Electron-driven instabilities

The electron temperature gradient and the density gradient can generate instabilities from the ion scales and up to the electron scales. The so-called trapped electron mode (TEM) can be destabilized either by the density gradient of by the electron temperature gradient, and the electron temperature gradient (ETG) mode, is destabilized when the electron temperature gradient is large as compared to the density gradient.

In TJ-II, typical experimental ion temperature profiles are almost flat and then, the ITG mode is not relevant. On the other hand, the electron temperature profile is usually peaked at the center of the plasma and exhibits large gradients in the plasma core. The density profiles also have significant gradients, usually. Thus, with typical profiles both TEM and ETG modes can be destabilized.

Figure 1. Electrostatic potential in a period of the device obtained in a linear simulation of electrostatic instabilities in the standard configuration of TJ-II, using kinetic electrons and ions.

The electron-driven modes have been studied in the TJ-II in global PIC simulations with EUTERPE using typical plasma scenarios [Sánchez et al. EPS 2014] and also in dedicated experiments in which the profiles were changed by changing the ECRH heating power and deposition location [Sánchez et al. NF 2019].

These simulations are carried out with two fully kinetic species, ions and electrons, and then are much more expensive computationally than ITG simulations as the fast electron dynamics has to be followed and smaller spatial scales have to be resolved with increased resolution. Some results if this kind of simulations are shown in the figures below.

Figure 2. Amplitude of potential at toroidal angle phi=0 in TJ-II.

Figure 1 shows the electrostatic potential in a period of the device obtained in a linear simulation of electrostatic instabilities in the standard configuration of TJ-II. Experimental density and temperature profiles were used in this simulation. The potential is shown for r/a=0.75 where the perturbation to the potential is maximum. The potential amplitude is localized poloidally and peaks at very narrow bands that are aligned with the magnetic field lines and coinciding with the location of bad (negative) magnetic curvature and small local magnetic shear.

Large amplitude stripes are located at regions where the modulus of the magnetic field has local minima, which betrays that this modes are associated with trapped particles (TEM).

Figure 2 shows the amplitude of potential is shown at toroidal angle phi=0 for a simulation in the standard configuration of TJ-II using experimental profiles and kinetic ions and electrons.

The localization of instabilities predicted by numerical simulations was observed in experimental measurements by Doppler reflectometry in dedicated experiments in TJ-II.

Figures 3 and 4 show the amplitude of potential in linear simulations in two configurations of TJ-II (the standard and a high rotational transform one, respectively) using experimental density and temperature profiles [Sánchez et al. NF 2019].

Figure 3. The amplitude of potential at the plane of measurement of the Doppler reflectometry system in the standard configuration of TJ-II, obtained in a linear simulation using experimental density and temperature profiles and kinetic ions and electrons.
Figure 4. The amplitude of potential at the plane of measurement of the Doppler reflectometry system in a high-iota configuration of TJ-II, obtained in a linear simulation using experimental density and temperature profiles and kinetic ions and electrons.