Resistive Wall Mode Studies in a Reversed Field Pinch with Rotating Helical Field

Transcription

1 J. Plasma FusirL Res. SERIES, Vl. 5 (22) Resistive Wall Mde Studies in a Reversed Field Pinch with Rtating Helical Field MASAMUNE Sada and IIDA Mtmi Kyt Institute f Technlgy, Matsugasaki, Kyt , Japan (Received: 12 December 2OOl I Accepted: 2 May 22) Abstract In standard RFP plasmas in STE-2, the magnetic fluctuatins are dminated by cre resnant tearing mdes which grw with the time scale f the resistive wall, and these mdes are identified as the resistive wall tearing mdes. The grwth f these mdes are shwn t be suppressed by the resnant rtating; helical field (RHF). The respnse f m=l mdes t the RHF has been studied in detail. In RFP plasmas, the RHF has the effect n the rtatin f neighbring mdes as well as f the resnant mde. In ULQ plasmas, where there is n m= resnant surface, nly the resnant mde tends t be influenced by the extr:rnal resnant perturbatin. The imprtance f the ra= mde in the mde cupling prcess is discussed. Keywrds: reversed field pinch, tearing mde, rtating helical field, mde cntrl, external kink mdes 1. Intrductin The rever;ed field pinch is characterized by lw-, (safety factr), high shear magnetic cnfiguratin, and believed t be drninated by anmalus transprt due t strng fluctuatins. Cntrl f the MHD mde dynamics is therefre essential t imprving the RFP experiments as a part f the, fusin research prgrams. The magnetic fluctuatins dtie t tearing mdes can be suppressed by current prfile mdificatin, the imprved cnfinement mdes being rcalized in large RFPs surrunded by an ideal cnducting wall [1]. As in tk.amaks, the resistive wall mdes (bth tearing and idcal kink mdes) are thught t be serius prblems in ftlture RFPs. Theries have predicted that the grwth f tearing mdes r their saturatin amplitudes can be reduced by mderate tridal rtatin f the plasnra clumn [2]. On the ther hand, stabilizatin c,f the external kink mdes require sub Alfv6nic rtatln speed which is much faster than the natural rtatin speed f the tearing mdes [3]. Thus, C r r e s p ndin g' aut h r' s e - mai I : mas amun dj. kit. ac.j p develpment f the techniques fr mde rtatin dnve rs ne f the urgent issues in the RFP research. We have prpsed the use f resnant rtating helical field (RHF) fr the mde r plasma rtatin drive [6]. The internally resnant RHF, applied frm utside f the resistive wall, may be able t prvide accelerating trque t the magnetic island, and eventually drive tridal rtatin f the plasma clumn, if the phase f perturbatin field is adequately cntrlled. In this paper, we describe the recent results n resistive wall mde studies frm Separatrix Test Experiment-2 (STE-2) with external helical fields. 2. Experiments The STE-2 [-6] (Rla =. rn/.1 m, 1 ( 6 ka), pulse length c6 < 1 ms) has been perated nly with a SS vacuum vessel (field penetratin time z* <.15 ms) t test the idea f driving tearing mde and/r plasma rtatin by using internally resnant RHF. In by The Japan Sciety f Plasma Science and Nuclear Fusin Research 59

2 Masamune S. et al., Resistive Wall Mde Studies in a Reversed Field Pinch with Rtating Helical Field fllws, m(n) and M(A) stand fr the plidal (tridal) mde numbers f the inherent mde and external field, respectively. Tw pairs f the helical cils cver the whle trus, prducing a rather sharp tridal mde spectrum f the external field; The amplitudes f the neighbring MIN=117,9 cmpnents are abut l V f the main MIN=\/8 cmpnent, while the rest is less than that. A pulsed scillatr prvides triangular shaped rthgnal scillating currents with variable frequency frm 1-2 khz. The perturbatin level is defined p-ll Beu, where lb,"l is the perturbatin amplitude and Bsu, the edge plidal field. The edge magnetic fluctuatins E,uwere measured with a tridal anay f sine/csine cils attached nt the uter surface f the vacuum vessel cvering ver half f the trus. 3. Results and Discussin 3.1 Suppressin f magnetic fluctuatin with RHF In STE-2 discharges withut a cnducting shell, the plasma current 1 is arund 6 ka with discharge duratin z f abut.7 ms. The discharge characteristics f the STE-2 tgether with the time behavir f magnetic fluctuatins have been described elsewhere [5,6]. Figure I shws the tridal mde spectrum f the m=l magnetic fluctuatins. Immediately after attaining the RFP cnfiguratin at abut t =.25 ms, the magnetic fluctuatins grw with the time scale f?*. The fluctuatin pwer distributes mainly amng the mdes with n>6. The mde with maximum amplitude changes frm sht t sht within the range f n frm 7-9. The fluctuatins remain almst nnrtating (i.e., lcked t the wall), r smetimes rtate very slwly in the directin f plasma current (c-directin). The measurement f radial prfile f the magnetic field has shwn that the mln=ll8 mde is the tearing mde whse resnant surface is lcated at rla-o.. Figure 2 shws the time evlutin f the amplitudes f these mdes tgether with the plasma current wavefrm withut the RHF. The amplitudes f the mdes cntinue t grw after setting up the RFP cnfiguratin with the time scale f t*. We shuld nte ur previus bservatin that in RFP plasmas with cnducting shell, the fluctuatin amplitude did nt cntinue t grw but rather remained almst cnstant during the discharge with lwer level than withut the cnducting shell [5]. Cmparing these different behavirs f magnetic fluctuatins, we may cnclude that these mdes are resistive wall tearing mdes whse saturatin amplitudes are enhanced by the resistive wall effect. When the RHF is applied at.3 ms with relative amplitude f.5 V, the time evlutin f the amplitudes f dminant mdes changes as shwn in Fig. 3. The grwth f the mdes is suppressed transiently fr.2-? 6 6l f 2l L. (ms) wr helbal lp- i=7 Fig. 2 Time behavir l the mlrcltt-9 mde amplitudes withut RHF.. a.3 g,i Fig. 1 Tridal mde spectrum. N 6 9 G 6f l 2l el. RHF t(ms) n= n{ Fig. 3 Time behavir l the mlrrllt-9 mde amplitudes with RHF. 51

3 Masamune S. et al., Resistive Wall Mde Studies in a Reversed Field Pinch with Rtating Helical Field.3ms, and, mrever, the amplitudes are reduced fr the rest f the discharge. Ensemble average ver several tens f shts has revealed that the amplitudes are reduced by 2t)-3 V at.5 ms (current peak). N significant influence n the lp vltage r discharge duratin has been bserved yet; It appears that careful ptimizatin ti the frequency and amplitude is required fr favrable effect n the RFP discharee. 3.2 Mde cupling studies The time behavir f the tridal phases f the ml n=tl6-ll mdes shws that the cre resnant (r internally nnresnant) mln=ll<8 mdes are almst lcked t the vessel. In bth cases, the higher mdes (z>9) tend t rtate in the ppsite directin t plasma current (ctr-directin) with a phase velcity f abut 5x132 rad/s. When the c-rhf is applied frm the start f discharge t RFP plasmas, as shwn in Fig., the ml n=1/8 mde is accelerated in the same directin (the phase increases with time). Mrever, the n=7 mde is als accelerated in the same directin. On the cntrary, mln=ll9 mde. which therwise rtate in the ctrdirectin, is lcked t the vessel, and the phase velcity f the mln=lll mde is decreased. That is, the lwer (n<8) mdes are accelerated, while the higher mdes are decelerated; It is evident that the effect f c-rhf can be bserved nt nly n the rtatin f resnant mde but als fr the neighbring mdes. We may nte that the rtatin velcity (phase velcity) is much lwer than the phase velcity f the applied RHF. The effect n the neighbring mdes are als bserved fr the ctr-rhf, as shwn in Fig. 5. In this case, the m=ll resnant mde rtates in the ctrdirectin: The resnant mde is accelerated in the same directin as the RHF. The neighbrirtg n=7 mde shws the similar trend. The higher mdes tend t rtate in the ppsite directin t the applied ctr-rhf; They tend t rtate in the c-directin in this case. A thery [7] predicts that the electrmagnetic trque Z1M acting n a magnetic island arises as a result f interactin between the magnetic fluctuatin f the mde -61 and nnlinearly prduced perturbatin culrent J"ilt n that mde ratinal surface. If we apply this idea, the trque n m=l/ mde can be written dwn as fllws, z,nt- '! 7-rt.ar rr.8t -.L,t. v I m.n t.lm -t., - gr 8(t.st Bt-.r B s 1^ - t. n - It tm,n t, sin[q-,,r - r,r, - 6<--r.,-u) (1) where C is the cupling cefficient. 8, are the magnetic fluctuatin amplitudes and 6, are the phases f the crrespnding mdes. The electrmagnetic trque n ther mdes can be expressed in a similar frm. Althugh we need simultaneus measurements f the m=l and m=o n=6 tt n=7 tt Pn -fi fi r-a!t rr-e E i',t ee n n= Fig. Tridal phase f m=1 mdes in RFP when c- RHF was applied frm the start f discharge. Fig.5 Tridal phase f m=1 mdes in RFP when ctr- RHF was applied frm the start f discharge. 511

4 Masamune S. et al., Resistive Wall Mde Studies in a Reversed Field Pinch with Rtatine Helical Field mde behavir t estimate the nnlinear electrmagnetic trque, the relatin shws the imprtance f the m=1 n=l mde. Here we will shw the imprtance f the m= mde ratinal surface (i.e., field reversal surface) fr the respnse f m=l mdes t the resnant helical perturbatin. The ultra-lw-q (ULQ) plasmas are prduced in STE-2 with the edge safety factr u f abut. 1 [6]. In ULQ plasmas in the STE-2, the dminant magnetic fluctuatin mde shifts t mln=116, (a) fr -tr t tr $ e -tl L Pfi E le a 6 att = fi 1l l n=6 n=7 n=1 Fig.6 (a): Tridal phase f the mln=1/6-1 mdes in ULO plasma withut helical parturbatin. (b): Tridal phase f the mln=1/6-1 mdes in ULO plasma with static helical parturbatin applied st.2ms. and m=l/ mde still has a nnnegligible amplitude. These mdes usually rtate in the ctr-directin, as shwn in Fig. 6(a). We applied static (nn-rtating) Ml N=l/8 resnant helical perturbatin t ULQ plasmas t see the m=i mde respnse. The static perturbatin was applied at t =.2 ms, with rise time f.5 msec and decay time f.5 ms. N significant influence has been bserved n the glbal parameters f the ULQ plasma. Figure 6(b) shws the time behavir f tridal phases f the mln=i/6-1 mdes with static helical field. As is evident, nly the m=ll resnant mde has a trend t be lcked (the phase remains cnstant with time) slightly after the helical field is applied. That is, in ULQ plasmas, where there is n m= mre ratinal surface, nly the resnant mde is influenced by the helical perturbatin. Thus, the imprtance f the zr= mde in the mde cupling prcess has been indirectly demnstrated by cmparing the different respnse f the n=1 mde(s) t external resnant helical perturbatins in RFP and ULQ plasmas. Imprvement f the magnetic diagnstics is in the prcess fr the simultaneus measurement f m= and m=1 mdes t estimate the electrmagnetic trque n the basis f eq. (1).. Summary In STE-2, when perated nly with a vacuum vessel, cre resnant tearing mdes are bserved t grw with the time scale f field penetratin time f the vessel, and these mdes are identified as the resistive wall tearing mdes. Resnant rtating helical field has been applied t cntrl the dynamics f these mdes. The grwth f the amplitudes f these mdes is shwn t be suppressed with the RHF. The effect f the RHF n mde rtatin is bserved nt nly fr the resnant mde but als fr the neighbring mdes, indicating the imprtance f cupling f m=l mdes. The rle f m= mde is studied by applying static (nn-rtating) helical perturbatin t ULQ plasmas, which have n m= mde resnant surface. In ULQ plasmas, nly the resnant m=l mde is affected by the perturbatin. These results suggest the imprtance f nnlinear cupling f the m=l mdes thrugh la= (and prbably n=l) mde. Detailed simultaneus measurements f the dynamics f m=l and z= mdes are in prgress. The effect f RHF n glbal discharge parameters has nt becme clear yet In STE-2, the resistance decreases with an increase in the plasma current irrespective f the RHF. N significant imprvement f 5t2

5 Masamune S. et al., Resistive Wall Mde Studies in a Reversed Field Pinch with Rtatins Helical Field the current dependence f discharge resistance has been made clear yet. Hwever, it might be nted that the plasma current tends t increase with the RHF. It appears that careful ptimizatin f bth the frequency (rtatin speed) and amplitude f the RHF is required. A linear stability analysis f the external kink mdes has shwn that m/n=ll mdes can be unstable in the STE-2 depending upn the current prfile [8]. We have shwn that the external helical current f several V f the tridal plasma current has a stabilizing efft:ct n these kink mdes. We lk fr the pssibility f sustaining a steady state with reduced amplitude f the external kink mdes by using externally nmesnant rtating helical field (M/N=l/). References tll S.C. Prager, Plasma Phys. Cntrl. Fusin 1, Al29 (1999). I2l T.C. Hender er a/., Nucl. Fusin 29, 1279 (1989). t3l S.C. Gt et a/., Phys. Plasmas 6, 3868 (1999). [] S. Masamtne et al., Plasma Phys. Cntrl. Fusin, r27 (1998). [5] S. Masamtne et al., Fusin Energy 1998 (IAEA, Vienna) 3,919 (1999). [6] S. Masamune et al., lsth IAEA Fusin Energy Cnf., IAEA-CN-77/EXP3/1 1 (2). t7l C.C. Hegna, Phys. Plasmas 3,67 (1996). [8] S. Masamwe et al., J. Phys. Sc. Jpn. 68, 216l (1999). 513