The FTU experiment at 8Ghz is the only Lower Hybrid Waves (LHW) experiment, running at present, providing a Current Drive (CD) and heating data base at reactor relevant densities (~1x1020m-3). The achievement of reversed magnetic shear configurations by partial Lower Hybrid Current Drive in fully relaxed current density conditions also represents an ITER relevant goal. Theoretically foreseen shear reversal configurations have been experimentally achieved in the high density FTU plasma on a time scale longer than the skin time by partial off axis LH Current Drive (LHCD) at 1 MW of power level. Experimental results are reported accompanied by a theoretical and numerical analysis of LHW power deposition and current density diffusion. Experiments are also presented of transient shear reversal configurations achieved by freezing the current density diffusion toward the plasma center during the ohmic current ramp-up phase by central Electron Cyclotron Resonant Heating (ECRH) (140GHz, 300KW, 100ms) and by LHW power injection. High central electron temperature up to 9keV are obtained during the ECRH heated current ramp phase. The confinement properties of the reversal region in this condition are briefly discussed.
To study relaxed states of the current density profile "low" temperature plasmas are considered in order to make the skin time less than the LH pulse length (<=1s). In FTU it turns out Te0<1.7 kev to have skin<300ms. In such conditions there is a large spectral gap between the parallel LHW phase velocity and the electron thermal velocity, so that first pass power absorption is expected to be small. Whatever it is the spectral gap filling mechanism, the dispersion relation and toroidal axis-symmetry impose to the launched parallel refractive index n||L a maximum upshift factor for each radial position, n||+/n||0, given by:
where x=r/a is the normalized minor radius, =a/Ro the inverse aspect ratio, q the safety factor, pe the electron plasma frequency, the LH frequency and n||0=(1+) n||L. Equation (1) also gives the spatial trapping region of all the rays with a given n . By comparing Eq. (1) with the upshift factor required for absorption, n||ELD(x)/n||0=6.5 T(x)-1/2, we can approximately determine the LHW power deposition region as the region where Eq. (1) and n||ELD(x)/n||0 overlap. Following this criterion three density region can be identified: 1) an high density region, defined as =pe(0)[2(q(0)q(a))1/2]-1>1, where deposition is expected to be central;
2) an intermediate density region, 1- n||0/n||ELD(0) <<1, where deposition is expected to be off axis; 3) a low density (low temperature) region (<1-n||0/n||ELD(0)) where absorption is expected to be negligible. It also turns out that, in the intermediate density region, the deposition is the more peripheral the flatter are the q and density profile, as indicated by the radial position of the maximum of Eq. (1), xmax2=[q(a)/q(0)+n]-1, becoming more peripheral for low q(a)/q(0) and n value. Here n=ln[ne(x)/(n(0)(1-x2))] is related to the density profile peaking. This picture, based on simple arguments, is fairly well confirmed by power depositions calculations based on toroidal ray-tracing and Fokker-Planck codes. In Fig. (1) an off axis deposition obtained in the intermediate density region is shown. According to such theoretical expectations, shear reversal configurations can be realized, in a low temperature plasma, by LHCD at intermediate density and by counter LHCD at high density, where, on the other hand, the runaway velocity can be well beyond the maximum velocity of fast electrons (c/n||acc). Resistive diffusion calculations , performed in the presence of all the current components, i.e. purely ohmic, purely non inductive, and cross term (hot conductivity), show that in the CD-scheme at least 40-50% of the current has to be driven at x~1/3 to get a shear reversal q profile and about 20-30% at the plasma center in the counter-CD scheme. Following these criteria two plasma targets have been selected and experimentally studied so far, suitable to undergo a shear reversal during the current flat-top by LHCD at n||=1.55 (=75o): 1) B=4T, IP=350kA (qa=5.5), nLINE=0.7x1020m-3, Te(0)=1.6keV, 1) B=5.2T, IP=350kA (qa=7), nLINE=0.85-1.2x1020m-3, Te(0)=1.3keV. The latter was a preparation plasma target for central ECRH. In both cases the sawtooth activity, when present, is suppressed and Double Tearing Modes (DTM) reconnections appear later on in the discharge. A different MHD behaviour marks the two kind of discharges, as discussed in ref. . In the B=4T case, the sawtooth is stabilized in 0.2-0.4 s, and, after a large MHD rearrangements of the discharge, a stable reversed configuration is achieved with a reversal radius rs/a=0.5 and a saturated m=2 mode. Data on these discharges have already been reported elsewhere. Deposition calculations for this kind of discharge give 150kA of current approximately driven between 1/3 and 1/2 of the minor radius (as shown in Fig.1) in agreement with the experimental Vloop drop. Resistive diffusion calculations, using such deposition as an input, give a temporal evolution of the q-profile in agreement with the q-profile reconstructed from the equilibrium data. Fig. 2a shows the
|Fig. 1 - LH deposition profiles at B=4T
||Fig. 2 - q-profile evolution a) from resistive
diffusion calculation, b) from equilibrium reconstruction
calculated q-profiles 100, 300, and 500ms after the RF switch on. Fig. 2b shows the reconstructed q-profile at the sawtooth stabilization (t=0.62s) and 400ms later.
In the higher B, q(a) discharges the sawtooth is stabilized very rapidly and irregular DTM crashes appear in the discharge which does not enter in the stable regime observed in the B=4T case. The DTM inversion radius is typically located at rs/a=0.2-0.25 thus indicating that a more central deposition profile is taking place with respect to the lower q(a) case, in agreement with the qualitative theoretical considerations given above. A density scan proved that this regime can be accessed only when density is larger than 0.85x1020m-3 while at q(a)=5.5 the density was 0.73x1020m-3. Such density values fall in the range 1-n||0/n||ELD(0) <<1. Concluding remarks are i) the LH deposition in low temperature plasmas, needed to study relaxed state of the current density profile within the RF pulse, can be controlled by a proper choice of the plasma parameters, according to theoretical expectations based on dispersion relation and axis-symmetry and confirmed by numerical deposition calculations; ii) in this way shear reversal configurations can be and, as a matter of fact , have been obtained in FTU by partial LHCD; iii) the plasma target at 5.2T has to be ameliorated lowering the q(a), thus making the off axis deposition more pronounced; a slightly off axis ECRH, rising the pressure profile, could have a stabilizing effects , allowing the discharge to enter the stable MHD regime found at B=4T.
Transient shear reversal configurations have been achieved by freezing the current density diffusion during the ohmic current ramp-up phase by central Electron Cyclotron Resonant Heating (ECRH). Typical plasma parameters of these discharges are: B=5.2T, dIp/dt=5MA/s-1, nLINE=0.4-0.7x1020 m-3. Very high central electron temperatures are measured by the Thomson scattering, in this phase (sawtooth-free) of the discharge, as shown in Fig. 3, where Te0~9keV is measured. A local transport analysis gives values of e around 0.2 m2/s at the plasma center. The achievement of a shear reversal configuration is marked by DTM reconnections and by simulations of the discharge evolution that gives the q-profile time
|Fig. 3 - Te profile during ECRH in current
ramp experiment a) t=42ms,b) t=70ms, c) t=119ms. ECRH starts at 45ms.
||Fig. 4 - simulated q-profile time evolution
in current ramp experiments a) t=65ms,
b) t=75ms, c) t=95ms, d) t=105ms. ECRH starts at 60ms.
behaviour reported in Fig. 4. Uncertainties in the q-profile are connected with the used resistivity (whether Spitzer or Neoclassical) and ZEFF values. In some of these discharges, at the end of the current ramp, an increase of the central electron temperature of about 1keV is observed in connection with the stabilization of an MHD mode that stops its activity when a very flat q-profile at the plasma center is established. Such temperature increase can be attributed to an improvement of the local electron confinement. Finally experiments have been done injecting LH power at the end of the current ramp on such ECR heated plasma targets, with the aim of further sustaining the shear reversal configuration. Up to now 200-400kW of LHW power has been injected at =75-120o (n||=1.55-2.4). Delays ranging between 30 and 100ms, on the onset of the sawtooth activity, have been observed so far. Generally the discharge without sawtooth stops in a disruption. Experiments are in progress to optimize the q-profile at the LH start in order to avoid disruptions.