The oscillatory modes of a sharply bounded plasma which involve surface charge are studied by a method which includes the behavior of the surface charge. It is found that these modes are "quasi· oscillations" -they do not persist indefinitely, eventually being destroyed by muliistreaming. They are inherently nonlinear, not even possessing a line~zeable limit if the density gradient is made finite. An important conclusion is that the surface charge modes probably play no role in laboratory experi· ments on the scattering and a-c probe resonances. On the other hand, there may be situations in which the surface charge modes would contribute importantly to an experiment, but would not be predicted by a linearized theory.

Th e Vl asov equati on has bee n solv ed for th e pl as m a reso na nce s pec tra of a re a li s ti c mod el by th e co ndu c tivit y ke rn e l me th od. Th e res ult s give a cle are r pi c ture of th e na ture of p las ma resona nce th a n he re tofore a vaila bl e. Th e calc ulation includ es Landau dampin g a nd does not ) m po se unphysi cal bo und a ry co nditi ons. The proble m of c hi ef inte res t here is th e sca ll e rin g I)f electromagne ti c radia· ti on ne ar th e e lec tron pl as ma fre qu e nc y from a cy lindri c a l pl a s ma whe n th e wa ve vec tor a nd pola ri · za ti on are per pe ndi c ul ar to th e c ylind e r a xis. Th e pl a s ma is nonuniform a nd bo und e d by a s hea th , a nd has di a me te r a s ma ll c omp a red to th e fr ee s pa ce wav e le ngth. Th e sca tt e rin g res ona nces a t th e lowe r frequ e ncies a re produ ce d b y c ha rge de ns it y pe rturb a ti o ns co nce ntrate d a t rela tiv ely la rge radii . But , th e prob le m of a pe rfec tl y c olli s ion less c ylindri c a l p las ma ca nn ot be red uced to a one·dim e ns io nal pro bl e m with out neglec tin g some of th e r esona nces with peri od ic e lec tron orbit s . It is argue d th a t we a k co ul o mb collj sions des troy th ese " tra ns it tim e resona nces," a nd th a t th e pro bl e m is ad equ a te ly desc ri bed b y keepin g ju s t one pe riod of th e elec tro n orb it in th e ca lc ul a ti on of the cond uc ti vit y ke rn e l. Th e c ylindri c a l pro bl e m th e n re du ces to th e p robl e m o f th e s te ad y, dri ve n, oscill a ti o'ns of a thin o ne· dim e ns iona l s lab of colli s ionl ess, Max we lli a n, pl a s ma , with a wa ll a t x= 0 whi c h e m it s e lec t ro ns a nd absorb s ali eleclJ"ons th a t re turn to x = O. a nd a n in s ul a ted wall a t x = x", whi c h a lso abso rbs e lec tro ns .A mod e l is used in whi c h the unperturbe d. e lec tri c fi eld , e ve ry wh e re in th e pos iti ve x·direc tio n, is unifo rm in th e plas ma , 0 ", X '" s. a nd join s s m oothl y to a ha rmoni c oscill ator fi e ld in th e s he a th , s '" X '" XIV ' T he cond uc tivit y kern els for a la rge num be r uf fre qu e nc ies hav e been ca lc ul a te d , a nd in ve rt e d , on la rge e lect ron ic co mp ute rs. Th e res ult s s how th a t mu c h of th e La nda u da mpin g w hi c h d e te rmin es th e lin e s hapes is co nce ntrate d near th e s he ath , a nd th e reso na nce fre q ue nc ies are de te rmin e d by th e pro pe rties of th e s he a th and th e ne ighbo rin g regions of th e pl as m a.

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The spectrum of undriven electron plasma oscillations of a realistic, nonuniform, collisionless plasma with a sheath is determined. The spectrum is found to be discrete.

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