Pis'ma v ZhETF, vol. 91, iss. 4, pp. 182 -185 © 2010 February 25
On interrelation between inward turbulent flux and lower order rational magnetic surfaces at plasma edge
S. V. ShchepetovV, Yu. V. Kholnov, D. G. Vasilkov
A. M. Prokhorov General Physics Institute RAS, 119991 Moscow, Russia
Submitted 1 December 2009 Resubmitted 15 January 2010
The interrelation between experimentally measured inward turbulent flux and lower order rational magnetic surfaces is demonstrated by the example of system with externally imposed magnetic surfaces - L-2M stellarator [Plasma Phys. Control. Fusion 50, 045001 (2008)]. In this note we show that average turbulent flux change sign from outward to inward in the vicinity of lower order rational magnetic surface located at plasma edge. There exists an upper threshold in plasma density for inward flux observation.
Nowadays it is commonly accepted that transport at the plasma edge is dominated by turbulence. Similarities in the characteristics and structure of edge turbulence between different confinement devices (tokamaks, stellarators, reversed field pinches) were found (see, e.g., Refs [1, 2], the reviews). It occurs quite often that for interpretation of experimental data in different confinement systems one must invoke inward turbulent transport. The most frequently used method of plasma edge turbulence analysis is based on the use of Langmuir probes as a method with high time and spatial resolutions. In a broad variety of these experiments turbulent flux measurements were performed. Normally, the observed turbulent flux is directed outwards. The observations of inward turbulent flux are considerably more rare. Most often experimentally measured inward turbulent flux is associated with shear electric field suppression of turbulence [3-7], including externally imposed electric fields [3,4,7]. In the vicinity of low order magnetic islands in TJ-II Heliac turbulent flux reverses from radially outwards to radially inwards [5]. In [6] was advanced a hypothesis that turbulent flux may reverse in the vicinity of low order rational magnetic surface. It is important to consider this hypothesis in more detail (and to verify or reject it) since such an information can help in choosing reliable mathematical model for plasma edge turbulence.
The prime purpose of this note is to clarify some peculiarities of interrelation between inward turbulent flux and lower order rational magnetic surfaces in the absence of visible magnetic islands around them as well as without use of externally imposed electric field. For this purpose an attempt will be made to analyze inward turbulent fluxes in L-2M - high-shear stellarator with externally imposed magnetic surfaces [8]. Two ra-
e-mail: shch0fpl.gpi.ru
tional magnetic surfaces where rotational transform /i is equal to 2/3 or 3/4 are located at the plasma edge and are observable with Langmuir probe technique. At plasma pressures relevant to for the experiment magnetic surfaces (with the exception of central region) are weakly disturbed by plasma pressure effects. Magnetic surfaces at the plasma edge coincide practically [8] with the vacuum magnetic surfaces that are measured periodically (since [9]). Inward turbulent flux is systematically observed within parameter region such that transport transitions to the regime with better confinement are possible [8]. During such transitions drastic changes in turbulence are observed in the region that is close to the plasma boundary. The region has definite sandwich structure being subdivided in three smaller zones with different plasma parameters dynamics. Thus we can compare inward flux behavior during different turbulent states.
L-2M is a medium size high shear classical stellarator with the multipolarity I = 2, the total number of magnetic field periods A" 14 and the major radius Ro = 100 cm. The vacuum magnetic surfaces have rotational transform /i = 0.18 at the magnetic axis and fi = 0.78 at the separatrix. It is convenient to characterize three-dimensional magnetic surfaces with the help of single-valued standardization. For this purpose we use average radius of magnetic surfaces a. At the magnetic axis a = 0 and lineary grows to its maximum value at the separatrix a = ap = 11.5 cm. The vacuum magnetic field at the magnetic axis is B0 ~ 1.34 T. The plasmas in these experiments were produced and heated by means of central ECH with a maximum power of 250 kW. The experiments were performed at boronized wall conditions. The plasma pressure was sufficiently small (3 < 0.2% (0 is the volume averaged ratio of the plasma pressure to the pressure of magnetic field). The vacuum magnetic configuration has magnetic hill all over
the plasma volume. However, plasma induced shifts of magnetic surfaces lead to creation of the magnetic well at x < 0.6, here x = a/ap [10]. For all the plasma pressures relevant to the experiment, plasma is stable with respect to ideal MHD modes. Resistive interchange modes that cannot be stabilized by shear are unstable at the plasma edge. Moreover, we can state that the relative gradients of plasma temperatures are significantly lower than that of density at the plasma edge and temperature gradient electrostatic instabilities are hardly probable. It is not to be supposed that resistive interchanges serve as the only source of plasma edge turbulence. We hypothesized in [8] that transport transitions can be triggered by non-MHD instabilities. Such instabilities can be found in the framework of two-fluid hydrodynamics [11] if coupling of drift modes with Alfven and acoustic waves [12] is taken into account.
For the purposes of this note we use movable triple Langmuir probe. Two tips of the probes aligned perpendicular to the magnetic surface and poloidally separated (aA6 = 0.4 cm) were used for measuring the value of floating potential Vf and its poloidal derivative. Here, 9 is the poloidal angle. Another tip is biased at a fixed voltage in ion saturation current Ip regime. Each tip is cylindrical with length equal to 0.2 cm. The probe penetrates transversely into plasma from the bottom of system (structure of magnetic surfaces and position of probe are presented in detail on Fig.l, where magnetic
80 85 90 95 100 105 110 115 120 r (cm)
Fig.l. Plasma induced changes of magnetic configuration. Vacuum magnetic surfaces (solid lines) and surfaces (broken lines) that are shifted due to plasma induced magnetic fields. Zero net current case, ¡3 = 0.2%, ¡3(x) ~ (1 — a2)3. Double line indicates vacuum chamber with branch tubes. Probe moving direction is depicted with bold line, r, z are cylindrical coordinates
surfaces at finite pressure are calculated with the procedure developed in [13]). In this position plasma induced changes of magnetic surfaces are minimal. Mov-
ing probe with distance 1.0 cm it covers 1.1cm in average radius of magnetic surfaces. The sampling frequency of the probes was 1MHz. It is necessary to mention that in order to guarantee correctness of Langmuir probe turbulent flux measurements we have limited their penetration depth inside separatrix by the value of 1.0 cm. In [3-7] transversive turbulent flux was investigated F ~ n^(A$_/aA0)^/£?o. Here, $ is the plasma electric potential, n is the plasma density, wavy subscript denotes oscillations. So that this value will correspond to normal component of electric drift, one must suppose that disturbances are electrostatic and strongly elongated along magnetic field lines. In cur-rentness equilibrium electromagnetic corrections to the formula is negligibly small (see, details and numbers in [8]). Therefore electromagnetic effects play role of additional degrees of freedom, making possible, e.g. resistive interchange instability. However, it is necessary to mention that Langmuir probes are measuring not n and # directly but floating potential Vf = # — AkTe/e and ion saturation current Ip ~ n^/Ti + Te. Here, A is the constant (A ~ 3 in the case of hydrogen), k and e are the Boltzmann constant and module of electron charge, respectively. Here as in majority of investigations [3-7] temperature fluctuations are postulated to be negligible. In order to move the probe deeply in plasmas we have used similar discharges with not very high parameters, where ne ~ 1.7-1013 cm"3 and W ~ 400 J. Here ne is the line averaged plasma density, W is the plasma energy. Fast transport event under these conditions usually occurs closer to the end of active heating phase. For all cases presented below the active heating phase begins at 48 ms and finishes at 60 ms. Let us present experimental results in the following order. Initially probe is located so that its taper crosses plasma boundary. In what follows probe is moved insight with spacing 0.2 cm (equal to probe taper length). Therefore, we define the penetration depth of probe with respect to its midpoint. In Fig. 2 we present turbulent flux obtained in duplicate discharges and two different probe locations x. Thus we show that turbulent flux may change direction at probe positions separated by small distance in 5x. Position of transport transition is marked with vertical line. Negative values correspond to the normal (outward) flux direction, positive values correspond to the inward flux. Since only the non vanishing part of turbulent flux is meaningful for transport studies the experimentally obtained turbulent flux was averaged with respect to time. We have used 1 ms window in the procedure of averaging and moved it over time scale. The results are also presented in Fig.2. It is pertinent to note that signal (depicted at Fig.2b) has time cell where negative values
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S. V.Shchepetov, Yu. V.Kholnov, D. G. Vasilkov
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