Electron Density Distribution in HSX

Transcription

1 Electon Density Distibution in HSX C. Deng, D.L. Bowe Electical Engineeing Depatment Univesity of Califonia, Los Angeles J. Canik, S.P. Gehadt, D.T. Andeson, P. Pobet, F.S.B. Andeson The HSX Plasma Laboatoy Univesity of Wisconsin-Madison

2 Abstact A multichannel intefeomete system is now outinely opeating on the new quasi-helically symmetic stellaato, HSX, to measue the equilibium pofile and electon density dynamics. The intefeomete system has 9 viewing chods with 1.5 cm spacing. The density spatial distibution is econstucted fom the measued line-integated density. At _ 12 3 high density [ ne > 2 10 cm ], an m=1 density oscillation with fequency of (1-2) khz is obseved. Petubative paticle tanspot studies will be caied out using modulated gas puffing. The paticle souce will be measued by a multichannel H α system. By using the continuity equation, the total adial paticle flux Γ can then be estimated. The diffusion coefficient D and convection velocity V will also be modeled. *Suppoted by USDOE unde gant DE-FG03-01ER-54615, Task II and DE-FG02-93ER54222.

3 Intefeomete Capabilities Intefeomete Capabilities Spatial esolution: 9 chods, 1.5cm spacing and width. Fast time esponse: analog: µsec, eal time digital: <10 µsec maximum bandwidth 250 khz [with 2 MHz sampling] Low phase noise: 24 mad (1.6 o ) ( n e dl) min = 9 x cm % level density fluctuations can be measued Density fluctuations: wavenumbe esolution (i) k < 2.1 cm -1, (ii) k < 0.07 cm -1

4 Solid State Souce Solid State Souce Solid State Souce: bias-tuned Gunn diode at 96 GHz with passive solid-state Tiple poviding output at 288 GHz (8 mw) Suppot of Optical Tansmission System: 2.5 mete tall, 1 ton eaction mass, mounted on stuctue independent of HSX device. Reduces stuctue vibation and minimizes phase noise. Dichoic Filtes: mounted on pot windows to shield intefeomete fom 28 GHz gyoton adiation Cut-off fequency: 220 GHz 10% loss attenuation anging fom 92db at 28 GHz to 68 db at 150 GHz. Edge Filtes: mounted inside pot windows to educe diffaction of the window

5 Intefeomete Schematic Intefeomete Schematic Gunn 96 GHz Tiple 288 GHz Sawtooth Modulato Refeence Plasma Filte Detection System 9 channels Pobe Phase Compaato Filte Amp. Mixe Lens Ø= n e dl

6 HSX Intefeomete Layout HSX Intefeomete Layout

7 HSX Intefeomete System HSX Intefeomete System

8 Beam Expansion Optics and Receive Aay Pobe Refeence Paabolic Beam Optics Plasma Cone Cube Mixe Aay Local Oscillato Beam Polyethylene Lens Aay Pobe Beam Receive (see inlet) Local Oscillato Beam

9 Flux Sufaces and Intefeomete Chods

10 Density Pofile Invesion Density Pofile Invesion Method: Abel invesion; Singula Value Decomposition - flexible bounday conditions - non-cicula geomety - plasma scape-off-laye SOL estimate Model: spline fit to 9 channel line-density pofile - no Shafanov Shift Path lengths: calculated fo twenty vacuum flux sufaces, SOL plasma contibution: One viewing chod is outside the sepaatix. This povides infomation on the SOL contibution. Refaction coection: necessay fo chod length and position

11 HSX Density Pofile (QHS) Measued Line-Integated Density Pofile and fitting Inveted Density Pofile

12 HSX Density Pofile (Mio) Measued Line-Integated Density Pofile and fitting Inveted Density Pofile

13 HSX Density Pofile (Anti-Mio) Measued Line-Integated Density Pofile and fitting Inveted Density Pofile

14 Petubative Paticle Tanspot Study Density petubation obtained by gas puffing modulation povide a good tool fo paticle tanspot study. Pevious successful expeiments on TEXT, ASDEX, W7-AS Diffusive and convective effects can be obtained by analyzing pofile time evolution: Sinusoidal wave is ideal fo this analysis, which give highe accuacy of the analysis. And a few cycles will be needed to obtain cetain accuacy. The amplitude will be aound less than 10% to educe the effects of plasma paametes dependency.

15 Continuity Equation The electon density can be constant on magnetic flux sufaces. We use cylindical geomety tanspot Equation: n t = 1 n(, t) D(, t) V(, t) n(, t) + S(, t) (1) Paametes n and S can be sepaated into two pat: (1) stationay pat n 0 and S 0, and (2) petubed pat and. n t n ne i ω = 0 + ω t whee ω is the fequency of the density petubation geneated by modulating the gas feed. Also assume D and V ae independent of time. Lineaizing equation (1) leads to: n S = S S 0+ S e i (2)

16 Lineaized Equations ), ( ) ) ( ) ( ( ), ( ) ) ( ) ( ( ), ( ) ( ), ( 2 2 S n V V n V D D n D n i = ω ω ω ω ω (5) e n im i n n + = The bounday conditions ae: at =0 ; at =a. 0 = = n n im e (6) 0 ; = = e n im cm n (7)

17 modulated gas feed

18 Fouie coefficients I The Fouie coefficients of the line-integated density wee obtained by fitting the following function to the measued data: + = N N im,2 e,1 N, cos( sin(2 Hee e iand ω ω N im, i t) + t) N + ( a 0 im,1 + sin( a t 1 ω + t) + a 2 t 2 ) N e,2 ae the eal and imaginay pats of the Fouie coefficients at the ith Hamonic of the modulation cos(2 fequency. The a0,a1 and a2 coespond to constant, linea and quadatic time dependence and take into account a possible slow time evolution. ω t)

19 Density Petubation Amplitude and Phase Amplitude and phase of the fist hamonic of the modulation fequency fo the line-integated densities

20 Estimated Souce At this moment, electon souce pofile unknown. Assume souce pofile has exponential fall-off. Amplitude and position of the Souce wee chosen (oughly) accoding to the Hα measuement. Line Integated Emmission (10-5 W/s*cm 3 ) Chod numbe (1 is outboad) n dl (10 cm ) e

21 Results fo D=const. and V=0 A ough estimate of D fom measued paticle confinement time, gives 3ms, D est =a 2 /(6 τ p ) 1.0m 2 /s τ p = n e S

22 Results fo stepped D, with V=0 The modeling is not sensitive to the detailed stuctue of D

23 Sensitivity of Modeling to D

24 Sensitivity of Modeling to V V = V1 1+ exp( ( v )/ ) + V 2 a

25 Sensitivity of Modeling to Souce Pofile if x<xc S=no*exp(-abs(x-xc)/xl1); if x>xc S=no*exp(-abs(x-xc)/xl2); xl2=5cm Peak position: xc=3.4cm

26 Density Petubation at diffeent fequencies The Paticle tanspot is unchanged with the fequency of gas feed modulations

27 Density Petubation with diffeent Densities The Paticle tanspot changes a little with density, which would give smalle D at highe density.

28 Modeling of the ecent expeiment D=2.0m 2 /sec V=0m/sec

29 Bette fit with outwad convection D=2.0m 2 /sec V=300m/sec Souce same as last slide

30 Summay Equilibium Density Distibutions fo QHS, Mio, Anti-mio modes wee obtained. The peliminay measuement and analysis shows the possibility of petubative paticle tanspot study on HSX,the modeling shows the D aound 1-2m 2 /s. Impoved Electon souce measuement (o modeling) equied to detemine D and V which povide best fit to intefeomete data.