Theoretical astrophysics and plasma physics at RPC

Abstract:

Breaking the up-down symmetry of tokamaks removes a constraint limiting intrinsic momentum transport, and hence toroidal rotation, to be small. Using gyrokinetic theory, we study the effect of different up-down asymmetric flux surface shapes on the turbulent transport of momentum. This is done by perturbatively expanding the gyrokinetic equation in large flux surface shaping mode number. It is found that the momentum flux generated by shaping that lacks mirror symmetry (which is necessarily up-down asymmetric) has a power law scaling with the shaping mode number. However, the momentum flux generated by mirror symmetric flux surface shaping (even if it is up-down asymmetric) decays exponentially with large shaping mode number. These scalings are consistent with nonlinear local gyrokinetic simulations and indicate that low mode number shaping effects (e.g. elongation, triangularity) are optimal for creating rotation. Additionally it suggests that breaking the mirror symmetry of flux surfaces may generate significantly more toroidal rotation

Abstract:

Divertor detachment may be essential to reduce heat loads to magnetic fusion tokamak reactor divertor surfaces. Yet in experiments it is difficult to control the extent of the detached, low pressure, plasma region. At maximum extent the front edge of the detached region reaches the x-point and can lead to degradation of core plasma properties. We define the `detachment window' in a given position control variable C (for example, the upstream plasma density) as the range in C within which the front location can be stably held at any position from the target to the x-point; increased detachment window corresponds to better control. We extend a 1D analytic model[1] to determine the detachment window for the following control variables: the upstream plasma density, the impurity concentration and the power entering the scrape-off layer (SOL). We find that variations in magnetic configuration can have strong effects; Increasing the ratio of the total magnetic field at the x-point to that at the target, Bx/Bt , (total flux expansion, as in the Super-X divertor configuration) strongly increases the detachment window for all control variables studied, thus strongly improving detachment front control and the capability of the divertor plasma to passively accommodate transients while still staying detached. Increasing flux tube length and thus volume in the divertor, through poloidal flux expansion (as in the snowflake or x-divertor configurations) or length of the divertor, also increases the detachment window, but less than the total ux expansion does. Thesensitivity of the detachment front location, zh, to each control variable, C, defined as δzh/δC , depends on the magnetic configuration. The size of the radiating volume and the total divertor radiation increase α (Bx/Bt)^2 and α Bx/Bt , respectively, but not by increasing divertor poloidal flux expansion or field line length. We believe this model is applicable more generally to any thermal fronts in flux tubes with varying magnetic field, and similar sources and sinks, such as detachment fronts in stellarator divertors and solar prominences in coronal loops.

Abstract:

A poloidal tilting symmetry of the local nonlinear δf gyrokinetic model is demonstrated analytically and verified numerically. This symmetry shows that poloidally rotating all the flux surface shaping effects with large poloidal mode number by a single tilt angle has an exponentially small effect on the transport properties of a tokamak. This is shown using a generalization of the Miller local equilibrium model to specify an arbitrary flux surface geometry. With this geometry specification we find that, when performing an expansion in large flux surface shaping mode number, the governing equations of gyrokinetics are symmetric in the poloidal tilt of the high order shaping effects. This allows us to take the fluxes from a single configuration and calculate the fluxes in any configuration that can be produced by tilting the large mode number shaping effects. This creates a distinction between tokamaks with mirror symmetric flux surfaces and tokamaks without mirror symmetry, which is expected to have important consequences for generating toroidal rotation using updown asymmetry.