REE7: Two-fluid modelling of large-scale rotation and internal transport barriers in tokamaks

Background

Magnetic confinement for fusion power production is being pursued through the ITER project. Generating strong magnetic fields to confine plasma is difficult and expensive, so reactor designers wish to maximise the plasma pressure that may be confined by a magnetic field. Experiments have shown that driving large-scale rotations of the plasma improves confinement. Gradients in the angular velocity are believed to suppress turbulence and create internal transport barriers, but measurements are difficult and current numerical simulations based on gyrokinetic theory provide little conceptual insight.

Techniques and Challenges

Existing numerical models solve the gyrokinetic equations for the evolution of the plasma distribution functions in a five-dimensional phase space. Numerical simulations are therefore very expensive, yet are still poorly resolved in velocity space. We are therefore studying different numerical methods for discretising velocity space, in particular truncated expansions in Hermite functions. Many natural discretisations of this system fail to capture Landau damping – an important phenomenon in plasma physics – due to their inability to resolve a cascade to ever finer scale structures in velocity space.

Results

We have applied hypercollisions – higher order diffusion terms in velocity space analogous to hyperviscosity in Navier–Stokes turbulence simulations – to dissipate disturbances at very small scales without noticeably affecting the larger scales. We have found that around ten Hermite moments accurately capture the growth and decay rates over the whole range of wavenumbers. This is a substantial reduction from the hundreds of degrees of freedom required by existing codes.

The Future

We are now studying more realistic models with more dimensions. In particular, we have restored degrees of freedom to the perpendicular velocity space. We believe a similar approach to the Hermite expansion used in parallel velocity space will lead to a drastic reduction in the number of degrees of freedom needed. Pursuing this work will guide us in the development of an accurate gyro-fluid or Landau-fluid model based on a very small number of degrees of freedom in velocity space.

References

Pueschel M.J., Dannert T., Jenko F.: On the role of numerical dissipation in gyrokinetic Vlasov simulations of plasma microturbulence, Computer Physics Communications, Volume 181, Issue 8, Pages 1428-1437, ISSN 0010-4655, DOI: 10.1016/j.cpc.2010.04.010, 2010

Zocco A., Schekochihin A.A.: Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection, and electron heating in low-beta plasmas, Physics of Plasmas 18, 102309, DOI:10.1063/1.3628639, 2011