and four-parameter probe techniques in fusion

Journal of Instrumentation

Advantages of the first-derivative probe technique over the three- and four-parameter probe techniques in fusion plasmas diagnostics To cite this article: E. Hasan et al 2018 JINST 13 P04005

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Published by IOP Publishing for Sissa Medialab Received: February 6, 2018 Revised: March 13, 2018 Accepted: March 23, 2018 Published: April 3, 2018

the three- and four-parameter probe techniques in fusion plasmas diagnostics

E. Hasan,a,b M. Dimitrova,b,c,1 T. Popov,a P. Ivanova,b R. Dejarnac,c J. Stockelc and R. Panekc a Faculty

of Physics, St. Kliment Ohridski University of Sofia, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria b Emil Djakov Institute of Electronics, Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, 1784 Sofia, Bulgaria c Institute of Plasma Physics, The Czech Academy of Sciences, Za Slovankou 3, 182 00 Prague 8, Czech Republic

E-mail: [email protected] Abstract: In this work, the advantages are presented and discussed of the first-derivative probe technique over the three- and the four-parameter conventional probe techniques for diagnostics of fusion plasmas. The conventional probe techniques for estimation of the plasma potential and the electron temperature and density can only be used when the electron energy distribution function (EEDF) is Maxwellian. The first-derivative probe technique can provide reliable results for the plasma potential and the real EEDF when the latter deviates from Maxwellian. To exemplify the application of the results obtained by different techniques, results on the parallel power-flux density distribution in the divertor region of the COMPASS tokamak, IPP.CR, are presented and discussed. Keywords: Plasma diagnostics - probes; Nuclear instruments and methods for hot plasma diagnostics

1Corresponding author.

c 2018 IOP Publishing Ltd and Sissa Medialab

https://doi.org/10.1088/1748-0221/13/04/P04005

2018 JINST 13 P04005

Advantages of the first-derivative probe technique over

Contents Introduction

1

2

Langmuir probe diagnostic techniques for divertor plasma studies 2.1 Conventional probe techniques 2.2 First-derivative probe technique

1 1 3

3

Experimental results and discussion

4

4

Calculation of the parallel power-flux density in the divertor region

9

5

Conclusions

1

Introduction

13

Electric probes still remain the most reliable diagnostic tools allowing one to obtain the local values of the important plasma parameters, namely, the plasma potential, Upl , and the electron energy distribution function. The application of the probe technique has been summarized in numerous reviews and monographs [1–7]. The Langmuir probe is seen as a rather simple and, thus, an attractive scientific instrument for diagnostic of gas discharge plasmas. To obtain meaningful results, the probe should operate at a very low gas pressure in the absence of a magnetic field and should not disturb the plasma. A number of requirements are to be fulfilled if one is to obtain correctly the plasma parameters, as discussed in [7]. The Langmuir probes applicability to magnetized plasmas is still a matter of discussion, e.g. [8]. The aim of the present work is to compare and consider in more detail the conventional and the advanced techniques now in use for estimating the plasma potential and the electron temperatures and densities in strongly magnetized turbulent fusion plasmas. As an example, results obtained by different techniques are used to estimate the parallel power-flux density distribution in the divertor region of the COMPASS tokamak, IPP.CR.

2 2.1

Langmuir probe diagnostic techniques for divertor plasma studies Conventional probe techniques

The Langmuir probe techniques process the measured current-voltage (IV) probe characteristics. In strongly magnetized fusion plasma, the electron part of the IV characteristics above the floating potential is strongly distorted due to the influence of the magnetic field − as the magnetic field increases, the electron branch is gradually depressed, so that the plasma potential position cannot be defined correctly [8]. On the other hand, in most of the cases the ion branch of the IV at large negative potentials is saturated. Therefore, in fusion plasmas, the ion saturation branch of the

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IV characteristics and the part around the floating potential are used when retrieving the plasma potential and the electron temperature and density [9, 10]. To approximate the probe current, I(Upr ), as a function of the probe potential, Upr , three parameters − the ion saturation current, Isi , the floating potential, U f l , and the electron temperature are used:
   e U f l − Upr i I(Upr )=Is 1 − exp − . (2.1) Te

Isi = 0.5ene cs Ap ;

(2.2)

Ap is the area of the probe projection in the direction of the magnetic field, B, and cs = [e (Te + Ti ) /mi ]1/2 is the ion acoustic velocity where, due to the lack of experimental data, the ion temperature in the most of the cases is assumed equal to the electron temperature. In some of fusion plasma modes, no saturation of the ion current is observed in the measured IV probe characteristic. This phenomenon is explained by probe sheath expansion, which is likely to depend on the plasma density, the ion and electron temperatures, the magnetic field and the probe bias [11–13]. In such cases, using the three-parameter fit and ignoring the sheath expansion, one can seriously overestimate the electron temperature and density. Thus, to process the probe data measured, it is usually sufficient to use the approach of linearly increasing the ion current as the probe bias becomes much more negative than the floating potential. Then, a fourth parameter, namely the slope of the ion current, ∆I/∆Upr , must be added to expression (2.1) to estimate the electron temperature and ion saturation current, Isi :
   e U f l − Upr ∆I i I(Upr )=Is 1 − exp − + (Upr − U f l ) (2.3) Te ∆Upr Here Isi is equal to the ion component of the total probe current at floating potential. Then, equation (2.2) is used again to obtain the electron density. In both approaches, the difference between the plasma potential and the floating potential is used to estimate the plasma potential, Upl . This difference [14] is given by     kTe me Ti −2 (1 − δ) Up f = ln 2π 1+ . (2.4) 2e mi Te Here me and mi are the electron and ion mass and δ is the secondary emission coefficient [15, 16]; again, the ion temperature is very often assumed as being equal to the electron one. It is clear that to obtain correctly the plasma potential and the electron density by these conventional probe techniques (CPTs), one must know the ion temperature, Ti . Additional experiments (usually using a retarding field analyzer, RFA) are required — the results obtained in different tokamaks show that in the edge fusion plasma the ion temperature can exceed the electron temperature by a factor of 2-4 [17–20]. It must be emphasized that the CPTs (either three- or four-parameter fits) do not measure the real EEDF, but only assume that it is Maxwellian.

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The ion saturation current and the floating potential are estimated from the measured IV probe characteristics; then, the electron temperature is estimated using this approximation. The electron density is found from the expression for the ion saturation current

2.2

First-derivative probe technique

where S is the probe surface area, W = 1/2mv2 + eU is the total electron energy in the probe sheath, v is the electron speed at the sheath edge. The probe is biased by a potential Upr , while the value of U in the equation (2.5) is the probe potential with respect to the plasma potential (U = Upr − Upl ). The value of the geometric factor γ is in the order of unity. The electron-energy probability function √ ∫∞ √ 4π 2 (EEPF), f (ε) = m3/2 f (W), is normalized to the electron density by 0 f (ε) εdε = n, ε being the electron energy. For a Maxwellian electron energy distribution function, the EEPF presented on a semi-log scale is a straight line [8]. The important parameter in equation (2.5) is the diffusion parameter ψ. It is a number increasing as the number of collisions in the probe sheath increases. In the presence of a magnetic field, B, at low gas pressures, ψ depends on the Larmor radius, RL (W, B), as well as on the shape, the size and the orientation of the probe with respect to the magnetic field lines. For cylindrical probes oriented perpendicularly to (ψ⊥ ) and along (ψ | | ) the magnetic field lines, the diffusion parameters for strongly magnetized turbulent fusion plasma can be expressed as: ψ⊥ (B, W) =

r ln (πL 0/4r) πL 0 and ψ | | (B, W) = 16γRL (B, W) 64γRL (B, W)

(2.6)

Here r is the radius of the probe and L’ is the characteristic size of the plasma inhomogeneities. In fusion plasmas, where the magnetic field is rather strong, the diffusion parameter value is much higher than unity (ψ(B, W)  1) and the EEPF is represented by the first derivative of the electron current Ie (U) of the IV probe characteristic measured: √ 3γ 2m ψ dIe (U) f (ε) = (2.7) 2e3 S U dU The accurate evaluation of the EEPF requires that the value of the plasma potential Upl be known. In [30], an iterative procedure for precise estimation of the plasma potential was proposed; it is reviewed in [8]. We will describe its main points below. It was shown in [26] that for strong magnetic fields, i.e. for high values of the diffusion parameter ψ, and for a Maxwellian EEDF, the position of the plasma potential is shifted to the positive side with respect to the minimum of the first derivative of the IV characteristics by a value of 1.1 ÷ 1.4T ∗ (the value of T ∗ being equal to the value

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The assumption for Maxwellian EEDF in fusion plasma is generally accepted and used in most cases of evaluating the main plasma parameters. However, there appeared theoretical predictions [21–23] and experimental evidence [24–29] that the EEDF can deviate from the Maxwellian in the vicinity of the last closed flux surface (LCFS) and in the divertor region of the tokamaks. To the best of our knowledge, only the first-derivative probe technique (FDPT), presented and discussed in detail in the review paper [8], could estimate the real EEDF if it deviates from the Maxwellian. We will outline now the FDPT main points only. Thus, the electron current flowing to a cylindrical probe when collisions in the probe sheath occur, as is typical for strongly magnetized plasma, is given [5–8] by: ∫ 8πeS ∞ (W − eU) f (W)dW (2.5) Ie (U) = − 2 −eU) 3me γ eU 1 + (W W ψ

b)

0 as the value corresponding to the Figure 1. a. Estimation of the seeded value of the plasma potential Upl half-height of the experimental first-derivative minimum. b. Comparison of the calculated first derivative 0 (dot-dashed line) with the experimental first derivative (solid line). The best fit obtained after the with Upl iterative procedure is presented by a dashed line.

of T e , expressed in volts). At the position of the plasma potential, a more or less pronounced change of the slope of the first derivative is seen. This is associated with the transition from diffusion of electrons to their drift due to the change of probe potentials from negative to positive with respect to the plasma potential. In the example presented in [30], one can easily identify the position of the bend. In others, more complicated cases, when the EEDF deviates from Maxwellian, the ion current does not saturate, and the bend is not well pronounced. For the iterative procedure, one can 0 as the value corresponding to the half-height of accept the seeded value of the plasma potential Upl the first-derivative minimum (figure 1 a). Then, using equation (2.7), one obtains the values of the electron temperatures and densities from the EEPF acquired in an absolute scale. With these values, the electron part of the IV probe characteristic is calculated using equation (2.5). Then with these data, the model second derivative 0 , is compared with the experimental first (dash-dot line) is calculated and, after being shifted by Upl derivative (solid line), as presented in figure 1 b. If the seeded value of the plasma potential is overestimated, for the next iteration it is decreased; iterations are thus performed until the best fit is reached between the measured and the calculated first derivatives. The offset of the first-derivative zero-level is due to the linear increase of the ion current measured and is taken into account during the iteration procedure. Our experience shows that overestimating or underestimating the seeded value of the plasma potential affects mostly the electron densities values obtained, rather than those of the electron temperatures. This procedure allows one to estimate the value of the plasma potential with an accuracy of 2–3 V.

3

Experimental results and discussion

The COMPASS tokamak has two divertor probe systems [27, 31]. The first one consists of 39 single graphite Langmuir probes (LP) embedded poloidally in the divertor tiles. They are oriented in parallel to the magnetic field lines and provide profiles with a spatial resolution in the poloidal direction down to 5 mm [27]. The probes are numbered from LP#1 at the high-field side (HFS) to

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a)

b)

c) Figure 2. a. EFIT reconstruction of the magnetic surfaces and the main discharge parameters at time 1170 ms. b. Temporal evolution of the NBI (cyan) and c. D-alpha (yellow curve) signal for discharge #12595.

LP#39 at the low-field side (LFS) in the divertor area. They are swept with respect to the tokamak chamber wall potential by a triangular voltage Upr (t) = −100 ÷ +60V at a frequency of 1 kHz [32]. In this work, we consider the results obtained by the first divertor probe system during NBIassisted ELMy H-mode deuterium discharge #12595 with toroidal magnetic field BT = 1.15 T, line-averaged electron density ne avr = 5.5×1019 m−3 and plasma current 220 kA. The discharge starts 970 ms after the data acquisition system is triggered. Figure 2 a shows a reconstruction of the magnetic surfaces by the Equilibrium FITing code (EFIT) and the main discharge parameters at time 1170 ms. The neutral-beam heating power is PNBI ~320 kW (I beam = 10 A), starting at 1075 ms and applied for 120 ms during the discharge (cyan curve in figure 2 b). The D-alpha signal, presented by a yellow curve in figure 2 c, indicates that the H-mode starts immediately after the NBI. To evaluate the plasma parameters by employing Langmuir probes, one has to record and process the IV probe characteristics measured. In the experiments described here, the probes are swept by a triangular voltage at a frequency of 1 kHz, so that one IV is recorded for 0.5 ms. This time is shorter than the duration of the inter-ELMs period [33, 34]. In addition, during the ELMs spikes, the plasma is not in a steady-state — even if the probes are swept quickly, one cannot estimate correctly the plasma potential and the electron temperature and density. This is the reason why the plasma parameters in this work are evaluated in the inter-ELMs periods. The probe data recorded show that the ion current is not saturated in the region of radial positions from 0.423 m to 0.442 m (probes LP#8 to LP#12) in the HFS, and from 0.506 m to 0.520 m (LP#25 to LP#28) in the LFS. For the rest of the probes, the ion current is saturated. Let us first consider how the IV is processed when the ion current is saturated. An example provided by probe LP#30 is presented in figure 3.

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a)

It seen that the three-parameter fit describes well the positive probe current up to the floating potential. The evaluated data are: floating potential U f l = 3.6 ± 0.2 V, electron temperature Te = 13 ± 1 eV and ion saturation current Isi = 0.070 ± 0.002 A. From these data one can obtain the values of the plasma potential and the electron density. Assuming Ti ≈ Te , the plasma potential is Upl = U f l + 2.8Te , i.e Upl = 40 ± 3V. The probe #30 projection area isAp = 6.52 × 10−6 m2 , so that for the electron density we obtain n = (3.8 ± 0.1) × 1018 m−3 . Let us now process the same IV by means of the first-derivative probe technique. After two iterations, the plasma potential value is estimated from the first derivative of the probe current (figure 4) as Upl = 37 ± 2 V. The EEPF obtained from the data acquired by LP #30 is presented in figure 5. It is clearly seen that the experimental EEPF (the solid line) deviates from Maxwellian. It can be approximated by a sum (dashed-dotted lines) of two Maxwellian distributions, i.e., by a bi-Maxwellian EEPF with a low-temperature fraction with electron temperature Tel = 4.0 ± 0.4 eV and density nle = (2.0 ± 0.2) × 1018 m−3 , and a fraction with electron temperature Teh = 12 ± 2 eV and density neh = (1.2 ± 0.3) × 1018 m−3 . The uncertainties in the values obtained during their variation in the iterative procedure are the maximal absolute errors. It is not possible to obtain the best fit with the experimental data using values out of the interval of errors. The best fit obtained of the model curve calculated by equation (2.5) using the experimental data presented above with the measured IV probe characteristic is presented in figure 6. Figure 7 shows the best fit of the model curve’s first derivative with the first derivative of the measured IV (solid line). We should note here that the ion saturation current must be added to the calculated electron probe current when one seeks the best fit between the measured IV and the model curve. This could introduce additional uncertainties in the values obtained because of the experimental error in the estimation of the ion saturation current. Using the first derivative, we do not need to use the value of the ion saturation current. The comparison with the results obtained by a three-parameter fit shows that the conventional technique can only estimate the temperature of the high-energy electron fraction. This is to

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Figure 3. IV characteristic measured by LP #30 at time 1170 ms (solid line). The dashed line presents the three-parameter fit.

Figure 6. Measured IV (solid line) and model curve Figure 7. First derivative of the measured IV (solid (dashed line), LP #30. line) and model curve (dashed line), LP #30.

be expected, since in the case of a bi-Maxwellian EEDF, the value of the floating potential is determined by the high-energy fraction of the bi-Maxwellian EEDF, even if it represents only a small percentage of the main low-energy electron group [35]. In the example presented, the plasma potential and the total electron density are slightly overestimated by the CPT. One can thus conclude that when the EEDF is Maxwellian, the results for the plasma potential and the electron temperature and density yielded by both the conventional and FDPT are in good agreement [8, 28]. As it was mentioned above, the ion current of the IV probe characteristics measured is not saturated both in the vicinity of the inner strike point and on the LFS close to the outer strike point. Figure 8 is an example of an IV curve measured by probe #26 displaced in the divertor low-field side, while figure 9 shows its first derivative and the estimated plasma potential Upl = 42 ± 2V. The evaluated EEPF is presented in figure 10. Because the ion saturation current is not defined, for corrections in the iteration procedure we use the comparison between the first derivatives of the experimental and the model IV characteristics. The best result is presented in figure 11.

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Figure 4. First derivative of the probe current mea- Figure 5. EEPF obtained from the data measured by sured by LP #30 and position of the plasma potential LP #30 (solid line) and its approximation by a sum of two Maxwellian distributions, with a low-temperature Upl . (dashed line) and a high-temperature (dotted line).

Figure 10. EEPF of the experimental IV probe char- Figure 11. First derivatives of the experimental (solid line) and model (dashed line) IV probe characteristics. acteristic.

Figure 12 and table 1 present a comparison of the results obtained by the FDPT with these obtained by the three- and four-parameter fits. In the FDPT case, the ion saturation current is obtained by fitting the electron probe current calculated using equation (2.5) with the electron branch of the IV curve measured. As seen, when the ion current does not saturate, the threeparameter fit overestimates all plasma parameters. The plasma potential and the ion saturation current values from the FDPT and four-parameter fit agree well, while the latter overestimates the total electron density by about 30%. Also, the four-parameter fit can only obtain the higher temperature of the bi-Maxwellian EEDF. Figure 13 a, b, c and d summarize the plasma parameters data for the entire divertor region during discharge #12595 in the inter-ELM period at time 1170 ms. The positions of the strike point are hereinafter indicated by dashed lines. With this set of data, one can obtain additional plasma parameters, e.g., the parallel power-flux density in the divertor region. The accurate evaluation of the parallel power-flux density in fusion devices is of paramount importance in what concerns the lifetime of the plasma-facing components. The radial distributions of the parallel power-flux density in the midplane of the COMPASS tokamak and in the TJ-II stellarator are presented in [28], where it was shown that they have a double exponen-

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Figure 8. Experimental IV characteristic measured Figure 9. First derivative of the experimental IV by probe LP#26 at 1170 ms, discharge #12595. characteristic measured by probe LP#26 at 1170 ms.

Table 1. Comparison of the plasma parameters obtained by the FDPT and the three and four-parameter techniques.

FDPT

Three-parameter fit

Four-parameters fit

Upl [V]

42±2

84±8

47±5

Isi [A]

0.114±0.006

0.197±0.005

0.114±0.005

28±3

15±2

7±2

4±1

Te [eV] n × 1018 [m−3 ]

4.5±0.5 15±2 0.9±0.1 1.9±0.3

tial character. Below we will present and discuss the poloidal distribution of the parallel power-flux density in the divertor region during discharge #12595 in the inter-ELM period at time 1170 ms.

4

Calculation of the parallel power-flux density in the divertor region

The parallel power-flux density at the sheath entrance is defined by equation [14]: Q | | = γkTe Γse or



Q | | = 2kTe + eUs f

 1 + kTe Γse + 2kTi Γse, 2

(4.1a)

(4.1b)

where the particles flux density is Γse = Jsi /e, Jsi being the ion saturation current density. The conventional probe techniques, assuming Maxwellian EEDF and, as usually accepted, Ti ≈ Te , provide a value of γ = 7.3 for the heat transition coefficient, which is in agreement with [14].

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Figure 12. Comparison of the experimental IV probe characteristic (solid line) with the model curves obtained by FDPT (short dashed line); three-parameter fit (dashed line) and four-parameter fit (dash-dotted line).

b) ion saturation current density.

d) electron densities.

c) electron temperatures.

Figure 13. Poloidal distribution of the plasma parameters in the divertor region of COMPASS tokamak in the inter-ELM period at 1170 ms, discharge #12595.

As shown in [28], when the EEDF is bi-Maxwellian, one should use an effective electron temperature Teeff to calculate the parallel power flux density: Teeff =

Teh Tel (nle + neh ) neh Tel +nleTeh

(4.2)

The radial distribution of the effective electron temperature is presented in figure 13 c by empty circles. It is clear that the Teeff can only be evaluated by using the FDPT, which provides the real EEDF. The parallel ion power-flux density term Qi| | = 2kTi Γse necessitates a more detailed discussion. As mentioned, due to the lack of information, in the CPTs the ion temperature is usually assumed equal to the electron one, i.e. Ti ≈ Te . However, results obtained using a retarding field analyzer (RFA) in different tokamaks have shown that in the edge fusion plasma the ion temperature can exceed the temperature of the main

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a) plasma potential.

electron population by a factor of 2–4 [17–20]. This difference varies at different locations. In the bi-Maxwellian case, the ratio between Teh and Tel is roughly the same, so that one can assume that Ti ≈ Teh . In fact, the problem is more complicated, since, as recent particle-in-cell simulations and analytic estimations [36, 37] have demonstrated, the ion energy distribution function also deviates from Maxwellian and can be approximated by a bi-Maxwellian. This is why, in our considerations we assume in first approximation an effective ion temperature Tieff ≈ Teh . Then, using equations (4.1a) and (4.1b) in the bi-Maxwellian case, we arrive at: Q|| =



2kTeeff

+

2.8kTeh

 1 eff + kTe Γse + 2kTeh Γse, 2

(4.3)

where it is assumed that the sheath drop is mostly influenced by the fast electrons; therefore, eUs f ≈ 2.8kTeh . Equation (4.3) can be rewritten as: 

Q | | = 2 + 2.8

Teh Teeff

   Teh Teh 1 eff + + 2 eff kTe Γse = 2.5 + 4.8 eff kTeeff Γse 2 Te Te

(4.4)

  Th Th and, thus, the sheath heat transition coefficient γ = 2.5 + 4.8 T eeff will depend on the ratio T eeff . e e Figure 14 presents the distribution of γ at different radial positions in the divertor region for discharge #12595 during the inter-ELM period at time 1170 ms. The radial distributions of the parallel power-flux densities for discharge #12595 during the inter-ELM period at time 1170 ms derived using the results for electron temperatures obtained by CPTs and the FDPT are presented in figure 15 a. It is seen that in the low- and high-field sides in the divertor region, the three-parameter fit vastly overestimates the parallel power-flux density.

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Figure 14. Poloidal distribution of the sheath heat transition coefficient γ in the divertor region of COMPASS tokamak for discharge #12595 in the inter-ELM period at 1170 ms.

Figure 15. Poloidal distributions of the parallel power flux densities in the divertor region of the COMPASS tokamak, in the inter-ELM period at 1170 ms derived using the results obtained by CPTs and FDPT. Table 2. The parallel power-flux densities parameters in the divertor region of the COMPASS tokamak obtained by CPTs and FDPT.

QLFS 0

λqLFS

QHFS 0

λqHFS

[MW/m2 ]

[mm]

[MW/m2 ]

[mm]

Three-parameter fit

20

17

12

14

Four-parameter fit

8.2

22

7.5

15

FDPT

5

23

6.5

23

The four-parameter fit results in the high- and low-field sides fall in between those obtained by the three-parameter fit and the FDPT. Figure 15 b shows the same results in a semi-logarithmic scale. The profiles derived for the high- and low-field sides clearly have an exponential shape. They can be approximated by the expressions:   LFS LFS QLFS = Q exp −R/λ in the low-field side (4.5a) q 0 || and

  HFS HFS in the high-field side QHFS = Q exp R/λ q 0 ||

(4.5b)

where λq is the decay length. The values obtained are presented in table 2. These results demonstrate that the three-parameter fit could overestimate substantially Q0 in comparison with the value obtained by the FDPT, while λq could be underestimated. The values obtained by the four-parameter fit are closer to those obtained by the FDPT, but the tendency is the same as in the case of the three-parameters fit. We should point out that, when applying the conventional techniques, one usually assumes that the ion temperature is equal to the electron one, Ti ≈ Te , the latter actually being the temperature of the high-energy electron fraction Teh . When considering the bi-Maxwellian case, we assume in first

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b)

a)

5

Conclusions

We present and discuss the advantages of the first-derivative probe technique over the conventional three- and four-parameter probe techniques for diagnostics of fusion plasmas. The techniques under discussion process the measured current-voltage probe characteristics. The conventional probe techniques for estimation of the electron temperature can only be used when the electron energy distribution function is Maxwellian. To obtain correctly the plasma potential and the electron density by these conventional probe techniques, one must know the secondary electron emission coefficient for the probe material and the ion temperature. Thus, additional experiments (usually using a retarding field analyzer, RFA) are required, the results obtained in different tokamaks showing that in the edge and scrape-off layer fusion plasma the ion temperature can exceed several times the temperature of the main electron group. In the Maxwellian case, the first-derivative probe technique provides results for the electron temperature in agreement with those from the conventional techniques, but does not require any additional information for the ion temperature to estimate the electron density and the plasma potential. When the electron energy distribution function deviates from Maxwellian and can be approximated by a bi-Maxwellian, the first-derivative probe technique yields correct results for the plasma potential and the real EEDF, respectively, for the electron temperatures and densities. In the case of a bi-Maxwellian EEDF and when the ion current of the measured IV probe characteristic saturates, the conventional three-parameter technique can only estimate the temperature of the high-energy electron fraction in agreement with the results obtained by the first-derivative probe technique. When the ion current in the measured IV probe characteristic does not saturate, the fourparameter conventional technique yields results for the ion saturation current, the plasma potential and the total electron density in agreement with those of the FDPT, while the electron temperature obtained corresponds again to the temperature of the high-energy electron fraction of the EEDF. If one then applies the widely-used three-parameter technique for processing the measured IV probe characteristic, the error in determining the electron temperature and the plasma potential reaches about 50%. Obviously, this technique cannot and should not be applied to such cases. The results obtained by the different techniques considered are used to calculate the radial distribution of the parallel power-flux density in the divertor region of the COMPASS tokamak. The results prove that the three-parameter technique could vastly overestimates the values of the

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approximation an effective ion temperature Tieff ≈ Teh . It is clear that a precise estimation of the heat transition coefficient would necessitate, besides probe measurements, additional measurements of the ion temperature. Different measured values of the ion temperature would alter the values of the parallel power — lux densities obtained by both approaches. On the other hand, when calculating the electron density by the conventional techniques, the value Ti ≈ Teh is used to estimate the value of the ion acoustic velocity cs = [e (Te + Ti ) /mi ]1/2 . The results for the electron densities provided by both CPTs and FDPT are in good agreement, so that one can conclude that assuming Tieff ≈ Teh is an adequate approximation. Of course, one should not use it as a way of evaluating the ion temperature, because, together with the electron temperature, they are under square root in the equation for the ion acoustic velocity.

parallel power-flux density around strike points, as compared with the values obtained by the FDPT, while the decay length λq could be underestimated. The values obtained by the four-parameter fit are closer to those obtained by the FDPT, but the tendency is the same as in the case of the three-parameter fit. A more precise estimation of the heat transition coefficient and the radial distribution of the parallel power-flux density in the divertor region would necessitate, besides probe measurements, additional measurements of the ion temperature.

Acknowledgments

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This research was partially supported by the Joint Research Project between the Institute of Plasma Physics of the CAS and the Institute of Electronics BAS BG, and by MSMT project # LM2015045.

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