Deok Kyo Lee

MOMCON: A spectral code for obtaining three-dimensional magnetohydrodynamic equilibria

Abstract A new code, MOMCON (spectral moments code with constraints), is described that computes three-dimensional ideal magnetohydrodynamic (MHD) equilibria in a fixed toroidal domain using a Fourier expansion for the inverse coordinates ( R, Z ) representing nested magnetic surfaces. A set of nonlinear coupled ordinary differential equations for the spectral coefficients of ( R, Z ) is solved using an accelerated steepest descent method. A stream function, λ, is introduced to improve the mode convergence properties of the Fourier series for R and Z . The convergence rate of the R - Z spectra is optimized on each flux surface by solving nonlinear constraint equations relating the m ≥ 2 spectral coefficients of R and Z .

Application of theta functions for numerical evaluation of complete elliptic integrals of the first and second kinds

Abstract An approximation method based on the use of theta functions is shown to be efficient and useful in the numerical evaluation of complete elliptic integrals of the first and second kinds, K ( k ) and E ( k ), respectively. The integrals are expressed in terms of power series of the form Σ a n q n 2 , 0⩽ q q is the nome determined uniquely from a given value of the argument k . The series converge very rapidly, except for small domains near | k | = 1, where they either converge slowly or fail to converge. When applied on Cray 2 computers for 0 ⩽ k 2 ⩽0.995, the procedure is found to be more efficient than both the Chebyshev approximations of the Hastings form and the standard Gauss arithmetic-geometric mean process. Numerical results that demonstrate the accuracy and efficiency of the approximation method are presented.

Absence of magnetic anomalies due to seepage-induced "magnetoelectric effects" and implications for sulfide self-potentials

The magnetic field due to an azimuthally symmetric distribution of subsurface electric current, which may be associated with vertical hydrocarbon seepage, vanishes above the ground surface. However, geologic conditions in general do not provide perfect isotropic conditions, and, in theory, some magnetic fields can be generated by the magnetoelectric effect. Sedimentary rock sections are relatively isotropic, particularly in the stratigraphic plane. Thus, hydrocarbon seepage‐induced magnetic fields above the ground surface may never be significant, even if strong electric currents are associated with the seepage. All current‐generated magnetic fields, of whatever origin, must obey Ampere’s law; no line integral operation can distinguish a magnetic field having one origin from that of any other origin. Therefore, seepage‐induced magnetic anomalies, if they exist at all, are probably useless for hydrocarbon exploration because it is virtually impossible to distinguish them from other anomalies of unknown ori...

Method of Folding a Piecewise Polynomial Function in the Delta Function Integral Representation

A simple procedure is presented for determining the folded form of a piecewise polynomial function in the delta function integral representation. The procedure is useful in evaluating the autocorrelation function by means of the algebraic convolution technique developed by Polge and Hays.