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A numerical model for predictive simulations of radiofrequency current drive in magnetically confined plasmas is developed. It includes the minimum requirements for a self-consistent description of such regimes, i.e., a 3-dimensional kinetic equation for the electron distribution function, 1-dimensional heat and current transport equations, and resonant coupling between velocity space and configuration space dynamics, through suitable wave propagation equations. The basic properties of this non-linear numerical system are investigated and illustrated by simulations applied to reversed magnetic shear regimes obtained by Lower Hybrid and Electron Cyclotron current drive for parameters typical of the Tore Supra tokamak.

Experiments on the effects of simultaneous injection of LH and ECH power have been carried out in FTU, with up to PLH=1 MW and PECH=0.75 MW. In the absence of the cold ECH resonance in the plasma, the ECH power is absorbed on the suprathermal electron tail sustained by LHCD, as predicted theoretically, and causes the central electron temperature Te0 to increase up to 1.2 keV. With the cold resonance at the center, in a sawteeth and MHD free plasma, almost fully sustained by LHCD, a quasi-stationary electron transport barrier is built-up in a region r/a

An analytical model for the evaluation of electron cyclotron current drive efficiency improvement in lower hybrid current drive regimes is presented. The adjoint equation is written and solved by a perturbation treatment, allowing to derive a response function including both collisional and lower hybrid effects, in the limit where the former still dominate. This allows an analytical demonstration of the current drive synergy effects, previously found by numerical solutions of the kinetic equation. The model is especially useful for the determination of appropriate wave parameters optimizing this synergy effect, such as the EC launching angles suitable for a given LH target plasma. Under these conditions, it is shown that a significant improvement of the ECCD efficiency can be obtained.

Neoclassical Tearing Modes stabilization is one of the main purposes for the implementation of an Electron Cyclotron Current Drive system on ITER-FEAT. Previous estimates have shown that a wave power level of 20–30 MW should be appropriate for a substantial reduction of the (3,2) and/or (2,1) modes. Here detailed calculations are presented combining, for the first time, the following elements: i) realistic antenna geometry resulting from detailed study of the implementation in an ITER upper port; ii) Gaussian beam-tracing calculations; iii) 3D Fokker-Planck calculations of the driven current density profile; iv) island evolution calculation, including island rotation effects. The power level necessary for complete stabilization of NTMs is evaluated for the ITER FEAT reference scenarios and the chosen wave frequency of 170 GHz. Optimization as a function of the injection poloidal and toroidal angles is discussed.

The kinetic theory of rf current drive in tokamak plasmas in the presence of magnetic turbulence is investigated. The main effect of the turbulence is to cause radial diffusion of the superthermal electrons. For typical parameters of large machines, the diffusion time can be of the same order of the slowing‐down time of the current carriers. In these conditions, a significant regime is identified in which the total driven current is enhanced by the effect of the radial diffusion. This is demonstrated analytically in the weak turbulence limit, and numerically confirmed in the general case, by means of a fully three‐dimensional Fokker–Planck code, for both parallel and perpendicular velocity‐space diffusion.

Noninductive current drive has been performed in the tokamak ASDEX upgrade by injection of radiofrequency waves at the second harmonic of the electron-cyclotron frequency in order to suppress unwanted disturbances of the magnetic-field configuration. The current has been driven parallel [co--electron cyclotron current drive (ECCD)] and antiparallel (counter-ECCD) to the plasma current to compare the effect of heating with direct current drive in the magnetic island. For the first time it has been shown experimentally that total stabilization of neoclassical tearing modes is possible with co-ECCD. The experiments verify the role of direct current drive as opposed to local heating.

Clear measurements of the localized current density driven by electron cyclotron waves have been made on the DIII-D tokamak. Direct evidence of the current drive is seen on the internal magnetic field measurements by motional Stark effect spectroscopy. Comparison with theoretical calculations in the collisionless limit shows the experimental current drive exceeds the predictions by a substantial amount for currents driven near the half radius. In all cases the experimental current density profile is broader than the predicted one.

The evolution of the wave polarization during the propagation of electron cyclotron waves in hot plasmas is investigated. The coupled mode equations are solved in slab geometry, including the relativistic corrections to the dielectric tensor. This formalism is applied to purely ordinary or extraordinary modes, propagating obliquely with respect to the magnetic field in tokamak plasmas, in order to determine the rate of change of the mode purity due to finite temperature effects. It is found that such an alteration of the mode purity can be one to three orders of magnitude larger than in a cold plasma. However, the overall effect remains tolerable for most applications and typical parameters of magnetically confined plasmas.

Control of tearing modes by means of heating and current drive inside the magnetic islands is one of the most important applications of RF power in tokamak reactors. The theoretical basis of this concept is reviewed, focusing on aspects related to RF-plasma interaction. Applications to the stabilization of neoclassical tearing modes in ITER by Electron Cyclotron Current Drive are presented to illustrate the basic physical dependences. The most significant experimental results and prospects for future applications are also discussed.

The suprathermal electron cyclotron radiation is used to investigate fundamental phenomena governing electron tail formation during LHCD. To this end, an approximate analytical solution of the 2-D time-dependent Fokker-Planck equation is found. Electron cyclotron emission (ECE) is analyzed with this model. The pitch-angle scattering time, the characteristic time of the quasilinear diffusion process and the perpendicular temperature are measured by fitting the temporal evolution of the ECE signal.

In a previous work the analysis1 on a possible CTS system on ITER has led to the following preliminary conclusions: two options can be taken into account seriously, i.e. i) CO2 (λ,= 10.6μm) extreme foreward scattering(scattering angle θ

Lower Hybrid Current Drive (LHCD) has been successfully employed in current profile control experiments and can be utilized to prevent MHD instabilities by tailoring the profile. Similarly, theory has shown that LHCD can be very effective in stabilizing MHD instabilities by feedback techniques: this experiments has not been tried yet. This paper addresses some of the practical aspects of such an experiment.

A new method for the analysis of tokamak discharges in which the plasma current is driven by the combination of high-power rf waves and a dc electric field is presented. In such regimes, which are the most usual in rf current drive experiments, it is generally difficult to separate the different components of the plasma current, i.e., purely Ohmic, purely noninductive and cross terms. If the bilinear (in wave power and electric field) cross term is the dominant one, an explicit relation between the loop voltage drop and the injected power can be found. This relation involves two parameters, the purely rf current drive efficiency and the hot (power dependent) electrical conductivity. These can be simultaneously determined from a simple two-parameter fit, if the loop voltage drop is measured at several rf power levels. An application to lower hybrid current drive experiments in the PBX-M tokamak is presented. It is shown that the method also allows the independent evaluation of the average power absorption fraction and n{sup {parallel}} upshift.

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The physical mechanisms for access to hybrid scenarios on JET are analysed by exploiting the role of the poloidal current density profile, which has been identified as critical for the transition to stationary advanced regimes in tokamaks. It is found that the low and high triangularity JET discharges access hybrid regimes via different physical mechanisms, involving the pressure in the core region for the low triangularity case and the pedestal pressure for high triangularity. However, these two regions, apparently different, are linked by a fixed point condition at zero poloidal current, which in the end is related to the particular pressure and q profiles characteristic of these regimes. These features are used, by means of a computational example, to show how to prepare and extrapolate hybrid regimes to other plasma conditions and devices.

Since its inception in 2002, the International Tokamak Physics Activity topical group on Integrated Operational Scenarios (IOS) has coordinated experimental and modelling activity on the development of advanced inductive scenarios for applications in the ITER tokamak. The physics basis and the prospects for applications in ITER have been advanced significantly during that time, especially with respect to experimental results. The principal findings of this research activity are as follows. Inductive scenarios capable of higher normalized pressure (beta(N)>= 2.4) than the ITER baseline scenario (beta(N) = 1.8) with normalized confinement at or above the standard H-mode scaling are well established under stationary conditions on the four largest diverted tokamaks (AUG, DIII-D, JET, JT-60U), demonstrated in a database of more than 500 plasmas from these tokamaks analysed here. The parameter range where high performance is achieved is broad in q(95) and density normalized to the empirical density limit. MHD modes can play a key role in reaching stationary high performance, but also define the limits to achieved stability and confinement. Projection of performance in ITER from existing experiments uses empirical scalings and theory-based modelling. The status of the experimental validation of both approaches is summarized here. The database shows significant variation in the energy confinement normalized to standard H-mode confinement scalings, indicating the possible influence of additional physics variables absent from the scalings. Tests using the available information on rotation and the ratio of the electron and ion temperatures indicate neither of these variables in isolation can explain the variation in normalized confinement observed. Trends in the normalized confinement with the two dimensionless parameters that vary most from present-day experiments to ITER, gyroradius and collision frequency, are significant. Regression analysis on the multi-tokamak database has been performed, but it appears that the database is not conditioned sufficiently well to yield a new scaling for this type of plasma. Coordinated experiments on size scaling using the dimensionless parameter scaling approach find a weaker scaling with normalized gyroradius than the standard H-mode scaling. Preliminary studies on scaling with collision frequency show a favourable scaling stronger than the standard H-mode scaling. Coordinated modelling activity has resulted in successful benchmarking of modelling codes in the ITER regime. Validation of transport models using these codes on present-day experiments is in progress, but no single model has been shown to capture the variations seen in the experiments. However, projection to ITER using these models is in general agreement with the favourable projections found with the empirical scalings.

Emission of cyclotron radiation at arbitrary wave frequency for diagnostic purposes is discussed. It is shown that the radiation spectrum at arbitrary frequencies is more informative than the first few harmonics and it is suited for diagnosis of superthermal electrons without any {open_quotes}ad hoc{close_quotes} value of the wall reflection coefficient. Thermal radiation from TFTR is investigated and it is shown that the bulk and the tail of the electron momentum distribution during strong neutral beam injection is a Maxwellian with a single temperature in all ranges of electron energies.

The spatial diffusion of fast electrons created by electron cyclotron resonant heating (ECRH) is examined using electron cyclotron emissions viewed along a nearly vertical chord in the TEXT-U tokamak. Enhanced emission at frequencies downshifted from the cold cyclotron frequency is attributed to non-thermal electrons. The emission spectra during ECRH are consistent with the presence of low density suprathermal electrons. Comparison of the spectra measured during ECRH with a bounce averaged Fokker-Planck code which incorporates the effects of magnetic and/or electrostatic turbulence on the distribution function, shows that the level of magnetic fluctuations in the center of TEXT-U is between 3 and 5 {times} 10{sup {minus}5}. This level of magnetic fluctuation is a factor of 2 to 5 too small to explain the transport of thermal electrons (E {approximately} 1 keV) in TEXT. Thus, magnetic fluctuations are an unlikely major cause of the transport of thermal electrons in TEXT.

The possibility of measuring the radial profile of fast-electron distributions from ECE spectra is discussed. The most usual ECE diagnostic set-up, i.e. the second-harmonic X-mode, observed by low-field side antennae in the equatorial plane, can be used by exploiting the reflection of spontaneously emitted radiation by the upper cut-off layer and the length of the sightline between the reflecting surface and the receiving antenna. The emitted intensity depends on this length, which introduces an element of spatial resolution in the suprathermal ECE spectra. Two methods are proposed. First, a dynamic method is described in which the length of the sightline is varied by density perturbations. Second, a spectral method is discussed that uses the length variation of the sightline with the observation frequency. A proof of the principle behind both methods is given for a lower hybrid current driven discharge in Tore Supra in which a pellet was injected.

Experiments to study inward heat transport phenomena have been performed in the Tore Supra tokamak with off-axis electron cyclotron resonance heating (ECRH). Both power balance and perturbation transport analysis have been done for low-frequency (1 Hz) ECRH modulation experiments. Heat diffusivity and heat pinch have been separately determined by fitting the experimental data of the amplitude and phase of the Fourier transform of the modulated temperature with a linear transport model including convection term. Comparison with the critical gradient model has shown that the heat pinch previously obtained could include a pseudo-pinch due to the non-linearity of the diffusivity and an additional non-diffusive heat pinch. The pinch effect is reduced for higher densities.

A transmission diagnostic system working in the frequency range 77–109 GHz has been implemented in the Tore Supra tokamak. It makes use of an ordinary mode launched along a vertical diameter, i.e., propagating along a nearly constant magnetic field. The purpose of the diagnostic is to measure electron cyclotron absorption (ECA) below the electron cyclotron frequency fc in the presence of the fast electron tails created during lower‐hybrid current drive. Transmission spectra measured by this method are compared with spectra obtained by Fokker‐Planck simulations and the relaxation properties of the tail are discussed.

Magnetically confined plasmas can be characterized by different operational regimes, i.e. distinctive features of the spatial distributions of pressure and current. The problem of the sustainment of high-beta plasma regimes for long times via proper alignment of the current sources is analyzed. A criterion involving the change of profile and sign of the poloidal current density is shown to be critical in order to discriminate the different plasma regimes and to prescribe precise plasma profiles for the establishment of such scenarios. The change of the properties of the poloidal current density profile is then linked to the breaking of the magnetic topology of a part of the plasma Hamiltonian. In the framework of the theory for phase transitions in equilibrium systems, this topology breaking could explain the phase-transition like behavior found in the access to stationary advanced plasma regimes.

Methods and tools for design and modelling of tokamak operation scenarios are discussed with particular application to ITER advanced scenarios. Simulations of hybrid and steady-state scenarios performed with the integrated tokamak modelling suite of codes CRONOS are presented. The advantages of a possible steady-state scenario based on cyclic operations, alternating phases of positive and negative loop voltage, with no magnetic flux consumption on average, are discussed. For regimes in which current alignment is an issue, a general method for scenario design is presented, based on the characteristics of the poloidal current density profile.

Recent progress on ITER steady-state (SS) scenario modelling by the ITPA-IOS group is reviewed. Code-to-code benchmarks as the IOS group's common activities for the two SS scenarios (weak shear scenario and internal transport barrier scenario) are discussed in terms of transport, kinetic profiles, and heating and current drive (CD) sources using various transport codes. Weak magnetic shear scenarios integrate the plasma core and edge by combining a theory-based transport model (GLF23) with scaled experimental boundary profiles. The edge profiles (at normalized radius ρ = 0.8–1.0) are adopted from an edge-localized mode-averaged analysis of a DIII-D ITER demonstration discharge. A fully noninductive SS scenario is achieved with fusion gain Q = 4.3, noninductive fraction f NI = 100%, bootstrap current fraction f BS = 63% and normalized beta βN = 2.7 at plasma current I p = 8 MA and toroidal field B T = 5.3 T using ITER day-1 heating and CD capability. Substantial uncertainties come from outside the radius of setting the boundary conditions (ρ = 0.8). The present simulation assumed that βN (ρ) at the top of the pedestal (ρ = 0.91) is about 25% above the peeling–ballooning threshold. ITER will have a challenge to achieve the boundary, considering different operating conditions (T e/T i ≈ 1 and density peaking). Overall, the experimentally scaled edge is an optimistic side of the prediction. A number of SS scenarios with different heating and CD mixes in a wide range of conditions were explored by exploiting the weak-shear steady-state solution procedure with the GLF23 transport model and the scaled experimental edge. The results are also presented in the operation space for DT neutron power versus stationary burn pulse duration with assumed poloidal flux availability at the beginning of stationary burn, indicating that the long pulse operation goal (3000 s) at I p = 9 MA is possible. Source calculations in these simulations have been revised for electron cyclotron current drive including parallel momentum conservation effects and for neutral beam current drive with finite orbit and magnetic pitch effects.

Real-time control is essential for many aspects of tokamak operation. A key parameter to control is the current profile, since both confinement properties and magneto-hydrodynamic (MHD) activity depend on it in quite a sensitive way. The long pulse capability of the Tore Supra tokamak has allowed a unique type of experiment, where successive stationary states of the safety factor profile, defined by their MHD activity, are established and controlled in real time. Multiple target stationary states could be requested and reached during the main heating phase of a single plasma discharge. Experiments have been carried out featuring (i) control of the presence/absence of sawteeth with varying plasma parameters, (ii) obtaining and sustaining a ‘hot core’ plasma regime without MHD activity and (iii) recovery from a voluntarily triggered deleterious MHD regime. During these experiments, the influence of fast ions on MHD stability could be observed and characterized, as well as indications of an enhanced ‘hot core’ confinement in electron heat transport during quiescent MHD states.

The impact of the radio-frequency heating and current drive systems on JET advanced scenarios at high density is analysed by means of the CRONOS suite of codes for integrated tokamak modelling. In particular, the performance of the proposed electron cyclotron heating and current drive system for JET is evaluated. As a first step, the code is applied in the interpretative mode to analyse two high power advanced scenario discharges of JET, in order to validate both the heating and current drive computational modules and the overall simulation procedure. Then, JET advanced scenarios are studied by predictive simulations on the basis of previous results. The simulations show that lower hybrid and electron cyclotron heating and current drive systems can together provide off-axis current in order to create and sustain steady-state scenarios on JET at high density. These results give deeper insight into the future advanced scenarios in ITER, since they establish a clear way to test some key aspects of them in present day devices such as JET.

Lower hybrid current drive (LHCD) experiments performed at a density close to that required for the steady-state (SS) scenario are reported. On C-Mod, FTU and Tore Supra, a strong decay of the bremsstrahlung emission is observed when the density is increased, much faster that the prediction of LHCD modelling. On JET, LH power deposition is also found to be sensitive to the plasma density: LH power modulation indicates that the power deposition moves to the very edge of the plasma (r/a similar to 0.9) when the density approaches the requirement of the JET SS scenario. From this experiment but also from the reconstruction of the electron cyclotron emission spectrum, the decrease in the LHCD efficiency with density is also found. From LHCD modelling of different JET pulses performed at different densities and wave parallel refraction indexes, it is concluded that the wave accessibility condition is not the key parameter for explaining the decrease in the efficiency. C-Mod, FTU and Tore Supra experiments indicate that the plasma edge parameters, namely density and temperature but also fluctuations, are affecting the efficiency via loss mechanisms which are likely to be collisional damping (C-Mod), parametric decay instabilities or wave scattering (FTU/Tore Supra).

A new concept of steady-state scenario for tokamak reactors is proposed. It is based on cyclic operations, alternating phases of positive and negative loop voltage with no magnetic flux consumption on average. Localized non-inductive current drive by electron cyclotron waves is used to trigger and sustain an internal transport barrier (ITB), whereas neutral beam current drive is used to periodically recharge the tokamak transformer. The fact of operating in cycles relaxes the hard constraint of simultaneous fusion performance maximization and full non-inductive operation, within the MHD stability limits. Integrated modelling simulations are performed to apply this concept for the ITER steady-state regime. A linear MHD analysis of the instabilities that could appear in this type of scenario is performed, showing that MHD stability would be strongly improved with respect to a steady regime with a strong ITB.

Issues related to the limitations and optimization of long pulse operation at high radiofrequency (RF) power levels in the Tore Supra tokamak are presented. An increasing operational limitation was encountered during the experimental campaigns in 2006–2007, affecting the high power and long pulse performance. This limitation was characterized by the sudden appearance of a multifaceted asymmetric radiation from the edge (MARFE), often followed by a disruption. The analyses revealed that the limitation could be linked to over-heating and flaking of the carbon re-deposition layers on the main plasma facing components (PFCs). The carbon deposits on all PFCs were therefore completely removed during the winter shutdown 2007–2008. Following this, a remarkable improvement in the injected power capability was observed, resulting in almost 12 MW of injected power during 10 s, without any of the previous signs of limitation (MARFE, disruption). Furthermore, the RF antennas are subject to localized heat loads due to RF sheath effects and interaction by fast particles, effects which need to be minimized in particular for long pulse operation. Experimental results concerning the heat load on the antennas, caused by fast ion losses in the presence of magnetic ripple, are presented in this paper.

The regime of nonlinear temperature oscillations (O-regime), characteristic of noninductive discharges on Tore Supra [Equipe Tore Supra, Proceedings of the 12th International Conference on Plasma Physics and Controlled Nuclear Fusion Research, Nice, France, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 1, p. 9], is investigated in its triggering and suppressing mechanism. This regime can be described by two nonlinearly coupled equations for the current density j(r) and the electron temperature Te(r) where the equation coefficients are functions of j and Te themselves. Both the integrated modeling code CRONOS [V. Basiuk et al., Nucl. Fusion 43, 822 (2003)] and a two-patch predator-prey system with diffusion and noise have been used and results have been compared to the experimental observations of the O-regime. A database of discharges is analyzed which features monotonic, flat, and reversed safety factor (q) profiles in order to characterize the action of external actuators on the regime d...

The characteristics of the safety factor profile (q) have been studied for a database of discharges featuring internal transport barrier phenomena under different heating and current drive conditions in the Tore Supra tokamak. The presence of a recurrent link between the time of formation of an internal barrier and the central safety factor (q0) crossing a low order rational surface is reported on and discussed for a database of ~40 discharges. Other relevant features of the current profile (e.g. the minimal q value, the magnetic shear and the presence of magnetic islands in the plasma) have been investigated, yielding to little or no correlation with the time and location of the barrier.

A new concept of steady-state scenario for a tokamak reactor is presented, which provides a solution of principle to the well-known problem of alignment of self-generated and non-inductively driven currents in the presence of an internal transport barrier. An effective control parameter is identified as the driven current at the barrier location, and the existence of a threshold in this parameter is demonstrated. This concept is applied in simulations to obtain a steady-state scenario within the specifications of the International Thermonuclear Experimental Reactor.

The CRONOS suite of codes and the GLF23 theory-based transport model are used to perform a 1.5D analysis of the DEMO design. The study uses plasma parameters similar to those obtained in the European Power Plant Conceptual Study in the case of a scenario with moderate inductive current, high bootstrap current fraction, relatively small major radiusR= 7.5 m and minor radiusa= 2.5 m and high elongation and triangularity. It is shown how it is possible to obtain a high fusion power of 2600 MW and high fusion gainQ= 26.5 by adding 98 MW off-axis neutral beam at a moderately high Greenwald fraction of 1.2. A non-inductive current fraction of 88% is obtained mainly from the bootstrap current at the plasma edge, where a high pedestal of 7.8 keV has been considered in order to optimize the alpha power. It is also shown how by adding 66 MW of electron cyclotron waves to the previous scenario a 100% non-inductive current steady-state scenario can be obtained with a reversedqprofile. However, in this case the fusion gain drops to 17.2 due to the higher input power. The application of LH waves is also discussed.

Electron cyclotron current drive (ECCD) at a low power level has been used on Tore Supra to induce local perturbations of the current density profile. Regimes with strong MHD activity have been analysed, and compared with similar stable discharges, in order to investigate the possible causes of their instability and relate the evolution of the discharge to the localization of EC power deposition. Both co- and counter-current drive pulses have been applied to dominantly or fully non-inductive discharges, sustained by a lower hybrid current drive. Detailed reconstructions by current diffusion calculations have been performed and the error bars evaluated. This method has proved valuable for shedding light on the complex interplay between the evolutions of temperature and safety factor profiles in steady-state tokamak plasmas. The crucial role of the dynamic evolution of rational surfaces has been identified. Moreover, we demonstrate that the operational domain in which ECCD can be employed must cope with the overall current profile characteristics, in particular the position where the safety factor has a minimum.

Recent results from the DIII-D tokamak have provided significant contributions to the understanding of many of the elements of tokamak physics and the application of this understanding to the design of next generation devices including ITER and CIT. The limitations of magnetohydrodynamic stability on the values of plasma beta (the ratio of kinetic pressure to the containing pressure of the magnetic field) that can be attained has been experimentally demonstrated and found to be described by existing theory. Values of beta (10.7%) well in excess of those required for proposed devices (ITER and CIT) have been demonstrated. Regimes of confinement (H-mode) have been established that scale favorably to proposed next generation devices, and experiments demonstrating the dependence of the energy confinement on plasma size have been completed. Understanding of confinement is rapidly developing especially in the areas of bulk transport and the role of turbulence in the plasma edge. Key experimental results in areas of plasma transport and edge plasma phenomena are in agreement with theories based on short wavelength turbulence. Control of the divertor heat loads and impurity influx has been demonstrated, and new progress has been made in the understanding of plasma edge phenomena. Experiments with ion Bernstein wave heating have not found regimes in which these waves can produce effective central ion heating. Electron cyclotron current drive experiments have demonstrated 70 kA of driven current in 400 kA discharges.

A 32-channel, 1GHz spaced heterodyne radiometer is used on the Tore Supra tokamak to measure electron cyclotron emission (ECE) in the frequency range 78–110GHz for the ordinary mode (O:E‖B,k⊥B) and 94–126GHz for the extraordinary mode (X:E⊥B,k⊥B). The radial resolution is essentially limited by ECE relativistic effects, depending on electron temperature and density, and not by the channels’ frequency spacing. The time resolution depends on the acquisition scheme: the system allows for both 1ms and 10μs acquisition. For example, this leads to precise electron temperature mapping during MHD activity. First experimental results obtained with this upgraded 32-channel radiometer are presented.

The analytical solution of the one-dimensional diffusion-convection equation in a cylinder has been found, for various functional forms of the diffusion coefficient, convection velocity and with an additional damping term. This is a significant generalization of a previous work [A. Clemencon, C. Guivarch, S. P. Eury, X. L. Zou, and G. Giruzzi, Phys. Plasmas 11, 4998 (2004)] on the diffusion equation, including now a convection term that can be constant, monomially increasing in the space coordinate, or have step-like variations. This type of equation has important applications in the field of magnetically confined plasmas, in which convection effects are experimentally observed in both particle and energy transports. Sharp variations of heat diffusivity, convection velocity, and damping term can result from the microturbulence which develops whenever the temperature gradient exceeds a critical value. A general scheme is developed to connect solutions in domains with different functional forms of the coefficients. The properties of the solutions are illustrated and discussed.

The conclusion reached in ref. 1 that the 3‐D Fokker‐Planck code verses the 2‐D bounce‐averaged code does not yield the correct current density is prove to be wrong. It is aruged that the results for the 3‐D code are very close to those of the 2‐D code that employs a bounce‐average procedure.(AIP)

A method for investigating the non-equilibrium kinetic processes which determine the formation of a non-Maxwellian electron distribution in tokamak plasmas is discussed. The case of a non-Maxwellian fast electron tail is considered in detail. It is shown that the study of the transient phase after modification of the tail by a short pulse of electron cyclotron wave energy yields valuable information on the mechanisms of tail formation.

Current drive by simultaneous injection of electron cyclotron waves and lower hybrid waves for the control of the current density profile in tokamaks is investigated. It is shown that this is a flexible method for large changes of q on axis and is therefore of relevance for studies on the access to the second stability regime.

Emission and absorption of electron cyclotron waves by the far end of a lower-hybrid flat tail are investigated. Using the tail structure obtained from the Fokker-Planck theory of the relativistic tail in the saturation regime, the salient features of the radiation spectra are computed. The results are suitable for an accurate verification of the kinetic theory of the tail formation.

Electron cyclotron resonance current drive in tokamak plasmas in the presence of a lower hybrid tail is investigated using a two-dimensional Fokker-Planck code. For an extraordinary mode at oblique propagation and down-shifted frequency it is shown that the efficiency of electron cyclotron current drive becomes (i) substantially greater than the corresponding efficiency of a Maxwellian plasma at the same bulk temperature, (ii) equal to or greater than that of lower hybrid waves, and (iii) comparable to the efficiency of a Maxwellian plasma at much higher temperatures. This enhancement of the efficiency results from a beneficial cross-effect of the two waves on the formation of the current carrying electron tail. The use of the ordinary mode for outside launching in the equatorial plane is also discussed and it is shown that the O-mode is generally not suited for current drive via the lower hybrid tail and that in a hot Maxwellian plasma the efficiency at down-shifted frequencies is comparable to that at up-shifted frequencies.

Wave damping near the electron gyrofrequency in a Tokamak plasma with the energetic tail generated by the electric field is investigated. The electron tail is computed by a Fokker-Planck initial value code as a function of the relevant parameter E/sub ////Ec=E/sub ///Te/(2 pi nee3 Lambda ). It is shown that strong damping of the e-mode occurs for oblique propagation. The results are of relevance for studies of ECRH in present-day Tokamaks and in future reactors where a mildly relativistic electron tail is naturally present for large Te. Special emphasis is therefore given to wave absorption for frequencies of significantly below the central electron gyrofrequency, and to the associated r.f.-driven current.

The combined effects of the dc electric field and electron‐cyclotron wave absorption in tokamak plasmas are investigated. The case of the ordinary mode for nearly normal propagation from the low magnetic field side is studied by a two‐dimensional Fokker–Planck code. It is found that the small fraction of the wave energy that goes into the superthermal electrons enhances the effect of the continuous pushing of the tokamak electric field.

Current drive by electron cyclotron heating of the far end of a lower-hybrid-sustained electron tail is investigated. The current density profile is determined by means of the kinetic theory and the ray-tracing code for the PLT and the Alcator C parameters. It is shown that the value of the ratio W/I for the combined effects of lower hybrid and electron cyclotron wave absorption can be improved compared to that of the present lower hybrid experiments. Suitable shaping of the current density profiles can be achieved by adjusting the wave-launching parameters.