# Presentation: 546163

## M3D Simulation Studies of NSTX

- W. Park, J. Breslau, J. Chen, G.Y. Fu, S.C. Jardin, S. Klasky,
- J. Menard, A. Pletzer, D. Stutman    (PPPL)
- H.R. Strauss    (NYU)
- L.E. Sugiyama    (MIT)

## Outline

- M3D code
-          MHD,  two-fluids,  hybrid models.
- NSTX studies including flow effects
-          2D steady states.
-          Evolutions of IRE’s.
-          TAE modes.

## =1.3  qo=0.8  qb=5

- MA=0
- Sh=0
- max=1
- min=0.5

- MA=0.2
- Sh=0.3
- max=1.1
- min=0.5

- MA=0.5
- Sh=0.4-0.07=0.33
- max=1.9
- min=0.2

- MA=0.8
- Sh=0.5-0.15=0.35
- max=5.2
- min=0.005

- Density profile dependence on sheared Rotation
-                                                                    MHD

- =1.3  qo=0.8  qb=5

## Density profile dependence on Physics model

- MA=0.2
- Sh=0.3
- max=1.1
- min=0.5
- RelSh=1

- MA=0.2
- Sh=0.3
- max=1.2
- min=0.5
- RelSh=0.8

- MA=0.2
- Sh=0.3
- max=1.8
- min=0.15
- RelSh=1.9

- MA=0.2
- Sh=0.3
- max=1.1
- min=0.5
- RelSh=1

- MHD

- Two-Fluids

- Hybrid

- Hybrid: trapped

- NSTX   =1.3  qo=0.8  qb=5

## Hot particle centrifugal force

-                     ~ Bulk plasma

- NSTX experimental data             agrees with MHD derived

##   Linear Instability Eigenmodes

- MA=0
- =0.03
- m=0

- With shear flow:  MA=0.2
- Reduced growth:  =0.01
- Rotating mode:m=0.13

-   Linear Instability Eigenmodes
-  Top view on the horizontal mid-plane

- U

##    Nonlinear Evolution without strong flow: similar to a sawtooth crash

-    Nonlinear Evolution without strong flow: similar to a sawtooth crash

## When the inversion radius is large or the plasma  is increased,

- When the inversion radius is large or the plasma  is increased,
- magnetic islands overlap and become stochastic.
- Disruption due to field line stochasticity.

## Soft X-ray signals compared:

- Theory agrees with experiment on general characters, but does not have wall locking and a saturation phase.

##   IRE

-   IRE

-  Sawtooth
-  Disruption due to stochasticity.
-  Disruption due to localized
-   steepening of *P* driven modes,
-       as in Tokamaks

- TFTR

- Stellarator

- P  profiles

##    Nonlinear Evolution with peak rotation of MA=0.2  

- if rotation profile is roughly maintained.
- However, with a normal momentum source rate,
- Vprofile flattens with reconnection,
- and full reconnection usually occurs.

-    Nonlinear Evolution with peak rotation of MA=0.2

- Pressure and V profiles
- are flattened inside island.
- Also seen in experiment.

##    Saturated steady state with strong sheared flow  

-    Saturated steady state with strong sheared flow

**B F**ield line
-       in the island
- Density (Pressure)
-       contours
- Temperature
-       isosurface
- Pressure peak inside the island together with shear flow causes the mode saturation.

## The simulation of an NSTX plasma show unstable TAEs consistent with observations

- NSTX shot #108530 at t=0.267sec;
- The calculated n=2 TAE mode frequency is 73 kHz which is close to the experimental value of 70 kHz (assuming 15kHz toroidal rotation)

- Hot particle/MHD hybrid simulation

- _Fu, et al., FP1.068 _

## Summary

- M3D code studies of NSTX.
- The relative density shift relation holds both in the simulation and experiment, with the centrifugal force of the hot component included.
- Toroidal sheared rotation reduces linear growth of internal kink. It is strongly stabilizing nonlinearly, but is normally flattened by reconnection. In some cases, pressure peaking in the island causes a mode saturation.
- IRE: Sawtooth, Disruption due to stochasticity, and Disruption due to nonlinear steepening of pressure driven modes, as in tokamaks.
- Resistive wall and coil currents are being added.