RADIOFREQUENCY WAVES, HEATING AND CURRENT DRIVE IN MAGNETICALLY CONFINED PLASMAS
6.2. THEORY OF RF WAVE PROPAGATION IN A MAGNETIZED PLASMA The theory of wave propagation in magnetized plasmas has been
6.3.3. Lower hybrid heating and current drive experiments
After the early classic work of Golant, who worked out the accessibility of lower hybrid waves in an inhomogeneous plasma [6.33], Bellan and Porkolab proceeded to verify the dispersion characteristics of lower hybrid waves [6.7]
(see Fig. 6.31). This work showed that lower hybrid waves can be launched effectively from the plasma edge with a phase array of loops surrounding a small plasma column, later to be replaced by a phase array of narrow waveguides in the TE10 mode of excitation in a tokamak plasma at the few GHz range of frequencies (see Ref. [6.156] and references therein), where TE10 stands for the
fundamental mode of excitation of a rectangular waveguide with the electric field pointing across the narrow dimension of the waveguide and the magnetic field perpendicular to it. While there were numerous attempts to use such waves in tokamaks to heat ions by mode conversion into hot ion plasma waves near the lower hybrid resonance layer in the plasma core (Fig. 6.3, region C), there was no convincing evidence ever of ion heating by mode converted waves. Instead, strong parametric decay instability (PDI) was observed in the plasma periphery as the density was raised so that the LH resonance condition would be satisfied and the so-called “density limit” was reached where strong PDI was observed near the plasma periphery [6.157]. Raising the source frequency well above the resonance layer greatly reduced the PDI and electron heating was observed by electron Landau absorption of the waves.
FIG. 6.31. Experimental verification of dispersion relationship of cold lower hybrid waves launched by a phased array of loops formed the basis for lower hybrid current drive experiments in tokamaks (after Ref. [6.7]). Plotted is the comparison of experimental data (horizontal lines) and theoretical predictions based on Eq. (6.48) (solid line).
The wave accessibility condition Eq. (6.58) and the Landau absorption Eq. (6.63) limit the minimum and maximum values of the slow wave index of refraction parallel to the magnetic field, N, to the range:
2 1/2
2 2 1/2
1 1 7
pe pe ce ci
ce ce e
n T
(6.133)
where Te is in keV.
Absorption is assumed to be due to the quasi-linear limit of Landau damping and is based on code results. It is typically at a phase velocity of about 2.4 times the thermal velocity (where the thermal velocity is defined as
(2 /T me e)1/2). The interpretation of Eq. (6.133) is that in ITER type plasmas the wave penetrates with an index of refraction of about 1.8 and absorption is around 12 keV, which typically is at r/a = 0.8, which is the ideal distance for a reversed shear AT regime. Clearly, modelling of the edge pedestal height will be critical for assessing LH wave penetration in a reactor type plasma and as the density is increased in reactor regimes beyond ITER’s values, wave penetration will be squeezed between accessibility and Landau absorption, unless the magnetic field is increased towards 8 T.
FIG. 6.32. Demonstration of the existence of LHCD in the PLT tokamak for a few skin times in the early 1980s. Copyright (2011) by the American Physical Society.
In the late 1970s the theory of current drive was worked out by Fisch and co-workers (Ref. [6.158] and earlier references therein) and a “feverish”
experimental search began to find such currents which were expected to reach hundreds of kA at a few hundred kW of power in low density plasmas.
Success followed in a number of experiments both in the USA and elsewhere.
We show here only a few results owing to space limitation. Some of the early experiments included JFT-2 [6.159], WT-2 [6.160], Versator-II [6.161], PLT [6.162], Petula [6.163], ASDEx [6.164] and Alcator C [6.165]. Soon thereafter, further experimental results were obtained demonstrating ramping of currents and plasma startup without ohmic drive [6.166], and even transformer recharging [6.167]. Many of these experimental results were summarized in review papers at the Varenna RF workshop in 1985 [6.168, 6.169]. In Fig. 6.32, PLT demonstrated current drive for 3.5 s, exceeding resistive diffusion time, a/rp, where a is the plasma minor radius and rp is the plasma resistance due to collisions. In Fig. 6.33, current ramp and transformer recharge is demonstrated from ASDEx [6.167].
FIG. 6.33. Plasma current ramp up with LH current drive. Solid lines correspond to:
Ip = constant; dashed lines correspond to: ohmic current IOH = constant; PRF = 675 kW.
Reprinted from Ref. [6.167]. Copyright (2011) by the American Physical Society.
In Fig. 6.34, currents have been demonstrated at ITER relevant densities in Alcator C [6.165]. The current drive efficiency increases with electron temperature and current as shown in Fig. 6.35 from JT-60 [6.170].
Depending on 2pe/ce2 , Fokker–Planck code results indicate efficiencies
20 –3
[10 m ] [MA] [m] / [MW] 0.1 [10 keV]e
n I R P = T . Many of the results were
summarized in additional review papers [6.1, 6.156, 6.171] and references therein. More recent experimental results may be found in Refs [6.64, 6.79]
(Alcator C-Mod) and [6.124] (JET).
FIG. 6.34. Demonstration of LHCD efficiency in Alcator C at densities up to 1020 m–3 at a frequency of 4.6 GHz [6.165]. Reprinted from Ref. [6.165]. Copyright (2011) by the American Physical Society.
FIG. 6.35. Lower hybrid current drive efficiency increases with Te in JT-60. Here CD is the the current drive efficiency, wL is the ratio of the minimum upshifted parallel phase velocity normalized to the electron thermal speed and L is the quasi-linear diffusion coefficient evaluated at wL, and normalized to the collisional diffusion coefficient. For details see Ref. [6.170]. Reprinted from Ref. [6.170]. Copyright (2011), IOP Publishing Ltd.
Recently, lower hybrid wave power injection demonstrated current drive for minutes at the 1GJ level in Tore-Supra (TS). In Fig. 6.36 we show recent results demonstrating current drive with lower hybrid waves at the 500 kA level for 6 min. Finally, impressive coupling results were obtained in JET, where, using gas injection, LH waves were coupled efficiently through a 14 cm scrape-off layer [6.172].
FIG. 6.36. Recent long pulse results from TS demonstrate non-inductive current drive for 7 min at 2.9 MW for 1 GJ [6.172]. Here, Cu is the relative copper impurity level and RC is the percentage of the radiated power due to impurities.