RFP BOUNDARY CONDTON STUDES ON TOKAPOLE JS Sarff J c Sprtt L Turner PLP 94 February 1985 Plasma Studies University f Wiscnsin These PLP reprts are preliminary and infrmal and as such may cntain errrs nt yet eliminated They are fr private circulatin nly and are nt t be further transmit ted withut cnsent f the authr and majr prfessr
_ ABSTRACT N RFP Bundary Cnditin Studies n Tkaple 11* JS SARFF JC SPROTT L TURNER** University f WiscnsinMadisn t has been as sumed that a reversedfield pinch (RFP) plasma requires a clse fitting cnducting shell fr gd stability and cnfinement t is nt knwn hwever the extent t which this bundary must be perfectly cnducting n rder t frm an RFP plasma bunded by a magnetic separatrix far frm a cnducting wall we have perated the Tkaple device which is nrmally a furnde plidal divertr tkamak with a prgrammedreversed tridal field We have btained plasmas in which a reversal surface is frmed far frm a cnducting wall up t 1 sec Cincident with reversal is a "quiet" perid seen n varius diagnstics sensitive t fluctuatins n additin we present tridal field prfiles and flux plts determined by an analytic slutin t xbab with cnstant A in a rectangular gemetry with a perfect ly cnducting bund ary including arbitrary internal filamentary currents Our experiments shw that althugh there is current utside the separatrix A is smaller there than inside the separatrix s that a cnstanta f rce free mdel des nt hld fr these plasmas **Permanent address: Ls Alams Natinal Labratry *This wrk is supprted by the USDOE
OUTLNE OF EXPERMENTAL WORK: JS SARFF and JC SPROTT The TOKAPOLE device The field vltage and current wavefrms used w in the "RFP mnett peratin f Tkaple Our measured magnetic field and current density prfiles V Other derive parameters: A F9 v Plasma fluctuatins V Summary
The TOKAPOLE device which we have perated with a frcedreversed trdal magnetic field Primary Windings J: Tridal Field Cils " "1 :t { :; :;"" Turb Mlecular pump
Tkaple has fur internal cpper hps which are inductively driven alng with the plasma current frming a flux plt with a magnetic separatrtx V1 item 2cm
The tridal vltage seen by the plasma is rughly nehalf the ttal applied The remaining half drives the hps 5V Cl N " OJ ec tt1 +J r! :> (j r! (j r! r evevsq t t the wl time lsec
The tridal plasma current applied vltage resulting frm the abve u c: Q) () Cj e C/} (!j 2)<A i J ct1 po +J reversal t ctt the waif tlme OOOAsec
The tridal field is reversed by reversing the winding current Pltted belw is the tridal field wavefrm seen at the wall and at the magnetic axis / KG "" "" i """"i c "t;;j s +J p:::l B Qt the w"l B9S n axis t ime /OOOAlsec
Prfiles f the tridal field taken with a (B) prbe t= bbo Msec 2 t" magnetic 15 D s :a Pt 1 5 72 " _ " (( sec ::: :=:= == =::: ::: _ 5 5 r (em) l J 1 15
Prfiles f the plidal field taken with a (B) prbe magnetic 125 r t T t:: "bomsec r fl :a fa " as :a CD :i t: 1 75 # 5 :;::: " 72 " " " 9 7 f Msec " 25 5 1 15 r (em)
td :a t:lt ""D 4 2 711 72«Sfe " " "" ;:: J 1 J_ il " 5 1 r (em) 15
Prfiles f the plidal current density btained _frm the tridal field prfiles 5 1 " t 2 """ S " N " a:s :a Q) Q +) tzr 1 72 / " / " / " " " 7LfOusec " 7 / /7 _/ / 1 j 5 1 r (em) 1 J 15
Prfiles f the A parameter fr the frcefree magnetic field (Vx BA B) calculated frm the field and current prfiles 1 r 1 f 1 74 AAec f t w Ei () d "d 8 6 4 72 7 " BO 2 = 5 1 r (em) 15
The"f i e"ld i everswii P Elr arne t e r (F ) and the pi nc h :parameter (9) are determined frm the tridal magnetic prfile and the prfile (e=a/2) We have used a=8 cm crrespnding t the psitin f the separatrtx and a=1 em crrespnding t where the plidal current density ges t "zer" 1 l 5 BFM "l"lt : J:: Pa: [ij t= 66 t= bho f! rd:a6so tb9 f! 5 a=1 em (a=a emf :7 1 f! t= 7 15 il 5 L L! l +4l_ 1 15 e 2 25
Plasma fluctuatins seen n a magnetic (B) prbe and a langmuir prbe shw a "quiet" perid cincident vith reversal f the tridal field at the wall n r 5 time t revevsal + B at the W H 1 ;efv f n saturatin current frm a langmutr prbe placed near the wall B frm a magnetic prbe placed near the wall
SUMMARY OF EXPERMENTAL WORK We have perated Tkaple with a frcedreversed tridal field and have btained unsustained RFP plasma states lasting up t 1 sec Cincident with reversal f the tridal field at the wall we see a "quiet" perid in plasma fluctuatins The frcefree field parameter A btained frm magnetic field prfile measurements has spatial structure resembling that f the Mdified Bessel Functin t1del (MBFM)
OUTLNE OF THEORETCAL WORK: J S SARFF and 1 TURNER Descriptin f a 2D mdel fr a frcefree plasma in Tkaple l Flux cnturs and field prfiles predicted by the mdel Summary
DESCRPTON OF OUR 2D MODEL We have btained a 2D analytic slutin fr the frcefree magnetic field within a rectangular dmain surrunded by a cnducting bundary Within this dmain the magnetic field satisfying VXBAR ex> with cnstant A is evaluated in the presence f filamentary current surces (an idealizatin f the cpper hps) Frm this slutin we btain the predicted magnetic field prfiles and flux cnturs which we can cmpare with the experimentally determined prfiles
Prfiles f ntridal in a square axa with fur hi??? enclsed filamentary currents fr the frcefree """""" " w " r t field paramter aa=os Three prfiles are shwn: y/a=5 (n the midplane) y/a=o16 (near the currents) and y/a=o3 14 t i 1 tn tn Et 12 1 / / / / / / = " >= / " " ; / 2 4 6 8 X/A SOLO: Y/A=5 DASH: Y/A=3 DOTDASH: Y/A=O16 1
Flux cnturs f Btridal in a square axa with f ur enclsed filamentary currents fr the frcefree field parameter aa=o 5 N < >t 1 8 6 4 2 : " : ::; " : :: :!: : h k " : " " til : " " " it # ; #! t! ; ;! :; ; ; " : : : :1 ;: :: : " : : " " : t " z = :: " "" :: :!! ::!;::: : : " " : w :: ) " :" 1:": " "! ::! : _ " f " ::: : <# _a _ : : : : : : : ; :!!:: " = ; : : 2"" _ ;;:: : : : " 41" " _ " ""a _ : ::: =: :::: :; f 2 4 6 X/A 8 1
M f r< / / / / / / t "C:j { +J < ( en % Q C2 tzl [ssnvd] La 21
M r:q / Cd " em S +J U rn Et Z (/) u t::_ () = M U "1"""1 * " t 1 1::_ ;t " : : " " ilḷ l " a t " " " t " t " f t t : : ::f: " 1 " t : ) : : lit " a l : tt _ 11 ezl:" :: # t «" t : 11 t : ;t fl " t t lit <X) c q N via 4f t CX) CO q N < >< 22
Prfiles f Btridal fr aa=1 BTORODAL VS X rfl rfl C L 8 1 5 / /1 4 J _ r / / / / / " " ; / / / / / / / / "" " " 2 4 6 X/A SOLD: Y/A=5 DASH: Y/A=O3 DOTDASH: Y/A=O16 8 1
c n $ t+4 M cd " 1 lfj &J Z en $/ = U W t:: () :;:1 i _ " ::::: : : : " " 1: : l : : t : ::l;):: t " " : :"" : : : " t t eta " : " " " " "! tj f " " " " ttl " " "! : : " " " " " : :::: : : : 11 : l J #: ;: t t" : " : " " : " t _ " " : : : : : " J! :! E : : " ::: : : : : " " _ t " t _ " " t : : h 1 " t at f " 1 t! t " " " " " " " : " i " t " " " : :a 2!! t : i : : t : " " " ::: :: l " : : : " : t c C1 via 24 t c C1
STTM}1ARY OF THEORETCAL WORK Frm ur 2n analytic s lutin f VxB=AB in a rectangular dmain with enclsed current sutces we have btained magnetic prfiles and flux plts characterizing cnstant A frcefree magnetic states in a Tkapleike gemetry The magnetic prfiles measured experimentally in Tkaple differ substantially frm the predicted prfiles which implies that if the plasma is frcefree A cannt be cnstant n fact the experimentally determined prfile shws A is nt cnstant