Tailoring the charged particle fluxes across the target surface of Magnum-PSI

Transcription

1 EUROFUSION WPPFC-PR(15) C Costin et al. Tailoring the charged particle fluxes across the target surface of Magnum-PSI Preprint of Paper to be submitted for publication in Plasma Sources Science and Technology This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme under grant agreement No The views and opinions expressed herein do not necessarily reflect those of the European Commission.

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3 Tailoring the charged particle fluxes across the target surface of Magnum-PSI C Costin 1, V Anita 1, G Popa 1, J Scholten 2, G De Temmerman 2,3 1 Iasi Plasma Advanced Research Center (IPARC), Faculty of Physics, Alexandru Ioan Cuza University of Iasi, Bd. Carol I nr. 11, 756 Iasi, Romania 2 FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, Association EURATOM-FOM, Trilateral Euregio Cluster, PO Box 6336, 56 HH Eindhoven, The Netherlands 3 ITER Organization, Route de Vinon-sur-Verdon - CS St Paul Lez Durance Cedex France claudiu.costin@uaic.ro Abstract. Linear plasma generators are plasma devices designed to study fusion-relevant plasma-surface interactions. The first requirement for such devices is to operate with adjustable and well characterized plasma parameters. In the linear plasma device Magnum-PSI, the distribution of the charged particle flux across the target surface can be tailored by the target bias. The process is based on the radial inhomogeneity of the plasma column and it is evidenced by electrical measurements via a 2D multi-probe system installed as target. Typical results are reported for a hydrogen discharge operated at 125 A and confined by a magnetic field strength of.95 T in the middle of the coils. The probes were biased in the range of -8 to -3 V, while the floating potential of the target was about -35 V. The results were obtained in steady-state regime of Magnum-PSI, being time-averaged over any type of fluctuations. Depending on the relative value of the target bias voltage with respect to the local floating potential in the plasma column, the entire target surface can be exposed to ion or electron dominated flux, respectively, or it can be divided into two adjacent zones: one exposed to electron flux and the other to ion flux. As a consequence of this effect, a floating conductive surface that interacts with an inhomogeneous plasma is exposed to non-zero local currents despite its overall null current and it is subjected to internal current flows. 1. Introduction Magnetically confined linear plasma devices are strongly contributing to plasma-surface interaction studies in nuclear fusion devices - a key area for the successful development of nuclear fusion as a large-scale energy source [1]. Magnum-PSI is such a facility designed to allow plasma-surface interaction studies under high heat and particle fluxes, mimicking the conditions expected in the ITER divertor [2]. The versatility of the plasma column is an important factor for the experimental value of such a device. By this we mean the ability to control the energy deposited on the target mainly by the fluxes of charged particles, ions and/or electrons. Consequently, knowledge of the spatial distribution of the ion/electron fluxes over the cross section of the plasma column versus different experimental conditions is of particular interest. The present work reports on recent experiments that revealed the possibility of tailoring the plasma column properties in Magnum-PSI. The cross sectional composition (electron vs. ion flux) of the

4 plasma column at the plasma-surface interface can be smoothly controlled by target biasing. The measurements were made with a 2D multi-probe system installed at the target location. 2. Experimental set-up A detailed description of Magnum-PSI and its capabilities can be found in [2]. The multi-probe system, as well as the diagnostic method used in this study, were also detailed in our previous work [3]. Briefly, the cross-sectional investigation of the plasma column was made by replacing the Magnum-PSI target with a 2D multi-probe system. A suite of 64 probes was assembled in a square matrix of 8 8, all probes being flush-mounted with a tungsten front plate. The probes were made of tungsten wire of.89 mm in diameter and 2 mm in length. The linear resolution of the multi-probe system was 4 mm in each direction of the matrix. The system composed of probes and front plate was used to register local currents or potentials across the plasma column. Each probe had its own biasing/measuring circuit, composed of resistors and capacitors. The registered signals were simultaneously acquired with a 64-channel National Instruments data acquisition system, at a maximum acquisition frequency of 1 MHz. All the results reported in this paper are time-averaged over any type of fluctuations and they were obtained during the steady-state operation phase of Magnum-PSI. 3. Results and discussion The multi-probe system was already used to obtain a detailed electrical characterisation of the Magnum-PSI plasma column, in terms of variation of the floating potential and ion saturation current for a large variety of operation conditions [3]. The present paper is focused on the flexibility of the plasma column, which can be achieved by target biasing. As it was already discussed in [3], the space charge sheath in front of the multi-probe system is developed on tens of μm and, consequently, plasma enters between probes and the front plate. Thus, the signals measured on the probes and on the front plate are independent of the different voltages that might be applied on the neighbouring collecting surfaces. 3.1 Current distribution to the surface of the floating target Magnum-PSI is often used in the floating target regime in order to mimic the plasma conditions at the ITER divertor during partially detached plasma operation. Thus, the first measurements were focused on measuring the 2D current distribution at the surface of the floating target. The results obtained in Magnum-PSI revealed an important aspect of the interaction of a floating conductive surface with nonhomogeneous plasma. In our experiments, the conductive target is substituted by the tungsten front plate. The entire surface of the front plate has the same potential, no matter if it is floating or biased. A typical radial distribution of the floating potential across the plasma column, measured with the multi-probe system, is plotted in Figure 1. It was obtained in a hydrogen discharge, characterized by a gas flow of 5.8 Pa m 3 /s which, in combination with the pumping system, assures a working pressure of.25 Pa in the target chamber when the magnetic field is applied. The discharge current delivered by the arc-source was 125 A. The applied magnetic field was about.95 T in the middle of the coils, which corresponds to.7 T at the measuring point (target position) [3]. At target position, the magnetic confinement of the plasma can be considered rather weak, since the cyclotron frequency of H + ions is in the same range as their collision frequency, but this doesn t limit the validity of the results. Similar distributions were also obtained at higher magnetic fields, both in Magnum-PSI [3] as well as in Pilot-PSI [4]. Moreover, the radial gradient of the floating potential is larger for higher magnetic field strengths [3]. Expressing the space coordinate as the radial position r is justified by the cylindrical symmetry of the plasma column, r = mm being assigned to the centre of the plasma column. Note that, depending on the operating conditions, the centre of the plasma column might not be aligned to the centre of the multi-probe system, as it will be further illustrated in Figure 3. The floating potential of the target (front plate), V f target = V, is also showed. The significance of the square symbols appearing in Figure 1 will be discussed later.

5 According to electrical probe's theory [5], when a probe is biased negatively with respect to the floating potential it will drain an ion dominated current from the plasma; when biased positively with respect to the floating potential it will drain an electron dominated current. In Figure 1 it can be noticed that in the central part of the plasma column (zone I) the probes measure a local floating potential more negative than the floating potential of the target while in the outer part of the plasma column (zone II) the probes measure a local floating potential more positive than the floating potential of the target. Thus, when all the probes are biased to the floating potential of the target, the probes should collect electron dominated currents in zone I and ion dominated currents in zone II. These aspects are schematically illustrated in Figure V f (V) V f target = V zone II zone I zone II Figure 1. Typical radial distribution of the floating potential across the plasma column (line + open circles); the horizontal line marks the floating potential of the target at V f target = V; the square symbols are explained in section 3.2 (H 2 gas;.95 T magnetic field strength; 125 A discharge current). Figure 2. Schematic illustration of the current flow from the plasma column toward and within the floating target in Magnum-PSI.

6 A further confirmation is provided in Figure 3. The 2D distribution of the current that reaches the target surface when all the probes were biased around the floating potential of the target, V probes = -35 V, (Figure 3a) is compared to the 2D distribution of the floating potential across the plasma column (Figure 3b). The black squares indicate the position of the probes. The discharge conditions are the same as for Figure 1. Even if the target is floating, which means that its total current is zero, the target collects non-zero local currents due to the inhomogeneity of the plasma column. The central zone of the target (zone I) collects electron dominated (negative) currents while the outer zone (zone II) collects ion dominated (positive) currents. The two zones are separated in Figure 3a by the black contour line, showing the local current I = ma. This line is well correlated to the black line in Figure 3b which shows the contour on the target surface where the local floating potential of the plasma column is equal to the floating potential of the target. Also, the two separated zones of positive/negative current in Figure 3a correspond with the two zones where the local floating potential is more positive/negative than the floating potential of the target in Figure 3b. The sum of all local currents that reach the floating target has to be zero and the negative charges have to neutralize the positive ones to the target surface. For this reason and because the conductive surface should preserve its equipotential nature, there should be an electron current flow within the floating target, as schematically drawn in Figure 2. Regarding the alignment of the measuring system, in Figure 3 can be noticed that the centre of the plasma column is shifted of about 2 mm with respect to the centre of the multi-probe system I (ma) V f target V f (V) y (mm) y (mm) x (mm) x (mm) (a) (b) Figure 3. (a) 2D distribution of the current flowing from the plasma column to the floating target (V probes = -35 V); (b) 2D distribution of the floating potential across the plasma column (H 2 gas;.95 T magnetic field strength; 125 A discharge current; V f target = V). The above mentioned result is generally valid for an inhomogeneous plasma which comes in contact with an equi-potential surface, no matter if the process is steady-state or not. It is particularly important for fusion reactors, such as tokamaks, where there will always be spots with plasma gradients along the wall/divertor. The inhomogeneous plasma, which in fusion reactors is floating, interacts with conductive surfaces (walls and divertor) which are usually grounded. Thus, significant currents are expected to flow locally through these surfaces in order to compensate the charge difference that arrives to the conductive surface in separate spots characterized by different plasma parameters. Moreover, the local heat flux to the surface will depend on whether the electron or ion flux is dominant. 3.2 Tailoring the current distribution to the target surface After explaining the interaction of an inhomogeneous plasma column with a floating target, the study was further focused on the interaction of the plasma column with a biased target. In order to

7 investigate the cross sectional distribution of the charged particle flux that bombards the target, all the probes were simultaneously biased at the same voltage with respect to the ground. The front plate was kept floating. The radial distribution of the probe current measured in the same discharge conditions is given in Figure 4, for different biasing voltage on the probes. The total current arriving to each probe is the sum of two currents carried by the charged particles: ions (positive current) and electrons (negative current). By varying the probe voltage from -8 to -3 V, the currents measured by the probes change from positive values (ion dominated) to negative values (electron dominated), passing successively through different types of radial distribution: (i) Gaussian ion current profile (V probes = V); (ii) flat ion current profile in the centre of the plasma column (V probes = -65 V); (iii) hollow ion current profile in the centre of the plasma column (V probes = -5-6 V); (iv) electron-dominated current in the centre and ion-dominated current on the sides (V probes = V); (iv) Gaussian electron current profile (V probes = V). A first conclusion that comes out from Figure 4 is that by biasing the target at different potentials with respect to ground it is possible to change the cross sectional distribution of ion and electron fluxes to the target. I (ma) V probes (V) Figure 4. Radial distribution of the probe current (H 2 gas;.95 T magnetic field strength; 125 A discharge current; probe bias as parameter). The dependence of the current distribution across the plasma column on the probe bias can be explained by analyzing the potential difference between the probe bias and the local floating potential (given in Figure 1). If a probe is biased sufficiently negative with respect to the floating potential, all the electrons coming from the plasma can be repelled and the probe will collect only the ion saturation current. Since the minimum local floating potential V f min in the plasma column is about -47 V (in the centre, according to Figure 1), and the electron temperature is below 3 ev (Figure 7b), we can assume that the local probe current measured with the probes biased at -8 V (Figure 4) is, exclusively, the local ion saturation current. Reducing the negativity of the probes, the bias of the central probes approaches the local floating potential and they will start to collect electrons. Accordingly, the total current in the central part of the plasma column decreases while it remains almost unchanged on the sides. It is thus possible to obtain hollow type distributions, with lower currents in the centre of the plasma column and higher on the sides (current curves for V probes = -5-6 V). However, as long as the bias of the probes remains negative with respect to V f min, all the probes will collect ion dominated currents. When the probe bias becomes more positive than this threshold, the plasma column is divided into the two zones described in section 3.1 and illustrated in Figures 1 and 2. This time, the limit between the two zones is set by the probe bias and not by the floating potential of the target. The local current is always zero at the radial position of this limit because, in this point, V probes should be

8 equal to the local V f. The latter statement is validated by Figure 1. The square symbols in Figure 1 are extracted from the current curves in Figure 4 and they correlate the probe bias (V probes = V) to the radial positions corresponding to I = ma. There is an excellent match between the curve drawn by the square symbols and the radial distribution of the floating potential across the plasma column, proving thus that at the target surface I = ma where V probes = V f. The zone I expands as the probe bias becomes less negative. An example of 2D map of the current that reaches the target is shown in Figure 5 for a probe voltage V probes = -45 V. This is the most complex distribution of the current on the target surface, having electron current in the centre of the plasma column (limited by the black contour line I = ma), a maximum ion current at intermediate radial position (r ~ 12 mm from the centre) and lower ion current at larger radius. As long as the probe bias is more negative than the plasma potential, the probe current is composed of the ion saturation current (the curve for V probes = -8 V in Figure 4) and an electron current. This is valid for the current curves having V probes -45 V. Consequently, the contribution of the electron current to these curves can be obtained by subtracting the local ion saturation current from the local probe current. The electron current intensities obtained as a result of this subtraction are plotted in Figure 6. The electron current was not calculated for the probe bias V probes -4 V because these values could be more positive than the local plasma potential for some of the probes and, in this case, the ion current that has to be extracted from the probe current is not known (it might be different from the local ion saturation current). y (mm) I (ma) x (mm) Figure 5. 2D map of the current that reaches the target (H 2 gas;.95 T magnetic field strength; 125 A discharge current; V probes = - 45 V).

9 I (ma) V probes (V) Figure 6. Radial distribution of the electron current that reaches the target (H 2 gas;.95 T magnetic field strength; 125 A discharge current; probe bias as parameter). 3.3 Estimation of the charged particles flux to the target surface For magnetically confined linear plasma generators, it is more relevant to describe the current density or the charged particle flux that interacts with the target. The estimation of these quantities, based on the current measured with a probe, is not straightforward in magnetized plasmas. When using a cylindrical probe aligned with the magnetic field lines, the knowledge of the probe's area is not enough. The current collected by the probe depends on the probe's length [6, 7], but it also depends on the ratio between the Larmor radius of the charged particles (a c ) and the probe's radius (r p ). If a c << r p, 2 probe's collecting area can be identified with probe's top area ( π r p ). If a c is comparable or larger than r p, obtaining probe's collecting area requires analytical or numerical solution. We will further estimate probe's collecting area for electrons (A ce ) and H + ions (A ci ). For the above mentioned discharge conditions, considering the electron temperature obtained from Thomson scattering measurements at 2 cm in front of the target (Figure 7b), the average values of electron Larmor radius at target position (B =.7 T) will vary from 34 μm for T e =.5 ev to 83 μm for T e = 3 ev. These values cannot be neglected with respect to probe s radius r p = 445 μm. The Thomson scattering system as well as the technique used for the diagnosis of Magnum-PSI were extensively described in [8]. 1. (a) 4 (b).8 3 n e (1 19 m -3 ).6.4 T e (ev)

10 Figure 7. Radial distribution of electron density (a) and temperature (b) measured from Thomson scattering (H 2 gas;.95 T magnetic field strength; 125 A discharge current; V probes = -8 V). Considering the ion temperature equal to the electron temperature, plasma being thermal at the plasma source [9], the average values of H + ion Larmor radius at target position will range between 1.5 mm (T i =.5 ev) and 3.6 mm (T i = 3 ev). These values are larger than the probe s radius r p =.445 mm. Consequently, the probe s collecting area for both electrons (A ce ) and ions (A ci ) is larger than probe's top area. Besides, the situation is even more complicated because the probe is surrounded by the front plate of the multi-probe system (Figure 8). Because plasma enters between the probe and the front plate, the probe collects electrons and ions also on its lateral area. Let's first estimate the probe s collecting area for ions (A ci ). To be collected by the probe, the ions should first enter in the hole around the probe. Since hole's top area (3.14 mm 2 ) is smaller than probe's lateral area (5.59 mm 2 - probe's length is 2 mm), the maximum collecting area of the probe is limited to the hole's top area and not to the probe's lateral area. Moreover, not all the ions that enter in the hole are collected by the probe. Therefore, a 2D Monte Carlo (MC) code [7] was used to estimate the probe's collecting area for ions. Solving a problem with cylindrical symmetry, the two dimensions considered in the model are radial r and axial z, the symmetry axis being identical with probe s axis, which is aligned to the magnetic field lines. The simulation box has R max = 2.5 mm and Z max = 2.1 mm (Figure 9a - sketch not at scale). The ions are introduced in the simulation domain at Z max and at different radial positions from r = mm to r = R max, having maxwellian distribution function corresponding to an ion temperature of.5 to 3 ev. The input current density j, simulating the current density coming from the plasma column, is uniform along the radial direction. Plasma is confined by an uniform axial magnetic field of.7 T. The code calculates the fraction of particles introduced in the simulation domain that is collected by the cylindrical probe, the front plate and the ceramic holder. This fraction, expressed in terms of current density, j(r)/j, is plotted in Figure 9b versus the input radial position r, for an ion temperature of 3 ev. Figure 8. Detail of a single probe: front picture and side view sketch. The probe's collecting area for ions is estimated as the cross sectional area in the plasma column which, multiplied by the current density j, assures the current collected by the probe:

11 R j = max probe ( r) Aci 2π rdr. (1) j Thus, the average collecting area calculated for ions is A ci = 1.1 mm 2. Using the same numerical procedure, the average probe s collecting area calculated for electrons is A ce =.82 mm 2, larger than 2 probe's top area ( π =.622 mm 2 ). r p 1. r probe =.445 mm front plate j(r) / j.5 probe. 2 ceramic (b) z (mm) 1 probe ceramic front plate 1 2 Figure 9. (a) The simulation box; (b) Normalized current density j(r)/j collected by the probe, the front plate and the ceramic holder, for T i = 3 ev. The ion flux density arriving to the target surface (Figure 1) can be now calculated by dividing the ion saturation current (curve for V probes = -8 V in Figure 4) by the product ea ci, where e is the elementary charge. (a) 4 Γ i (1 23 m -2 s -1 ) Figure 1. Radial distribution of the ion flux density to the target surface (H 2 gas;.95 T magnetic field strength; 125 A discharge current; V probes = -8 V). The electron thermal flux density in the plasma column can be estimated as

12 1 n 8kT e Γ e = e. (2) 4 πme The radial distribution of this flux density (curve TS in Figure 11) can be obtained by introducing n e and T e from Figure 7 in relation (2). This information is not enough when we need the radial profile of the charged particle flux that bombards the target. The latter one strongly depends on the target bias. For illustration, Figure 11 also shows the electron flux density calculated from probe measurements. It was obtained by dividing the highest electron current that was correctly estimated (curve for V probes = -45 V in Figure 6) by the product -ea ce. This flux density is lower than the thermal one because the bias of the probes was more negative than the local plasma potential corresponding to each probe. Moreover, knowing that between the Thomson scattering location and the multi-probe system there is a distance of 2 cm and the magnetic field is diverging in this region, it is possible to have particle losses and plasma column broadening between the two locations TS TS fit V probes = -45 V Γ e (1 24 m -2 s -1 ) Figure 11. Radial distribution of the electron flux density calculated from Thomson scattering results (TS curve) and from probe measurements for V probes = -45 V (H 2 gas;.95 T magnetic field strength; 125 A discharge current). 3.4 Estimation of the plasma potential When analyzing the elementary processes accompanying the interaction of the plasma column with the target surface, the fact that the target might be locally exposed to a combination of ion and electron current must be considered. Both ion and electron bombardment produce thermal heating of the target but, due to their larger mass, the ion bombardment might have many additional effects as sputtering, recombination, secondary electron emission or chemical reaction with target material. Moreover, the processes induced by ion bombardment are strongly related to the kinetic energy of the ions which, besides the thermal component, also includes the energy gained within the electrostatic sheath formed in front of the floating target. If the thermal energy might be considered equal to the electron one, the evaluation of the second component of the ion energy requires knowledge of the plasma potential, on one side, and of the ion moving regime within the ionic sheath, on the other side. Measuring the local plasma potential V p in strongly magnetized plasma is not a trivial task. A frequent evaluation of this parameter is obtained from probe measurements as [1]: I e sat V = + p V f Te ln (3) I i sat

13 where the electrons are assumed to have Maxwellian velocity distribution function corresponding to the temperature T e (expressed in ev). I e sat and I i sat are the electron and ion saturation current, respectively. As it was already assumed, the ion saturation current I i sat is given by the current curve for V probes = -8 V in Figure 4. The electron saturation current I e sat can be obtained by multiplying the electron thermal flux density (curve TS_fit in Figure 11) with the product ea ce : 1 8kTe I e sat = ene Ace. (4) 4 πme Thus, the estimated radial distribution of the plasma potential is plotted in Figure 12. It has to be mentioned that the estimated plasma potential has to be considered with prudence since its value can be affected by several factors: - possible non-maxwellian electron velocity distribution function; the velocity of the electrons might have a drift component along the magnetic field lines in which case the plasma potential would be more positive than it was found; - electron density and temperature are measured at 2 cm in front of the target, where the plasma column diameter is narrower than at the target due to the divergence of the magnetic field in this region [3]; thus, the electron saturation current I e sat is underestimated at larger radii and, consequently, the estimated plasma potential is more negative than it should be; this could be the reason why V p = V f at larger radii V f V p Potential (V) V f target = V Figure 12. Radial distribution of the measured floating potential and the estimated plasma potential across the plasma column (H 2 gas;.95 T magnetic field strength; 125 A discharge current). 3.5 Estimation of the current flowing through the floating target The distribution of the current over the surface of the floating target was discussed in section 3.1. Based on this distribution and knowing how to estimate the current density from the probe measurements (section 3.3), it is possible to calculate the current that flows through the floating target as: I ft r = zonei I( r) 2π rdr, (5) A ce where I(r) is the absolute value of the local current measured in zone I - a disc of radius r zonei (Figure 2). As this current is electronic, the current density was calculated using the probe's collecting area for electrons, A ce.

14 The current flowing through the floating target was calculated for the same magnetic field strength (.95 T) and different discharge currents (Figure 13). This current is of the order of Ampéres and it is larger at lower discharge currents. When the discharge current increases there is a decrease of (i) the radial gradient of the floating potential in the plasma column and (ii) the difference between the local floating potential measured by the probes and the floating potential of the target [3]. Thus, the local currents received by the floating target diminish and so does the current that flows through the floating target I ft. Because the entire floating target is exposed to a total zero current, the electron current I ft from zone I is balanced and limited by an equivalent ion current from zone II I ft (A) Figure 13. The current flowing through the floating target as a function of the discharge current (H 2 gas;.95 T magnetic field strength). Conclusion The spatial distribution of the charged particles that come from the plasma column and interact with the target in Magnum-PSI can be smoothly tailored by modifying the target bias. This is a great advantage when investigating plasma-surface interaction due to the good control of the charged particle fluxes on the surface. For a chosen operation condition, the target can be entirely exposed to ion/electron fluxes, or it can be partially exposed to electron flux and partially to ion flux. Ion and/or electron currents were measured with a 2D multi-probe system. The corresponding flux density was obtained by dividing the measured current to the numerically estimated collecting area of the probe. A floating conductive surface that interacts with an inhomogeneous plasma collects non-zero local currents despite its total null current. This fact generates electron current flows within the conductive surface, from the zones which collect electron dominated currents to the zones collecting ion dominated currents. These zones are determined by the difference between the local floating potential in the plasma column and the floating potential of the conductive surface. This result is of great importance for understanding fusion reactors operation. In such reactors, a floating inhomogeneous plasma interacts with the grounded walls, divertor or other biased electrodes. Consequently, phenomena which are similar to those described in this paper are expected to appear at the plasmasolid interface in fusion reactors. Acknowledgements This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme under grant agreement No I d (A)

15 This work has been performed under EUROfusion WP PFC. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] De Temmerman G, Bystrov K, Liu F, Liu W, Morgan T, Tanyeli I, van den Berg M, Xu H, Zielinski J 213 Plasma-surface interactions under high heat and particle fluxes Acta Polytechnica 53(2) [2] De Temmerman G, van den Berg M A, Scholten J, Lof A, van der Meiden H J, van Eck H J N, Morgan T W, de Kruijf T M, Zeijlmans van Emmichoven P A and Zielinski J J 213 High heat flux capabilities of the Magnum-PSI linear plasma device Fusion Engineering and Design [3] Costin C, Anita V, Ghiorghiu F, Popa G, De Temmerman G, van den Berg M A, Scholten J, Brons S 215 Cross-section analysis of Magnum-PSI plasma beam using 2D multi-probe system Plasma Sources Sci. Technol [4] Solomon M L, Anita V, Costin C, Mihaila I, Popa G, van der Meiden H, Al R, van de Pol M, van Rooij G and Rapp J 21 Multi-Channel Analyzer Investigations of Ion Flux at the Target Surface in Pilot-PSI Contributions to Plasma Physics 5(9) [5] Schott L 1968 Electric probes, in Plasma Diagnostics, ed. by W. Lochte-Holtgreven, Elsevier, New York, Chap. 11 [6] Mihaila I, Solomon M L, Costin C, Popa G 213 On Electrical Probes Used in Magnetized Plasma Diagnostics Contrib. Plasma Phys. 53(1) [7] Mihaila I, Costea S, Costin C, Popa G 214 On Negative Slope of Probe Characteristics in Magnetized Plasmas Contrib. Plasma Phys. 54(3) [8] van der Meiden H J, Lof A R, van den Berg M A, Brons S, Donné A J H, van Eck H J N, Koelman P M J, Koppers W R, Kruijt O G, Naumenko N N, Oyevaar T, Prins P R, Rapp J, Scholten J, Schram D C, Smeets P H M, van der Star G, Tugarinov S N and Zeijlmans van Emmichoven P A 212 Advanced Thomson scattering system for high-flux linear plasma generator Rev. Sci. Instrum [9] van de Sanden M C M, Janssen G M, de Regt J M, Schram D C, van der Mullen J A M, van der Sijde B 1992 A combined Thomson Rayleigh scattering diagnostic using an intensified photodiode array Rev. Sci. Instrum [1] Schrittwieser R, Ionita C, Adamek J, Stockel J, Brotankova J, Martines E, Popa G, Costin C, van de Peppel L, van Oost G 26 Direct measurements of the plasma potential by Katsumata-type probes Czech. J. Phys. 56 (Issue 2 Suppl.) B145-5