Magnetic topology effects on Alcator C-Mod scrapeoff layer flow

Transcription

1 PSFC/JA Magetic topology effects o Alcator C-Mod scrapeoff layer flow Simakov, A.N.*, Catto, P.J, LaBombard, B. ad Glasser, A.H.* May 2008 *Los Alamos Natioal Laboratory, Los Alamos Plasma Sciece ad Fusio Ceter Massachusetts Istitute of Techology Cambridge MA USA This work was supported by the U.S. Departmet of Eergy, Grat No. DE-FG02-91ER Reproductio, traslatio, publicatio, use ad disposal, i whole or i part, by or for the Uited States govermet is permitted. Submitted for publicatio i Plasma Physics ad Cotrol. Fusio (May 2008)

2 Magetic topology effects o Alcator C-Mod scrape-off layer flow Adrei N. Simakov Los Alamos Natioal Laboratory, Los Alamos, New Mexico 87545, USA Peter J. Catto ad B. LaBombard MIT Plasma Sciece ad Fusio Ceter, Cambridge, Massachusetts 02139, USA Ala H. Glasser Los Alamos Natioal Laboratory, Los Alamos, New Mexico 87545, USA (May 1, 2008) Abstract Recet iterest i the experimetal study of tokamak plasma flow for differet magetic field geometries calls for theoretical uderstadig of the effects of tokamak magetic topology chages o the flow. The cosequeces of total magetic field reversal ad/or X-poit reversal o divergece-free plasma flow withi magetic flux surfaces is cosidered ad the results are applied to iterpret recet Alcator C-Mod scrape-off layer (SOL) flow measuremets. 1

3 I. Itroductio Plasma flow i a tokamak ca be beeficial i may ways ad is therefore importat to uderstad. Strog plasma rotatio ca stabilize resistive wall modes 1 ; ad sheared plasma flow ca ehace global plasma stability ad icrease the achievable ratio of plasma kietic pressure to magetic pressure by ifluecig mode couplig. I particular, sheared flow ca icrease the threshold for triggerig eoclassical tearig modes. 2 Sheared flow is also kow to ehace particle ad heat cofiemet by suppressig ad regulatig turbulet trasport. 3 I additio, plasma flow i a tokamak scrape-off layer (SOL) is believed to affect SOL trasport of eutrals ad impurities 4 as well as the ivetory of tritium ad products of fusio reactios, ifluece material migratio, 5 ad set boudary coditios for the tokamak core plasma rotatio. 6 I the last few years measuremets of the compoet of the SOL flow parallel to the magetic field have bee made i a umber of tokamaks throughout the world, icludig Alcator C-Mod, 6 JT-60U, 7 JET, 8 TCV, 9 ad Tore Supra. 10 The parallel flow was measured usig Mach probes situated at differet poloidal locatios, so that poloidal variatio of the flow could be studied, for differet magetic field topologies. I particular, for diverted tokamaks, measuremets were made for lower sigle ull (LSN), upper sigle ull (USN), ad double ull (DN) operatio. I additio, measuremets were made for both possible directios of toroidal magetic field ad plasma curret (which are usually kept co-directed to preserve magetic field helicity). The measured flow is foud to be strog, especially at the ier (high field side) far SOL where it may possibly reach Mach umbers of order uity. Moreover, the SOL flow ca have strog poloidal variatio. For diverted discharges, the ier SOL flow 2

4 has a tedecy to remai directed towards a ier divertor, reversig directio for X-poit reversal, but idepedet of the total magetic field directio. Meawhile, the outer (low field side) SOL flow teds to be co-curret ad to reverse for total magetic field reversal, idepedet of the X-poit positio. The basic uderstadig that emerges from these measuremets is that the SOL flow has two compoets: a up-dow symmetric compoet, which is isesitive to the LSN/USN/DN topology, but cares about the directio of the total magetic field; ad a up-dow asymmetric compoet, which respods primarily to the LSN/USN/DN magetic field topology. The symmetric compoet is ormally assumed to be associated with the early divergece-free ature of plasma flow withi a magetic flux surface, which requires parallel io flow to close io diamagetic ad E B flows. The asymmetric compoet is assumed to be coected with the strogly poloidally asymmetric ballooig ature of radial plasma trasport, which results i a local icrease i plasma pressure o ope field lies about the outer midplae with a correspodig parallel plasma flow directed from the outer midplae toward both ier ad outer divertors. Although certai aspects of this basic uderstadig have bee cofirmed by umerical modelig results, see e.g., 11,12 some detailed questios about the SOL flow remai uaswered. I particular, 11 did ot ivestigate the effects of magetic topology chages ad eglected particle drift effects; ad 12 did ot cosider X-poit reversal ad eglected heat flux cotributios to the gyroviscosity as well as the perpedicular viscosity, thereby obtaiig a questioable radial electric field. The work preseted here uses a simple model 13 of divergece-free plasma flow withi a magetic flux surface, havig symmetric ad asymmetric compoets. It predicts plasma flow chages resultig from X-poit reversal ad/or total magetic 3

5 field reversal (Sec. II) ad iterprets recet Alcator C-Mod SOL flow measuremets (Sec. III). Our fidigs are summarized ad coclusios are preseted i Sec. IV. II. Flow symmetries for X-poit ad/or B field reversal Divergece-free plasma flow i a axisymmetric tokamak is geerally a excellet approximatio withi the magetic flux surfaces that reside iside the separatrix. O the ope field lies outside the separatrix, however, plasma flow ca exhibit a strog divergece, particularly i regios where ioizatio ad/or cross-field trasport is balaced by parallel flows to the divertor surfaces. I additio, i may tokamaks, a pheomeo of mai-chamber recyclig takes place i which radial plasma fluxes oto wall surfaces are balaced by recyclig ad associated ioizatio sources. Yet i this case, large-scale flow withi the flux surfaces is ot sigificatly affected sice material flux that is covected radially to the wall must be balaced by local ioizatio sources. I view of this picture, we expect the strog, large-scale plasma flows that are observed i the tokamak edge, which are far removed from divertor surfaces ad which coect from outer to ier midplaes i sigle-ull discharges, to be well approximated by a divergece-free flow field, V = ωr 2 ζ + K(ψ) B, (1) where ω is a toroidal rotatio frequecy, R is the cylidrical radial coordiate, ζ is the toroidal agle variable, K(ψ) is a fuctio of the poloidal magetic flux coordiate ψ, is plasma desity, ad the tokamak magetic field is take i the form B = I(ψ) ζ + ζ ψ. I double-ull cofiguratios, SOL flux tubes do ot coect outer ad ier midplaes. Nevertheless, expressio (1) is valid for such cofiguratios iside the separatrix ad by cotiuity we expect it to approximately 4

6 hold just outside the separatrix as well. Based o these argumets, we will assume that (1) approximately holds for ear-sol flows i both sigle ad double-ull cases ad use it to study whether we ca simply explai the observed tokamak flow symmetries related to X-poit ad/or the total magetic field reversal. It will be apparet shortly that our simple model based o (1) describes Alcator C-Mod flow-symmetry observatios very well, thereby justifyig a posteriori our use of (1) to explore the pheomeo. We allow the flow i (1) to have both symmetric (s) (i.e. idepedet of the X-poit positio) ad asymmetric (a) (i.e. depedet o the X-poit positio) cotributios ad briefly summarize the relevat tokamak flow symmetries, amely those related to X-poit ad/or the total magetic field reversal, as obtaied i. 13 By defiitio, the flow i a up-dow symmetric DN cofiguratio has oly a symmetric cotributio that we write as V D = ω s R 2 ζ + K s(ψ) B. (2) The flow i the LSN ad USN cofiguratios has both symmetric ad asymmetric cotributios ad ca be writte for cross-sectios of the same shape as V L = (ω s + ω a )R 2 ζ + K s(ψ) + K a (ψ) B (3) ad V U = (ω s ω a )R 2 ζ + K s(ψ) K a (ψ) B, (4) respectively. Clearly, X-poit reversal reverses the sig of the asymmetric flow portio, leavig the symmetric portio uchaged. Reversig (R) the total magetic field, B R = B, i a DN cofiguratio is equivalet to simply turig the up-dow symmetric tokamak over, thereby reversig 5

7 the etire flow to obtai V R D = ω s R 2 ζ + K s(ψ) B R = ω s R 2 ζ K s(ψ) B. (5) However, turig a up-dow asymmetric tokamak over reverses ot oly the total magetic field but also the X-poit. Therefore, to oly reverse the total magetic field i a up-dow asymmetric tokamak we have to both reverse the X-poit (reversig the asymmetric flow portio) ad tur the tokamak over (reversig the total flow), thereby reversig the symmetric flow portio to fid V R L = (ω s ω a )R 2 ζ K s(ψ) K a (ψ) B, (6) V R U = (ω s + ω a )R 2 ζ K s(ψ) + K a (ψ) B. Flow symmetry properties (2) (6) associated with X-poit ad total B reversals are clearly idepedet of the exact expressios for ω s, ω a, K s, ad K a. The flux fuctios K s ad K a ca be obtaied from eoclassical theory o closed flux surfaces (i.e. iside the separatrix) for differet collisioality regimes, 14,15 but are otherwise uavailable. Expressios for ω s ad ω a ca be easily obtaied for all collisioality regimes from the io equatio of motio for both closed ad ope flux surfaces without ivokig eoclassical theory assumptios (except for axisymmetry) to fid ( ϕ ω s = c ψ + 1 ) p i, ω a = c ϕ s e ψ ψ, (7) a where c is the speed of light, e is the magitude of electro charge, ϕ is electrostatic potetial, ad p i is the io pressure. I (7) ω a does ot cotai the pressure gradiet term sice for matched discharges the desity ad io temperature profiles are lowest order flux fuctios ad therefore, by defiitio have to be the same i LSN ad USN ad for reversed B operatio. Cosequetly, oly the electric field term i ω ca have a asymmetric cotributio. 6

8 III. Aalysis of Alcator C-Mod SOL flow measuremets A. Flow symmetries Recet Alcator C-Mod SOL parallel flow measuremets were performed for LSN ad USN discharges with ormal ad reversed B (io grad-b drift towards the lower ad the upper divertors, respectively) for closely matched plasma poloidal crosssectios with the same lie-average desity, as well as other discharge parameters. A few DN flow results for ormal ad reversed B are also available. Flow measuremets were performed with scaig Mach probes situated 5.8 cm below the plasma midplae o the high field side ad 11 cm above the plasma midplae o the low field side, so that parallel flow at these two differet positios is available for a umber of SOL flux surfaces. Typical error bars, based o the shot-to-shot variatio i the parallel flow measuremets, are i the rage of ±10 km/s for the high-field side SOL flow measuremets ad ±5 km/s for the low-field side SOL flow measuremets. Desities ad electro temperatures are also deduced from the probe measuremets. The diagostics, probe desig, as well as the data aalysis procedure are described i detail i. 6 Due to iaccuracies i the probe geometry, desity measuremets o the high-field side may be systematically high or low by ±50%. Otherwise, typical desity ad temperature measuremets error bars are i the rage of ±10%. To determie the four ukows ω s, ω a, K s, ad K a from (3), (4), ad (6) oly measuremets for two magetic topologies eed be employed, assumig ω s ad ω a are approximate flux fuctios. The measured desity (ad electro temperature) profiles support the lowest order flux fuctio approximatio. It ca be see from Fig. 1 that for LSN ad USN cases electro desity varies by at most a factor of two or less betwee locatios of the low ad high field side probes (i.e. over a legth 7

9 qr 3.4 m). At the same time, it varies by a factor of two i the radial directio over a distace of oly about 4 mm, so the radial variatio is about 850 times faster tha the parallel variatio. Therefore, for may practical purposes (icludig our simple lowest order theory) the flux fuctio approximatio should be excellet. Cosequetly, the symmetric ad asymmetric portios of ω ad K ca be evaluated usig (3), (4), ad (6) i four differet ways from the followig measuremets: (i) V L ad V U, (ii) V L R ad V U R, (iii) V L ad V L R, ad (iv) V U ad V U R. As a qualitative check, ω s ad K s ca be also evaluated usig (2) ad (5) from V D ad V R D (this check would be quatitative if the flux surfaces of DN discharges were better matched to be the oes recovered whe field asymmetry is removed). Close matchig of the radial profiles of ω s, ω a, K s, ad K a obtaied i the four differet ways would cofirm the correctess of our uderstadig of the flow respose to X-poit ad/or B reversals i the absece of ay complicatios. Before begiig our aalysis of the flow data we check the symmetry properties of the Alcator C-Mod flow measuremets. If the vacuum chamber ad the fuellig were up-dow symmetric, discharge parameters were ideally matched (icludig radial profiles), ad measuremets were i the midplae, the the radial profiles of V L ad V R U, ad of V U ad V L R, would be idetical sice these two cases would the correspod to turig over Alcator C-Mod. Figure 2 shows the compariso of these quatities o the low ad high field sides. The quatity ρ measures the distace from the separatrix ito the SOL projected alog flux surfaces oto the outer midplae. Except for the high field side V U ad V R L data, the measured parallel flows do ot possess the desired symmetry, ad the high field side data for V R U is possibly questioable. The lack of symmetry i the parallel flow may be due to the differet geometries of the upper ad lower divertors ad other vacuum vessel asymmetries i 8

10 Alcator C-Mod, up-dow asymmetries i fuellig ad i the Mach probe locatios, ad iadequate matchig of the discharges. Cosequetly, we aticipate less tha ideal results. Usig the plasma SOL flow ad desity data as well as our kowledge of magetic field geometry (from EFIT equilibrium recostructio data) for each shot we ca employ (2) (6) to evaluate ω s ad K s five differet ways (icludig the DN shots) ad ω a ad K a four differet ways. The results are show i Fig. 3. Normalizatio costats are chose as follows: B 0 = 4.1 T, I 0 = 3.5 T m, ad 0 = cm 3. Solid lies represet quatities obtaied from V L ad V U, dashed-dotted lies are from V R L ad V R U, dotted are from V L ad V R L, dashed are from V U ad V R U, ad dashed-dotted-dotted are from V D. If our simple picture of the flow symmetries, as give by (2) (6), were correct ad all the parameters for differet magetic field geometry discharges were ideally matched, all the curves for ω s, ω a, K s, ad K a would be idetical. Clearly, there is a complicatio. The mai reaso is, that eve though the lie itegrated desities are matched for all the discharges, the SOL radial desity profiles are quite differet (they differ by factors of two to three) ad so the discharges are ot ideal matches. Figure 1 illustrates this poit by comparig high ad low field side desity profiles for the discharges of Fig. 2. Show are desity profiles for the LSN cofiguratio with ormal ad reversed B, L ad R L, respectively; the USN cofiguratio with ormal ad reversed B, U ad R U, respectively; ad the DN cofiguratio with ormal B, D. We expect K(ψ) θ sice whe multiplied by B it represets io flux, with θ the flux surface averaged desity. Therefore, K(ψ) is sesitive to differig desity profiles, whereas K(ψ)/ is ot. Assumig that θ we ca approximately 9

11 replace K s,a (ψ)/ with u s,a (ψ) = K s,a (ψ)/ θ i (2) (6) ad thereby avoid most of the difficulty with umatched desity profiles. The experimetal justificatio for us to adjust the local desity profiles to coform to a flux-surface average oe comes from the clear isesitivity of the measured flow profiles to variatio i plasma desity. Figure 7 from 6 shows what happes to the SOL flows as the lie-averaged desity is chaged. Withi error bars, the high-field side flows are essetially uchaged for a factor of 2 variatio i lie-averaged desity. Therefore, we have good reaso to believe that if we could have obtaied a set of discharges with precisely matched SOL desity profiles, the resultig flow profiles would ot be ay differet (withi error bars) from those that employed the flux surface averaged desity profile rather tha the local oe. Also, replacig the questioable data for V R U o the high field side with its couterpart V L [recall Fig. 2 (b)] ad evaluatig ω s, ω a, u s, ad u a we obtai rather remarkably improved agreemet amog differet curves, as show i Fig. 4. The impressive agreemet (excludig the DN curves sice they are oly for qualitatively matched flux surfaces) idicates that our model of the flow symmetries with respect to X-poit ad B reversals is quite good. Some of the remaiig differeces betwee the curves is presumably caused by up-dow asymmetries of the vacuum vessel, fuelig ad probe locatio, ad/or poloidal desity variatio. B. Radial electric field Employig the ω s (ρ) ad ω a (ρ) profiles show i Fig. 4 ad usig (7) we should i priciple be able to evaluate the symmetric ad asymmetric portios of the radial electric field ad cosequetly the full radial electric field for all the differet magetic field topology cofiguratios discussed, provided the io pressure ad desity profiles 10

12 are kow (the latter is measured by the probe). This turs out to be o-trivial sice (i) the measured profiles of the io temperature, T i (ρ), are uavailable; ad (ii) the pressure ad desity profiles for the discharges with the differet magetic field topologies are ot precisely matched. To overcome these difficulties we (i) assume T i = T e (with the electro temperature, T e, beig measured); ad (ii) use expressios V = ω(ψ)r 2 ζ +K(ψ)B/, V R = ω(ψ)r 2 ζ K(ψ)B/, ad ω(ψ) = c( ρ/ ψ)[e r (e) 1 ( p i / ρ)] together with the high ad low field side measuremets of the parallel flow velocities ad ad T e profiles for each magetic field cofiguratio (i.e. without splittig quatities ito symmetric ad asymmetric). We first evaluate ω ad the E r ( ϕ/ ρ) idividually for each case, where [ ] V E r = cm 10 {[cm 3 ] T e [ev]} [cm 3 ] ( ωi0 B 0 ) [ km s ] ( ) ψ [T m] (8) ρ is ot a flux fuctio because of ψ/ ρ. For the discharges uder cosideratio ψ/ ρ 0.57 T m for the low field side ad 0.45 T m for the high field side, respectively. The results are show i Fig. 5. I particular, Figs. 5 (a) ad (b) preset the low field side ad high field side E r for the LSN discharge with ormal B (solid lies) ad USN discharge with reversed B (dashed lies), respectively; while Figs. 5 (c) ad (d) preset the low field side ad high field side E r for the USN discharge with ormal B (solid lies) ad LSN discharge with reversed B (dashed lies), respectively. While the solid ad the dashed lies are relatively well matched, as expected from the symmetry cosideratios, they are ot i agreemet with the experimetally deduced values E r 40 V/cm i the far SOL for all the magetic field topology cofiguratios cosidered (see Fig. 11 of 6 ). Although the Mach ad E r probe mea- 11

13 suremets have their ow difficulties (see e.g. discussio i Sec of 6 ), the large discrepacies betwee these measuremets ad our results show i Fig. 5 suggest other uderlyig causes. Oe of these may be that the assumptio T i T e is ivalid i the SOL (as is the case i the tokamak pedestal regio 16,17 ) ad the procedure for evaluatig E r described herei ca oly be reliable ad useful whe accurate T i (ρ) profiles are available. The sesitivity of E r to T i arises ot just because of the ormalizatio of the flow to the soud speed. The more importat effects are the tedecy of the symmetric ad asymmetric cotributios i ω ad u to cacel for ormal LSN ad reversed USN, ad the tedecy of the total ω ad K = u θ cotributios to the flow to cacel for ormal USN ad reversed LSN. Hece small errors i these derived quatities lead to large errors i the iferred values of E r. IV. Coclusios A simple theory for plasma flow modificatios due to the X-poit reversal ad the total magetic field reversal is discussed ad used to iterpret Alcator C-Mod SOL flow measuremets. The theory employed is rather basic ad summarized by (2) (6). Accordig to these expressios, X-poit reversal is expected to cause reversal of the asymmetric flow portio, while B reversal is expected to result i reversal of the symmetric flow portio. We demostrate that these expressios are all that is required to aalyze recet high ad low field side Mach probe SOL flow measuremets i the Alcator C-Mod tokamak for LSN, USN, ad DN magetic field cofiguratios with ormal ad reversed magetic field (io grad-b drift towards the lower ad the upper divertors, respectively). Equatios (3), (4), ad (6) are used to evaluate the symmetric ad asymmetric 12

14 portios of ω ad K i four differet ways by usig the iboard ad outboard probe measuremets for the followig cases: (i) V L ad V U, (ii) V R L ad V R U, (iii) V L ad V R L, ad (iv) V U ad V R U. Also, ω s ad K s are evaluated from V D by usig (2). If the theory were rigorously correct ad the discharges were ideally matched the all the curves for ω s,a ad K s,a would be the same. However, the raw agreemet is oly suggestive as ca be see from Fig 3. To improve the agreemet we must accout for the order uity differeces i the radial desity profiles (see Fig. 1), sice the data was take by matchig oly the lie average desity. If the desity is assumed to be a approximate flux fuctio ad K(ψ)/ is replaced with u(ψ) i (2) (6) the the agreemet betwee the curves improves dramatically (see Fig. 4), idicatig that our model of the flow symmetries is rather good. We expect that the agreemet could be further improved by matchig the radial desity ad temperature profiles rather tha the lie-average desity i the discharges with differet magetic topologies. Kowledge of plasma desity ad io temperature profiles allows determiatio of the radial electric field, as show i Fig. 5. The results obtaied by assumig T i = T e (sice the T i profiles are ot available while the T e profiles are) are cosistet with our symmetry cosideratios (e.g. E r for the LSN discharge with ormal B ad USN discharge with reversed B are very similar), but disagree with the far SOL experimetal measuremets, which typically fid E r 40 V/cm. This leads us to believe that the assumptio T i = T e is ivalid, as is the case i the tokamak pedestal regio, ad that the kowledge of accurate T i profiles is essetial for determiig the radial electric field profiles by our procedure. 13

15 V. ACKNOWLEDGEMENT This research was supported by the U.S. Departmet of Eergy grats DE-AC52-06NA at Los Alamos Natioal Laboratory, DE-FG02-91ER ad DE- FC02-99ER at the Plasma Sciece ad Fusio Ceter of the Massachusetts Istitute of Techology. 14

16 Refereces 1 Garofalo A M et al 2002 Phys. Rev. Lett Buttery R J et al th EPS Coferece o Cotr. Fusio ad Plasma Physics (Fuchal, Portugal, 2001) Europea Coferece Abstracts vol 25A ed C Silva, J Pies, ad R Nóbrega (Europea Physical Society) p Burrell K H et al 1992 Plasma Phys. Cotrol. Fusio ad refereces therei 4 Parker R et al 1997 J. Nucl. Mater Pitts R A et al 2005 Plasma Phys. Cotrol. Fusio 47 B303 6 LaBombard B et al 2004 Nucl. Fusio Asakura N et al 2000 Phys. Rev. Lett Erets S K et al 2004 Plasma Phys. Cotrol. Fusio Pitts R A et al 2007 J. Nucl. Mater Gu J P et al 2006 It. Cof. o Research ad Applicatios of Plasmas (Opole- Turawa, Polad, 2005) AIP Coferece Proceedigs vol 812 ed M J Sadowski, M Dudeck, H-J Hartfuss, ad E Pawelec (America Istitute of Physics) p Pigarov A Yu, Krasheiikov S I, ad LaBombard B 2006 Cotrib. Plasma Phys Boi X et al 2005 J. Nucl. Mater Catto P J ad Simakov A N 2006 Phys. Plasmas Catto P J ad Simakov A N 2007 Phys. Plasmas

17 14 Hirshma S P ad Sigmar D J 1981 Nucl. Fusio Hito F L ad Hazeltie R D 1976 Rev. Mod. Phys Maggi C F et al 2007 Nucl. Fusio Kaga G ad Catto P J 2007 Bull. Am. Phys. Soc

18 FIGURE CAPTIONS Figure 1. SOL plasma desity profiles o the (a), (c) low ad (b), (d) high field sides with solid lies for LSN cofiguratio desities L ( ormal B) ad R L ( reversed B), dashed lies for USN cofiguratio desities U ( ormal B) ad R U ( reversed B), ad dotted lies for DN cofiguratio desity D ( ormal B). The ormalizatio factor 0 = cm 3. Due to iaccuracies i the probe geometry, desity measuremets o the high-field side may be systematically high or low by ±50%. Otherwise, typical desity measuremets error bars are i the rage of ±10%. Figure 2. Compariso of Alcator C-Mod data for V L (solid lies) ad V R U (dashed lies) i (a), (b) ad V U (solid lies) ad V R L (dashed lies) i (c), (d) o the low [see (a), (c)] ad high [see (b), (d)] field sides. Error bars are oly preseted for oe curve of each pair to avoid clutterig the figure. The errors are idetical for the other curve. Figure 3. Profiles of ormalized (a) ω s, (b) ω a, (c) K s, ad (d) K a. Solid lies represet quatities obtaied from V L ad V U, dashed-dotted lies are from V R L ad V U R, dotted from V L ad V L R, dashed lies are from V U ad V U R, ad dashed-dotteddotted from V D. Figure 4. Profiles of ormalized (a) ω s, (b) ω a, (c) u s, ad (d) u a usig the same labelig as i Fig. 3. Figure 5. Low field side (a), (c) ad high field side (b), (d) radial electric field 17

19 profiles evaluated for the LSN discharge with ormal B [(a), (b), solid lies], USN discharge with reversed B [(a), (b), dashed lies], USN discharge with ormal B [(c), (d), solid lies], ad LSN discharge with reversed B [(c), (d), dashed lies]. 18

20 5 4 0 low field side L high field side 3 2 D U R L R U D (a) (b) U D low field side D high field side 3 2 R L U R L (c) (d) Figure 1.

21 V [km/s] low field side V L R 12 V U ρ [mm] V [km/s] high field side R V U V L (a) (b) low field side high field side V [km/s] V [km/s] R -20 V L R V 10 L V 7.5 U V U (c) (d) Figure 2.

22 ω S I 0 [km/s] B ω A I B 0 0 [km/s] (a) (b) K S 0 B 0 [km/s] K A 0 B 0 [km/s] (c) (d) Figure 3.

23 ω S I 0 [km/s] 50 B 0 ω A I B 0 0 [km/s] (a) (b) u S B 0 [km/s] u A B 0 [km/s] (c) (d) Figure 4.

24 E [V/cm] r 50 E [V/cm] r (a) (b) E [V/cm] r E r [V/cm] (c) (d) Figure 5.