Nondiffusive transport regimes for suprathermal ions in turbulent plasmas

The understanding of the transport of suprathermal ions in the presence of turbulence is important for fusion plasmas in the burning regime that will characterize reactors, and for space plasmas to understand the physics of particle acceleration. Here, three-dimensional measurements of a suprathermal ion beam in the toroidal plasma device TORPEX are presented. These measurements demonstrate, in a turbulent plasma, the existence of subdiffusive and superdiffusive transport of suprathermal ions, depending on their energy. This result stems from the unprecedented combination of uniquely resolved measurements and first-principles numerical simulations that reveal the mechanisms responsible for the nondiffusive transport. The transport regime is determined by the interaction of the suprathermal ion orbits with the turbulent plasma dynamics, and is strongly affected by the ratio of the suprathermal ion energy to the background plasma temperature.

Figure 1

View of the TORPEX vessel with magnetic field line and suprathermal ion detection system. TORPEX contains open, helical magnetic field lines (violet) with a radial gradient in field strength that terminate on the vessel. Also shown are the suprathermal ion source on a toroidal sliding track and one detector mounted on a two-dimensional movable system that can also be displaced toroidally. This combination allows measurement of a three-dimensional suprathermal ion current profile. Computed examples of simulated suprathermal ion trajectories with an initial energy of 30 eV are shown in red, emitting from the source. Gyromotion and the irregular spreading of the ion beam due to interaction with the plasma turbulence is apparent. Simulated snapshots of the plasma potential are also displayed at two toroidal positions.

Figure 2

Poloidal suprathermal ion current profiles at different toroidal distances [(a), (d) $d=0.2\mathrm{m}$; (b), (e) $d=0.6$ m; (c), (f) $d=2.2$ m]. Top: $E=70$ eV; bottom: $E=30$ eV. The vertical drift due to the curvature and gradient of the magnetic field is apparent. The spreading due to the interaction with the turbulent plasmas is revealed and is more important for 30 eV ions. Ion current is stated in ${\mathrm{A}/\mathrm{m}}^2$.

Figure 3

Radial width of suprathermal ion current profiles as a function of toroidal distance traveled. Red squares and blue circles represent experimental measurements for ions emitted at 30 and 70 eV, respectively. Continuous bands are drawn from a synthetic diagnostic of numerical simulations for 30 eV (red) and 70 eV (blue) ions [19]. The beam width oscillates due to the gyromotion of the ions. A slight discrepancy between measurements and simulations in the phase and amplitude of these oscillations is visible. This comes from the fact that they depend on the injection angle and energy, which can slightly vary from one measurement to the other. The width of the bands is obtained by varying the simulations input parameters within experimental uncertainties. On top of this oscillation, the beam spreads due to the interaction of the ions with the turbulence. The different trends of the spreading indicate different transport regimes. The ballistic phase, lasting approximately one gyroperiod (first three measurements), is in good agreement with the simulations for both energies. Then, the 30 eV ion beam spreads strongly until a toroidal distance of $\simeq 1$ m. The accumulated spreading of the 70 eV ion beam is less than the 30 eV beam. Error bars are computed by modeling the measurement with a finite size detector inlet (4 mm radius) and 2 mm absolute positioning accuracy.

Figure 4

Simulated suprathermal ion trajectories projected on the poloidal plane of TORPEX. Ions with an initial energy of 30  eV (in red) have a smaller Larmor radius and are transported by the plasma turbulence. Ions with an initial energy of 70 eV (in blue) have larger Larmor radii and larger vertical drifts. They average the turbulent fluctuations during their gyromotion, which effectively reduces their radial transport. As they drift upward, 70 eV ions perform consecutive steps in opposite radial direction. A snapshot of the simulated plasma potential, displayed in the background, shows the interchange mode positioned approximately at $r=-12$ cm with a vertical wavelength $\lambda \simeq 18$ cm and the turbulent structures propagating toward the low field side.

Figure 5

Variance of the ion radial positions as a function of time. Results obtained from the numerical simulations reproducing the experimental data in Fig. 3, for ions at 30 eV (red) and 70 eV (blue). Fits of the different phases, shown in dashed lines, provide the values of the transport exponent ${\gamma }_R$. A slope corresponding to ${\gamma }_R=2$ is shown next to the initial ballistic phase. For ions of 30 eV, the transport is then superdiffusive with a transport exponent ${\gamma }_R\simeq 1.20$ during approximately four gyromotions and finally close to a diffusive process with ${\gamma }_R\simeq 0.92$. For ions of 70 eV, the transport is subdiffusive with ${\gamma }_R\simeq 0.51$. Time is normalized to the ions gyroperiod.