Particle-in-cell simulations of parametric decay instabilities at the upper hybrid layer of fusion plasmas to determine their primary threshold

Parametric decay instabilities (PDIs) are nonlinear processes by which energy from a strong pump wave may be directed into other waves at other frequencies, in particular natural modes of the medium, provided that energy and momentum are conserved. The particle-in-cell (PIC) code EPOCH is used to simulate PDIs in a magnetically confined fusion plasma converting a 105 GHz microwave X-mode pump wave into electrostatic daughter waves at the upper hybrid (UH) layer. Modes associated with the PDIs as well as a linearly converted electron Bernstein wave (EBW) are identified in f- and k-space. The PDI daughter modes are found to agree with experimental observations from ASDEX Upgrade as well as with analytical predictions, showing a nonlinear increase in power above a predicted threshold

On the selection rules for three-wave interactions along ray trajectories

Three-wave interactions may occur in media with quadratic nonlinearities, which allow for a flow of power between linear waves. The interactions require selection rules similar to conservation of energy and momentum to be satisfied. Equations are presented to solve these selection rules efficiently along the ray trajectory of a pump wave via integration similar to how ray trajectories are determined numerically. This is convenient when dealing with large amplitude beams which may interact with waves along its trajectory. Reformulating the selection rules as a system of ODEs means that the selection rules may be solved using dispersion relations for the three waves, even if the dispersion relations cannot be solved for frequency or wavevector, which would otherwise be needed. In numerical implementations, root-finding algorithms, which may be unstable for complicated dispersion relations, can be avoided. A simple set of equations valid in one-dimensional are presented first. The corresponding equations in arbitrary dimension, including 2D and 3D, are then derived. A set of equations are also derived to find different solutions to the selection rules at a fixed point. Examples with the derived equations applied to plasma physics are presented.</p

Cascades of Parametric Instabilities in the Tokamak Plasma Edge during Electron Cyclotron Resonance Heating

We report observations of nonlinear two-plasmon decay instabilities (TPDIs) of a high-power microwave beam, a process similar to half-harmonic generation in optics, during electron cyclotron resonance heating in a tokamak. TPDIs are found to occur regularly in the plasma edge due to wave trapping in density fluctuations for various confinement modes, and the frequencies of both observed daughter waves agree with modeling. Emissions from a cascade of subsequent decays, which indicate a generation of ion Bernstein waves, are correlated with fast-ion generation. This emphasizes the limitations of standard linear microwave propagation models and possibly paves the way for novel microwave applications in plasmas.</p

Letter

We present novel experimental evidence of parametric decay instability of microwave beams in the plasma edge of the Wendelstein 7-X stellarator. We propose that the instability is sustained by trapping of only one daughter wave in the non-monotonic density profile measured with high spatial resolution within a stationary magnetic island. The power levels and spectral shapes of the detected microwave signal are reproduced by numerical modelling and a theoretical power threshold is predicted around 300 kW, comparable with observations. We predict a fraction of power drained by daughter waves around 4% in the experiments, potentially increasing above 50% for more hollow edge density profiles. Such absorption levels could significantly reduce the efficiency of the microwave heating and current-drive system in tokamaks and stellarators