RFP BOUNDARY CONDITION STUDIES ON TOKAPOLE II. J.S. Sarff J. c. Sprott L. Turner

Size: px

Start display at page:

Download "RFP BOUNDARY CONDITION STUDIES ON TOKAPOLE II. J.S. Sarff J. c. Sprott L. Turner"

Darrell Stafford
5 years ago
Views:

1 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

2 _ 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

3 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

4 The TOKAPOLE device which we have perated with a frcedreversed trdal magnetic field Primary Windings J: Tridal Field Cils " "1 :t { :; :;"" Turb Mlecular pump

5 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

6 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

7 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

8 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

9 Prfiles f the tridal field taken with a (B) prbe t= bbo Msec 2 t" magnetic 15 D s :a Pt " _ " (( sec ::: :=:= == =::: ::: _ 5 5 r (em) l J 1 15

10 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 " r (em)

11 td :a t:lt ""D «Sfe " " "" ;:: J 1 J_ il " 5 1 r (em) 15

12 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

13 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 " BO 2 = 5 1 r (em) 15

14 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

15 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

16 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)

17 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

18 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

19 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 / / / / / / = " >= / " " ; / X/A SOLO: Y/A=5 DASH: Y/A=3 DOTDASH: Y/A=O16 1

20 Flux cnturs f Btridal in a square axa with f ur enclsed filamentary currents fr the frcefree field parameter aa=o 5 N < >t : " : ::; " : :: :!: : h k " : " " til : " " " it # ; #! t! ; ;! :; ; ; " : : : :1 ;: :: : " : : " " : t " z = :: " "" :: :!! ::!;::: : : " " : w :: ) " :" 1:": " "! ::! : _ " f " ::: : <# _a _ : : : : : : : ; :!!:: " = ; : : 2"" _ ;;:: : : : " 41" " _ " ""a _ : ::: =: :::: :; f X/A 8 1

21 M f r< / / / / / / t "C:j { +J < ( en % Q C2 tzl [ssnvd] La 21

22 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 / / / / / "

23 Prfiles f Btridal fr aa=1 BTORODAL VS X rfl rfl C L / /1 4 J _ r / / / / / " " ; / / / / / / / / "" " " X/A SOLD: Y/A=5 DASH: Y/A=O3 DOTDASH: Y/A=O16 8 1

24 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

25 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

GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin

GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS J.e. Sprtt PLP 924 September 1984 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.