Fast ion transport phenomena in turbulent toroidal plasmas

In the field of plasma physics, suprathermal ions are encountered e.g. in astrophysical jets, the solar wind, as well as fusion plasmas, where they originate from neutral beam injection or fusion reactions. One aspect of shared interest with astrophysical settings is their transport by different forms of plasma turbulence that may generally exhibit non-diffusive character. Therefore, fast ion cross-field transport by electrostatic turbulence is investigated on the TORoidal Plasma EXperiment (TORPEX), in the simple magnetized torus geometry. Lithium ions in the 30-70 eV range are injected toroidally into hydrogen plasmas, with electron temperatures of typically below 5 eV. Previous studies identified sub- to superdiffusive regimes of transport, depending on the fast ion energy and related gyro- and drift-averaging effects.

The first part of this thesis investigates the phenomenon of local intermittency, as quantified by the skewness of fast ion time-series. A comprehensive data-set of fast ion time-series is presented to establish observations of intermittency across all non-diffusive transport regimes. Through the development of an experiment-based particle tracing algorithm, the physical picture of a small, but meandering fast ion beam is clarified and the generation of local intermittency demonstrated through synthetic time-series. Furthermore, an analytical model is presented to predict the skewness of such time-series solely based on their time-average value and two basic beam parameters. Its application to the experimental data shows very good agreement between the predicted and the measured skewness. These combined findings demonstrate conclusively how intermittency is generated across all transport regimes in our system, or by any type of meandering beam.

The second part of this thesis advances the statistical description of non-diffusive fast ion transport through Fractional Diffusion Equations (FDEs). To improve upon physical shortcomings of models that assign distributions with infinite variance to the random jumps of particles, we utilize tempered Lévy distributions that exponentially truncate jumps beyond a chosen scale. The FDE and propagator of Truncated Asymmetrical Fractional Lévy Motion (TAFLM) are derived by judiciously adapting earlier path-integral methods. Being generally non-Gaussian at early times, the propagators converge arbitrarily slowly to Gaussians in the long-time limit, while preserving their overall non-diffusive behaviour. Very good agreement with fluid-tracer results from the Global Braginskii Solver is found in the most strongly spread, quasi-diffusive regime. Here, the finite domain size of the turbulent plasma structures can now take effect through the truncation scale. Further use of these statistical methods can be discussed across the wider field of bounded, non-diffusive transport.

Suprathermal ion transport in turbulent magnetized plasmas

Alexandre Dominique Bovet

Suprathermal ions, which have an energy greater than the quasi-Maxwellian background plasma temperature, are present in many laboratory and astrophysical plasmas. In fusion devices, they are generated by the fusion reactions and auxiliary heating. Controlling their transport is essential for the success of future fusion devices that could provide a clean, safe and abundant source of electric power to our society. In space, suprathermal ions include energetic solar particles and cosmic rays. The understanding of the acceleration and transport mechanisms of these particles is still incomplete. Basic plasma devices allow detailed measurements that are not accessible in astrophysical and fusion plasmas, due to the difficulty to access the former and the high temperatures of the latter. The basic toroidal device TORPEX offers an easy access for diagnostics, well characterized plasma scenarios and validated numerical simulations of its turbulence dynamics, making it the ideal platform for the investigation of suprathermal ion transport. This Thesis presents three-dimensional measurements of a suprathermal ion beam injected in turbulent TORPEX plasmas. The combination of uniquely resolved measurements and first-principle numerical simulations reveals the general non-diffusive nature of the suprathermal ion transport. A precise characterization of their transport regime shows that, depending on their energies, suprathermal ions can experience either a superdiffusive transport or a subdiffusive transport in the same background turbulence. The transport character is determined by the interaction of the suprathermal ion orbits with the turbulent plasma structures, which in turn depends on the ratio between the ion energy and the background plasma temperature. Time-resolved measurements reveal a clear difference in the intermittency of suprathermal ions time-traces depending on the transport regime they experience. Conditionally averaged measurements uncover the influence of field elongated turbulent structures, referred to as blobs, on the suprathermal ion beam. A theoretical model extending the Brownian motion to include non-Gaussian (Lévy) statistics and long-range temporal correlation is developed. This model successfully describes the evolution of the radial particle density from the numerical simulations and provides information on the microscopic processes underlying the non-diffusive transport of suprathermal ions.

EPFL2015

Self-consistent interaction of fast particles and ICRF waves in 3D applications of fusion plasma devices

Jonathan Marc Philippe Faustin

Tokamaks and stellarators are the most promising reactor concepts using the magnetic confinement to contain the plasma fuel. Reactors capable of sustaining deuterium-tritium (D-T) fusion reactions requires the confinement of a very high temperature plasma (above 100 millions kelvin). In addition to external heating methods, the slowing down of alpha particles (helium-4 nuclei) born from D-T fusion reactions on the background plasma represents a significant source of plasma heating. The good confinement of fast particles is therefore one of the most important aspect of magnetic fusion devices. Furthermore, long plasma operation in future fusion reactors requires the control of inherent plasma instabilities. These instabilities are particularly dangerous in tokamaks because of the large plasma current necessary to establish the confining magnetic field. In this thesis we use the numerical code package SCENIC to study the application of Ion Cyclotron Range of Frequency (ICRF) waves to tokamak and stellarator devices. This numerical tool was built to self-consistently solve, in three dimensional configurations, the plasma magnetohydrodynamic (MHD) equilibrium, the ICRF wave propagation and the resonant ion distribution function. SCENIC is used to interpret how the sawtooth instability can be controlled in tokamaks by appropriate application of ICRF waves. This control method was successfully tested in the JET tokamak and it is foreseen to be applied in the future ITER tokamak. Such plasma degrading instabilities are not, however, expected in stellarators because they operate with no plasma current. The recently started stellarator Wendelstein 7-X (W7-X) must however prove experimentally that fast particles particles can be confined in an optimised quasi-isodynamic magnetic configuration. An efficient auxiliary source of fast ions is required in W7-X since it is not designed to procude alpha particles via D-T fusion reactions. In this thesis, we address the possibility of generating a significant fast ion population with ICRF waves in W7-X. SCENIC simulations are employed in order to identify relevant fast ion loss channels that may still exist in the W7-X quasi-omnigenous equilibrium. These simulations show that ICRF minority heating may not be suitable for producing fast ions in W7-X plasmas. It is found that a high energy tail is more likely to be developed if a three-ion species scheme is applied.

EPFL2017

Modelling of sawtooth-induced fast ion transport in positive and negative triangularity in TCV

Marcelo Baquero Ruiz, Basil Duval, Alexander Karpushov, Antoine Pierre Emmanuel Alexis Merle, Dmytry Mykytchuk, Mario Podesta, Olivier Sauter, Lorenzo Stipani, Duccio Testa, Matteo Vallar

Internal kinks are a common magneto hydro-dynamic (MHD) instability observed in tokamak operation when the q profile in the plasma core is close to unity. This MHD instability impacts both the transport of the bulk plasma (current, particle and energy transport) and minority species, such as fast ions. In tokamak a configuration variable (TCV) (R (0)/a = 0.88 m/0.25 m) the fast ion population is generated in the plasma by neutral beam tangential injection of energies up to 28 keV. TCV features 16 active shaping coils permitting a great flexibility in plasma shape, including negative triangularity (delta) configurations that show surprisingly high confinement. This study focuses on the transport of fast ions induced by sawteeth, by comparing two triangularity cases and simulation results with experimental data. Comparison of two equilibria with opposite delta shows that the fast ion drifts are larger for delta < 0. Furthermore, the sawtooth-induced transport in this case is larger than delta > 0 in similar conditions. Comparison with experimental data confirms the dominance of the modification of thermal kinetic profiles following the sawtooth crash in explaining drops in the neutron rates and fast ion D-alpha signals. Additional fast ion diffusion, however, improves the interpretation of the experimental data. For delta < 0, the amplitude of the perturbation better representing the experimental data is larger. Finally, an exploratory study for 50 keV particles (soon available in TCV) shows that the situation does not worsen for such particles.