Assessment of antenna parameters for current drive in thermonuclear reactors by radio-frequency power

The most challenging conceptual problem of thermonuclear energy research based on deuterium plasmas magnetically trapped in toroidal machines, named tokamaks, consists in how to control and actively shape during operations the current density radial profile of plasma column. To achieve this control is of paramount importance, indeed, for the following reasons: i) to prevent the onset of unstable modes that detriment the figures of stability and fusion power gain from thermonuclear reactions, which are necessary for a reactor; ii) to remove the obstacle of tokamaks of being intrinsically inductive machines, i.e., capable of producing only transient plasma regimes, in front of the reactor’s need of operating in steady- state. In regard to the former problem, data of modelling and experiments available in the last 25 years showed that the growth rate of pernicious unstable plasma modes, of magneto-hydro-dynamic (MHD) nature, is strongly depressed when a relative maximum of the plasma current density is suitably located at radii close to the region that interests the unstable modes. They make challenging the possibility of achieving the desired thermal insulation that is necessary for allowing thermonuclear conditions of high temperatures (∼100 million of degrees) and high density (∼1020 m-3) of plasma. The limitation of pulsed operation was, instead, well known since the assessment (half century ago) of the tokamak concept, and this was soon perceived as the major conceptual obstacle against the development of a thermonuclear fusion reactor. Indeed, at that time, the further problem of the onset of unstable modes (which produces anomalous transport effects, on heat and matter, via micro-turbulence and MHD modes) did not appear yet. The discovery in 1981 at Princeton (USA) of the lower hybrid current drive (LHCD) effect was considered very attractive for facing both the mentioned major problems of a reactor. The LHCD effect consists in the capability of multimegawatt microwave power at several gigahertz, coupled to quasi-electrostatic natural modes of plasma, named lower hybrid (LH) waves, of non- inductively producing current in tokamak plasma. Consequently, the plasma current can flow with continuity in a tokamak under RF power injection. The antenna consists in phased arrays of rectangular waveguides that suitably fit the gaps of the tokamak’s magnet. Via electronic setting of the waveguide phasing, the refractive index (n//, in the direction parallel to the confinement magnetic field) of the RF power spectrum can be usefully determined in order to Landau-resonate with a tail of the electron distribution of plasma electrons, for the temperature that corresponds to the radial layer where the current drive effect would be desirably produced. As further support of attractiveness of the LHCD effect, it should be considered that other methods utilising radiofrequency power in the ion-cyclotron and electron-cyclotron resonant frequencies, as well those that exploit strong power injection of energetic ion beams, present much lower efficiency in driving plasma current than that possible by the LHCD effect. Unfortunately, for long time the LHCD effect was observed to occur successfully only when operating at too low plasma densities – of about a factor three lower than that required by reactor – despite of the many attempts carried out for decades in many laboratories in the world. In these experiments, the RF power was however successfully coupled by the antenna, but remained unexpectedly deposited at the plasma periphery, as a consequence of parasitic effects of plasma edge. Only recently, an original research performed in the ENEA-Frascati Lab. – whose results have been published on Nature Communications: 5,55,2010 – has assessed a new method for enabling the occurrence of the LHCD effect at reactor graded high plasma densities. This method is based on previous theoretical predictions of reduced parasitic effect under higher temperature of plasma edge (ENEA Laboratory work published on Physical Review Letters in 2004). These works demonstrated that the parasitic damping of the coupled RF power is produced by non-linear wave-plasma interaction, named parametric instability (PI), which is capable of strongly altering (namely, broadening) the n// spectrum launched by the antenna. Consequently, the temperature required for Landau-resonance of the RF power spectrum with plasma electrons is strongly diminished, which causes absorption in the cold region of plasma periphery. This Thesis is focused on helping solution of an important conceptual problem, which is part of this challenge, by means of a noticeable application of strong radiofrequency power coupled to quasi- electrostatic plasma waves (LH waves). From the engineering point of view, results produced by an originally developed numerical code (LHPI) have backed solving the problem (existing for decades) of how to enable the antenna parameters determining the deposition of the coupled RF power (of several gigahertz) at a desired radial layer of the plasma column. This task would be ideally required indeed by an antenna. With respect to other current drive tool, based on electron cyclotron resonance (at about 150 GHz), this cannot guarantee the coverage of the outer half radius of plasma necessary for a reactor. Thanks to results reported here, new understanding is provided that for the first time enables a waveguide antenna for current drive in tokamaks to tailor the deposition in the plasma, in different operating conditions, by electronically acting on the launched spectrum (via feeding/phasing of waveguides). In particular, a) in case of too high plasma densities at the plasma edge, as occurs in running experiments, operation with higher temperature of plasma is recommended to avoid parasitic effects of spectral broadening. b) in case of too high plasma temperature at the plasma periphery, as envisaged in a future reactor, the assessment of a new antenna parameter, Δn//, allows however guaranteeing useful penetration of the coupled RF power into the plasma bulk. More specifically, the following issues have been considered in the Thesis. 1) Available data of RF power spectral broadening, kept during experiments carried out on the EAST tokamak (China), have been interpreted on the basis of the parametric instability modelling. This work has been performed thanks to a new version of a numerical code (developed on the basis of a previously version available since 1989 at ENEA-Frascati) having much improved qualities of velocity and precision. 2) The work has also focused on the key problem of how to enable the occurrence of the LHCD effect also in conditions of high electron temperature of reactor plasmas. Indeed, precisely the high temperature that in a reactor is expected to occur even at large radii of the plasma column which usefully prevents the occurrence of the parasitic effects observed in the experiments – would also produce an undesired RF power deposition too far out in the plasma, owing too strong electron Landau damping, as shown by numerical results. This circumstance is in contrast with the primary goal of a reactor of being equipped by current profile control, so that the too high plasma temperature of reactor represents the remaining major conceptual problem preventing the exploitation of the LHCD tool. This problem has been solved by the new outcome described in the Thesis. This result consists in having identified in a sufficiently narrow n// antenna power spectrum the way for reducing the wave-plasma interaction at high temperatures, thus enabling the penetration of the coupled RF power in the hot and dense regions of reactor plasmas. This diminished wave-plasma interaction is consequence of the content of standard quasi-linear theory of plasma waves: this aspect remained singularly undisclosed so far. 3) Finally, the thesis has analysed the problem of how to design an antenna capable of producing the required power spectra necessary for envisaging a current profile control system in a thermonuclear reactor. For carrying out this work, a numerical code has been utilised capable of treating waveguide antenna geometries however complex. Consequently, the desired sufficiently narrow n// power spectrum can be produced, indeed, by suitable array of active and passive phased array of rectangular waveguides. Moreover, the scan of the main antenna parameters (power reflection coefficient, directivity, etc,) performed assuming realistic conditions of plasma edge, has shown that all requirements should be satisfied for envisaging a current profile control system for a tokamak reactor based on the exploitation of the LHCD effect. The lower hybrid current drive tool in now fully supported by know how necessary for enabling the current profile control in the warm and dense plasma of thermonuclear reactor. The current drive method assessed here is of paramount importance for conceiving antennas to be implemented in the system of current profile control, which a reactor mandatorily requires.