Isotopic effect in experiments on lower hybrid current drive in the FT-2 tokamak

To analyze factors influencing the limiting value of the plasma density at which lower hybrid (LH) current drive terminates, the isotopic factor (the difference in the LH resonance densities in hydrogen and deuterium plasmas) was used for the first time in experiments carried out at the FT-2 tokamak. It is experimentally found that the efficiency of LH current drive in deuterium plasma is appreciably higher than that in hydrogen plasma. The significant role of the parametric decay of the LH pumping wave, which hampers the use of the LH range of RF waves for current drive at high plasma densities, is confirmed. It is demonstrated that the parameters characterizing LH current drive agree well with the earlier results obtained at large tokamaks.


Result of the LHCD efficiency study
The most efficient method for sustaining the quasisteady plasma current by means of lower hybrid (LH) waves can be implemented only at relatively low plasma densities not exceeding a certain density limit, n DL . The existence of the density limit for LH current drive (LHCD) was attributed to various mechanisms: linear absorption by ions, which increases as the density tends to the resonance LH value; collision losses; scattering by drift turbulence; parametric instabilities; etc. The density limit effect has been studied and discussed for several past decades; however, it has not received comprehensive physical explanation [1].
In the present work the main attention is paid to investigation of current drive by lower hybrid waves on the FT-2 (R = 0.55 m, a = 0.08 m, B T ≤ 3 T, I p = 19÷40 kA, f 0 = 920 МHz) tokamak. The results of experiments carried out at the FT-2 tokamak allow us to conclude that the most probable reason for LHCD termination in both hydrogen and deuterium plasmas at a relatively low plasma current of I = 22 kA and, accordingly, a low electron temperature is an additional reduction in T e at the periphery of the plasma column during the LH pulse [2]. This results in a lower threshold for the parametric decay (~T e /n e ) of the pumping wave. The parametric decay satellites, the frequencies of which are down-shifted, (f sat = f 0kf Ci ), (k = 1, 2, 3…), are slowed down more than the pumping wave. Therefore, the plasma density, at which linear conversion of slowed down satellite waves occurs, is lower than that for the pumping wave; hence, the LH wave after parametric decay can be absorbed by ions even at the plasma periphery, without penetrating into the plasma column. At a higher plasma current (I OH = 32 kA) and higher electron temperature (T e0 = 600 eV), the density at which the LHCD in hydrogen plasma terminates is close to the resonance value (n DL H ≈ n LH H ≈ 3.5 10 19 m -3 ). After the plasma density reaches this value, the interaction of the LH wave with electrons is replaced with direct absorption by ions, when ω 0 ~ ω pl, i . As a result of the experimental study of the influence of the plasma isotopic composition on the LHCD efficiency, it is established that the efficiency η CD D in deuterium plasma on FT-2 is higher than in hydrogen plasma η CD H [2]. As it is seen from Fig. 1 (I OH = 32 kA), within the density range from <n e > = = 10 19 m -3 to <n e > = 2.5 10 19 m -3 in deuterium, we have η CD D ≈ 0.4 A m -2 W -1 , whereas in hydrogen plasma, this value is appreciably smaller, η CD ≈ 0.3 A m -2 W -1 . The resonance value n LH of the density for deuterium at ‫||‪N‬‬ ≈ 2 is substantially higher, n LH D ≈ 10 20 m -3 ≥ n DL D ≈ 4.5 10 19 m -3 . So, the obtained value n DL D ≈ 4.5 10 19 m -3 is smaller by more than one-half of the n LH D . Nevertheless, in contrast to hydrogen plasma, the density at which the sharp increase in the high-energy chargeexchange (CX) atomic flux (Fast Neutral (FN) with E CX = 1575 eV) <n e > FN D ≈ 5 10 19 m -3 , takes place proved to be higher than n DL D . There is an appreciable gap between the values of n DL D and <n e > FN D . Apparently, the main reason for LHCD termination in this case is the parametric decay of the pumping wave. The experimental results confirm that parametric processes intensify with increasing density during the RF pulse (see Fig. 3 in [2]). Nevertheless, we cannot exclude the influence of a substantial slowing down (up to ‫≈||‪N‬‬ 10) of the pumping wave as it propagates into the plasma column. The experimental evidence of influence of isotopic effect on characteristics of the ion heating observed at <n e > rise and after LHCD termination, which demonstrates Fig. 2 for H/D plasmas. A significant part of the LHCD experimental studies on FT-2 were performed at relatively low densities of <n e > = 10 19 m -3 , when, the parametric decay of the pumping wave is absent and the highest LHCD efficiency is observed. It is established that, at relatively large values of the plasma current (I OH = 32 ÷ 35 kA, P RF ≈ 100 kW, T e0 ≈ 550 ÷ 600 eV), the quantities η CD and I RF N and their dependences on the plasma parameters are close to those obtained at large tokamaks [2].

Parametric processes intensify with increasing plasma density
Parametric process on the periphery of the plasma column are considered as the main mechanism of growth ‫||‪N‬‬ resulting in a significant reduction of LHCD efficiency and depletion of the pump wave power due to the absorption of ions in the peripheral plasma [3,4]. The To assess the impact of isotopic effect on the development of parametric processes on the tokamak FT-2 a comparative measurements were carried out using the movable RF probe-antenna placed in the poloidal limiter shadow at the poloidal angle θ = 310°, which corresponds to the ICR in the plane of a large radius R = 0.6 m. Normalized spectra of the LH pump wave measured by the RF probe at different densities of the H/D plasma are shown in Fig. 3. It is noted that the increase in density results in a significant change in the intensity of IC satellites as well as the frequency width (FWHM) ∆F, MHz of the broadened pump wave. As shown in Fig. 4, maximum values for these dependencies as a function of <n e > are achieved with plasma densities of <n e > ~ 3 ÷ 4 10 19 m -3 . Under these conditions, according to Fig. 1, the efficiency generation of LHCD is reduced almost to 0.
Characteristically, those IC satellites in deuterium plasma appear at a density higher, than the density in hydrogen plasma. With increasing density its level is approximately 2 times higher than the level of the same dependencies measured in hydrogen plasma. This fact, in particular, may indicate a significantly larger pump wave depletion effect, when large fraction of LHW power falls in sidebands. Shift down frequencies (f sat = f 0kf Ci ), (k = 1, 2, 3...), at substantial rise of ‫||‪N‬‬ for f sat could result in additional heating of the ions on periphery of discharge. Most of the LHW power of f 0 in the course of propagation along the magnetic field lines with the gradual penetration in the plasma column reaches it central regions. During such penetration of LHW the effect of spectral broadening ∆F (Fig. 4) and additional slowdown result in decrease of the efficiency generation of the LHCD. With increasing density, more effective additional heating of the deuteron are observed Fig. 1, 2.
These and other experimental data presented in the report allows the use of isotope effect to conduct a comparative analysis for obtaining more information about the mechanisms affecting the efficiency of generation of LHCD and ion heating.
This work is executed at partial financial support by Russian Science Foundation grant 17-12-01110