A DC probe diagnostics for fast electron temperature measurements in tokamak edge plasmas *)

Transcription

1 A DC probe diagnostics for fast electron temperature measurements in tokamak edge plasmas *) J.P. GUNN, P. DEVYNCK, J.-Y. PASCAL Association EURATOM-CEA Cadarache sur la fusion Saint Pan1 Lez Durance, France J. ADAMEK, I. DURAN, M. HRON, J. STOCKEL, F. ZACEK Institute of Plasma Physics, Association EURATOM/IPP.CR, Praha, Czech Republic O. BAI~INA, R. HRACH, M. VICHER Faculty of Mathematics and Physics, Charles University, Praha, Czech Republic G. VAN OOST Department of Applied Physics, Ghent University, Gent, Belgium Received 11 September 22 The tunnel probe is a new kind of Langmuir probe for use in the tokamak scrape-off layer. It provides simultaneous measurements of electron temperature and parallel ion current density with high frequency at the same point in space. We describe ongoing work to characterize the ion flows within the probe, and to calibrate the diagnostics using 2D kinetic simulations. PACS: Ra, Gj Key words: tokamak, edge plasma, plasma fluctuations, tunnel probe 1 Introduction: the tunnel probe The tunnel probe (Fig. 1) is a new kind of Langmuir probe for use in the tokamak scrape-off layer (SOL). It provides simultaneous measurements of electron temperature Te and parallel ion current density Jll at the same point in space with high frequency up to about 1 MHz. It consists of a hollow conducting tunnel a few millimetres in diameter and typically 5 mm deep that is closed at one end by an electrically isolated conducting back plate (BP). The time response of the probe is given by the ion parallel transit time through the tunnel. Both conductors are biased negative~ to collect ions and repel electrons. The tunnel axis is parallel to the magnetic field B. Plasma flows into the open orifice and the ion flux is distributed between the tunnel and the BP. The ratio of the two ion currents is determined by the magnetic sheath (MS) thickness at the concave surface of the tunnel, and is therefore a pronounced function of T~. The self-consistent, two-dimensional kinetic code XOOPIC [1] is used to determine the theoretical relation between the current ratio Rc = ITUN/IBp and Te. Combined with the measured sum of the two currents *) Presented at 5th Workshop "Role of Electric Fields in Plasma Confinement and Exhaust", Montreus, Seitzerland, June 23-24, 22. Czechoslovak Journal of Physics, Vol. 52 (22), No

2 J. Gunnet a/. II Q...Q O} t-.i.-,.) -I " t- O conducting tunnel E e--- (l) -~.t- Fig. 1. Schematic of the tunnel probe. Ions near the tunnel surface are diverted from their guiding center trajectories by the strong radial electric field gradient in the magnetic sheath. The ratio of the currents flowing to the tunnel and to the back plate is a sensitive function of electron temperature. /TUN -~- ~/BP : 4t 7r?'2, ne at the sheath entrance can also be estimated. A detailed description of the kinetic simulations and a convincing experimental validation in the Tore Supra tokamak have already been published [2]. The purpose of that study was to calibrate the effective ion collecting area of a large Langmuir probe tip shielded by a thick conducting plate through which a cylindrical orifice was drilled. A large fraction of the ions flowing along/~ lines through the orifice was neutralized on the shield, which resulted in an attenuation of the ion flow to the pin. The calibration is needed to calculate the unperturbed JIq incident on the shield surface. It turns out that the calibration factor depends strongly on Te and weakly on JIt" These findings inspired the design of the tunnel probe. Here we report on the first tests of a prototype tunnel probe in the CASTOR tokamak. The primary goals of the experiments were to find the optimal tunnel radius that gives a significant variation of Rc as a function of Te (Section 2), and to investigate the effect of angular misalignment between/~ and the tunnel axis (Section 3). The latter cannot be tested theoretically because we do not yet have a 3D kinetic code, although 2D calculations [2] indicate that the probe should tolerate small misalignments of roughly 5. The probe was mounted on a manipulator that could be moved radially and rotated between shots. 2 Optimization of the tunnel probe Tunnel diameters of 2.5 mm, 4. mm, and 5. mm were investigated. The tunnels were 5 mm long in all cases (this length must be larger than the helix length of the ion orbits for our analysis to be valid). A good rule of thumb is to choose the tunnel radius to be roughly twice the MS thickness [3], rtunnel = 2~MS Ce/Wci (where C 2 e kte/mi is the cold ion sound speed and wci is the ion cyclotron frequency). In this case, the plasma inside the tunnel is divided into two regions. On axis, outside the MS boundary, the plasma flows unperturbed to the back plate. Near the concave surface inside the MS, all the ions are deviated from their guiding center trajectories 118 Czech. J. Phys. 52 (22)

3 A DC probe diagnostics for fast electron temperature measurements... by the strong radial electric field and collected by the leading edge of the tunnel. If the tunnel is too large, Rc is not sufficiently sensitive to Te; if it is too small, the radial electric field penetrates to the axis and the plasma remains attached to the entire length of the tunnel with the result that almost all the current drains to the tunnel, and none to the back plate. The following table compares the ratio of MS thickness to probe radius between the various probe diameters that were tested in CASTOR (hydrogen gas, B = 1 T) and Tore Supra (deuterium gas, B = 3.5 T), assuming Te = 2 ev: Exp. device CASTOR CASTOR CASTOR TS Probe diameter 2.5 mm 4 mm 5 mm 3 mm LMPS/TTUNNEL This is, of course, a crude simplification of the physical picture; in reality there is no sharp division between the two regions, and the MS scaling derived from 1D simulations in planar geometry is certainly modified by the strong cylindrical curvature of the probe. Nonetheless, the rule of thumb proves to be a good guide. The importance of choosing the correct diameter is illustrated in Fig. 2. The back plate was biased to -1V to collect ions, and the tunnel voltage was swept. For large voltages, the ion current to the 2.5 mm back plate is completely suppressed, whereas it saturates to a measurable value in the 5 mm case. 2 tunnel back plate (swept) (-1 V) tunnel + back plate t-q E < C tj v- (D '1 r-.= L shot1388 r= 2.5 mm shott319 r = 5. mm l nominal operating point ' tunnel bias voltage [ V ] Fig. 2. Comparison of current distribution inside 2.5 mm and 5. mm tunnel probes. Bias voltage is swept on tunnel, fixed on back plate. (left panel) I-V characteristic of tunnel. (center panel) Current throughput to back plate. (right panel) Total current passing through the orifice (sum of two previous panels). Currents are normalized by the orifice cross-sectional area. Czech. J. Phys. 52 (22) 119

4 J. Gunnet a/. The XOOPIC code was run for the CASTOR 5 mm tunnel probe geometry over the expected ranges of plasma parameters 5 < Te < 5eV and.5 < Jl] < 2 A/cm 2. The analysis procedure is straightforward. First, one calculates J]l from the sum of the two ion currents, and the ratio Re. Then T~ is calculated by interpolation within the numerical results. Raw data from the 5 mm tunnel are shown in Fig. 3, with the XOOPIC results superimposed. The probe was oriented in the 5 mm tunnel D.. "" 6 O E 4 O JII [ Acm'2 ] Fig. 3. Ion current ratio as a function of parallel current density for two radial positions in the plasma. Theoretical kinetic calculations are superimposed for comparison. ion drift direction. Two cases are shown: in shot the probe was placed in the SOL at normalized minor radius r/a = 1.1, and inside the last closed flux surface at r/a =.8 in shot In each case, there is a progression from low JII and high Rc through the density ramp-up phase at the beginning of the shot towards the cluster of points that correspond to the stationary ohmic phase. The average Te can be estimated from the XOOPIC isothermal contours. In the first case we find Te ~ 5 ev, and in the second Te ~ 2 ev. These values are reasonable and correspond to measurements by swept Langmuir probes that were made in the past. The vertical and horizontal widths of each cluster is a measure of the level of T~ and JII fluctuations, respectively. In the Tore Supra investigation of Ref. [2] it was reported that the ion current ratio was insensitive to JIl" This is also the case in CASTOR for similar values of JIl" However, for very low values that occur during the density ramp-up at the beginning of the shot, R increases sharply because the Debye length becomes comparable to the dimensions of the tunnel and the plasma is no longer able to shield the probe potential; the vacuum electric field dominates and most ions are attracted to the tunnel, independently of T~. This effect imposes a lower limit on the exploitable range of JII, but fortunately such low values never occur during the stationary phase of the discharge. 111 Czech. J. Phys. 52 (22)

5 A DO probe diagnostics for fast electron temperature measurements... For the purpose of illustration, we show preliminary measurements from CAS- TOR discharge to which overlapping pulses of electrode biasing (+1V) and lower hybrid heating were applied. The 5 mm tunnel probe was positioned at r mm in the region of large EXB shear, facing in the ion direction. The tunnel and BP were biased to -2V and the currents were sampled at 1 MHz. The measured JII, Te and ne are plotted in Fig. 4. The relative fluctuation amplitudes BIAS 1., E shot t,.) <.5 I,,ILL.~.~,,~,,.,A...,~. i I LH. ' I, ' I I - _ ~_ 2 i g" 2 I ' ' I ' I ' m.,l.,..,,.,,i, T-,..-.~,,~p,..,ee~ p'rlr r.r.~rm" ~rlrpl "~ "I,w~-r,~" I'~.-~, i i, time [ms] Fig. 4. Tunnel probe measurements of parallel ion current density (top panel), electron temperature (middle panel), and sheath-edge density assuming equal ion and electron temperatures (bottom panel) during a shot with electrode biasing and lower hybrid heating. of Te and ne are both around 2% except during the bias phase, when they drop to 1%. The positive bursts that are observed on Te are completely suppressed during the bias phase. The calculation of sheath edge density depends, as usual, on some assumed value for ion temperature. Its interpretation will be further complicated by its dependence on the Mach number of the parallel flow. 3 Sources of error In this section we comment on sources of error that could give rise to experimental uncertainty in the determination of Te. Some are due to incomplete parameter scans using the XOOPIC code, which can simply be corrected by performing more runs; others are due to physical phenomena that are not taken into account in the idealized model; for these special investigations they are needed. The XOOPIC code calculates the ratio of ion currents flowing to the negatively biased collectors. Despite the probe bias, a small current of energetic electrons is also present, so the measured electrical current will be slightly smaller than the Czech. J. Phys. 52 (22) 1111

6 J. Gunnet M. pure ion current. One must prescribe the magnitude of voltage required in order to minimize this effect, given the expected maximum Te in the plasma. The effective electron collecting area of each conductor is well approximated by its geometrical projection along /~ due to the small gyroradius of electrons. For slight angular misalignment of the order of ±5, the collecting area of the BP is much larger than that of the tunnel, so we can safely neglect electron collection by the tunnel. The totm electrical current to the BP is IBp= IoRIF [5--exp( e(v-vtbp+tun)~]kte ]J (1) where Tg~,BPwTUN is the floating potential that would be measured if the tunnel and BP were short-circuited together, equivalent to the floating potential of a classical disk-shaped Langmuir probe. IORIF is the ion or electron current flowing into the tunnel orifice at that particular value of probe voltage, and 5 = 1/(1 + Re) is the current attenuation factor as defined in Ref. [2]. The applied voltage V is defined with respect to this floating potential that typically corresponds to (within values of the order of the electron temperature) the ground voltage of the vacuum vessel if the probe is located in the unbiased SOL. The ratio of electron to ion currents on the BP is then /e,bp 1 (e(v - ~/f,bp+tun) /i,bp 5 exp kte " (2) It is apparent from this expression that the floating potential of the BP is lower than the classical floating potential due to the ion current attenuation (see Eq. (9) of Ref. [2]). The necessary applied voltage is V=Vf,sP+TuN+kTeln~SIe'BP~ e \ (3) If for example we want the measured BP current to be not more than 1% lower than the pure ion current for Te bursts up to 5 ev and for ion current attenuation around 5 ~.2, then we need to apply -2V to both conductors. If the floating potentials were measured simultaneously, for example by averaging the floating potentials of two small Langmuir probe tips located on either side of the tunnel orifice, then it would be simple to correct the BP current and greatly improve the accuracy of the Te calculation. The conductor voltages were set to - 1 V with respect to the floating potential for all XOOPIC runs. We suppose that for sufficiently negative voltages, the ion current to the BP saturates. In Fig. 2, we saw that the current does saturate fairly well if the tunnel radius is appropriately chosen, but more code runs are needed to ascertain whether this is true for all plasma parameter regimes. If it turns out not to be so, then the analysis forcibly becomes more complicated, but remains possible in principle; the degree of non-saturation Would have to be tabulated in order to estimate the resulting error. This work is in progress Czech. J. Phys. 52 (22)

7 A DC probe diagnostics for fast electron temperature measurements... ~ 1. II! : ',' '. Io ~ :..8 ee / i : /.', Shadowing: measured geometric Fig. 5. Comparison of current reduction to the back plate with a geometrical calculation of magnetic shadowing as a function of the angle between the magnetic field and the tunnel axis. Preliminary XOOPIC simulations show that ion temperature does not significantly influence the current ratio. It is because the current attenuation is principally governed by the MS radial electric field that extends over several thermal Laxmor radii; the radial ion flow is not due so much to interrupted gyro-orbits, but rather to the radial polarization drift induced by the strong electric field gradient. One would expect ion temperature to play a role, however, for large ion-to-electron temperature ratios. The ion temperature does play a role in the estimation of sheath-edge density, since the latter is derived from the ratio of parallel current density to ion sound speed. The parallel ion temperature manifests itself in the axial distribution of radial ion flux within the tunnel (see Fig. 8 of Ref. [2]). The higher the ion temperature, the deeper ions will penetrate into the tunnel before neutralizing on its surface. Perhaps this dependence could be exploited by implementing a segmented tunnel. The ratio of the currents to the fore and aft tunnel segments could then be linked to the parallel ion temperature. This problem is under investigation. Stangeby [4] investigated the influence of a small population of suprathermal electrons on the current voltage characteristic of a Langmuir probe, and found that a tiny population can strongly increase the apparent electron temperature. The tunnel probe might be subject to the same problems. What we need to know is whether the MS electric field is controlled by the hot or the thermal population. Simulations axe foreseen in order to address this question. The effect of angular misalignment between the tunnel axis and/~ was studied in detail. Magnetic shadowing by the tunnel, characterized experimentally by the ratio 5 = x[bp/(/tu N -]- IBp), impedes charge flow to the BP. As shown in Fig. 5, the geometric calculation of the magnetic shadow gives a highly peaked function, but the measurement is found to be insensitive to the angle as long as the misalignment is less than 5. This was predicted by 2D XOOPIC simulations in rectangular geometry and 3D Monte Carlo calculations without electric fields [2], and is due to Czech. J. Phys. 52 (22) 1113

8 J, Gunnet al.: A DC probe diagnostics for fast electron temperature measurements... the perpendicular motion of the ions. Such tolerances are easy to achieve, leaving a wide margin for variations of edge safety factor with negligible error on the measurement of Rc. Finally, the effects of omnipresent plasma-surface interactions must be considered. What is the role of recycling, secondary electron emission, and sputtering? These phenomena are present around all types of probes, but are usually ignored. In principle, they can be investigated using the XOOPIC code, but until now no effort has been made in this area. 4 Summary Because of the simple geometry of the tunnel probe, it is possible to carry out precise kinetic simulations in order to calibrate it. Even with a highly idealized model, we have seen that the simulation results behave remarkably like the experimental measurements, indicating that we have correctly identified the essential physical features. Classical cylindrical probes that are commonly used in today's tokamaks cannot be easily modelled because enormous simulation domains are required to correctly treat the plasma around the probe. As an example, consider the calibration of the probe's effective collecting area. Sheath expansion likely puts a minimum uncertainty of 1% on this quantity in the case of classical convex probes, but that of the concave tunnel probe is much more precisely known due to the simple fact that all ions that enter the tunnel are collected, independent of sheath geometry. The tunnel probe has a fundamental advantage over classical probes due to its geometry. One limitation on the use of tunnel probes arises from the need to correctly dimension them. A given tunnel diameter is needed for a certain range of magnetic field and electron temperature. If the magnetic field is lower than about 1 T, then the diameter approaches 1 cm, and the probe size is comparable to typical plasma structures. Rather, the tunnel probe is best suited for high magnetic fields. For example, in deuterium plasmas in Alcator C-Mod, tunnel radii of (.5-1)mm would be suitable, opening the way to arrays of tunnel probes to measure electron temperature structures with good radial and poloidal spatial resolution. Authors are indebted to F. Jir~nek, J. Zelenka, K. Rieger, and M. Satava for technical assistance with the experiments. References [1] J.P. Verboncoeur, A.A. Langdon, and N.T. Gladd: Comput. Phys. Commun. 87 (1995) 199. [2] J.P. Gunn: Phys. Plasmas 8 (21) 14. [3] J.P. Gunn: Phys. Plasmas 4 (1997) [4] P.C. Stangeby: Plasma Phys. Contr. Fusion 37 (1995) Czech. J. Phys. 52 (22)