Ivo Furno and the CRPP Basic Plasma Physics Group
Centre de Recherche en Physique des Plasmas, Ecole Polytechnique Fédérale de Lausanne (EPFL), Association EURATOM – Confédération Suisse, CH-1015 Lausanne

Introduction

At the edge of tokamaks, the most promising magnetic confinement concept to obtain controlled nuclear fusion on Earth, a large fraction of the particle and heat transport is attributed to the presence of plasma blobs. These are isolated filamentary non-linear structures with increased density and temperature with respect to the surrounding plasma. Blobs are intermittently ejected and transported away from the main plasma into the outermost region of the device, dubbed Scrape-Off Layer (SOL), where particles are rapidly lost flowing along the magnetic field lines to the wall, thus "eroding" the last plasma layer, as the name suggests it. Blob transport may affect divertor heat loads and wall recycling and possibly the overall performance of future burning plasmas such as ITER. Thus, in recent years, there has been an increasing experimental, theoretical, and numerical simulation effort to understand the physics of blobs. From the experimental point of view, the investigation in fusion devices is hampered by the intrinsic difficulty of having diagnostic access in the region of interest with adequate temporal and spatial resolution. To overcome these limitations, an extensive investigation of blob physics has been undertaken in the basic plasma physics device TORPEX [1] at the Centre de Recherche en Physique des Plasmas at the EPFL. TORPEX is a device much simpler than tokamaks, but in which full diagnostics access with high spatial and temporal resolution is obtained.

Fig. 1. The TORPEX device at the CRPP-EPFL

The TORPEX device and the experimental setup

A picture of TORPEX is shown in Fig. 1. TORPEX is a toroidal device with major and minor radius R = 1 m and a = 0.2 m respectively. For the present experiments, hydrogen plasmas are generated and sustained by microwaves at 2.45 GHz in a magnetic configuration with a dominant toroidal (B_T = 73 mT) and a small vertical field component (B_z=2.3 mT). This simple magnetic configuration, with open helical field lines, features ∇B and magnetic curvature similarly to the SOL of fusion devices. It is characterized by the presence of plasma blobs [2] exhibiting universal statistical properties with strong similarities with observations in tokamaks [3]. The plasma has typical electron temperatures T~ 5-15 eV and densities in the range n ~ 2 - 15×10¹⁵ m^-3. These low temperatures and densities permit high spatial and temporal resolution in-situ measurements using electrostatic probes over the entire plasma cross-section. These measurements are not achievable in typical fusion experiments. This experimental setup represents, therefore, a unique starting point to investigate the physics of blobs and associated transport with unprecedented diagnostics capabilities.

Fig. 2. (a) Poloidal profile of skewness of signals from electrostatic probes. In (a) the profile of spectral power in the frequency range 3.9 ± 1 kHz is shown in white and localizes the interchange mode. (b,c) Signals at the two locations indicated in Fig. 2 (a) show coherent fluctuations in the main plasma region (blue cross) and intermittent bursts associated with blobs at the edge (green cross). (d,e) Power spectral densities of the two signals in (b,c).

Plasma waves and blobs

The main features of this configuration are shown in Fig. 2. We identify two distinct poloidal regions with different plasma dynamics: (1) a main plasma region for r < 5 cm, where the plasma source is localized, dominated by a coherent interchange wave for -5 <r <5 cm; (2) a region for r > 5 cm with negligible plasma production and broadband fluctuation spectra, dubbed source-free region, characterized by the propagation of blobs. In Fig. 2 (a), we illustrate the nature of the fluctuations in the

two regions using 2D profiles of the skewness S (normalized third order moment of the probability density function) of signals from electrostatic probes [4]. In the main plasma region, fluctuations are characterized by coherent oscillations at a frequency of ~3.9 kHz as shown by a probe signal in Fig. 2(b). These oscillations are associated with an interchange mode [5], which is localized around the position of maximum plasma pressure gradient. Interchange modes involve the exchange of fluid elements with different densities and tend to be unstable in the “unfavorable” curvature region where ∇B⋅∇P>0, P being the plasma pressure. In the source-free region, the fluctuation spectrum is broad and exempt from coherent modes, Fig. 2 (e). The skewness is positive (S ~ 1) indicating the occurrence of positive intermittent bursts, as shown in Fig. 2 (c). These bursts are associated with the presence of blobs that originate in the main plasma region and propagate outward into the source-free region as individual coherent structures over distances of the order of the minor radius.

Mechanism for blob generation

To investigate the mechanism for blob generation, time resolved 2D profiles of electron density, pressure, plasma potential and velocity fields are required. These are obtained by performing a conditional sampling over many blob events of the I-V characteristic of an electrostatic probe in a time window centered on the blob detection [5]. The results of the conditional sampling are shown in Fig. 3. We show the time evolution of the fluctuating density, δn, in the mode (red) and in the source-free (black) regions.

Figure 3 shows 2D profiles of the fluctuating density, in panels (b) – (d) and plasma potential, δV, in panels (e) – (g) at three different times during the ejection of the blob together with the velocity field of the plasma, which corresponds to the E×B drift velocity. The coherent structures are identified with the interchange wave, based on their spatiotemporal properties. The dynamics of blob formation and ejection from the interchange wave is captured by frames (c) – (e). A radially elongated density structure forms from the positive cell of the wave, Fig. 3 (c).
The formation of this structure follows from the convection of plasma by the E×B flow in a corridor that extends radially over a distance of the order of the minor radius, Fig. 3 (f), in which the velocity is mainly in the radial direction. In Fig. 3 (c - d), the elongated density structure is convected upward in a sheared velocity field that moves different parts of the density structure with different vertical velocities. A relative displacement between them is obtained, Fig. 3 (c). Eventually, the original density structure breaks into two parts, Fig. 3 (d). The new structure on the low field side forms a plasma blob.

Fig. 3. Plasma dynamics from the conditional sampling technique. Shown are (a) time history of δn in the mode region (red) and in the source free region (black). 2D profiles of (b)–(d) and (e)–(g) δV at different times during blob ejection. The arrows show the instantaneous E×B velocity.

Fig.4. A zoomed view of the instantaneous fluctuating v_E×B velocity field at t = -184 μs shows the convective cells interchanging zones of high and low plasma pressure. (b) Time evolution of the interchange drive.

In Fig. 4, we illustrate the mechanism driving the elongation of the density wave crest. The instantaneous pattern of the fluctuating v_E×B in Fig. 4 (a) shows a text-book example of the interchange mechanism that exchanges a zone of high plasma pressure with a zone of low plasma pressure. The time evolution of the pressure gradient, which provides the drive for the interchange mode, is shown in Fig. 4 (b) and reveals that the elongation of the density cell follows a sudden increase of the interchange drive.

Conclusions

These results detail a fundamental phenomenon in plasmas. The accurate measurements can be used to validate theories and numerical simulations of blob dynamics. Similarly to the tokamak SOL, the magnetic configuration features open field lines, a ∇B and magnetic field curvature. Blobs in TORPEX exhibit universal statistical properties with strong similarities with observations in the tokamak SOL. Thus, the observed dynamics sheds light on the blob ejection mechanism in tokamaks and may open new venues for controlling edge turbulent transport.

This work was partly supported by the Fonds National Suisse de la Recherche Scientifique.

References

[1] A. Fasoli, et al., Phys. Plasmas 13, 055902 (2006).
[2] S. H. Müller, et al., Phys. Plasmas 14, 110704 (2007).
[3] B. Labit, et al., Phys. Rev. Lett. 98, 255002 (2007).
[4] I. H. Hutchinson, Principles of Plasma Diagnostics, Cambridge University Press, New York, 1987.
[5] I. Furno, et al., Phys. Rev. Lett. 100, 055004 (2008); I. Furno, et al., Phys. Plasmas 15, 055903 (2008).

[Released: July 2008]