Eigenfrequencies in an electromagnetic spheroidal cavity

Kokkorakis Gerassimos, C; Roumeliotis John, A

dc.contributor.author	Kokkorakis Gerassimos, C	en
dc.contributor.author	Roumeliotis John, A	en
dc.date.accessioned	2014-03-01T02:41:12Z
dc.date.available	2014-03-01T02:41:12Z
dc.date.issued	1996	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/30418
dc.subject.other	Boundary conditions	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Mathematical models	en
dc.subject.other	Perturbation techniques	en
dc.subject.other	Vectors	en
dc.subject.other	Abstract only	en
dc.subject.other	Electromagnetic spheroidal cavities	en
dc.subject.other	Vector wave functions	en
dc.subject.other	Electromagnetic field effects	en
dc.title	Eigenfrequencies in an electromagnetic spheroidal cavity	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1109/AEM.1996.873054	en
heal.identifier.secondary	http://dx.doi.org/10.1109/AEM.1996.873054	en
heal.publicationDate	1996	en
heal.abstract	The eigenfrequencies fnsm in an electromagnetic spheroidal cavity, are determined analytically by a shape perturbation method. The analytical determination is possible in the case of small v = 1-a2/b2, (\|v\|<<1), where 2a and 2b are the lengths of the rotation axis and the other axis of the spheroidal cavity, respectively. In this case exact, closed-form expressions are obtained for the expansion coefficients gnsm(1) and gnsm(2) in the resulting relation fnsm(v) = fns(0)[1+gnsm(1)v+g nsm(2)v2+O(v3)], where g's are independent of v, while fns(0) are the eigenfrequencies of the corresponding spherical cavity with v = 0(b = a). There is no need for the spheroidal vector wave functions. The electromagnetic field is expressed in a series of spherical vector wave functions. The equation of the spheroidal boundary is given in terms of the spherical coordinates r and Θ. After the satisfaction of the boundary conditions we obtain an infinite determinant equation, from which the above relation for fnsm(v) is found after lengthy manipulation. This relation is valid for each small value of v and for all modes, while all numerical techniques require repetition of the evaluation for each different v. It is valid for a prolate spheroidal cavity (v<0),as well as for an oblate one (v>0).	en
heal.publisher	IEEE	en
heal.journalName	Trans Black Sea Region Symposium on Applied Electromagnetism	en
dc.identifier.doi	10.1109/AEM.1996.873054	en