# Presentation: 815517

## Recent Studies of NSTX Edge Plasmas: XGC0 Modeling, MARFE Analysis and Separatrix Location

- F. Kellya, R. Maquedab, R. Maingic, J. Menarda, B. LeBlanca, R. Bella, S. Paula, C. S. Changd
- and the* *NSTX* *Research Team
*a**Princeton Plasma Physics Laboratory, Princeton, NJ  *
*b**Nova Photonics, Princeton, NJ  *
*c**Oak Ridge National Laboratory, Oak Ridge, TN*
*d**Courant Institute of Mathematical Sciences, NYU*

- NSTX Results/Theory Review
- August 6-7, 2008
- Princeton, NJ

## Modeling of NSTX with XGC0

- Equations of ion polarization drift and continuity1,

- 1 C.S. Chang, S. Ku, H. Weitzner, Phys. Plasmas **11** (2004) 2649.

- can be combined

- The ion polarization density is then proportional to

- (1)

- (2)

## Modeling of NSTX with XGC0 (2)

- Using measured Te , Ti and ne profiles with NSTX 127533 equilibrium in XGC0 resulted in simulations with very large ion polarization densities after 40 ITTTs.  Combination of low magnetic field and low temperature leads to a fast growth rate of the ion polarization density in XGC0.
- Other problems: ion and electron transport are neoclassical and no capability to model impurities.

## Figure 1     MARFE evolution in NSTX shot #117125

**661.415 ms**

**661.502 ms**

**661.589 ms**

**1(b)**

**660.879 ms**

**660.458 ms**

**1(a)**

- ‘average frame’ subtracted to enhance contrast
- 68000 frames/s
- or  ~14.7 s
- between frames
- with  a D-line
- bandpass filter

## MARFE/ELM cycle in NSTX shot #117125 (900 kA, 6.2 MW, Double Null, ~ 656-665 ms )

- Poloidally and toroidally localized MARFE remnant (plasmoid) moves upward following magnetic field line
- Plasmoid (MARFE precursor) upward movement stagnates and expands into a toroidally symmetric ring
- MARFE ring moves downward in ion         drift direction
- ELM activity in divertor region coincides with burn through of most of MARFE
- Type I ELM (at ~665.5 ms) burns through MARFE

- Downward drift in ion grad-B direction places stable MARFE position near lower divertor.2   Velocity of background plasma (poloidal ExB drift) is equal to the MARFE velocity.3
- 2 Asakura, et al., NF **36** (1996) 795.
- 3 Chankin, Phys. Plasmas **11** (2004) 1484.

## Figure 2    ELM cycle drives dynamics of MARFE

- ELM cycle and MARFE cycle are directly linked.  Precursor of Type I ELM slows, then reverses MARFE movement and then ELM burns through MARFE4.

**2(a) Center column wide slit “streak” image of shot 117125**

**Upper divertor**

**Lower divertor**

**2(b) Divertor D******** (a.u.)**

**Time (ms)**

**Midplane**

**2 m**

- 4 Maqueda, et al., JNM 363-366, 1000 (2007).

## MARFE theory

- Drake4 found the MARFE to be a radiative condensation instability governed by
- 															(1)
- Wesson and Hender5 observed that the most unstable mode     varies as cos θ and wave number k|| = 1/qR
- 															(2)

- parallel and perpendicular conduction

- radiative condensation

- 4 Drake, PF **30** (1987) 2429.
- 5 Wesson and Hender, NF **33** (1993) 1019.

## MARFE density limit

- Mahdavi6, et al. and Maingi and Mahdavi7, incorporated non-equilibrium radiation effect of neutrals in a uniform edge distribution to obtain

- (4)

- 6 Mahdavi, et al., in *Proc. 24**th** European Conf. on Controlled Fusion and *
*Plasma Physics*, Berchtesgaden, Germany, 1997, Vol. 21A, p. 1113.
- 7 Maingi and Mahdavi, Fusion Sci. and technol. 48 (2005) 1117.* *

- (3)

##  Table 1   MARFE condition for NSTX discharge 117125 at Thomson Scattering times and separatrix data used in calculation of MARFE Index if | tTS – tCHERS | < 1.5 ms.

- 	**TS time ****(s)**** ****	****Condition ****	****    CHERS time    ****	****T****e,sep****[eV]****	****n****e,sep****[m****-3****]****	****f****C****[%]****	****	****MI**
- 	0.326662  	no marfe 		0.32525		93		2.5E19	7.2		0.07
- 	0.343345	no marfe		0.33525
- 	0.359992	no marfe		0.35525
- 	0.376685	upward move		0.37525		34		2.2E19	6.4		0.82
- 	0.393332	no marfe		0.38525
- 	0.410015	no marfe		0.40525
- 	0.426662	no marfe		0.42525		51		1.8E19	5.2		0.20
- 	0.443345	no marfe		0.43525
- 	0.459992	no marfe		0.45525
- 	0.476685	onset		0.47525		38		3.0E19	6.2		0.83
- 	0.493322	stagnation		0.48525
- 	0.510025	stagnation		0.50525
- 	0.526662	no marfe		0.52525		147		3.4E19	4.9		0.04
- 	0.543345	onset		0.53525
- 	0.559992	no marfe		0.55525
- 	0.576685	onset		0.57525		31		1.9E19	6.8		0.96
- 	0.593332	onset		0.58525
- 	0.610025	no marfe		0.60525
- 	0.626662	burn		0.62525		34		1.8E19	10.7		0.96
- 	0.643355	stagnation		0.63525
- 	0.660002	move down		0.65525
- 	0.676685	stable at top		0.67525		41		2.2E19	11.3		0.71
- 	0.693332	no marfe		0.68525
- 	0.710015	onset		0.70525
- 	0.726662	onset		0.72525		41		2.2E19	4.8		0.41
- 	0.743355	no marfe		0.73525
- 	0.759992	no marfe		0.75525
- 	0.776685	no marfe		0.77525		61		2.6E19	5.9		0.19
- 	0.793332	no marfe		0.78525
- 	0.810015	stagnation		0.80525

## Figure 3    Conditions observed in NSTX discharge 117125

-  no marfe; t = 0.326662 s

-  marfe onset; 0.726662 s

-  move up; 0.376685 s

-  stagnation; 0.493322 s

-  move down; 0.660002 s

-  burn; 0.626662 s

-  stable at top; 0.676685 s

- Figure 3    Conditions observed in NSTX discharge 117125

- Center image is
- nearest to TS time,
- left image -72.5 ms,
- right image +72.5 ms

## Figure 4    MARFE Index vs time for NSTX 117125

## Experimental estimates and assumptions

- Shot 110077 of NSTX: DN, D fueled, BT(0) = -0.45 T, Ip = 1 MA and PNBI up to 5.1 MW during an H-mode edge during which the LFS radial electric field has been estimated8 to be between 0 and -5 kV/m.
- From Fig. 2(a), ring MARFE at 660 ms has an experimental poloidal velocity of -1.54 km/s (downward).    From Fig. 4 case 2, ring MARFE at 377 ms moves upward 0.273 m in 0.145 ms for an experimental poloidal velocity of 1.88 km/s (upward).
- Neutral fraction, n0/ne, was estimated to be 1x10-3.
- Electron thermal diffusivity e at separatrix was assumed to be 50 m2/s and conductive fraction 0.5.  Perpendicular thermal conductivity was calculated from
- Thomson scattering resolution insufficient to resolve pedestal. Assumed HFS separatrix accurately determined by LRDFIT04 with  shifted LFS profiles to make HFS + LFS Te profiles smooth.

- 8 T. M. Biewer, et al., Rev. Sci. Instr. **75** (2004) 650.

##  Heat flux driven Diamagnetic Drift

- 9 M. Z. Tokar, Contrib. Plasma Phys. **32**  (1992) 341.

-   Tokar9 - MARFE movement is due to one MARFE border cooled and the other heated by diamagnetic heat flows in the magnetic surface.
-   Non-stationary heat balance equation with conductive diamagnetic heat flux and terms describing the dependencies of the pressure, P, on time, t, and poloidal angle, θ, and assuming the other terms constant

- conductive heat flux density through plasma edge

- and

- Qb is conductive power transported through area *A**p*

- (5)

## Using Thomson measurements of ne and Te and CHERS measurements of Ti at LFS separatrix we estimate for shot 117125

-  poloidal diamagnetic heat flux driven drift velocity is

- MARFE Movement due to Diamagnetic heat flux drift

- Taking perturbations of P of the form

- at 660 ms  => Vθd = 1.0 km/s upward

- at 377 ms  => Vθd = 3.6 km/s upward

- and

- and

- (6)

- (7)

## MARFE Movement = Diamagnetic heat flux + ExB Drift 

- Total poloidal velocity of MARFE will be diamagnetic heat flux driven drift relative to the ExB drift.
- If MARFE velocity is due to the sum of the ExB and diamagnetic heat flux driven drifts, this implies ExB drift is
- 		-2.6 km/s (downward)  => HFS Er = -4.6 kV/m at 660 ms
- 		-1.7 km/s (downward)  => HFS Er = -3.3 kV/m at 377 ms

## Discussion of Results

- CHERs measurements of carbon C6+ are averaged over ~7 ms and Thomson scattering measurements occur at 60 Hz.  Temporal and spatial resolution of the data not quite sufficient.  LFS separatrix location not accurately determined by equilibrium code. Experimental data was adjusted by assuming innermost HFS TS channel was placed on correct poloidal flux surface and shifting LFS Thomson Te profiles to match HFS profiles.
- General tendency of MARFE threshold confirmed by NSTX experimental data.
- Theory strictly applies to conditions _before_ MARFE formation and poloidal asymmetries not considered.
- Movement of MARFEs in NSTX consistent with the sum of diamagnetic heat flux and ExB drift, if conductive fraction is 0.5 and χe is 50 m2/s, then Er is about -4 kV/m.

## Conclusions

-  Modeling of NSTX by XGC0 limited by fast growth of ion polarization density at low magnetic fields and temperatures, neoclassical e-transport and no impurities.
-   MARFE onset in NSTX is found to roughly agree with basic MARFE theory, but uncertainties in the data limit the comparison.
-   MARFE movement in NSTX shot 117125 is consistent with diamagnetic heat flux driven motion relative to the background plasma velocity, i.e. ExB drift.
-   Separatrix placement yielded separatrix Te in the range 31 to 41 eV during MARFE activity, consistent with observations in TEXTOR at MARFE onset10.

- 10 F.A. Kelly, W.M. Stacey, J. Rapp and M. Brix, Phys. Plasmas **8** (2001) 3382.