# Presentation: 544749

## Confinement, Power Balance and Local Transport Results in NSTX 

- <date/time>

**Stanley M. Kaye**
- PPPL, Princeton University
**R. Bell, C. Bourdelle, B. LeBlanc, S. Paul, M. Redi, S. Sabbagh, D. Stutman**** **
**APS-DPP Meeting**
**Albuquerque, N.M.**
- October 2003

**Confinement, Power Balance and Local Transport Results in NSTX**** **

***Columbia U***
***Comp-X***
***General Atomics***
***INEL***
***Johns Hopkins U***
***LANL***
***LLNL***
***Lodestar***
***MIT***
***Nova Photonics***
***NYU***
***ORNL***
***PPPL***
***PSI***
***SNL***
***UC Davis***
***UC Irvine***
***UCLA***
***UCSD***
***U Maryland***
***U New Mexico***
***U Rochester***
***U Washington***
***U Wisconsin***
***Culham Sci Ctr***
***Hiroshima U***
***HIST***
***Kyushu Tokai U***
***Niigata U***
***Tsukuba U***
***U Tokyo***
***Ioffe Inst***
***TRINITI***
***KBSI***
***KAIST***
***ENEA, Frascati***
***CEA, Cadarache***
***IPP, J******ü******lich***
***IPP, Garching***
***U Quebec***

## Abstract

- 	Neutral beam heated, low aspect ratio NSTX discharges exhibit global and thermal confinement times that exceed the values given by conventional aspect ratio scalings in plasmas both in the H-mode and with L-mode edge profiles. While only modest changes in confinement are seen going from the L-phase to the H-phase, both types of plasmas have global confinement enhancement values up to 2.5 relative to L-mode scalings and up to 1.5 relative to H-mode scalings. Under the assumption of classical collisional energy transfer in these plasmas, the plasma transport is governed by the electrons, with electron thermal diffusivities exceeding the ion thermal diffusivities by up to an order of magnitude. The ion thermal diffusivities are comparable to the neoclassical values as given by the NCLASS model, consistent with gyrokinetic results indicating a suppression of the ITG/TEM modes. The momentum diffusivity is less than both the electron and ion thermal diffusivities, which supports the hypothesis that long wavelength turbulence is suppressed in these low aspect ratio plasmas.  Unlike the thermal diffusivities in plasmas at conventional aspect ratio, the ion and electron thermal diffusivities in NSTX decrease towards the outside of the plasma, raising the possibility that some non-classical heating process may be active.
- 	This work was supported in part by U.S. Dept. of Energy Contract No. DE-AC02-76-CH03073.

## Confinement and Local Transport Results

- Determination of thermal confinement times and local transport properties requires TRANSP runs to estimate fast ion energy/losses and power balance
- Ran 25 cases using detailed kinetic profiles
- MPTS (Te, ne)
- CHERS (Ti, v)
- Additional atomic physics
- Carbon density profiles for Zeff
- Ran each case with data mapping leading to best match to measured diamagnetic flux
- Set Ti=Te in outer region
- Computed internal equilibrium using magnetic diffusion calculation and ESC equilibrium solver
- Regions of “anomalous” i in outer region virtually eliminated
- Large uncertainty in i in this region

## Both L- and H-mode Plasmas Form The Basis for the Confinement and Local Transport Studies

- • Density profile becomes hollow after
- transition, but then fills in in 0.3 to 0.5 s

- • H98pby,2>1 observed routinely
-     (Emag ~ 60 msec)

- High-quality, “steady-state” H-modes are observed on NSTX

## Confinement Gain in Steady-state After the H-mode Transition is Often Modest

- One aim of this study is to determine whether improvement is due
- to lower core transport or an increase in pedestal stored energy

## L-Modes Are High-Quality, but More Transient

- 2

- 1

- 0

## Comparison of Calculated to Measured Displaced Toroidal Flux Reflects Accuracy of TRANSP analysis

- meas (Wb)

- TRANSP (Wb)

- -0.08    -0.06   -0.04    -0.02    0.00    0.02

- Measurement uncertainty in displaced flux (2 mWb)

- L-mode:
- <TRANSP – meas> = -5.4 1.4 mWb
- H-mode:
- <TRANSP – meas> = -2.8 1.2 mWb

*TRANSP underpredicts plasma diamagnetism in L-mode*
*On average, close to measurement uncertainty*
*In H-mode*

- L-mode

- H-mode

## Agreement Between TRANSP and EFIT Gives Confidence

- Only a ~15 kJ Difference Between Stored Energy Calculated
- by TRANSP and That From Magnetic Reconstruction

- Relatively Little Fast Ion Loss Compared to Fraction of Fast Ion Stored Energy

- 0.0     0.1     0.2      0.3     0.4    0.5

- Wfast/Wtot

- 0.25

- 0.20

- 0.15

- 0.10

- 0.05

- 0.00

- Pf, loss/PL

- E,thermal reduced from E,global

- In Using TRANSP Results to Estimate Fast Ion Stored
- Energy And Losses

## Energy Confinement Times Can Exceed Predictions from Conventional Aspect Ratio Scalings

- Global

- • Quasi-steady conditions
- • E,global from EFIT magnetics reconstruction
-        - Includes fast ion component
- • E,thermal determined from TRANSP runs

- 1.5x

- 0.5x

- 1.0x

- Thermal

## Confinement Enhancements(L, H-Modes Combined)

- 2T, TC – Two term thermal
- conduction model (Cordey et al.,
- Nuc. Fusion, Vol. 43, p. 670, 2003)

## L- vs H-Mode Transport

- The density profile exhibits the largest difference
- between the two phases

## Ion Energy Balance Indicates Thermal Conduction Loss Dominant in Core During Both Phases

- dW/dt, ion-electron coupling can be large near edge

## Electron Power Balance Indicates Thermal Conduction is Primary Energy Loss in Both Phases (For Both Channels)

## Little Change in Core Transport Going From L- to H-Phase

- Changes in are
- generally within
- uncertainties
-  (discussed later)
-       i  neoclassical
-       e > i

## In General: i,neo  i < e In Core (r/a~0.4)

- Neoclassical based on NCLASS

## The Relation Between andi Is Unclear

## The Ion Behavior (Low i) Consistent With Long-Wavelength Turbulence Being Suppressed

- Short wavelength modes may dominate transport
-   - Electron transport physics is a critical area of
-     research for NSTX

- C. Bourdelle,
- M. Redi

## Is There Evidence That Transport is Controlled By a Critical Temperature Gradient?

- 	If this is the case, we would  expect to see a zero heat flux at a non-zero temperature gradient
- 	(e.g., Hoang et al., PRL, 87, 125001-1, 2001)

## NSTX Data Do Not Exhibit Behavior Consistent With the Critical Gradient Paradigm (Electrons or Ions)

- Source of electron transport under active investigation
-     - Short- turbulence diagnostic to be implemented in FY05

## Power Balance/Diffusivity Uncertainty Analysis

- Focus on uncertainties due to equilibrium/data mapping
- Uncertainties due to random/systematic uncertainties in data discussed in LeBlanc et al. (Poster LP1.005)
- Variations examined (give rise to  15 kJ variation of stored energy)
- Use of EFIT equilibrium vs internal solution of poloidal field diffusion and Grad-Shafranov equations
- EFIT constraints based on pure magnetic vs partial kinetic reconstructions
- Sauter vs standard neoclassical electrical resistivity
- Mapping of Te, ne
- Uncertainties in power balance (Qie, Pcond) in outer half of plasma can be large (several hundred kW)
- Translates to factors of up to 2 to 3 uncertainty in i, e (discharge dependent)
- Uncertainty can be large enough to lead to a “reversal” in the direction of ion conduction power flow (i.e., power into vs power out of ions) – see results for discharge 108211

## Large Uncertainty in Power Balance Components in Outer Half of Plasma

## Factor of 2 to 3 Uncertainty in i, e; e Well Constrained For This Case

## Large Uncertainty in Qie (and dW/dt) Can Lead to a “Reversal” in the Direction of Conduction Power Flow

- Energy flow out of ions

- Energy flow into ions

## Uncertainty Can Lead To “Anomalous” Result (i < 0) 

- Do not want to rule out non-classical heating physics in outer region
-  	Higher time/spatial resolution CHERS implemented in FY04 will
-   	help quantify i uncertainty/ion transport physics further

## Conclusions

- NSTX confinement times are enhanced over those given by conventional aspect ratio tokamak scalings
- H-mode thermal confinements in excess of H-mode scaling values by 20 to 30%
- H-mode confinement (normalized) better than that of L-mode
- Local transport analysis performed, indicates little change in core transport going from L- to H-mode
- Ion transport less than electron transport
- Ion transport at or slightly above neoclassical level
- Data and analysis indicate long- turbulence may not be the source of ion transport
- Relatively low ion thermal diffusivity
- Gyrokinetic analyses
- Large uncertainties in power balance, thermal diffusivities in outer half of plasma due to uncertainties in equilibrium/data mapping
- MSE q(r) measurement (FY04) will help constrain equilibrium