Time intermittency in nondiffusive transport regimes of suprathermal ions in turbulent plasmas

Intermittent phenomena have long been studied in the context of nondiffusive transport across a variety of fields. In the TORPEX device, the cross-field spreading of an injected suprathermal ion beam by electrostatic plasma turbulence can access different nondiffusive transport regimes. A comprehensive set of suprathermal ion time series has been acquired, and time intermittency quantified by their skewness. Values distinctly above background level are found across all observed transport regimes. Intermittency tends to increase toward quasi- and superdiffusion and for longer propagation times of the suprathermal ions. The specific prevalence of intermittency is determined by the meandering motion of the instantaneous ion beam. We demonstrate the effectiveness of an analytical model developed to predict local intermittency from the time-average beam. This model might thus be of direct interest for similar systems, e.g., in beam physics, or meandering flux-rope models for solar energetic particle propagation. More generally, it illustrates the importance of identifying the system-specific sources of time-intermittent behavior when analyzing nondiffusive transport.

Figure 1

Fast ion experimental setup in TORPEX. The poloidal coordinates $R$ and $Z$ are indicated, with $R=Z=0$ on axis and the toroidal source-detector distance $D$. The gridded energy analyzer (GEA) can be displaced over most of the poloidal cross section. Fast ion trajectories are shown in red for an injection energy $E$ of 30 eV, and in dark blue for 70 eV. A magnetic field line is indicated in purple. A plasma density profile interpolated from ion-saturation current measurements with the Langmuir probe arrays HEXTIP-U [26] is shown on the left, and its floating potential profile is shown on the right.

Figure 2

Segments of the local time series of fast ion current density $J\left(t\right)$ that feature the highest skewness at $D=171\text{cm}$ and respective energy. The ion-source on-phases are indicated in red, and the off-phases are in black. Distinct peaks are visible during the on-phase. The on-phase mean $\mu$ and skewness ${\gamma }_{\mathcal{S}}$ are given. For the mean, the off-phase value was subtracted. The locations $(R,Z)$ of the GEA where these time series were collected are marked in Fig. 3.

Figure 3

Normalized mean and skewness profiles at $D=171\text{cm}$. Note the larger spread and reduced vertical drift at $E=30\text{eV}$, as well as the lower peak current density and higher maximum skewness. The gray circles in (a) indicate detector positions, and green crosses denote the positions at which the time-series samples in Fig. 2 were acquired. The noise contributions from the background plasma increase significantly toward the interchange mode on the HFS, and reduce the on-phase skewness here compared to the LFS.

Figure 4

Maximum normalized skewness for different source-detector distances $D$ and fast ion energies $E$ of 30, 50, and 70 eV in red, yellow, and dark blue (circles, top to bottom), respectively. Crosses show values before normalization [see Eq. (2)] and are offset by $D=+2\text{cm}$ for clarity. The dotted line indicates the maximum background value of ${\gamma }_{\mathcal{N}}=2.2$.

Figure 5

Schematic of quantities in the analytical model, comprising the mean profile $J\left(\mathbf{R}\right)$ and smaller instantaneous profile $j\left(\mathbf{R}\right)$, which is deflected rigidly through the displacement PDF $f\left(\mathbf{R}\right)$ toward a particular measurement position ${\mathbf{R}}_0$, where the detector area (aperture) is centered.

Figure 6

Fits (blue) of the second (a) and third (b) central moment of the fast ion time series at 70 eV and $D=171\text{cm}$, as a function of the mean profile value $J(R,Z)$, as detailed on the right-hand side of Eqs. (8) and (9). The crosses represent experimental data points calculated from measurements on each time series as detailed on the left-hand side. The corresponding (normalized) profile is given in Fig. 3.

Figure 7

On-phase skewness ${\gamma }_{\mathcal{S}}$ at $D=\{126,146,171\}\text{cm}$ (a)–(c) for 70 eV profiles as predicted from Eq. (10) vs measured values. The estimated total fast ion currents are $I=\{5.04,2.97,2.36\}\mu \text{A}$.

Figure 8

On-phase skewness ${\gamma }_{\mathcal{S}}$ at $D=\{126,146,171\}\text{cm}$ (a)–(c) for 30 eV profiles as predicted from Eq. (10) [with $J_{C[2,3]}$ from Eqs. (12) and (13)] vs measured values. The estimated total fast ion currents are $I=\{2.35,2.5,3.2\}\mu \text{A}$.