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approvedsher19.pdf2019-04-13 12:07:46Alan Glasser

Abstracts

Author: Alan H. Glasser
Requested Type: Poster
Submitted: 2019-02-18 12:47:26

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Contact Info:
FTCI
24062 Seatter Lane NE
Kingston, WA   98346
USA

Abstract Text:
Resistive tearing modes are constructed by matching a sequence of ideal and resistive regions, [A.H. Glasser, Z.R. Wang, and J.-K. Park, "Computation of resistive instabilities by matched asymptotic expansions," Phys. Plasmas 23, 112506 (2016)] at each singular surface matching the small-x asymptotic behavior in the ideal MHD outer region to the large-x asymptotic behavior of the resistive MHD inner region. The 6th-order resistive region equations ] A.H. Glasser, J.M. Greene, and J.L. Johnson, "Resistive instabilities in general toroidal plasma configurations," Phys. Fluids 18, 7, 875 (1975)] have previously been treated as a set of 3 coupled second-order ordinary differential equations, ignoring the exponentially large and small solutions.

A careful study of these solutions reveals problems. The leading-order terms in the two series are identical, i.e. degenerate. The solutions fail to converge as the position x and the degree n get large. The width of the inner region is too broad, failing to overlap with the outer region. Verification studies with the straight-through MARS code indicate broad ranges of unsatisfactory agreement.

A new analysis is presented, based on a method given by Wasow. [Wolfgang Wasow, "Asymptotic Expansions for Ordinary Differential Equations," Dover, Mineola, NY, 1965, 1993, Chapter V] The equations are treated as a coupled system of 6 first-order equations, expressed in terms of 6x6 matrices. The leading-order matrix is transformed to Jordan canonical form, revealing that the power-like solutions are degenerate, with 0 on the diagonal and 1 above the diagonal, the most difficult case to treat. Wasow presents an order-by-order splitting procedure to separate the power-like solutions from the exponential solutions and obtain a asymptotic power series solution. Details will be presented.

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