a Wave-Radiation Model for the Onset of Dissipation in Superfluid Helium at the Roton Critical Velocity.

Abstract

in g the o n s e t of d is s ip a tio n at th e ro to n c r i t ic a l v e lo c ity in s u p e r flu id h e liu m .T h is is a c la s s ic a l , c o r r e s p o n d e n c e -p r in c ip le -lim it po in t of v iew and is q u ite an alo g o u s to th e c la s s ic a l d e s c r ip tio n that i s w idely a c c e p te d fo r u n d e rs ta n d in g the e m is s io n of photons by an e le c t r i c c h a rg e th a t m o v e s at a c o n s ta n t v e lo c ity g r e a t e r th a n the sp e e d of lig h t in a d ia le c tr ic m e d iu m .A fte r f i r s t d e riv in g a th e o ry f o r th e w ave e x c ita tio n s and b o u n d a ry -v a lu e p ro b le m s of the c o rre s p o n d e n c e p rin c ip le lim it fo r a co n d en se d -b o so n s y s te m , th is p a p e r show s th a t a w ave r a d i a tio n field f o r m s a ro u n d a fo re ig n body m o v in g th ro u g h the s u p e r fluid m e d iu m w hen the fo re ig n body m o v e s f a s t e r th an the m in im u m p h a se v e lo c ity , {w/k )m jn » w ave e x c ita tio n s in the m e d iu m .M o re o v e r, the sp a tia l d e p e n d e n c e of th is w ave fie ld and the lo s s of e n e rg y r a d ia tin g th ro u g h it a r e c a lc u la te d a s fu n ctio n s of the f r a c tio n a l in c r e a s e of the fo re ig n b o d y 's v e lo c ity above the th r e s h o ld v e lo c ity In s p ite of a p p ro x im a tio n s m a d e in th e c a lc u la tio n s , th e r e s u l t s in d ic a te th a t it is im p o s s ib le , e x p e r i m e n ta lly , to f o r c e an io n c o m p lex to m ove th ro u g h the s u p e rflu id c o m ponent o f h e liu m a t a v e lo c ity o b s e r v a b ly g r e a t e r th an th e ro to n c r i t i c a l v e lo c ity .ACKNOWLEDGMENTS I would lik e to thank P r o f e s s o r R. L. M ills fo r h is c o n trib u tio n s to m y g ra d u a te ed u catio n and fo r h is p e rc e p tiv e c o u n s e l w hile th is r e s e a r c h w a s b e in g c o n d u cted , e s p e c ia lly r e g a r d in g th e re s o lu tio n of s e v e r a l m a th e m a tic a l d iffic u ltie s w hen no so lu tio n s s e e m e d to e x is t.T h e N a tio n a l A e ro n a u tic s and Space A d m in is tr a tio n i s th an k ed f o r i t s fin a n c ia l su p p o rt d u rin g the y e a