Alexandre Bovet

Transport equation describing fractional Lévy motion of suprathermal ions in TORPEX

Suprathermal ions, created by fusion reactions or by additional heating, will play an important role in burning plasmas such as the ones in ITER or DEMO. Basic plasma experiments, with easy access for diagnostics and well-controlled plasma scenarios, are particularly suitable to investigate the transport of suprathermal ions in plasma waves and turbulence. Experimental measurements and numerical simulations have revealed that the transport of fast ions in the presence of electrostatic turbulence in the basic plasma toroidal experiment TORPEX is generally non-classical. Namely, the mean-squared radial displacement of the ions does not scale linearly with time, but 〈r2(t)〉 tγ, with γ ≠ 1 generally, γ > 1 corresponding to superdiffusion and γ < 1 to subdiffusion. A generalization of the classical model of diffusion, the so-called fractional Levy motion, which encompasses power-law (Levy) statistics for the displacements and correlated temporal increments, leads to non-classical dynamics such as that observed in the experiments. On a macroscopic scale, this results in fractional differential operators, which are used to model non-Gaussian, non-local anomalous transport in a growing number of applied fields, including plasma physics. In this paper, we show that asymmetric fractional Levy motion can be described by a diffusion equation using space-fractional differential operator with skewness. Numerical simulations of tracers in TORPEX turbulence are performed. The time evolution of the radial particle position distribution is shown to be described by solutions of the fractional diffusion equation corresponding to asymmetric fractional Levy motion in sub- and superdiffusive cases.

Investigation of fast ion transport in TORPEX

Basic aspects of fast ion transport in ideal interchange-mode unstable plasmas are investigated in the simple toroidal plasma device TORPEX. Fast ions are generated by a miniaturized lithium 6+ ion source with energies up to 1 keV, and are detected using a double-gridded energy analyser mounted on a two-dimensional movable system in the poloidal cross-section. The signal-to-noise ratio is enhanced by applying a modulated biasing voltage to the fast ion source and using a synchronous detection scheme. An analogue lock-in amplifier has been developed, which allows removing the capacitive noise associated with the voltage modulation. We characterize vertical and radial transport of the fast ions, which is associated with the plasma turbulence. Initial experimental results show good agreement with numerical simulations of the fast ion transport in a global fluid simulation of the TORPEX plasma.

Basic investigations of electrostatic turbulence and its interaction with plasma and suprathermal ions in a simple magnetized toroidal plasma

Progress in basic understanding of turbulence and its influence on the transport both of the plasma bulk and of suprathermal components is achieved in the TORPEX simple magnetized torus. This configuration combines a microwave plasma production scheme with a quasi-equilibrium generated by a toroidal magnetic field, onto which a small vertical component is superimposed, simulating a simplified form of tokamak scrape-off layers. After having clarified the formation of blobs in ideal interchange turbulence, TORPEX experiments elucidated the mechanisms behind the blob motion, with a general scaling law relating their size and speed. The parallel currents associated with the blobs, responsible for the damping of the charge separation that develops inside them, hence determining their cross-field velocity, have been measured. The blob dynamics is influenced by creating convective cells with biased electrodes, arranged in an array on a metal limiter. Depending on the biasing scheme, radial and vertical blob velocities can be varied. Suprathermal ion transport in small-scale turbulence is also investigated on TORPEX. Suprathermal ions are generated by a miniaturized lithium source, and are detected using a movable double-gridded energy analyser. We characterize vertical and radial spreading of the ion beam, associated with the ideal interchange-dominated plasma turbulence, as a function of the suprathermal ion energy and the plasma temperature. Experimental results are in good agreement with global fluid simulations, including in cases of non-diffusive behaviour. To investigate the interaction of plasma and suprathermal particles with instabilities and turbulence in magnetic configurations of increasing complexity, a closed field line configuration has recently been implemented on TORPEX, based on a current-carrying wire suspended in the vacuum chamber. First measurements indicate the creation of circular symmetric profiles centred on the magnetic axis, and instabilities driven in the region of strong gradients, with a strong ballooning character.

Plasma turbulence, suprathermal ion dynamics and code validation on the basic plasma physics device TORPEX

The TORPEX basic plasma physics device at the Center for Plasma Physics Research (CRPP) in Lausanne, Switzerland is described. In TORPEX, simple magnetized toroidal configurations, a paradigm for the tokamak scrape-off layer (SOL), as well as more complex magnetic geometries of direct relevance for fusion are produced. Plasmas of different gases are created and sustained by microwaves in the electron-cyclotron (EC) frequency range. Full diagnostic access allows for a complete characterization of plasma fluctuations and wave fields throughout the entire plasma volume, opening new avenues to validate numerical codes. We detail recent advances in the understanding of basic aspects of plasma turbulence, including its development from linearly unstable electrostatic modes, the formation of filamentary structures, or blobs, and its influence on the transport of energy, plasma bulk and suprathermal ions. We present a methodology for the validation of plasma turbulence codes, which focuses on quantitative assessment of the agreement between numerical simulations and TORPEX experimental data.

Three-dimensional measurements of non-diffusive fast ion transport in TORPEX

In the basic plasma physics device TORPEX, progress in the fundamental understanding of supra-thermal ion transport is achieved by extensive sets of three-dimensional (3D) data, together with numerical simulations of supra-thermal ion tracers in fluid turbulent fields. A miniaturized lithium 6+ ion source injects fast ions with energies up to 1 KeV and a double-gridded energy analyzer is used as a detector. The source is mounted on a toroidally movable system and the detector can be moved in the poloidal cross-section, allowing one to reconstruct 3D fast ion current profiles. Synchronous detection is used to enhance the signal-to-noise ratio. A modulated biasing voltage is applied to the fast ion source and an analog lock-in amplifier is used to demodulate the detector signal. The analog lock-in amplifier is specially designed to remove the capacitive noise associated with the voltage modulation. Radial transport of the fast ions, associated with plasma turbulence, is characterized. A synthetic diagnostic allows comparing the experimental results with numerical simulations of the fast ion transport in a global fluid simulation of the TORPEX plasma. A good agreement is shown.

Measurements of interactions between waves and energetic ions in basic plasma experiments

To measure the transport of fast ions by various types of waves, complementary experiments are conducted in linear and toroidal magnetic fields in the large plasma device and the toroidal plasma experiment. Lithium sources that are immersed in the plasma provide the energetic ions. Spatial scans of collectors measure the transport. Techniques to find the beam and optimize the spatial sensitivity are described. Measurements of Coulomb scattering, resonant ) (

Non-diffusive transport of suprathermal ions by intermittent turbulent structures

We report on recent experimental, numerical and theoretical investigations of suprathermal ion transport and turbulent plasma dynamics in TORPEX. TORPEX is a toroidal device in which field-aligned blobs are intermittently generated and propagate across a confining magnetic field. Suprathermal ions are locally injected using a miniaturized source and detected using gridded energy analyzers. We show evidence for subdiffusive and superdiffusive transport of suprathermal ions, using an unprecedented combination of uniquely resolved three-dimensional measurements and first-principles numerical simulation. We present time-resolved measurements of suprathermal ion current fluctuations, which exhibit a clear causality relation with blobs, as revealed by a transfer entropy method for the superdiffusive case. This link is further investigated by using a conditional sampling technique, which allows resolving the cross-field dynamics of both blobs and the suprathermal ion beam, revealing that suprathermal ions experiencing superdiffusive transport are associated with bursty displacement events, resulting in highly intermittent time traces. This work links observations usually inaccessible in fusion devices and astrophysical plasmas, namely energy resolved three-dimensional time-averaged measurements, with Eulerian time-resolved measurements, which are often the only accessible measurements in such systems.