CONDITION OF DAMPING OF ANOMALOUS RADIAL TRANSPORT, DETERMINED BY ORDERED CONVECTIVE ELECTRON DYNAMICS

Transcription

1 CONDITION OF DAMPING OF ANOMALOUS RADIAL TRANSPORT DETERMINED BY ORDERED CONVECTIVE ELECTRON DYNAMICS VIMaslv SVBachuk VILapshin YuVMlnsv* EDVlkv NSC Khakv Insiu f Physics and Tchnlgy Khakv 608 Ukain *Kaain Khakv Nainal Univsiy Khakv 608 Ukain vmaslv@kipkhakvua I is shwn ha a dvlpmn f insabiliy du a adial gadin f dnsiy in h cssd lcic and magnic filds in nucla fusin insallains ding cnvciv clls can b xcid I pvids anmalus paicl ansp Th spaial sucus f hs cnvciv clls hav bn cnsucd Th adial dimnsins f hs cnvciv clls dpnd n hi ampliuds and n a adial gadin f dnsiy Th cnvciv-diffusin uain f adial dynamics f h lcns has bn divd A h cain valu f h univsal cnlling paam h cnvciv cll xciain and h anmalus adial ansp a suppssd PACS Rf: 57Lw INTRODUCTION Anmalus plasma paicl ansp du lw-funcy pubains in h css-fild dg gin f h idal dvics is invsigad nw innsivly (s f xampl [] Nw als h l f h lcic fild fmd in nucla fusin insallains and suling cssd filds is innsivly invsigad In h labay xpimns in cssd filds h vx fmain in lcn plasma was bsvd [] in magnn dischag in ECR plasma suc [] in and lay f h Pnning dischag Th chagd plasma lns inndd f fcusing f high-cun in bams has h sam cssd cnfiguain f filds [] and h vics a fmd in i Thus h cssd cnfiguain f filds als can b n f h asns f h vics xciain in nucla fusin insallains In ubulnc f small ampliuds h lcn ajcis a schasic A achivmn f h lag ampliuds whn funcy Ω f h lcn scillains in h cnvciv cll f h pubain xcds h gwh a f is xciain Ω(>γ h cll changs in is viciniy h lcn dnsiy gadin n which snghns h nx clls Thus n h cll bundais h jumps f n ( ais On hs jumps h gwh as f h nx cll xciain a much m han h gwh a dmind by n pubd n Thus ding f clls aiss simila invsigad

2 in [5] I pvids fas lcn ansp In h wds h slfcnsisn xciain f h lwfuncy cnvciv clls in h nnuilibium plasma difing in cssd lcic and magnic filds in slaa by a adial gadin f dnsiy is unsabl cncning ccunc f clains Thus cnvciv-diffusin adial lcn ansp and paly dd laic f cnvciv clls in spac ( ais DESCRIPTION OF EXCITATION AND STRUCTURE OF CONVECTIVE CELLS L us cnsid dvlpmn f insabiliy f cnvciv lcn dynamics xciain in adial lcic E and lngiudinal magnic H filds in h gin f dnsiy gadin and suppssin f h anmalus ansp causd by his cnvciv dynamics W us cylindical appximain F dscipin f h lcn cnvciv dynamics w us hy dvlpd in [6] f plasma lns Th lcn dynamics in cssd filds is dscibd by h uains [6-8] d ω n d V ϕ φ E V α V [( ] 0 α ( E V ω T n φ is h lcic pnial f h pubain 0 m E 0 V n h 0 n 0 mω [ φ] V [ φ] Fm his uain w div similaly [6] h lina dispsin lain dscibing h insabiliy dvlpmn ( ω ω k ( l ( ω ω 0 ωpi ω p l φ F mbil pubains V ph V n can bain [6] ω ω ( δω ( ω ω l pi ω δω iγ γ [( ω k ( l ( ω ω ] / pi p Th gwh a is ppinal n A is baining w usd a validiy f h inualiy [( E ( T / n0 / πnω] ( ωp ω << m mi I is fulfilld a h small n and ω ωp >> L us cnsid h chain n f h mbil cnvciv clls A small dviains fm aking in accun h fis mmb f ( E ( ( T / n ( ω ( h adial si f h cnvciv cll - hl f h lcns 0 n δ w bain

3 [ φ ( (( ( ( ( ( ] / ω E T / n0 ω δ h F lag ampliuds in h gins f h lcn bunchs h cnaflws a fmd On can shw ha in h s fam ad wih funcy ω ph h lcns appd by h lcn hl and h lcns fming h lcn bunch a ad in h ppsi dicins W bain fm h cndiin δ δ φ φ cl h bunday f h cll - hl f h lcns δ ± ω ( φ φ (( E T / n ω ( ( ( ( ( δ cl is h adial widh f h cnvciv cll-bunch f h lcns 0 ( δ L us cnsid h ffc n n bhavi f clls Fininss f im f h cnvciv cll symmiain and h flcin f snan lcns fm cnvciv clls - bunchs sul ha h cnvciv clls a paly asymmical [6] I suls in fmain f cl / E and adial dif f clls This bhavi f h cnvciv clls has bn bsvd in xpimns [] Th cnvciv clls a shifd n adius gh wih appd lcns lading addiinal mchanism f cnvciv adial lcn ansp CONVECTIVE DIFFUSION EQUATION F alid nw in nucla fusin valus ω ω and E h paam dmining yp p f xcid cnvciv clls is small I mans ha mbil clls shuld b fmd Thn f fini bu n s lag ampliuds h cll hls f h lcns a fmd Thf fuh w cnsid cnvciv ansp alid by clls - hls f h lcns Fig Singl cnvciv cll A achivmn f h lag ampliuds h appas ding f clls (s Fig simila invsigad in [5] Insid bds f a cll dd cnvciv mvmn f h lcns ccus Hwv hy a influncd by nvinmnal filds Als i is impan ha ampliuds f clls a n sainay Insad f avag n ( which ds n ak in accun clains w us fu dnsiis f h lcns n k ( avag n small-scal scillains: n ( (n ( is h

4 avag dnsiy f h lcns lcad in gin (s Fig in dph f a cll n > v (in gin in dph f a cll n < v ; n ( (n ( is h avag dnsiy f h lcns placd in gin na bd f a cll n > v (in gin na bd f a cll n < v Th impanc f us f diffn n k ( is als dmind by ha angula spds f lcn ain insid a cll a diffn in dpndnc n disanc fm is axis Als in w cnal aas f h cnvciv clls h fllwing pcsss a sill alid: plaau fmain n n ( du diffnc f angula spds f lcn ains; a n ( jump fmain a h cain mmns f im in h gins and h is an acclad diffusin and an xchang by lcns bwn gins and (fac β and als bwn gins and Fig Th dd chain f cnvciv clls Fm h abv w hav appximaly ( τ ( α n ( n ( ( τ ( α n ( n ( n αβ ( τ αn ( β( α n ( n αβ ( β [ n ] n n ( τ αn ( β( α n ( ( β [ n ] n n α is h fac f mixing du n idal ding influnc f flucuains gwh f ampliuds diffncs f chaacisic ims f h lcns In viciniis f cll bds n jumps a fmd nc n hs n jumps nw clls wih h gas gwh as a xcid I suls in ding f cnvciv clls Fm hs uains ning ( n n ( n n N δ N n n w div ( N βn ( β ( α n δ n n n τ n α τ β( α αδn β α ( n N Fm hs uains w hav simila [5] τ τ τ N α β τ δn ( α δn αβ [ ] ( n [( β( α αδn] β( α α( N βn ( α β

5 W sach h ms favabl paams whn h cnvciv clls a n xcid and anmalus ansp is suppssd W shw ha h cnvciv clls a n xcid if h valu f h magnic fild is cls h ms favabl S l us cnsid such ampliud f h cnvciv cll a which h magnic fc can n ap h lcns f h cll aing aund is axis n h clsd ajcy and lcns can mv acss h magnic fild In h wds h lcn bunch f h cll can xnd acss h magnic fild Thus h lcn bunch fmain is sppd Thus fm balanc f h fcs pviding mvmn f h lcns n clsd ajcis n can find simila [6] ha if h magnic fild is cls pimum ( E ( T / n m ω 0 h cnvciv clls a n xcid CONCLUSION S a insabiliy dvlpmn du h adial gadin f dnsiy in h cssd lcic and magnic filds in nucla fusin insallains h ding f h cnvciv clls can ais I pvids anmalus paicl ansp Th spaial sucus f hs uickly mving cnvciv clls hav bn cnsucd I has bn shwn ha h adial dimnsins f hs cnvciv clls dpnd n hi ampliuds and n a adial gadin f dnsiy Th cnvciv-diffusin uain dscibing hs cnvciv-diffusin adial dynamics f h lcns has bn divd Th is h univsal paam cnlling h xciain f hs cnvciv clls A h cain valu f his paam h xciain f hs cnvciv clls and h anmalus adial ansp a suppssd Th bsvd fings f dnsiy can b xplaind by h fmain f hs cnvciv clls REFERENCES TSPdsn al Plasma Phys Cn Fus 996 V 8 P YKiwam al Phys Rv L 000 V 85 P 7 MKn MYTanaka Phys Rv L 000 V 8 P 69 AAGnchav al Plasma Phys Rp 99 V 0 P 99 5 ASBakai YuSSigv DAN USSR 977 V 7 P 6 6 AAGnchav VIMaslv INOnishchnk Plasma Phys Rp 00 V 0 P 66 7 VIPviashvili OAPhlv Plasma Phys Rp 986 V P 7 8 MVNlin GPChnikv Plasma Phys Rp 995 V P 975