean-reverting process for the fuel prices. Basic parameter values refer to an actual IGCC power plant currently in operation.