Sheared Flow Generation by RF Waves

Introduction

There has been considerable interest in the possibility of employing rf waves, particularly in the ion cyclotron range of frequencies (ICRF), to induce shear in the poloidal flow velocity of tokamak plasmas. Theory suggests that rf-induced sheared flows may allow access to high confinement regimes and thus be a key to greatly improved tokamak performance.  Confinement improvement as a result of the application of rf power has been reported on a number of experiments, and at least in some cases, rf-induced sheared flows provide a plausible explanation of the observations. Such novel applications of ICRF waves could provide a degree of active external control over an internal transport barrier, which would be important for advanced tokamaks.

In particular, spontaneously occurring sheared flow layers are believed to be important in establishing the H-mode edge transport barrier and may play a role in some tokamak internal transport barriers. Applied ICRF waves could provide a flexible and practical means of transport barrier control because of the ease with which rf power can be controlled and deposited at desired locations.  The use of rf waves to control transport is of interest both for the practical achievement of fusion relevant conditions, and as a "knob" which can be used for fundamental physics investigations of the plasma response to applied forces and flows.

 

 

Fig. 1 RF driven flows are “open loop”, making them easier than “closed loop” turbulence problems. Thus rf allows the study of fundamental nonlinear physics in a controlled context.

 

 

  

Fig. 2 Results of a 1D model for sheared flows generated by IBW absorption at the ion cyclotron resonance layer here located at x = 0.  Here x is a radial variable and the wave is incoming from the right.  Ex is the wave electric field, S and P are the Poynting flux and absorbed power. The right panels show the toroidal (z) and poloidal (q) components of the rf-generated force and the resulting plasma flows. Taken from Ref. 3.

Recent results

Work at Lodestar in collaboration with ORNL and the RF SciDAC project has advanced the theory of rf-driven flows by extending previous publications.[1‑3] A general frequency gyrokinetic formulation has been developed which calculates the nonlinear forces on the plasma using a kinetic moment approach that is valid to first order in the ratio of the gyroradius compared to the wave envelope scale length and the plasma equilibrium scale length.  We obtain a compact form for the nonlinear rf-induced force on the plasma for tokamak geometry.[4]  Numerical results [5] based on this work show that ICRF mode conversion process can be used to produce short wavelength modes that are suitable for generating rf forces.

Both the nonlinear stress tensor and the Lorentz force contribute to the net force on a fluid element. Flux-surface-averaged flows are driven by two classes of terms: direct absorption of wave momentum and dissipative stresses.  Furthermore, the general kinetic expression for the force reduces to the standard cold-fluid ponderomotive force in an appropriate limit, but in this limit no flows are driven.

The topic of rf-driven sheared flows is emerging as a natural area of collaboration between the rf, turbulence and transport communities.  The results of an integrated effort in this area could be interesting from a physics perspective, providing a deeper understanding of interaction of nonlinear forces, flows, and the plasma response; and important from a practical perspective, giving experiments a flexible knob for control of transport barriers.

More on the basic physics

Three basic mechanisms for nonlinear rf forces are:
                        1) photon absorption
                        2) photon reflection, reactive ponderomotive forces
                        3) momentum redistribution

Plasma flows in a tokamak can be driven by 1) and 3) but not 2).  The basic physics of rf-forces on plasma has been discussed in the pioneering work of Ref. 6.  See also several recent Lodestar Reports and slides from meeting presentations and seminars:

·        Momentum Conservation and Nonlinear RF-Induced Flows, J.R. Myra, D.A. D'Ippolito, L.A. Berry, E.F. Jaeger and D.B. Batchelor, 15th Topical Conference on Applications of Radio Frequency Power to Plasmas, Grand Teton National Park, Moran, WY, May 19-21, 2003.

·        Nonlinear radio-frequency generation of sheared flows, J.R. Myra, D.A. D'Ippolito, L.A. Berry, E.F. Jaeger, D.B. Batchelor and the Rf SciDAC Team, presented at the Transport Task Force Meeting, April 2-5, 2003, Madison, WI.

·        Nonlinear radio-frequency generation of sheared flows, J.R. Myra, D.A. D'Ippolito, L.A. Berry, E.F. Jaeger, D.B. Batchelor and the Rf SciDAC Team, presented at the MIT/PSFC Spring Seminar Series, May 9, 2003, Cambridge, MA.

References

  1. E.F. Jaeger, L.A. Berry and D.B. Batchelor, Phys. Plasmas 7, 641 (2000); E. F. Jaeger, L. A. Berry, and D. B. Batchelor Phys. Plasmas 7, 3319 (2000).
  2. J.R. Myra and D.A. D’Ippolito, Phys. Plasmas 7, 3600 (2000).
  3. J.R. Myra and D.A. D’Ippolito, Phys. Plasmas 9, 3867 (2002).
  4. J.R. Myra, L.A. Berry, D.A. D'Ippolito, E.F. Jaeger and D.B. Batchelor, report in preparation.
  5. E.F. Jaeger, L.A. Berry, J.R. Myra, D.B. Batchelor, et al., Phys. Rev. Lett. 90, 195001 (2003).
  6. G.G. Craddock and P.H. Diamond, Phys. Rev. Lett. 67, 1535 (1991); G.G. Craddock, P.H. Diamond, M. Ono and H. Biglari, Phys. Plasmas 1, 1944 (1994).