Institute for Plasma Research, Bhat, Near Indira Bridge, Gandhinagar , INDIA of the main author:

Transcription

1 1 Plasma Turbulence Studes n ADITYA tokamak R. Jha, P. Kaw, D. Raju, A. Sen and the ADITYA Team Insttute for Plasma Research, Bhat, Near Indra Brdge, Gandhnagar -3848, INDIA Emal of the man author: rjha@pr.res.n Abstract. A summary of results from measurements and analyss of edge turbulence n ADITYA tokamak s presented. The floatng potental s found to be postve n the scrapeoff layer as well as n the edge plasma wth a mnmum near the shear layer. The electrostatc Reynolds stress, estmated by a condtonal averagng technque, s found to be hghest near the shear layer. Measurements wth gas-puff show strong suppresson of edge fluctuatons wth concomtant reducton n Reynolds stress. The fluctuaton data s further examned wth a novel scheme of data analyss based on the `emprcal mode decomposton' and Hlbert transform. It s found that the edge fluctuatons can be well represented by a fnte number of about 10 dscrete modes. Ther nstantaneous energes show ntermttent bursts and the hgh frequency modes are non-statonary. The technque s further developed to study three-mode nteractons and employed to show that trplet nteractons are statstcally sgnfcant among hgh frequency modes of the fluctuaton data. 1. Introducton The study of edge fluctuatons s an actve area of research for fuson devces and s motvated by the desre to gan a better understandng and ultmately a better control of anomalous transport processes. In ths paper, we present two of our recent efforts n ths drecton: one descrbng expermental measurements of Reynolds stress and the other related to characterzaton of fluctuaton data usng a Hlbert transform-based technque.. Measurement of Reynolds Stress It s now wdely recognzed that the exchange of energy between large-scale sheared ExB mean flows and small-scale turbulent fluctuatons s crucal for controllng anomalous heat and partcle losses n fuson devces [1]. In order to gan a better understandng of ths process, we have carred out measurements of the Reynolds stress (RS) experenced by turbulent eddes n the tokamak edge plasma. Measurements of RS are carred out n a normal flattop current plasma dscharge as well as n conjuncton wth edge modfcaton usng gaspuff. For ths purpose, a hgh throughput (500 SCCM) pezo-electrc valve s mounted on a bottom port that s about 00 degrees from the probe system n the electron drft drecton. The fluctuaton measurements are carred out durng ms at the flattop plasma current. The pezo valve s opened for 1.7 ms and molecules of hydrogen gas are released nto the plasma. Concdng wth the gas-puff, there s sgnfcant ncrease n the chord-averaged central plasma densty, n the H α emsson and also n the soft X-ray emsson [see Fg. (1)]. The quantty of the puffed gas s adjusted such that the plasma current and hence the plasma equlbrum s not affected sgnfcantly. It s observed that the gas-puff reduces potental fluctuaton n the edge regon but t does not cause sgnfcant reducton n densty (or, on saturaton current) fluctuaton. We have carred out measurements of radal profles of floatng potental wth and wthout gas-puff to see f fluctuaton suppresson s caused by change n potental or E B flow gradents. The electrostatc RS s determned from fluctuatng velocty components n radal and polodal drectons.

2 FIG. 1: Tme-seres of (a) plasma current, (b) chord-averaged plasma densty, (c) bolometer sgnal and (d) H α sgnal. The vertcal dotted lne ndcates the tme when gas-puff valve s opened. The blocks on the rght shows: (e) Voltage on the gas-puff valve, (f) Soft X-ray, (g) floatng potental and (h) on-saturaton current. For ths purpose, we use a set of nne Langmur probes n cross (+) confguraton: fve probes spaced n the polodal drecton and another fve n the radal drecton, the central probe beng common. Ths confguraton s sutable for smultaneous measurement of radal and polodal veloctes experenced by a turbulent eddy. The probe system can be moved n the radal drecton near the edge plasma and by collatng data from many smlar dscharges t allows measurement of radal profles of floatng potental, E B velocty, shear rate etc. Fgure shows the floatng potental profle at a tme when there s no gas-puff and that durng the gas-puff. We note that the floatng potental s postve n the edge as well as n the SOL plasma wth a mnmum near the separatrx. Fgure 3 shows RMS (root mean square) values of fluctuaton levels. It s observed that durng the gas-puff when there s a suppresson of fluctuaton, the mean floatng potental profle also gets flattened. However, both wth and wthout gas-puff, the fluctuaton level s mnmum at radal dstance between 0-0 mm from the separatrx. We have determned the radal profles of E B flow velocty as well as ts gradent n both dscharge condtons (.e., wth and wthout gas-puff). It s observed that near 5 1 the shear layer, the maxmum shear V E B / r 4 10 s n the normal dscharge and s durng the gas-puff. FIG. : Radal profles of mean floatng potental (a) wthout gas-puff, and (b) durng gaspuff. The open crcle shows the mean value over several dscharges and error bar ndcates the total spread.

3 3 5 1 These values are larger than the de-correlaton frequency 10 s and explan fluctuaton suppresson n the shear layer. We had expected that durng gas-puff the velocty gradent would ncrease but we do not observe such a thng. In the present experment, the duraton of fluctuaton suppresson s small (5 ms compared to ms confnement tme). It s lkely that gas-puff causes confnement mprovement, but conclusve evdence can come only f we get fluctuaton suppresson for a longer tme. Another pont to study n detal wll be to determne the cause of fluctuaton suppresson. Future experments would be drected towards measurement of torodal flow velocty usng a Mach number probe. FIG. 3: Radal profle of the root mean square (RMS) value of potental fluctuatons n dscharges (a) wthout gas-puff and (b) durng gas-puff. FIG. 4: (a), (c), (e) and (g) are ensemble averages of condtonal eddes seen by the central probe at dfferent radal locatons, r p0 from the separatrx. Even when the probe s placed at a certan radal dstance, ts dstance from the separatrx can be dfferent n dfferent dscharges because of lack of poston control. Fgures (b), (d), (f) and (h) show condtonally averaged radal ( δ vr ) and polodal ( δv θ ) veloctes. The estmates Reynolds stress, RS= δv r δvθ s also shown. In the turbulent edge plasma, the electrostatc RS (= δv r δvθ ) represents radal flux of polodal momentum and may be responsble for drvng the mean flow. Ths s one of the mechansm by whch the small-scale fluctuatons can get suppressed. As a part of ths study we have measured RS n a normal dscharge. To mprove accuracy, we had to use data from several dscharges so that the number of ensembles [N ens, see Fgure nset] s large. The data

4 4 length durng gas-puff s too small to allow an unambguous measurement of RS at dfferent radal locatons. For collectng ensembles, an eddy s pcked up on the central pn of the cross (+) probe by mposng the followng condtons: () the ampltude of the eddy exceeds 1.5σ above the mean level, and () the slope ( φ / t ) s postve. Other detals of condtonal averagng are same as n Ref. []. We also have smultaneous measurement of fluctuatng radal velocty ( δ vr ) and polodal velocty ( δv θ ) experenced by the reference eddy. A large number of ensembles of these quanttes are collected from the tme-seres. Fgure 4 shows the ensemble averages of these quanttes when the probe s placed at dfferent radal dstances from the separatrx [ndcated n Fgure 4(a,c,e,g)]. The postve value of δvr s n the outward and postve δvθ ndcates electron damagnetc drecton. It s observed that n the far-sol (r p0 = 30±14 mm), eddes move radally outward but polodal velocty s bpolar. One half of the eddy moves n electron damagnetc drecton and the other half n on damagnetc drecton- ndcatng a spnnng moton. It s noted that δvr s outward n the SOL but nsde the separatrcs t s ether neglgbly small or drected nward. The values of RS are shown n Fg. 4(b,d,f,h). It s observed that a strong gradent n the RS exsts between the radal locatons r p0 = 4±6 mm and r p0 = -5±4 mm from the separatrx, gvng δ v r δv θ / r 7 10 m s. Usng the value of V E B / r 7 10 m s as 1 derved from Fg. (a) n the shear regon, one obtans vscosty η m s. Future f exp 1 experments wll now focus on ncreasng the duraton of fluctuaton suppresson wth gaspuff and studyng relatons between flows and turbulence. 3. Hlbert transform based tokamak data analyss To obtan further nsght nto the turbulence characterstcs we have analyzed the fluctuaton data usng a novel technque based on the Hlbert transform developed by Huang et al. [3]. The method has two major components - a shftng process known as 'emprcal mode decomposton' that extracts a fnte number of mono-frequency modes (the ntrnsc mode functons, IMFs) and subsequent applcaton of the Hlbert transform on the IMFs that permts evaluaton of nstantaneous frequences and ampltudes. In contrast to Fourer transform-based technques, the present method can be appled to non-statonary data as well as to data sets that have a relatvely small number of data ponts. The method s also superor to wavelet-based technques n many respects. A detaled descrpton of ths technque and ts applcaton on tokamak data has been presented n Ref. [4]. Here we descrbe some key results that llustrate the strength of ths technque. The Hlbert transform of an IMF X(t) can be wrtten as: 1 + X ( τ ) Y ( t) = Ρ dτ.(1) π t τ where, P s the Cauchy prncpal value of the ntegral. By takng Fourer transforms of X(t) and Y(t), t can be shown that Y ( ω) = jx ( ω). Thus, all frequency components of Y(t) are delayed n phase by π/ and hence are orthogonal to X(t). The analytc sgnal, Z ( t) = X ( t) + jy ( t) allows an approprate defnton of nstantaneous ampltude, 1 A ( t) = X + Y also known as the envelope, and nstantaneous phase Θ ( t) = tan ( Y / X ). The nstantaneous angular frequency ω (t) s the local slope of Θ (t). When we analyze edge fluctuaton data usng ths technque, we fnd that the edge fluctuaton data contan a fnte number of IMFs n contrast to the huge number of modes that a Fourer transform analyss

5 5 would yeld. Some of these modes are not correlated wth the raw data, and hence they are spurous. The physcally relevant modes are those that are correlated wth the raw data wth a normalzed correlaton coeffcent of > 10 %. These are physcally relevant modes and hence they can be used for further analyss. FIG. 5: (a) Un-wrapped phases of IMF components of φ f data, and (b) Hlbert-Huang (HH) spectrum of a small segment of the data. The colored dots represent the varaton of ampltude on a tme frequency plot (the HH spectrum). Fgure 5(a) shows the nstantaneous phases of these modes and the mean frequency of a mode s nearly constant. However undulaton on a phase clearly shows that nstantaneous frequency wanders around the mean frequency. The mode ampltude can be represented on tme-frequency plane and such a representaton s known as Hlbert-Huang (HH) spectrum, H ( t, ω ) = Re A ( t)exp[ j ω ( t) dt where the summaton s over the relevant IMFs. Fgure 5(b) shows the HH spectrum for fluctuaton data and t s characterzed by ntermttent varaton of nstantaneous frequency. FIG. 6: The mean margnal spectrum h(ω), the devaton spectrum SDV(ω) and the degree of non-statonarty spectrum DNS(ω) of the φ f data from ADITYA SOL plasma. The devatons from the mean margnal spectrum and the degree of non-statonarty are hgher for hgher frequency components. The HH spectrum can be used to extract several ntegral or averaged quanttes that are senstve measures of turbulence characterstcs. One such measure s the mean margnal spectrum, h (ω ) whch s comparable to the Fourer spectrum but more meanngful because t s based of the emprcal modes present n the data. Lkewse, another ntegral quantty, the degree of non-statonarty (DNS), shows how dfferent frequency components devate from

6 6 the mean margnal spectrum. The devaton spectrum SDV (ω ) s shown n Fg. (6) along wth DNS (ω ). It s observed that the low frequency modes (< 0 khz) are nearly statonary, but hgher frequency modes become non-statonary. Ths concluson can also be made from the vsual nspecton of dfferent IMFs. We have further generalzed ths technque to explore the occurrence of phase couplng n the turbulence data. The basc dea s to assocate the IMFs as the basc nonlnear modes of the system and examne ther mutual nteractons. Snce IMF components are represented as, Z ( t) = A ( t)exp[ jθ( t)], nteractons among them can be studed by evaluatng the IMF bcoherency factor, namely, * Z Z + 1Z + γ =.() A A A where, the angular bracket represents tme averagng. If the phases, * Θ, + 1 Θ, and Θ + are random, the numerator Z Z + 1Z + 0 and f Θ = Θ + 1+ Θ +, the numerator s equal to A A + 1A =. Thus, the b-coherency factor γ s bound n the range [0,1] and t can be used to detect phase couplng. The error ε (γ ) s estmated by countng the number (M) of the largest wave n the trplet (.e., the number of π phases). It s assumed that each wave perod s ndependent and thus M represents the number of ndependent ensembles for averagng so that the error, σ ( γ ) = 1/ M. FIG. 7: The coherency factor of trplet couplng n three data sets obtaned from the ADITYA tokamak, (a) floatng potental (φ f ) data from the SOL plasma, (b) on saturaton current (I s ) data from the SOL plasma and (c) the I s data from the edge plasma (6 mm nto the man plasma). The dotted lne ndcates 3σ error n the estmates of the coherency factor, γ. Fgure 7 shows measurement of IMF b-coherency for three data sets of fluctuatons n the SOL and edge plasmas. It s observed that the IMF b-coherency s statstcally sgnfcant among a few hgh frequency modes n the SOL plasma but the edge plasma close to the lmter has neglgble trplet coherency. Ths s consstent wth the wdely accepted noton that the edge plasma behnd the lmter has a velocty shear layer whch can de-correlate turbulent fluctuatons whereas the SOL plasma s rch n coherent structures. The HH spectrum can be used to estmate the nstantaneous energy, IE ( t) = H ( t,ω), whch truthfully tracks the fluctuaton actvty n the tme-seres. Snce ths quantty s domnated by low frequency modes, the IE demonstrates the tme-scales of modulaton energy present n the data. We have estmated IE for the edge fluctuaton data and observe that t correlates wth the fluctuaton actvty and has a characterstc tme-scale of about 00 ω

7 7 µs. Ths can be compared wth the auto-correlaton tme of the fluctuaton that s about 10 µs. Thus, the energy of edge turbulence modulates at a tme-scale that s 0 tmes larger than the tme-scales of turbulent fluctuaton. FIG. 8: The Mrnov col data, db θ /dt n ADITYA tokamak and the nstantaneous energy (IE) durng plasma current flattop, and (b) ts Hlbert-Huang spectrum takng only the frst two IMFs. We have also carred out smlar measurements for the Mrnov col data. When the magnetc oscllaton data are decomposed nto IMFs, we fnd that only two of the several IMFs are strongly correlated wth the raw data. These modes have mean frequency of 10 khz and 30 khz respectvely. The HH spectrum and the nstantaneous energy (IE) are obtaned from these modes. To facltate easy nterpretaton, only Mrnov data durng plasma current flattop s used when we expect mean plasma pressure profle to have been well establshed. We observe that whenever IE s large, there s only one frequency component at 10 khz [see Fg. 8(a), and 8(b)]. However, n between successve events of hgh IE, there are perods of low IEs when the second frequency at about 30 khz also appears. The ntermttent burstng of the hgh frequency component (the second IMF) would not have been physcally sgnfcant f the IE was close to zero. A sgnfcant level of IE at the tme of the hgh frequency bursts mples that ths phenomenon has a physcal orgn. As s well known, the mode frequency of a Mrnov oscllaton s related to the plasma damagnetc frequency that n turn depends on the plasma pressure gradent. The bursts n hgh frequency components can therefore be nterpreted as beng due to ntermttent changes n the local plasma pressure gradent - remnscent of sand-ple avalanches that mantan profle consstency.

8 8 Reference: [1] E. Sanchez, C. Hdalgo, B. Gonzalves et al., J. Nucl. Mater , 96 (005). [] B. K. Joseph, R. Jha, P. K. Kaw et al., Phys. Plasmas 4, 49 (1997). [3] N. E. Huang, M. C. Wu, S. R. Long et al. Proc. R. Soc. London A 459, 317 (003). [4] R. Jha, D. Raju and A. Sen, Phys. Plasmas 13, 8507 (006).