1 INTRODUCTION

The formation of the regimes with improved plasma confinement is one of the necessary conditions for the implementation of efficient (in terms of energy) operating regimes of the new-generation tokamaks, including the reactor-grade facilities [1]. Improved confinement regimes include the regimes with the external (H-mode) and internal transport barriers. A region with the reduced anomalous transport of heat and/or particles is usually called the transport barrier, which occurs due to the partial or complete suppression of turbulence that determines transport in this region. If the reduced transport (reduced turbulent flows and corresponding transport coefficients) is observed in the central region of the plasma column, 0.1 < ρITB < 0.8, then we speak of the formation of the internal transport barrier (ITB) [2]. The regimes with ITBs were obtained at all operating tokamaks in the course of ion, electron, and combined heating [3–6]. The characteristic features of ITB formation under different conditions and theoretical approaches to describing the physical mechanisms for ITB formation are discussed in detail in [3]. Numerous experiments [7–9] have shown that the configuration with low magnetic shear near the rational surface is favorable in terms of the ITB formation. This is especially critical in the regimes with predominant electron plasma heating. The ITB formation is detected when at the constant sources, the region with increased gradients of temperature, density and plasma rotation velocity appears in the plasma. If the appropriate measurements in the ITB region are performed, it can be observed that the peculiarity appears on the profile of the radial electric field Er [3] and the turbulence is suppressed inside of the barrier [7, 10].

For reliably observing and studying the transport barriers, the following diagnostics are used [3]:

—the active spectroscopy (CXRS) was used for determining the ion temperature profiles, plasma rotation velocity, and reconstructing the Er profile;

—the heavy ion beam probing of plasma (HIBP) was used for measuring the plasma potential profile and determining the Er(r) profile;

—the reflectometry diagnostics was used for registering changes in turbulence in the ITB region;

—the electron cyclotron emission (ECE) diagnostics was used for detecting the time of ITB formation and time evolution of the electron temperature profile;

—the Thomson scattering (TS) diagnostics providing for data on the electron density and temperature profiles was used for studying the ITB formation.

In experiments at the T-10 tokamak, the ITB formation was observed in the course of the electron cyclotron resonance heating (ECR heating) in the operating regimes with negative magnetic shear [11], in the regimes with low shear near the rational surface q = 1 [7, 8], and in the regimes with injection of deuterium pellets [12]; the ITB events were also detected during the spontaneous injection of impurities into the plasma [13] and restructuring of the q profile during the sawtooth oscillations [14]. We note that in the T-10 experiments, the occurrence of peculiarities on the profiles of electron temperature and X-ray radiation near the surface q = 1 was already noted in [15].

In [7], using the off-axis ECR heating, the region with low shear was created near the rational surface q = 1 in the region ρ = 0.6. An increase in the electron temperature gradient was observed using the TS and ECE diagnostics. The TS system had only 9 measurement points along the minor radius, which made it possible to obtain the spatial resolution of ~2 cm in the region of ITB formation.

This paper presents new diagnostic capabilities of the TS system at the T-10 tokamak [16]. For demonstrating the upgraded system capabilities, the results of detecting ITB in the regimes with the off-axis ECR heating are presented. For determining the correlation between the positions of the ITB and rational surface, time evolution of the current profile was simulated using the ASTRA code [17].

2 DIAGNOSTIC SYSTEM

At the T-10 tokamak, the upgraded TS diagnostics is based on the Nd:YAG laser with the pulse repetition frequency of 100 Hz, energy of 2.5 J per pulse, and the wavelength of λ = 532 nm (second harmonic). The signals were detected using the television system based on the CMOS camera and image intensifier. Laser beam is injected into the tokamak chamber along the vertical direction using the multipass system. The geometry of probing and light collection is shown in Fig. 1. The technical equipment of the upgraded diagnostics is discussed in detail in [16].

Fig. 1.
figure 1

Geometry of probing and light collection of TS system at the T-10 tokamak.

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The laser can operate for several seconds, making it possible to observe the changes in temperature and density profiles during the plasma discharge at 10-ms time intervals. In discharges with low density, due to the insufficient amount of collected light and low signal-to-noise ratio, it is preferable to determine temperature profiles using the frames averaged over several laser pulses. Averaging was performed in the stationary discharge stages with constant or slightly varying plasma parameters. We note that in this work, the Thomson scattering diagnostics was used only for measuring the electron temperature profile. The density profiles were reconstructed from the data of interferometric measurements. The density measurements using the Thomson scattering were not performed because of the engineering features of the system; this is discussed in detail in [16].

3 EXPERIMENTAL CONDITIONS

The experiments were carried out at the T-10 tokamak (with the major radius R = 1.5 m, minor radius a = 0.3 m, and circular plasma cross-section) in the regimes with off-axis EC current drive. In these experiments, plasma was heated using two groups of gyrotrons. The first group included gyrotrons with the frequencies of 139.9 and 140.4 GHz. The power of these gyrotrons was injected obliquely to the major radius of the torus (with a toroidal angle of 18° at the plasma boundary), so they simultaneously heated the plasma and provided for the electron cyclotron current drive. The second group included gyrotron with the frequency of 129 GHz. The power of this gyrotron was injected strictly along the major radius, so it did not contribute to the EC current drive. In the range of magnetic fields under consideration, power of the 129‑GHz-frequency gyrotron was absorbed near the axis of the plasma column, rheat ~ 5−6 cm.

For the shots under consideration, the parameters are presented in Table 1.

Table 1. Parameters of typical T-10 shots with ITB in regimes with off-axis EC current drive
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Here, Ip is the plasma current, BT is the magnetic field at the axis of the plasma column, qa=2πa2BT/(μ0IpR) is the Safety factor at the plasma boundary, μ0 is the magnetic permeability of vacuum, rcd is the radius of location of the EC-driven current peak (over the profile) measured from the magnetic axis of the plasma column, fcd is the frequency of gyrotron used for the EC current drive, Pcd is the EC power used for non-inductive current drive, and PECRH is the total power spent for ECR heating and current drive: PECRH = Pcd + Pheat, where Pheat = 0.45 MW is the power of 129-GHz-frequency gyrotron spent on the plasma heating only and giving no contribution to the current drive.

Figure 2 shows time evolutions of the central electron temperature measured using the ECE diagnostics [18], the average density measured along the central chord using the interferometer, and the total ECR heating power. We note that the gyrotrons are switched on at the plasma current flat-top (time of reaching the current flat-top is tp = 400−430 ms). In the stage of the electron cyclotron resonance heating/current drive, the ohmic heating power does not exceed 200 kW.

Fig. 2.
figure 2

Time dependences of (a) Te(0) temperature measured by ECE diagnostics, (b) average density, and (c) injected microwave power.

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In all shots under consideration, the sawtooth oscillations (SO) are observed in the ohmic stage of the discharge (before switching on the EC power). This indicates the presence of the q = 1 surface in the plasma. The radius corresponding to the phase reversal of the sawtooth oscillations, determined from the data of multichannel X-ray measurements, was rs ~ 8−10 cm (taking into account the presence of measuring channels in the region of the SO phase reversal). From the high magnetic field side, the radius of the SO  phase reversal is in the range between –7 and ‒10.5 cm; from the low magnetic field side, it is in the range between 7.5 and 9 cm. Switching on the off-axis current drive results in the stabilization (termination) of the sawtooth oscillations (in shots nos. 72766 and 72767, t = 550 ms; and in shot no. 70289, t = 750 ms). Subsequent switching on the on-axis heating in shots nos. 72766 and 72767 initiates the sawtooth oscillations again. In the stage of ECR heating (t > 680 ms), the radius of the sawtooth oscillations phase reversal is rs ~ 7.5−8.5 cm.

4 RESULTS OF TEMPERATURE PROFILE MEASUREMENTS

The results of measuring the temperature profiles using the Thomson scattering diagnostics are presented in Figs. 3, 4, and 5 for each of the shots under consideration at several characteristic times before and during the auxiliary heating phase. For comparison, the profiles measured using the ECE diagnostics at the same times are shown. For characterizing the temperature gradient, we calculated the profiles of the normalized electron temperature gradient R/\({{L}_{{{{T}_{e}}}}}\) = (R/Te)dTe/dr and the density profiles obtained from interferometric measurements by means of solving the inverse problem. The pulses are shown in order of increasing toroidal magnetic field, which corresponds to the shift of the region of microwave power deposition and the region of electron-cyclotron current drive from the edge towards the axis of the plasma column.

Fig. 3.
figure 3

Profiles of (a) electron temperature, (b) normalized temperature gradient; and (c) electron density in shot no. 70289 at BT = 2.26 T.

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Fig. 4.
figure 4

Profiles of (a) electron temperature, (b) normalized temperature gradient; and (c) electron density in shot no. 72767 at BT = 2.28 T.

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Fig. 5.
figure 5

Profiles of (a) electron temperature, (b) normalized temperature gradient; and (c) electron density in shot no. 72766 at BT = 2.31 T.

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In all shots under consideration, in the ohmic stage, the temperature profiles have no considerable peculiarities. The normalized gradients are moderate, R/\({{L}_{{{{T}_{e}}}}}\) ≤ 10, which corresponds to those typically observed in the regimes without ITB. In shot no. 70289 during the off-axis ECR heating (PECRH = 0.8 MW), the normalized temperature gradient increases to R/\({{L}_{{{{T}_{e}}}}}\) ~15 by time t ~ 830 ms (Fig. 3b), which may indicate the ITB formation. In shot no. 72767, in 50 ms after switching on the off-axis heating (PECRH = 0.75 MW), the gyrotron is additionally turned on, providing for the on-axis power deposition (PECRH = 0.45 MW), which results in the formation of a zone with the increased gradient of R/\({{L}_{{{{T}_{e}}}}}\) ~ 22 (Figs. 4a and 4b). After the resumption of sawtooth oscillations, at t > 680 ms, the region of increased gradient disappears (see profiles at t = 713 ms in Figs. 4a and 4b). In shot no. 72766, in which the heating scenario is similar, the increase in the temperature gradient is much less pronounced (Fig. 5). Shot no. 72766 is characterized by the highest magnetic field, which means that the region of the EC current drive becomes more on-axis. Apparently, this results in the difference of the barrier fo-rmation.

5 SIMULATIONS

For determining the transport barrier position relative to the rational surfaces and verifying the assumptions made above, time evolutions of the current profile and the profile of the safety factor q were calculated using the ASTRA transport code.

The electron temperature and density profiles and their variation in time were the input data for calculations and were taken from experimental data obtained using the TS and interferometry diagnostics, respectively (Figs. 3−5). Time evolution of the current profile was simulated under the assumption of neoclassical conductivity using the Sauter–Angioni formula [19] with allowance for the bootstrap current. The magnitude and profile of the electron cyclotron current were calculated using the OGRAY code [20] (Fig. 6). The driven current at each instant was corrected taking into account the changes in temperature and plasma density:

$${{I}_{{{\text{cd}}}}}\left( t \right) = ~{{I}_{{{\text{cd}}}}}\left( {{{t}_{{{\text{calc}}}}}} \right)\frac{{{{T}_{e}}\left( t \right)}}{{{{T}_{e}}\left( {{{t}_{{{\text{calc}}}}}} \right)}}\frac{{{{n}_{e}}\left( {{{t}_{{{\text{calc}}}}}} \right)}}{{{{n}_{e}}\left( t \right)}}.$$
Fig. 6.
figure 6

Profiles of electron cyclotron driven currents calculated using OGRAY code: (a) shot no. 70289, t = 833 ms, BT = 2.26 T; (b) shot no. 72767, t = 643 ms, BT = 2.28 T; and (c) shot no. 72766, t = 633 ms, BT = 2.31 T. The values of EC driven currents are shown in figures.

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The effective plasma charge was taken to be Zeff ≈ 3, which corresponds to the Zeff estimation obtained from the visible-range continuum in the ohmic stage before switching on the gyrotrons.

The correspondence between the calculations and experimental data was controlled by means of monitoring the time dependence of the loop voltage. As will be shown below, for all three shots, the loop voltages obtained in the calculations are in satisfactory agreement with the measured ones. For shots nos. 70289 and 72766, on the Ip flat-top, the calculated and experimental βp values and plasma energy contents W were compared. The deviations of the calculated parameters from the measured ones do not exceed 15%.

The calculation results are shown in Figs. 7, 8, and 9. The calculated changes in the profiles of the safety factor q(r) are shown in Figs. 7a, 8a, and 9a. For these q(r) profiles, the magnetic shear distributions shear(r) = (r/q)dq/dr are shown in Figs. 7b, 8b, and 9b. Time dependences of the loop voltage, demonstrating satisfactory agreement between the calculated and experimental data, are shown in Fig. 7c, 8c, and 9c.

Fig. 7.
figure 7

Calculated profiles of (a) safety factor q and (b) magnetic shear, and (c) time dependences of loop voltage for two times in shot no. 70289. For convenience, Fig. 7b shows electron temperature profile measured using TS diagnostics. Arrow in Fig. 7a shows position of peak current density of EC driven current; in Figs. 7a and 7b, dotted lines indicate radii of phase reversal of sawtooth oscillations in ohmic phase.

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Fig. 8.
figure 8

Calculated profiles of (a) safety factor q and (b) magnetic shear, and (c) time dependences of loop voltage for two times in shot no. 72767. For convenience, Fig. 8b shows electron temperature profile measured using TS diagnostics. Arrow in Fig. 8a shows position of peak current density of EC driven current; in Figs. 8a and 8b, dotted lines indicate radii of phase reversal of sawtooth oscillations in ohmic phase.

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Fig. 9.
figure 9

Calculated profiles of (a) safety factor q and (b) magnetic shear for two time instants, and (c) time evolution of loop voltage in shot no. 72766. For convenience, Fig. 9b shows electron temperature profile measured using TS diagnostics. Arrow in Fig. 9a shows position of peak current density of EC driven current; in Figs. 9a and 9b, dotted lines indicate radii of phase reversal of sawtooth oscillations in ohmic discharge phase.

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From the figures presented, it is clear that in the ohmic stage, the calculated position of the q = 1 surface is consistent with the rs estimate of its position obtained from the multichannel X-ray measurements. Switching on the off-axis ECR heating and current drive results in a decrease in the magnetic shear in the region of power deposition. In the experiments under consideration, it corresponds to the region near the rs surface. According to the simulation results, when the heating and current drive are switched on, the q = 1 surface does not disappear, but the magnetic shear near it decreases. This may explain the appearance of a region with increased temperature gradient in shots nos. 70289 and 72767. In accordance with the theoretical concepts [3, 7, 22], in the region with low magnetic shear near the rational surface, the transport barrier formation is associated with the rarefaction of rational surfaces (the formation of the so-called “gap”). Figure 10 illustrates the rarefaction of rational surfaces in shot no. 70289. The figure shows the calculated q(r) profile and the locations of rational surfaces q = m/n for the poloidal mode numbers m ≤ 20 at time t = 833 ms. The rarefaction of magnetic surfaces near the q = 1 surface is clearly visible. In shot no. 72767, situation looks similar. The simulation results make it possible to explain the difference between shots nos. 72766 and 72767. In shot no. 72766, due to the higher toroidal magnetic field, the region of EC current drive turns out to be located inside the surface q = 1. This leads to not a decrease, but an increase in the magnetic shear near the surface q = 1 (compare Figs. 8b and 9b), and as a consequence, to the lesser rarefaction of magnetic surfaces near the q = 1 surface.

Fig. 10.
figure 10

Calculated profile of safety factor q and locations of rational surfaces (vertical lines) at 833th ms in shot no. 70289. Surfaces q = 1; 1.5; 2; 2.5; 3 are marked in red.

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As mentioned above, the ITB formation is the result of a decrease in the turbulent transport and a-ssociated transport coefficients. Within a somewhat simplified consideration (without separating transport into its diffusive and non-diffusive components), the changes in the transport coefficients during the tra-nsport barrier formation can be quantitatively characterized using the effective transport coefficients. Figure 11 shows the result of estimating the effective electron thermal diffusivity χe,eff for one of the shots presented (no. 70289). To determine the effective thermal diffusivity, the following formula was used:

$${{\chi }_{{e{\text{,eff}}}}}\left( r \right) = \frac{{Q_{e}^{{{\text{TOT}}}}\left( r \right)}}{{V{\kern 1pt} '\left( r \right){{n}_{e}}\left( r \right){\text{grad}}\left( {{{T}_{e}}\left( r \right)} \right)}},$$

where \(Q_{e}^{{{\text{TOT}}}}\) is the heat flux through the surface with radius r, and V ' is the volume element.

Fig. 11.
figure 11

(a) Calculated profiles of effective electron thermal diffusivity in shot no. 70289 before transport barrier formation and in the stage of already formed ITB; and (b) time evolution of effective electron thermal diffusivity inside and outside barrier region (r = 11 and 14 cm, respectively).

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Figure 11a shows the χe,eff and Te profiles at time instants before the transport barrier formation (813 ms) and during the existing ITB (833 ms). It can be seen that the region of increased electron temperature gradient corresponds to the region of reduced effective electron thermal diffusivity, as would be expected during the transport barrier formation. Figure 11b shows time evolutions of the χe,eff coefficient inside and outside the region of increased temperature gradient, at the radii of 11 and 14 cm, respectively, during the ECRH pulse driving the current. An important feature can be noted: at r = 11 cm, the thermal diffusivity coefficient does not decrease immediately after the gyrotron is switched on, but with a delay of ~50 ms. The simulations performed make it possible to attribute the observed time delay to the restructuring of the q(r) profile.

In the regimes under discussion, the plasma energy lifetimes are as follows: τE = 24 ms (no. 70289, 833 ms, total heating power Ptotal = 1 MW), τE = 15 ms (no. 72767, 643 ms, Ptotal = 1.4 MW), and τE = 11 ms (no. 72766, 633 ms, Ptotal = 1.4 MW). They turn out to be slightly lower than those predicted by the scaling for the L-mode [1], but correspond to typical energy confinement times observed at the T-10 in the L-mode regimes in discharges with densities \({{\bar {n}}_{e}}\sim 0.3{{n}_{{{\text{Gw}}}}}\) (see, [23], nGw is the Greenwald density). The changes in the energy confinement time due to the ITB formation are within the experimental accuracy. In the regimes of this type, the changes in plasma confinement were analyzed in [7, 8] and are beyond the scope of this article.

6 CONCLUSIONS

New diagnostic capabilities of the upgraded Thomson scattering system of the T-10 tokamak made it possible to observe time evolution of the plasma electron temperature profile throughout the entire plasma discharge at 10-ms time intervals with the spatial resolution of up to 5 mm. This made it possible to trace in more detail time evolution of temperature profiles and describe the dynamics of ITB formation in the regimes with off-axis heating and electron-cyclotron current drive, studied in [7, 21].

It was shown that in the regimes with off-axis ECR heating and current drive (power is deposited near the q = 1 surface), the formation of regions with increased electron temperature gradient is observed, which can be interpreted as the formation of the internal transport barrier.

The ASTRA code was involved for simulating time evolution of the plasma current profiles using the electron temperature profiles measured. It was shown that the formation of regions with increased temperature gradient correlates with a decrease in the magnetic shear near the q = 1 surface. This does not contradict the existing ideas concerning the mechanism for the transport barriers formation in the regions with low magnetic shear near the rational surfaces and is consistent with the interpretation of the T-10 results previously published in [7, 21].