Lower Hybrid Power Research Articles

Estimation of heat loads on the wall structures in parasitic absorption of lower hybrid power

Parasitic absorption of the short wavelength modes of the LH spectrum is a probable reason for the hot spots seen in the grill region of several tokamaks. Experiments suggest that the heat loads on the wall structures depend on the coupled power. In this work, the parasitic absorption of LH power was studied with self-consistent particle-in-cell simulations. The launched spectra were obtained from the SWAN coupling code. The power and temperature dependences of the absorption in the near field of the LH grill were investigated with a series of simulations. The parasitic absorption was found to grow from 0.6 to 1.1% when the coupled power increased from 26 to 67 MW/m2. When the edge temperature rose from 12.5 to 100 eV, the absorption increased from 0.4 to 1.7%. The maximum kinetic energies were between 0.6 and 1.8 keV. Estimates for the heat loads and surface temperature of the grill limiter are also obtained. The absorption leads to heat loads between 1.5 and 13 MW/m2 and surface temperatures of 510-2390° C.

Role of fast waves in the central deposition of lower hybrid power

In tokamaks, lower hybrid (LH) waves are routinely used for current drive and heating of plasmas. The LH waves have two modes of propagation that are called the slow and the fast wave. Usually, the lower hybrid waves are launched as slow waves into a tokamak, but during the propagation part of the wave power can be transformed to fast waves. General characteristics of the mode transformation of slow waves to fast waves are first investigated with a simple quasitoroidal ray-tracing model. Next, the effect of mode transformed LH power on the deposition profiles in a JET-like tokamak is analysed by using the fast ray-tracing code FRTC. When the launched spectrum is at small values of the toroidal refractive index (1.6 n0 2.0), the contribution of the fast wave to the deposited power is found to be significant and responsible for most of the absorption at the centre. When n0 is large , the effect of the mode transformed fast waves is small or negligible. At modest central densities (ne0 ~ 0.5 × 1020 m-3), the contribution of the fast wave to the power deposition can be more than 50% in the plasma centre. In consequence, the significant amount of wave energy absorbed in the fast mode must be carefully taken into account in modelling LH current drive experiments in the future. At low central densities (ne0 0.3 × 1020 m-3), practically no absorption of fast waves occurs.

Particle-in-cell simulation of parasitic absorption of lower hybrid power in edge plasmas of tokamaks

In lower hybrid (LH) current drive experiments at Tore Supra and Tokamak de Varennes (TdeV), hot spots and the generation of impurities have been observed. Melting of the grill mouth has also occurred in LH current drive experiments. A possible explanation for these observations is parasitic absorption of the short-wavelength part of the LH spectrum close to the grill mouth. In this work, we investigate the parasitic absorption of the LH power in the edge plasma of Tore Supra and JET with particle-in-cell (PIC) simulations. The LH spectra are calculated with the SWAN coupling code and used in the self-consistent electrostatic PIC code XPDP2 which calculates the absorption. The absorption was calculated for different edge densities and density scale lengths when the coupled LH power densities varied between 25 MW m-2 and 50 MW m-2. The high-n|| part of the LH spectrum was found to be absorbed near the edge within a few millimetres. The absorbed power density varied from 65 kW m-2 to 420 kW m-2 which corresponds to 0.2-0.8% of the coupled power. In an edge plasma having a temperature of 25 eV, the maximum energies of the fast electrons generated by the parasitic absorption were between 0.4 keV and 1.6 keV.

Transport of intense LH pulses into a tokamak plasma

Application of lower-hybrid (LH) power in short, intense pulses in the 5–10 GW range should overcome the limiting effects of Landau damping, and thereby permit the penetration of LH power into the interior of large-scale plasmas. We show that, under such very intense LH pulses, wave coupling may deteriorate because of nonlinear density changes due to the ponderomotive force effects in front of the grill. Ponderomotive forces are also likely to induce strong plasma bias and consequent poloidal and toroidal plasma rotation. Although backward electric currents, created in the plasma by intense LH pulses, dissipate a large portion of the radio frequency power absorbed, the current drive efficiency is acceptable. We use a numerical simulation of wave–particle interactions to analyse the applicability of standard quasilinear theory to the case of large energy flux densities. The initial results indicate the existence of important restrictions on the use of the quasilinear approximation. The results of the present paper also indicate that some of the effects considerably alter some ideas of Cohen et al.

Localized heat flux due to lower hybrid wave coupling in the Ergodic Divertor configuration on Tore Supra

Lower hybrid (LH) current drive experiments were carried out in the ergodic divertor (ED) configuration. In this configuration, at low density (〈 n e〉=1.7 × 10 19–2.3 × 10 19 m −3), up to 4.5 MW of LH power was coupled and 65% of the plasma current (here equal to 1.4 MA to match the resonant edge safety factor needed for divertor operation) was driven by the LH waves. With an optimized position of the grills, it was possible to obtain a reasonable steady state temperature of the neutralizers ( T neut < 800°C) and 3.9 MW were coupled for 20 s leading to a record total injected energy of 93 MJ in this configuration. The power deposition can be derived from the surface temperature of the boron carbide coating of the neutralizers by infrared thermography. A well localized heat flux is observed on the divertor neutralizers magnetically connected to the grills. Such heat flux is known, from previous work, to be due to LH power dissipation near the grills. This heat flux is here studied in detail. In the shots analyzed here, parallel heat fluxes up to 15 MW/m 2 were measured, but values exceeding 50 MW/m 2 have been recorded. The use of the field line tracing code MASTOC allows one to link the power deposition on the neutralizer plate to specific regions in front to the grills, thus underlying the importance of the electromagnetic fields there. The edge density is shown to be a key parameter. Not-well-understood local effects arise when the LH is activated, and accurate measurement and analysis of local density and electric field are needed. It has to be noted that a trade-off between the decrease of the edge density at the grill and its coupling capability which drives the electric fields quoted above has to be dealt with; the positioning of the grill has then to be optimized and eventually feedback controlled. In order to increase the operational margin, the spreading of the heat flux was efficiently obtained by a moderate modulation of the divertor current by less than 30%.

Measurement and interpretation of interaction of MeV energy protons with lower hybrid waves in JET plasmas

Experiments with simultaneous lower hybrid (LH) current drive and ion cyclotron resonance frequency heating of minority protons in JET deuterium plasmas showed efficient coupling of LH power to the MeV energy anisotropic protons. Such an interaction represents parasitic loss of LH power, intended for electron current drive, to the proton population, with important implications for the efficiency of LH current drive schemes in fusion devices containing high-energy charged fusion products. We solve the hot-plasma dispersion relation in the LH range of frequencies for plasmas containing high-energy minority anisotropic protons and electrons, and find that multiple solutions of the dispersion relation with perpendicular refractive index exist in the plasma centre due to the presence of the protons. These hot-plasma modes give damping of LH input power onto the protons by perpendicular Landau damping. Combinations of background plasma and LH antenna parameters exist for which no solutions of the LH dispersion relation are found with , thus reducing damping of LH power to the protons to . This suggests ways of reducing the parasitic loss of LH power to high-energy charged fusion products.

Real time current profile control at JET

A plasma current profile control system has been designed and tested at Joint European Torus (JET). The system uses the one turn loop voltage for lower hybrid current drive (LHCD) control, and the normalised second current moment of the plasma current distribution for off-axis current control. These provide relatively simple measurements and calculations suitable for real time operation. Models for the response of the loop voltage and second current moment to Lower Hybrid power input are derived and validated against JET data. Based on these models, the components of the second current moment and loop voltage control systems are designed to suit prescribed performance. Loop voltage has been controlled in 2.5 MA discharges at 66% reduction, providing the means for LHCD regulation. Second current moment control during the current rise phase has contributed to 60% improvement of the neutron yield performance of shear optimisation discharges at JET.

Profile control experiments in JET using off-axis lower hybrid current drive

In lower hybrid current drive (LHCD) experiments in JET, up to 7.3 MW of lower hybrid (LH) power has been coupled to X point plasmas, resulting in sawtooth suppression and full current drive up to 3 MA. The current drive efficiency reached ηCD = 0.26 × 1020 m-2·A/W in these experiments. The LH power deposition and driven current profiles can be quite well reproduced with the ray tracing and Fokker-Planck code in JET, even when multipass absorption of the LH wave is dominant. Profile control with off-axis LHCD has been used for increasing q above 1, thereby suppressing sawteeth before the edge localized mode (ELM)-free hot ion H mode. In optimized shear plasmas, a broad q profile with central negative shear was formed with moderate LH power (∼2 MW), applied in the low density phase during the current rampup. An internal transport barrier with improved electron confinement was produced, which resulted in a peaking of the electron temperature profile and Te0 up to 10 keV at ne0 ⩽ 1.5 × 1019 m-3.

Generation of hot spots by fast electrons in lower hybrid grills

Generation of hot spots on plasma facing components magnetically connected to the grill is a main limiting factor in high-power operation of a lower hybrid system. A possible explanation for the hot spots is the sputtering caused by fast electrons generated by parasitic absorption of lower hybrid power near the grill mouth. The behavior of the edge plasma near the grill mouth is investigated with a new tool in this context: the self-consistent particle-in-cell (PIC) code XPDP2 [V. Vahedi et al., Phys. Fluids B 5, 2719 (1993)]. The PIC simulations provide the key parameters of the problem: the absorbed power, the radial deposition profiles, and the energy spectrum of the accelerated particles close to the grill.

Full wave modelling of lower hybrid current drive in tokamaks

Full wave calculations based on the use of eikonal trial functions that are locally solutions of the homogeneous problem are carried out for solving the lower hybrid (LH) current drive problem in tokamaks, when geometrical optics assumptions are no longer valid in the description of the wave dynamics. The LH power deposition profile as well as the non-inductive driven current are determined self-consistently with a two dimensional (2-D)relativistic Fokker-Planck solver. The first consistent simulations are performed for the high aspect ratio tokamak TRIAM-1M, when the toroidal n|| upshift is bounded and insufficient to bridge the large spectral gap and cause wave damping.

Enhanced heat flux in the scrape-off layer due to electrons accelerated in the near field of lower hybrid grills

As a result of experimental observations of localized heat flux on components magnetically connected to radiating waveguides in Tore Supra and in TdeV, the acceleration of electrons near lower hybrid (LH) antennas has been investigated. A simple analytical model has been developed to compute the dynamics of the particles in the near field approximation. Landau damping of the very high N|| (20 < N|| < 100) component of the launched spectrum on the thermal electrons of the scrape-off layer (SOL) is found to occur. Simulation of a typical LH pulse in Tore Supra indicates that the electrons can be accelerated up to 2-3 keV. Modelling of the interaction of this fast electron population with the edge plasma allows a calculation of the heat flux on plasma facing components that are magnetically connected to the antenna. Model results and the results of experiments in Tore Supra and TdeV are compared. The calculated heat fluxes are found to be fairly consistent when the variation of convective heat flux at the grill aperture is taken into account. From this analysis, it is concluded that, for an LH power density of 25 MW/m2, the resulting heat flux along the field lines (3.5 MW/m2) is manageable for the components connected to the antenna, provided that good coupling can be maintained at a low density in front of the grill.

Functional dependence of the lower hybrid power absorption coefficient in JET

The fraction of the coupled lower hybrid (LH) power absorbed in divertor plasmas in JET has been determined experimentally with a method utilizing the time derivative of the total stored energy (plasma and magnetic). This method can account for the power absorbed inside a normalized flux coordinate . The experimental LH absorption coefficient reaches 100% at low plasma densities, , and decreases to 25% at . The LH wave accessibility to the plasma core has been found to play an important role in determining the power absorption and the radial deposition profile. The decreasing absorption is correlated with a gradual shift of the LH power deposition profile, as determined by the hard x-ray profiles, towards the plasma periphery. Similar behaviour is found in ray-tracing + Fokker - Planck code calculations. The frequency spectrum of the LH pump wave, as determined by a probe outside the tokamak vessel, broadens strongly as the wave accessibility is reduced and the absorption drops.

Full steady-state operation in Tore Supra

In order to produce fully non-inductive, lower hybrid (LH) driven discharges in a systematic and reproducible manner, new operation modes have been studied on the superconducting Tore Supra tokamak. To cope with some uncertainties in the LH current drive efficiency (e.g. profile dependences), the plasma current is not imposed a priori, but evolves freely until the equilibrium (which depends on the LH power level) is reached. The voltage applied on the primary circuit no longer controls the plasma current. In an `open loop' scenario in which this voltage is preset and constant, the timescale required to attain the equilibrium is the longest characteristic time of the coupled plasma - poloidal field coils system ( s). In order to obtain a stationary state faster, a new feedback scheme has been implemented in which the primary circuit voltage is controlled in such a way that the flux consumption vanishes. It is shown that this operation mode allows full steady-state to be reached within a characteristic time of a few seconds. The underlying physics is described and a detailed analysis of the experiments is made. It is shown, in particular, that this operation scenario generates stable stationary plasmas with improved confinement, so that the so-called `LHEP' regime can be extrapolated to continuous operation.

Stationary regimes of improved confinement in Tore Supra

Recent stationary improved confinement experiments with current density profile modifications in non-inductive Tore Supra operation are reported. Significant progress has been obtained by achieving long duration discharges using lower hybrid (LH) waves: (i) 2 min in the 4 T improved confinement LHEP (LH enhanced performance) regime, at a current MA, loop voltage V, LH power MW (, are the electron energy content and Rebut - Lallia - Watkins L-mode prediction), (ii) 75 s long in a fully non-inductive LHEP regime (, V, MA, MW) using a new plasma control scheme, (iii) 30 s at 1.7 MA ( V, MW) in the L-mode regime. MHD stability in full current drive operation and the role of weak - or reversed - central magnetic shear in the central LHEP electron temperature transition (reproduced in full current drive in a systematic manner and measured by independent electron temperature diagnostics) are discussed. Stationary high- experiments were performed with fast-wave direct electron heating (FWEH) in a large range of operation: 42 - 76 MHz and - 3.9 T. Maximum coupled power of 9.5 MW is obtained in the 48 MHz/2T configuration with good electron heating performance and improved confinement at high density (central density ). By increasing the magnetic shear in the gradient region, stationary improved confinement states (6 MW during 5 s, ) are reached in a reproducible manner with poloidal beta, , approaching 1 and 40% of bootstrap current. The high-bootstrap FWEH experiments have been recently combined with LHCD at reduced loop-voltage ( V and up to 70% of non-inductive current). A total injected power up to 7.2 MW (LH: 3.6 MW, FW: 3.6 MW) has produced stationary improved confinement with a peaked electron temperature profile (central value up to 8.0 keV) at a central density of .

Radially localized measurements of superthermal electrons using oblique electron cyclotron emission

It is shown that radial localization of optically thin electron cyclotron emission from superthermal electrons can be imposed by observation of emission upshifted from the thermal cyclotron resonance in the horizontal midplane of a tokamak. A new and unique diagnostic has been proposed and operated to make radially localized measurements of superthermal electrons during lower hybrid current drive on the Princeton Beta Experiment-Modified (PBX-M) tokamak [Bernabei, et al., Phys. Fluids B 5, 2562 (1993)]. The superthermal electron density profile as well as moments of the electron energy distribution as a function of radius are measured during lower hybrid current drive. The time evolution of these measurements after the lower hybrid power is turned off are given and the observed behavior reflects the collisional isotropization of the energy distribution and radial diffusion of the spatial profile.

Magnetic ripple and the modeling of lower-hybrid current drive in tokamaks

Using ray tracing, a detailed investigation of the lower-hybrid (LH) wave propagation in presence of toroidal magnetic field ripple is presented. The local ray behavior is first depicted for a cylindrical equilibrium periodically modulated along the axial direction. Variations along ray trajectories in the component of the wave vector parallel to the equilibrium magnetic field are observed, with a maximum relative amplitude that is locally of the order of the ripple level. For the full rippled toroidal equilibrium, a similar local behavior is found when the ray trajectory crosses a high ripple region. Despite the modest amplitude of the local ray perturbation, its global influence on ray trajectories may be strong, as a consequence of the combined effects of toroidal and poloidal inhomogeneities. By coupling ray tracing with a one-dimensional relativistic Fokker–Planck code, simulations of LH experiments have been performed for the TORE SUPRA tokamak [Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 105, Paper IAEA-CN-60/A1-5]. It is shown that magnetic ripple may induce significant modifications in the LH power deposition profiles, mainly in the ‘‘few passes’’ regime when the wave makes some, but not many, passes inside the plasma before being absorbed. The effect of magnetic ripple leads then to a broadening of the power deposition profile and a shift towards the center of the plasma, and a better coupling with high energy electrons. This behavior may be explained by an increase in the overall ray stochasticity. Taking into account magnetic ripple in LH simulations, a better agreement is found between numerical predictions and experimental observations.

Characteristics of ergodic divertor plasmas in the Tore Supra tokamak

The characteristics of ergodic divertor (ED) deuterium plasmas in the Tore Supra tokamak are discussed. The divertor volume is a relatively well limited region between the ED modules and ρ = τ/a equivalent to 0.8. The core (ρ ⩽ 0.8) plasma confinement is not degraded by the presence of the ED (by comparison with similar limiter, non-ED plasmas): the electron density and temperature profiles are not modified. The ED configuration compares well with a classical X point divertor: intrinsic impurities are screened out, the power load is deflected to dedicated surfaces, and density control through particle pumping is possible. Up to 5.5 MW of ion cyclotron resonance power and 3 MW of lower hybrid power have been successfully used, power exhaust being mainly by radiation (80%)

Fast electron transport and lower hybrid absorbed power profiles from hard x-ray imaging in the Princeton Beta Experiment-Modified

Recent hardware improvements on the hard x-ray camera of the Princeton Beta Experiment-Modified (PBX-M) expand the capabilities for observing bremsstrahlung radiation from fast electrons during lower hybrid current drive (LHCD) experiments, thereby allowing accurate fast electron transport studies. Developed methods to directly invert two-dimensional x-ray images reveal radial profiles of the emitted intensity and isotropy. Such profiles extracted from lower hybrid (LH) modulation experiments permit computation of the lower hybrid power absorption profile. Results from application to the LH phase scans demonstrate the ability to control the peak location of the driven current. Incorporating these results into simulations using both a three-dimensional Fokker–Planck code and a simple modulation model provides lower and upper bound estimates for the hot electron diffusion coefficient D*.

Theory and experiments on r.f. plasma heating, current drive and profile control in Tore Supra

The combination of r.f. waves in the lower hybrid (LH) and ion cyclotron frequency ranges offers a versatile and efficient way of heating tokamak plasmas while controlling their properties and magnetohydrodynamic stability through the control of the current density profile. Experimental and theoretical studies on the applications of such plasma waves have been carried out on Tore Supra during recent years and are reported here. The LH system coupled up to 6.5 MW during 2 s at 3.7 GHz through two multijunction launchers. In the longest plasma shot, the total injected LH energy reaches a record value of 170 MJ during a 62 s LH pulse, at a power level of 2.8 MW, corresponding to an average power density of 17 MW m −2 . The ion cyclotron resonant frequency (ICRF) system (35–80 MHz) is composed of three resonant double-loop antennae. Up to 4 MW have been coupled with a single antenna, allowing a record power density through the Faraday screen of 16 MW m −2 to be reached. 30 s steady-state r.f. pulses have been obtained with up to 54 MJ delivered to the plasma. One of the major observations has been the transition to the so-called “stationary lower hybrid enhanced performance (LHEP) regime” ( I P = 0.8 MA; n e0 = 2.8 × 10 19 m −3 ; P LH = 3.2 MW) in which the (flat)_central current density ( q 0 ∼2) and (peaked) electron temperature profiles ( T e0 ∼ 6–8 keV) are fully decoupled. This regime exhibits a significant improvement of the global confinement (40%) owing to the increase in l i , i.e. in the magnetic shear in the outer half of the discharge, supplemented by a large reduction in the electron thermal diffusivity in the central zone where the magnetic shear vanishes because of the slight off-axis character of the LH power and current deposition. Transp analyses show that LHEP plasmas provide access to the second ballooning stability regime. At higher current and density ( I p = 1.5 MA; n e0 = 6 × 10 3 m −3 ), ICRH stabilization of sawteeth (4 MW) combined with lower hybrid current drive (LHCD) current profile modifications has allowed to extend the stabilized phase for up to 1 s with 3.4 MW of LH power, the duration of sawtooth-free periods increasing with increasing LH power. The dynamical properties of fast electrons during LHCD have been investigated recently on Tore Supra through power modulation experiments. It is shown that slowing down always predominates and, from the long-time evolution of the hard X-ray emission, the radial diffusion rate of the fast electrons is estimated to be 0.1–0.3 m 2 s −1 . Theoretical developments have focused on the modelling of LHCD and also on fast wave current drive (FWCD) and fast wave heating. The effect of intrinsic stochasticity on the propagation of LH waves is discussed and a fully developed statistical theory of stochastic wave diffusion and multipass absorption, with applications to Tore Supra through a wave diffusion-Fokker-Planck (WDFP) numerical code, is briefly presented. This model provides a simple explanation for the temperature dependence of the LHCD efficiency in small tokamaks. The ion cyclotron resonant heating (ICRH) full-wave code Alcyon has been upgraded to compute the power and current deposition profiles from direct electron absorption of the fast wave (electron Landau damping-transit time magnetic pumping). The code has been used to study FWCD in Tore Supra, the Joint European Torus and the International Thermonuclear Experimental Reactor. Finally a new concept of an efficiently cooled reflector antenna for LHCD applications in a steady-state reactor is briefly described.

Current drive studies for the ARIES steady-state tokamak reactors

Abstract Steady-state plasma operating scenarios are designed for three versions of the ARIES reactor, using non-inductive current drive techniques that have an established database. R.f. waves, including fast and lower hybrid waves, are the reference drivers for the D–T burning ARIES-1 and ARIES-II/IV, while neutral beam injection is employed for ARIES-III which burns D–3He. Plasma equilibria with a high bootstrap-current component have been used, in order to minimize the recirculating power fraction and cost of electricity. To maintain plasma stability, the driven current profile has been aligned with that of equilibrium by proper choices of the plasma profiles and power launch parameters. Except for ARIES-III, the current-drive power requirements and the relevant technology developments are found to be quite reasonable. The wave-power spectrum and launch requirements are also considered achievable with a modest development effort. Issues such as an improved database for fast-wave current drive, lower-hybrid power coupling to the plasma edge, profile control in the plasma core, and access to the design point of operation remain to be addressed.