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A new method for obtaining analytical eigenfunctions and growth ratesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2001 (English)Conference paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

2001.
##### National Category

Fusion, Plasma and Space Physics
##### Identifiers

URN: urn:nbn:se:kth:diva-78597OAI: oai:DiVA.org:kth-78597DiVA: diva2:492672
##### Conference

28th EPS Conference on Controlled Fusion and Plasma Physics, Madeira, 18-22 June 2001, P4.106, p. 516
#####

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#####

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##### Note

NR 20140805Available from: 2012-02-08 Created: 2012-02-08Bibliographically approved

By use of computer math programs, the MHD stability properties of fusion confinement plasmas can now be determined analytically, without further approximations, to high orders in time and space coordinates. We here present results from expanding the linearized ideal and resistive MHD eigenvalue equations for cylinder geometry in radius *r*. The effect of sheared fluid flow on stability is also included. Not only analytical growth rates, but also analytical forms of the eigenfunctions are obtained. As expected, we find that moderately large expansions provide high accuracy for mildly localized eigenfunctions.

The method, for linearized eigenvalue problems, is based on expansions of the dependent perturbed variables in powers of the spatial independent variables; e.g. *u _{r}*,

By successively solving the MHD equations at higher orders of *r*, solutions being exact up to this order are obtained. The indicial equation (at *r* = 0) is automatically solved in this method. By applying boundary conditions at *r* = *r _{wall}*, an implicit equation for the eigenvalue

Our method can be used for any geometry, and also for nonlinear systems of equations. It thus has a very large potential for efficient and exact analytical investigations of (one- or many-fluid) MHD equations, also including additional physical effects. The calculations require efficient math program routines and high speed and memory computer platforms, wherefore they were difficult to perform earlier.

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