1. Generation of Toroidal Rotation by Gas Puffing
Generation of Toroidal Rotation by Gas Puffing. Simulation with B2SOLPS5.0
V. Rozhansky1, E. Kaveeva1, S. Voskoboynikov1,
G. Counsell2, A. Kirk2, D. Coster3, R. Schneider4
1St.Petersburg State Polytechnical University, Polytechnicheskaya 29, St.Petersburg, Russia
2EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxon, OX14 3DB, UK
3Max-Planck Institut für Plasmaphysik, EURATOM Association, D Garching, Germany
4Max-Planck Institut für Plasmaphysik, EURATOM Association, D Greifswald, Germany

2. Motivation
1.   Toroidal rotation in the co-current direction has been observed in Alcator C-MOD, JET, MAST in the absence of NBI (in the Ohmic regime and during ICRF).
2. In Alcator C-MOD the velocity was proportional to plasma pressure and inversely proportional to plasma current.
3. In MAST co-current toroidal rotation has been observed during outboard gas puffing and counter-current rotation during inboard gas puffing.
4. Existing models (Glaassen et al, Fullop et al ) are based on neoclassical approach and contain several assumptions, their applicability is not clear.
5. Impact of the gas puffing on the toroidal rotation may be understood from the simulations by B2SOLPS5.0 with drift and currents, which contain all neoclassical effects, neutral viscosity etc.

3. Simulations
Typical
simulation mesh

4. Modeling parameters
Two L-regime MAST discharges N6467 and N6468 with similar geometry (lower divertor, the distance between separatrixes 3.5 mm and 4 mm at the outer midplane accordingly) but different fuelling conditions.
N6467 – outboard puffing
N6468 – inboard puffing
N6467 – the toroidal rotation at the outer midplane was almost zero in the core region and negative in the SOL.
N6468 – the plasma rotated in the counter-current (positive) direction with velocity of the order of 5 km/s in the core and again was negative in the SOL.
(Field et al, 30EPS Conf. Plasma Phys. & Contr. Fusion) St.Petersburg 2003)
In the calculations anomalous viscosity was either or to test the sensitivity of velocity profile to its value.
The gas puff was

5. Parallel velocity at the outer midplane for MAST shots N6467 and N6468,
Radial electric field at the outer midplane for MAST shots N6467 and N6468,

6. Experimental profiles of parallel velocities at the outer midplane.
Curve for shot N6467 is blue, for shot N6468 is red.
Parallel velocity at the outer midplane for MAST shots N6467 and N6468, the anomalous viscosity is twice smaller,
The observed profiles of toroidal rotation velocity in the core are close to the experimental values

7. Are parallel fluxes in the core close to neoclassical fluxes?
Poloidal profile of parallel velocity in the core
15 mm from the inner separatrix (at the outer midplane):
shot N 6467, outboard puffing.
shot N 6468, inboard puffing.
For inboard puffing completely different!

8. Neoclassical predictions
Neoclassical Pfirsch-Schlueter fluxes
Poloidal projection
of Pfirsch-Schlueter fluxes:
For inboard puffing due to large
neutral viscosity should be
(Fulop et al)
is counter-current directed.
According to simulations:
1. Parallel fluxes are completely different.
2. Neutral viscosity does not play significant role

9. Model It is counter-current directed for inboard puffing
The toroidal torque is connected with radial transport of the inboard/outboard particle fluxes by vertical drifts
It is counter-current directed for inboard puffing

10. Analytical model The model continuity equation
Here represents the diffusive escape of particles.
Velocity associated with the location of particle source is
subscript ‘in’ denotes the values at the inner midplane.
From the parallel momentum balance
where
is a drift velocity
and is a radial diffusive velocity.

11. The convective flux caused by drift is
Estimation for momentum fluxes ( is the radial scale of the ion source)

12. Generated toroidal rotation
Toroidal rotation is
counter-current directed for the inboard puffing
and co-current directed for outboard puffing.
The suggested parallel velocity pattern and the main role of radial transport of the inboard/outboard particle fluxes by vertical drifts is verified by simulations results.

13. Relative role of various mechanisms of toroidal momentum transport
shot N6468
shot N6467
Components of average flux of parallel momentum through the flux surface.
1- the flux associated with anomalous viscosity and diffusion;
2- the flux associated with drift;
3-parallel momentum flux for neutrals;
4- change of the radial flux of toroidal momentum due to neoclassical torque.

14. Conclusions
Simulations predict change of the sign of toroidal rotation from the co-current to the counter-current direction when switching from the outboard to the inboard puffing in accordance with MAST experiments.
The absolute value of toroidal rotation is of the order of the experimentally observed.
Parallel fluxes in the core are completely different from neoclassical predictions.
Toroidal rotation is generated mainly due to radial transport of the inboard/outboard particle fluxes by vertical
drifts.
Neoclassical torque and neutral viscosity plays modest role in the process of toroidal rotation generation in contrast to the existing theories.