Estimation of Tokamak Plasma Position and Shape in TOKASTAR-2 Using Magnetic Field Measurement )

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1 Estmaton of Toama Plasma Poston and Shape n TOKASTAR-2 Usng Magnetc Feld Measurement ) Kouhe YASUDA, Hde ARIMOTO, Atsush OKAMOTO, Taaa FUJITA, Masato MINOURA, Ryoma YOKOYAMA and Taahro YAMAUCHI Graduate School of Engneerng, Nagoya Unversty, Furo-cho, Chusa-u, Nagoya , Japan (Receved 28 December 2017 / Accepted 7 May 2018) The toama plasma poston and shape were estmated for the frst tme n TOKASTAR-2 based on external magnetc measurement usng flament current approxmaton method. Data of a magnetc probe array and flux loops was used. Effects of the helcal feld on the toama plasma radal poston were nvestgated. The oscllaton of the radal poston and the outer dsplacement of the plasma under the wea vertcal feld were suppressed by the helcal feld. c 2018 The Japan Socety of Plasma Scence and Nuclear Fuson Research Keywords: helcal feld applcaton, TOKASTAR, magnetc measurement, plasma poston and shape DOI: /pfr Introducton Helcal feld s thought to provde mproved postonal stablty and the stablzaton of the plasma poston by applyng the helcal feld to the toama plasma was shown [1, 2]. A toama-stellarator hybrd confnement called TOKASTAR was proposed [3], whch s a compact system wth a low aspect rato (A < 3) and has smple helcal cols. TOKASTAR-2 s a hybrd plasma confnement devce based on TOKASTAR concept [4]. One of the man purposes of TOKASTAR-2 s to study the stablzaton effect of the toama plasma poston by applyng the helcal feld of the smple helcal cols. Fgure 1 shows the col systems of TOKASTAR-2. Toama and stellarator col systems can be operated ndependently or smultaneously. The stellarator col system conssts of two HF (Helcal Feld) cols n parallelogram shape, four AHF (Addtonal Helcal Feld) cols n fan shape and two crcular VF (Vertcal Feld) cols. These cols are connected to DC power supples. The HF cols are located outsde n the radal drecton whle the AHF cols are located on upper and lower sdes. They were desgned so that the magnetc surfaces are generated wthout the plasma current. The toama col system conssts of three-bloc OH (Ohmc Heatng) cols and two PVF (Pulse Vertcal Feld) cols. The PVF cols are used to generate a varyng vertcal feld for the toama equlbrum. Eght TF (Torodal Feld) cols and two SC (Shape Control) cols are commonly used for toama and helcal operatons but SC cols are not used n ths study. The OH cols, the PVF cols and the TF cols are connected to pulsed power supples wth capactor bans. Fgure 2 shows the stablzaton of the toama author s e-mal: yasuda-ohe16@ees.nagoya-u.ac.p ) Ths artcle s based on the presentaton at the 26th Internatonal To Conference (ITC26) Fg. 2 Fg. 1 Col systems of TOKASTAR-2. Stablzaton of the toama plasma poston by applyng the helcal feld. plasma poston by applyng the helcal feld conceptually. The toama equlbrum of TOKASTAR-2 s shown n Fg. 2 (a) whle the helcal vacuum magnetc surface s shown n Fg. 2 (b). The effectve axsymmetrc polodal feld component of the helcal feld s n the same drecton as the polodal feld generated by the plasma current when the rotatonal transform by the helcal feld and that by the plasma current are n the same drecton. Ths effectve c 2018 The Japan Socety of Plasma Scence and Nuclear Fuson Research

2 axsymmetrc polodal feld pushed the plasma column toward the magnetc axs of the helcal feld through Lorenz force and then the stablzaton effect on the plasma poston s expected. The effect of the helcal feld applcaton on the plasma radal poston was observed by an nternal magnetc feld measurement [5] and by a hgh-speed camera [6] n TOKASTAR-2. However, the plasma current and poston were nfluenced by nserton of the magnetc probe n [5]. No precse poston of the plasma was obtaned n [6] snce the camera mage was based on lght ntensty ntegrated along the tangental sght lnes. Moreover, t was dffcult to estmate the toama plasma shape by these two methods. In ths paper, usng an external magnetc feld measurement newly nstalled, the toama poston and shape n TOKASTAR-2 are obtaned wthout nfluence on the plasma. The effect of the helcal feld on the plasma radal poston s nvestgated. 2. Measurng Methods Fgure 3 shows the locaton of magnetc sensors n TOKASTAR-2. A magnetc probe array (MPA) was nstalled n Aprl The 16 sensor cols are located n ceramc rods for protecton from the plasma. The rods are located along the TF cols. All sensor cols on the nner and outer sdes and one sensor col on the upper and lower sdes (CH 5 and 13) measure the vertcal magnetc feld and two sensor cols on the upper and lower sdes (CH 4, 6, 12 and 14) measure the radal magnetc feld. The crcuts of two sensor cols (CH 9 and 12) have become open and the other 14 sensor cols are used. The product of the number of turns N and the effectve col area S, NS, ofthe sensor cols s m 2. The resonant frequency of the sensor cols s 90 Hz, whch s hgh enough for measurement of the TOKASTAR-2 toama plasma whose duraton tme s 0.5 ms. The magnetc feld was obtaned by numercally ntegratng the voltage of the sensor cols. We also used four magnetc flux loops located at R = 0.06 m, Z = ±0.13 m and R = 0.18 m, Z = ±0.10 m. The magnetc flux was also obtaned by numercally ntegratng the voltage of the flux loops. 3. Method of Analyss We used flament current approxmaton method [7] to estmate the toama plasma poston and shape. The toama plasma shape s obtaned from contours of the polodal magnetc flux ψ total = ψ p + ψ vac, (1) where ψ p s magnetc flux generated by the plasma current and ψ vac s that generated by the external cols current and the eddy current. We modeled the plasma current by the sx rng flaments. In TOKASTAR-2, a large eddy current s drven n the vacuum vessel, whch cancels the vertcal feld [8] and hence t s dffcult to obtan ψ vac by calculaton. In ths paper, ψ vac s determned from measured by MPA and the magnetc flux ψ vac,exp measured by flux loops n the shot wthout plasma, where subscrpts ( and ) denote the channel numbers of the sensors. The ψ p s determned by the measured values of the polodal magnetc feld B p,exp and the magnetc flux ψ p,exp generated by the plasma current. We evaluate B p,exp and ψ p,exp by B p,exp = B total,exp B vac,exp, the magnetc feld B vac,exp ψ p,exp = ψ total,exp ψ vac,exp, where B total,exp and ψ total,exp are the sgnal obtaned n the toama dscharge. Contrbuton from the dfference n the PVF cols current and eddy current between the cases wth and wthout the plasma s modeled by addtonal flaments located at the poston of the PVF cols. 3.1 Sngle flament An ntal guess of the plasma poston, whch s needed to locate the sx flaments, s determned by modelng the plasma by a sngle rng flament. The flament current s fxed to the measured value of the plasma current, I p. The resdual sum of squares between the measured value and the calculated value Fg. 3 Measurng nstruments E 1fla = 1 =1 (B p,cal B p,exp ) 2 + a p (ψ p,cal =1 ψ p,exp ) 2, s calculated for a sngle flament located at a grd pont n the RZ plane. The grd spacng s 2 mm both n R- and Z- drectons. The coeffcent a p s fxed to T 2 /Wb 2. B p,cal and ψ p,cal are the calculated values of the polodal magnetc feld and magnetc flux, respectvely. The number of summaton for the frst and second terms, 14 and 4 are the numbers of the feld sensor cols and the flux loops, respectvely. The poston (R 1fla, Z 1fla ) where E 1fla s mnmzed s determned and the sx rng flaments are located around (R 1fla, Z 1fla ). (2)

3 3.2 Sx flaments and addtonal flaments The polodal magnetc feld and flux at sensors generated by unt current n the sx rng flaments and two addtonal flaments are calculated. The followng error E p = 1 (B p,cal =1 B p,exp ) 2 + a p =1 (ψ p,cal ψ p,exp ) b p I 2, (3) =1 s mnmzed where I s flament currents. The thrd term s added to prevent the flament currents from beng large. The coeffcent b p s adusted so that I 1 6 > 0 and I I p I p Smultaneous equatons on I, obtaned from E p / I = 0, are solved. The poston of the current centrod s then obtaned by =1 R centrod = Rf I =1 =1 I, Z centrod = Zf I =1 I, (4) Fg. 4 Contour plot of polodal flux. Red lne s the last closed flux surface and blac dots are sx rng flaments. where (R f, Zf ) s the poston of sx flaments. 3.3 Vacuum magnetc feld We used multpole magnetc feld to calculate ψ vac.by Maxwell equaton, ψ vac satsfes Δ ψ vac = 2 ψ vac R 2 1 ψ vac R R + 2 ψ vac = 0. (5) Z 2 The soluton of Eq. (5) s expanded to multpole feld ncludng dpole, quadrapole, hexapole, octpole and decapole felds wth even and odd modes. The ψ vac s expressed by a lnear combnaton of these felds ψ vac = c 0 + c 1 ψ even d + c 2 ψ odd d +. (6) To determne the coeffcent c l, resdual sum of squares Fg. 5 Comparson between measured values and calculated values of the magnetc feld and flux. In (a), the horzontal axs s the channel number of MPA. In (b), sold lnes denote the calculated values and dotted lnes denote the measured values. E vac = 1 (B vac,cal =1 + a vac B vac,exp ) 2 (ψ vac,cal =1 ψ vac,exp ) 2, (7) s mnmzed. Smultaneous equatons on c l, obtaned from E vac / c l = 0, are solved. The coeffcent a vac s fxed to T 2 /Wb 2. B vac,cal and ψ vac,cal are the calculated values of the vacuum magnetc feld and magnetc flux, respectvely. 4. Results 4.1 Toama plasma shape Fgure 4 shows the contour of the polodal magnetc flux of the toama dscharge at t = 2.8 ms whch s close to the tme of the plasma current pea. The chargng voltages of capactor bans for the PVF cols, the TF cols and the OH cols are V PVF = 0.33 V, V TF = 1.1 V and V OH = 2.0 V. Ntrogen gas was used as worng gas. The toama plasma poston and shape were obtaned for the frst tme n TOKASTAR-2. In ths case, the plasma maor radus R = m, the plasma mnor radus a = m, the aspect rato A = 3.15 and the elongaton κ = Fgure 5 shows comparson between the measured value and the calculated value of (a) the magnetc feld and (b) magnetc flux. The calculated values are consstent wth the measured values. 4.2 Applcaton of the helcal feld To study the effect of the helcal feld, the external helcal feld was appled to the toama plasma. The V PVF was scanned wth constant V TF = 1.1 V and V OH = 2.0 V. The currents of the stellarator col systems were I HF = 2.5 Aturn, I AHF = 2.88 Aturn, I VF = 0.15 Aturn by whch closed magnetc surfaces were generated. Fgure 6 shows tme evoluton of the plasma current I p wth and wthout the helcal feld for several values of V PVF. Fgure 7 shows maxmum of I p as a functon of the vertcal feld at R = 0.12 m at t = 2.8 ms when the PVF

4 Fg. 6 The plasma current (top) wth and (bottom) wthout the helcal feld. Fg. 8 Comparson between the postons of the current centrod wth and wthout the helcal feld. Fg. 7 The maxmum of the plasma current as a functon of the vertcal feld at R = 0.12 m at t = 2.8ms. Fg. 9 The radal poston as a functon of the vertcal feld at I p = 1.0A. cols current becomes maxmum. As shown n Fg. 7, the plasma current becomes 1.9 A around B v = 4mT both wth and wthout the helcal feld. The plasma current was reduced drastcally under the strong vertcal feld (B v < 5 mt) for the case wthout the helcal feld. In contrast, the plasma current was reduced more gradually wth the vertcal feld for the case wth the helcal feld. Fgure 8 shows the tme evoluton of the poston of the current centrod and of the plasma current wth and wthout the helcal feld at V PVF = 0.30 V. The poston of the toama plasma wth the helcal feld was obtaned gnorng the three-dmensonalty of the plasma current dstrbuton. The oscllaton of the radal poston observed n a shot wthout the helcal feld s suppressed by applyng the helcal feld. Fgure 9 shows the radal poston as a functon of the vertcal feld B v (= B PVF +B OH +B eddy )atthe poston of the current centrod for the specfc plasma current (1.0 A). The several data n V PVF scan at V OH = 1.6, 1.7, 1.8, 2.0 V was analyzed. The outer dsplacement of the plasma under the wea vertcal feld B v 1.5mT s observed n plasmas wthout the helcal feld, but t s suppressed n plasmas wth the helcal feld. These results show that the toama plasma radal poston s sta blzed by applyng the helcal feld for large plasma maor rad, typcally R centrod 0.11 m (radal postons of outer plasma edge > m) under the wea vertcal feld. The effectve vertcal feld of the helcal feld on the equator plane s wea (less than 0.2 mt) n a range m < R < m but t ncreases rapdly wth R n a range R > m. Quanttatve valuaton of the helcal feld needs more detaled analyss ncludng averagng the effectve vertcal feld over the plasma cross secton. It s out of the scope of the present paper and s regarded as future wor. 5. Summary The toama plasma poston and shape were estmated for the frst tme n TOKASTAR-2 by magnetc measurement and flament current approxmaton method. The polodal magnetc flux generated by the plasma current was modeled by sx rng flaments and the vacuum magnetc flux was modeled by multpole felds. We nvestgated effects of the helcal feld on the toama plasma poston. The oscllaton of the radal poston observed n a shot wthout the helcal feld s suppressed

5 by applyng the helcal feld. The outer dsplacement of the plasma under the wea vertcal feld was also suppressed by the helcal feld. The helcal feld by the smple helcal cols contrbutes to the postonal stablty to the radal poston n the toama plasma. Acnowledgments Ths wor s performed wth the support and under the auspces of the NIFS Collaboraton Research program (NIFS14KOAP027, NIFS17KLEP026). [1] K. Saura and S. Tanahash, J. Phys. Soc. Jpn. 49, 759 (1980). [2] H. Iez, K.F. Schwarzenegger and C. Ludescher, Phys. Fluds 22, 2009 (1979). [3] K. Yamaza and Y. Abe, Nagoya Research Report IPPJ- 718 (1985). [4] T. Osh, K. Yamaza, K. Oano et al., J. Plasma Fuson Res. SERIES 9, 69 (2010). [5] T. Ueda, H. Armoto, T. Futa et al., J. Plasma Fuson Res. 10, (2015). [6] T. Sato, H. Armoto, T. Futa et al., Plasma Fuson Res. 11, (2016). [7] D.W. Swan and G.H. Nelson, Nucl. Fuson 22, 1015 (1982). [8] R. Nshmura, H. Armoto, T. Futa et al., Plasma Fuson Res. 9, (2014)