Table of contents

Report on the Fourth IAEA Technical Committee Meeting held at Princeton Plasma Physics Laboratory, Princeton University, Princeton, New Jersey, United States of America.

Experiments with plasmas having nearly equal concentrations of deuterium and tritium have been carried out on TFTR. To date (September 1995), the maximum fusion power has been 10.7 MW, using 39.5 MW of neutral beam heating, in a supershot discharge and 6.7 MW in a high beta _P discharge following a current ramp-down. The fusion power density in the core of the plasma has reached 2.8 MW/m³, exceeding that expected in the International Thermonuclear Experimental Reactor (ITER). The energy confinement time tau _E is observed to increase in DT, relative to D plasmas, by 20% and the n₁(0).T₁(0). tau _E product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter H mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high beta _P discharges. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP simulations assuming classical confinement. Measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from helium gas puffing experiments. The loss of energetic alpha particles to a detector at the bottom of the vessel is well described by the first-orbit loss mechanism. No loss due to alpha particle driven instabilities has yet been observed. ICRF heating of a DT plasma, using the second harmonic of tritium, has been demonstrated. DT experiments on TFTR will continue both to explore the physics underlying the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor

Results from recent DT experiments on TFTR to measure the energy distribution and radial density profile of fast confined alphas with the use of Li pellets and neutral particle analysis are presented. When a pellet is injected into the plasma, a toroidally extended ablation cloud is formed. A small fraction of the fusion alphas incident on the cloud is converted to helium neutrals as a result of electron capture processes. The escaping energetic helium neutrals are analysed and detected by the neutral particle analyser. Radially resolved energy spectra of trapped confined alphas in 0.5-2 MeV range and radial alpha density profiles are presented in this paper. The experimental data are compared with modelling results obtained with the TRANSP Monte Carlo code and with a specially developed Fokker-Planck post-processor (FPP) that uses the alpha source distribution produced by TRANSP. Comparison of the experimental data with TRANSP and FPP shows that the alphas in the plasma core of sawtooth free discharges in TFTR are well confined and slow down classically. The energy and radial profiles distributions outside the plasma core show the influence of stochastic ripple losses on alphas. Measurements for sawtoothing plasmas show a significant outward radial transport of trapped alphas

Measurements of DT alpha particle loss to the outer midplane region of TFTR have been made using a radially movable scintillator detector. The conclusion from this data is that mechanisms determining the DT alpha loss to the outer midplane are not substantially different from those for DD fusion products. Some of these results are compared with a simplified theoretical model for TF ripple induced alpha loss, which is expected to be the dominant classical alpha loss mechanism near the outer midplane. An example is given of plasma driven MHD induced alpha particle loss to the outer midplane, but no sign of any `collective` alpha instability induced alpha particle loss has yet been observed at this location

Experimental observations are presented of a new branch of the toroidal Alfven eigenmode spectrum during ICRF heating of plasmas on TFTR. The identification of the second branch is based largely on direct measurements of the toroidal mode numbers of the toroidal Alfven eigenmodes and by the differences in the time evolution of the frequency spectrum between the new branch and the original toroidal Alfven eigenmodes. The new branch has so far only been observed in relatively low edge q (=4-4.5) plasmas

Experiments to destabilize the toroidicity induced Alfven eigenmode (TAE) by energetic alpha particles were performed on the Tokamak Fusion Test Reactor using deuterium and tritium fuel. To decrease the alpha particle pressure instability threshold, discharges with an elevated value of q(0)>1.5 were used. By raising q(0), the radial location of the low toroidal mode number TAE gaps moves towards the magnetic axis and into alignment with the region of maximum alpha pressure gradient, thereby (in theory) lowering the value of the central alpha particle beta _alpha required for instability. No TAE activity was observed when beta _alpha (0) reached 0.08% in a discharge with fusion power of 2.4 MW. Calculations predict that the alpha driven TAE was weakly unstable

An Alfven frequency mode (AFM) is very often seen in TFTR neutral beam heated plasmas as well as in ohmic plasmas. This quasi-coherent mode has so far only been seen on magnetic fluctuation diagnostics (Mirnov coils). A close correlation between the plasma edge density and the mode activity (frequency and amplitude) has been observed, which indicates that the AFM is an edge localized mode with r/a>0.85. No direct impact of this mode on the plasma global performance or on fast ion loss (e.g., the alpha particles in DT experiments) has been observed. This mode is not the conventional TAE (toroidicity induced Alfven eigenmode). The present TAE theory cannot explain this observation. Other possible explanations are discussed

In high beta DIII-D plasmas with intense neutral beam injection, beta induced Alfven eigenmodes (BAE modes) are observed. These instabilities cause concentrated losses of >50% of the fast ions and thus are of concern for future devices. The authors have now observed BAE modes and resultant fast ion loss in full field (2.0 T) discharges where the ratio of parallel velocity to Alfven speed is v_||/v_A ≈ 0.3. In a few discharges, they have also observed a new instability, a `chirping' mode. These modes have frequencies between 50 and 200 kHz that `whistle' down a factor of two in a single 2 ms burst. They occur in plasmas with relatively large values of fast ion β((β_f) ⩾ 1%), Alfven speed (v_||/v_A ⩽ 0.5) and plasma rotation (f_rot > 20 kHz). In contrast to the usual Alfven modes, which are fluid modes of the background plasma, the chirping instabilities seem to be beam modes that are nearly stationary in the plasma frame

Results from the first experiments to drive Alfven eigenmodes (AEs) with antennas external to a tokamak plasma are presented. In ohmically heated plasma discharges, direct experimental measurements of the damping of toroidicity induced AEs (TAEs) have allowed an identification of different regimes corresponding to different dominant TAE absorption mechanisms with a wide range of damping rates, 10^-3 ⩽ γ/w ⩽ 10^-1. In plasmas heated by ion cyclotron resonance heating, neutral beam injection heating, lower hybrid heating and high plasma current ohmic heating, a new class of weakly damped Alfven eigenmodes, the kinetic Alfven eigenmodes, predicted in theoretical models that include finite Larmor radius and finite parallel electric field effects, has been identified experimentally

A TFTR supershot with a plasma current of 2.5 MA, a neutral beam heating power of 33.7 MW and a peak DT fusion power of 7.5 MW is studied using the TRANSP plasma analysis code. Simulations of alpha parameters such as the alpha heating, pressure and distributions in energy and v₁/v are given. The effects of toroidal ripple and mixing of the fast alpha particles during the sawteeth observed after the neutral beam injection phase are modelled. The distributions of alpha particles on the outer midplane are peaked near forward and backward v₁/v. Ripple losses deplete the distributions in the vicinity of v₁/v=-0.2. Sawtooth mixing of fast alpha particles is computed to reduce their central density and broaden their width in energy

Modelling of TF ripple loss of alphas in DT experiments on TFTR now includes neoclassical calculations of first orbit loss, stochastic ripple diffusion, ripple trapping and collisional effects. A rapid way to simulate experiment has been developed which uses a simple stochastic domain model for TF ripple loss within the TRANSP analysis code, with the ripple diffusion threshold evaluated by comparison with more accurate but computationally expensive Hamiltonian co-ordinate guiding centre code simulations. Typical TF collisional ripple loss predictions are 6-10% loss of alphas for TFTR DT experiments at Ip=1.0-2.0 MA and R=2.52 m

A search is made for signs of enhanced beam ion transport in a set of TFTR plasmas heated with various numbers of tritium and deuterium beams. Our investigation is based on the time dependent, 1½-D simulation code TRANSP, and an ad hoc diffusion model of enhanced fast ion transport. Spatially constant and spatially variable diffusion models are used (the code was upgraded to allow for D_f(r) modelling). Simulations with spatially constant diffusion coefficients resulted in an upper bound of D_f ⩽ 0.2 m²/s for a set of high power DT supershots. One discharge is analysed in particular detail, in terms of both various diffusion models and the effects of systematic errors. Best agreement between the measured neutron flux in this discharge and the corresponding TRANSP predictions is obtained by assuming that D_f has low values in the inner half of the plasma column (D_f 0.1 m²/s) and then rises rapidly in the outer half, suggesting that stochastic ripple diffusion is the likely mechanism for the enhanced beam ion transport. This hypothesis is supported by the modelling results from two other plasmas with large major radii

The results of a 3-D (in constants of motion space) Fokker-Planck simulation of the collisional losses of fusion products in axisymmetric DT and DD discharges in TFTR are presented. The distributions of escaped ions over poloidal angle and pitch angle, and their energy spectra, are obtained. Axisymmetric collisional losses of fusion products are found to be less than 2 to 5%. The distribution of confined fusion products is shown to be strongly anisotropic and non-uniform in the radial co-ordinate, mainly for slowed-down fusion products with small longitudinal energy. A comparison between these modelling results and experimental data is made

The evolution of the alpha particle distribution function in a TFTR DT supershot is simulated using a 3-D Fokker-Planck code that allows for a time varying alpha particle source and for collisions with the evolving thermal plasma. It is important to include large orbit width effects as these lead to differing distribution functions in velocity space at the high and low field sides of the tokamak. The predicted time variations of the profiles of alpha particle density and of the heating of the background plasma agree well with Monte Carlo calculations by the TRANSP plasma simulation code, though the Fokker-Planck approach has the advantage that it gives smoother distribution functions

The paper reports recent results concerning the 3 MeV fusion proton trajectories in the Tore Supra tokamak. The orbit computations were made in a new and unusual manner on the basis of a topological equation which governs these trajectories. The method avoids both the problem of computing precision and the need to follow a large number of particles along their orbits; it permits a topological map of trajectories to be drawn, i.e. all possible trajectory classes, without any numerical computation to be found. It also gives the transitions occurring between the various classes. The confinement of the proton orbits and the optimization of the detector location were studied under the same topological rules. The need to develop this subject comes from the necessity to explain a large quantity of experimental data recorded by a silicon detector system on Tore Supra. Experimental analysis of the charged fusion products is ensured by this unique detection system, which allows simultaneously energy and pitch angle resolution to be obtained

The stability of toroidal Alfven eigenmodes (TAEs) is presented for steady state plasmas in the JT-60 Super Upgrade (JT-60SU). Studies are carried out by using the ACCOME code for calculating self-consistent MHD equilibria and by using the NOVA-K code for analysing the TAE stability. Characteristics of the TAE stability are obtained for non-inductive steady state plasmas (3 MA/3 T) with a large bootstrap current and a 500 keV neutral beam (NB) current. Above the density value corresponding to V_hV_A~1, the TAE becomes unstable owing to the large pressure gradient, ΔP_h, and the large β of the hot particles, (β_h). Here, V_hV_A is the ratio of the hot particle velocity to the Alfven velocity. As the density and the temperature increase, the bootstrap current increases so that the NB power required for the current drive decreases. Consequently, both ΔP_h and (β_h) decrease and the TAEs are stabilized by ion Landau damping. In the high current and high toroidal field plasma (10 MA/6.25 T) case, because ΔP_h is small, owing to high density, and (β_h) is small, owing to high toroidal field, the TAE is stable for low n to medium n (⩽15)

The confinement of fusion produced or high energy particles is one of the most important issues to be studied in the helical confinement system. A preliminary study has been carried out on the possibility of developing techniques for simulation experiments for the study of high energy particle physics in the Large Helical Device (LHD) project. Candidate methods have been considered as follows: (a) a high energy (~3.5 MeV) He⁰ beam injection method; (b) a medium energy (~200 keV) H⁰ beam injection method; (c) a method involving high energy rail production by an ICRF wave and/or a method of reaction rate enhancement by an ICRF wave; and (d) a method involving the combination of neutral beam injection and ICRF wave. Various features of each method have been considered. Although the high energy He⁰ beam injection method has some advantages, the technique for production of this beam is extremely difficult because of the difficulties of the production of both negative helium and ground state neutral helium by neutralization. It is pointed out, on the other hand, that a wide range of simulation experiments for fast particle physics may be carried out even by the medium energy beam method, because the typical orbit deviation (e.g. equivalent super-banana size in a classical sense) can be largely controlled by controlling the magnetic field configuration in the case of a helical system, for example by shifting the magnetic axis. This is one of the unique features of a helical system in contrast to an axisymmetric system

A qualitative model is given to describe the redistribution of ICRF heated minority ions at sawtooth crashes in tokamak plasmas. A crucial feature of the model is that it takes into account profile broadening effects due to the finite width of the ICRF heated particle orbits. Predictions of the model are compared and found to be in agreement with numerical simulations as well as with experimental results from JET

The work deals with the fast ion transport during crashes of sawtooth oscillations. A kinetic equation for the distribution function of fast ions valid for the whole region of sawtooth mixing is derived. Special attention is paid to clarifying the behaviour of near-axis particles

Experiments have been carried out in JT-60U to verify the modelling of fast ion ripple transport. The ripple induced loss was estimated from the neutron decay following neutral beam pulse injection and the loss related heat load on the first wall. Comparison of the lost fraction and the hot spot positions between measurements and orbit following Monte Carlo calculations exhibited good agreement, indicating that the ripple transport governing fast ion losses is explained within the framework of existing theory. Neutral beam heating experiments in JT-60U also indicate that H modes free of ELMs are still obtainable for ripple amplitudes of up to 2.2%

Direct losses of ions trapped in the toroidal field ripple of Tore Supra were studied, using two techniques. The first (DRIPPLE I) correlates the ion loss current measured by an electric probe with the ion loss power measured by a calorimeter. As the calorimeter integrates over all particle energies and time, it yields only the averaged lost ion energy. The second technique (DRIPPLE II), still under development, uses a Faraday cup positioned and filtered so as to select ions by their Larmor radius. Preliminary results are useful but the currents measured are small (1-100 nA), aid improvements in instrumentation are needed to take full advantage of the data. During ICRH (hydrogen minority regime, resonance on-axis), a direct correlation between the lost ion mean energy and the density of hydrogen (n_H) is observed. The energy increases when the hydrogen minority density decreases. Moreover, the line integrated density and the lower hybrid (LH) heating also affect the fast ion losses

Ion cyclotron emission (ICE) has been observed during D-T discharges in the Tokamak Fusion Test Reactor (TFTR), using RF probes located near the top and the bottom of the vacuum vessel. Harmonics of the alpha cyclotron frequency ( Omega _a,) evaluated at the outer midplane plasma edge are observed at the onset of the beam injection phase of TFTR supershots and persist for approximately 100-250 ms. These results are in contrast with observations of ICE in JET, in which harmonics of Omega _a evolve with the alpha population in the plasma edge. Such differences are believed to be due to the fact that newly born fusion alpha particles are super-Alfvenic near the edge of JET plasmas, while they are sub-Alfvenic near the edge of TFTR supershot plasmas. In TFTR discharges with edge densities such that newly born alpha particles are super-Alfvenic, alpha cyclotron harmonics are observed to persist. These results are in qualitative agreement with numerical calculations of growth rates due to the magnetoacoustic cyclotron instability

Edge localized magnetoacoustic-cyclotron instability excited through bounce resonances with the fast ions is shown to be consistent with the spectrum of ion cyclotron emission in tokamaks. In particular, it is shown that the instability growth rate is maximum and vanishes for a wave frequency close to the cyclotron harmonics of fast ions near the outer and inner circumferences of the torus, respectively. The analysis takes into account both the radial structure of the eigenmodes and the finite orbit width of fast ions

A comprehensive set of fast particle diagnostics is routinely used at JET. Some are in the process of being upgraded and others, completely new, are being prepared for use during the forthcoming tritium experiments. For fusion product studies, the strength and profile of the charged particle birth distribution is obtained by measuring the neutron emission with three pairs of absolutely calibrated fission chambers and a two-camera profile monitor. Information on the DD neutron energy spectrum is deduced from a time-of-flight neutron spectrometer. Neutrons of 14 MeV energy from triton burnup are measured using silicon diodes and a high energy branch of the profile monitor. Absolute calibration is obtained with an activation system. A prototype lost alpha particle detector (Faraday cup) has been tested in the laboratory and has been installed inside JET so that its noise immunity can be tested. Two 14 MeV neutron spectrometers are under commissioning and a third is under construction. A high energy neutral particle analyser is routinely used to diagnose fast RF driven particles and will also be available for alpha particle studies. The intensity of RF driven fast particles is also deduced by the spectroscopy of gamma rays emitted in reactions with impurity ions in the plasma. The gamma ray measuring branch of the neutron profile monitor adds spatial resolution to the measurement. A new antenna for measuring ion cyclotron emission (ICE) and a gyrotron for alpha particle scattering experiments are in the process of being commissioned. Active charge exchange spectroscopy to investigate the low energy range of the alpha particle population is being considered. Where appropriate, information gathered with these systems is presented to illustrate their performance

A study is conducted of the feasibility of alpha particle measurement using a high energy diagnostic beam in combination with a neutral particle analyser for an ITER plasma. In order to measure alpha particles over an energy range of 0.5 to 3.5 MeV, the required beam energy is approximately 1 MeV for a ³He⁰ beam and 3 MeV for a ⁶Li⁰ beam, the beam current density being about 1 mA/cm² for both cases. Among the various methods of producing such a high energy neutral beam, the acceleration of negative ions is the most favourable. Recent results of relatively small scale experiments with these negative ion sources reveal that the required current density is now attainable. Technical problems as to how to scale the ion sources used on an ITER sized experiment are also discussed for these experiments

To understand the reason for the possible losses of the fusion products, it is necessary to obtain experimental information on their energy distribution function during slowdown. The method proposed in the present paper is based on the detection of gamma rays produced by nuclear reactions between decelerating alpha particles and nuclei already present in the plasma. The feasibility of this diagnostic for both low and high background radiation fields is considered

A majority of the planned fusion product diagnostics for the T-15 tokamak are described. These include a few dozen silicon diodes to detect escaping charged fusion products with high energy resolution. They will resolve the charged particle fluxes in radial, pitch angle, energy and time dependences. In addition, measurements of DD neutron birth profiles are proposed to be carried out using two independent system-a bubble chamber and a `sandwich` radiometer that have not been used in tokamaks to date. A new method of plasma current profile measurement is suggested, based on the detection of `test` alpha particles emitted by radioactive sources at the vessel wall

High-n, toroidal Alfven eigenmodes (TAEs) are studied on the basis of a kinetic model that includes full thermal ion finite Larmor radius effects, trapped electron collisions and fast particle instability drive. Lower kinetic TAEs (KTAEs) are shown to be non-existent in the nearly collisionless limit. Like TAEs, upper KTAEs are shown to exist because of thermal ion finite Larmor radius effects in the dissipationless limit. Dissipation effects on the stability of both TAEs and upper KTAEs can be treated perturbatively. However, owing to their extended mode structure in the ballooning space, upper KTAEs usually remain stable or weakly unstable even with large fast particle free energy. On the other hand, TAEs can be strongly destabilized. A new resonant TAE (RTAE) can be excited when the fast particle drive is significantly large. The RTAE is a beam-like mode, with its frequency determined mainly by the wave-particle resonance condition. The frequency of the RTAE can be much less than the TAE gap frequency and may be interpreted as the BAE observed in DIII-D experiments. As plasma beta increases, the TAE, RTAE and kinetic ballooning modes strongly couple; the TAE changes into the RTAE and eventually connects to the kinetic ballooning mode. Numerical results and analytical analysis on the stability of the RTAEs and KTAEs will be presented and compared with the TAE stability

In the present work, we analyse the two dimensional (2-D) mode structures and global stability of the Alfven branches, whose frequencies are close to the toroidicity induced Alfven continuum gap. The fully 2-D problem is solved using a two spatial-scale WKBJ formalism without employing perturbation theory in treating drive and damping terms. A code that solves the 2-D mode structures and global stability of the Alfven branches is presented. Applications to a model toroidal equilibrium with ITER relevant plasma parameters are analysed. Results indicate that no unstable modes are present in the considered reference scenario

A quasi-linear model is developed to produce realistic self-consistent saturation levels when modes do not overlap, and give self-consistent diffusion and wave evolution when modes do overlap. Both regimes give steady or pulsating behaviour in weakly driven systems with classical relaxation and background dissipation present. An avalanche response is demonstrated: wave momentum release caused by the overlap of closely spaced modes can produce mode overlap of more widely spaced modes (a domino effect) or the growth of modes which would be stable in systems unaffected by the diffusion of closely spaced modes. Detailed analysis and calculations are performed for the bump-on-tail instability, and extension of the method to more general problems is briefly discussed

A consistent numerical simulation is performed to study the dynamics in a steady state plasma with improved core confinement which is sustained by a bootstrap current and external drive. A new non-linear link between the profiles of the pressure, current and thermal conductivity is investigated. A self-organized oscillation (i.e. Spatiotemporal limit cycle oscillation) of the plasma pressure and current, coupled by the variation of the confinement enhancement factor, is predicted to occur. In the presence of alpha particle heating, the time variation of the plasma parameters causes a change in the alpha heating power. This provides a new picture of the thermal instability in burning plasmas

The upper limit of local and global energy losses of alpha particles induced by TAE instability is evaluated. Both numerical results and a simple analytical expression for the lost fraction are presented. It is shown that the increase of particle resonance velocities with radius minimizes the alpha losses, preventing the escape of alphas from the plasma core

Two methods are examined for influencing the stability thresholds of alpha driven toroidal Alfven eigenmode (TAE) instabilities in the deuterium-tritium (DT) operation of the Tokamak Fusion Test Reactor (TFTR). These are: (a) increasing the TAE drive through raising the central q(0) value (in order to centre the peak alpha pressure gradient on the lower m gap locations) and (b) decreasing the TAE damping rate on the background ions through cooling perturbations such as helium puffs or injected pellets. A gyrofluid model of the TAE is used that is inherently non-perturbative and includes continuum damping, ion/electron/neutral beam Landau damping, ion FLR effects and a generalized resistivity (finite E₁ effects). Specific TFTR DT cases are analysed using a combination of measured and inferred profiles. The resulting predicted thresholds are generally consistent with an observed lack of strong TAE activity. However, it is found that special techniques, especially increasing q(0), can significantly lower the alpha driven TAE threshold into ranges that should be experimentally accessible

A Hamiltonian guiding centre particle following code has been developed to study the fast particle motion in the presence of arbitrary time dependent electromagnetic perturbations. In conjunction with an MHD stability code, this code was used to analyse TAE/KTAE induced alpha orbit diffusion and alpha losses in JET plasmas. Resonant alpha orbits are studied below and above the stochasticity thresholds, in the presence of single or several TAEs and KTAEs. Monte Carlo randomized ensembles of alpha particles in the presence of finite amplitude TAE/KTAEs are followed and estimates for the stochastic diffusion coefficients are obtained. Generalization of the method towards the self-consistent wave-particle evolution is described

A fast and efficient numerical algorithm using energy conservation is developed to study the interaction of high energy particles with a toroidicity induced Alfven eigenmode (TAE). A Hamiltonian guiding centre code is used to simulate the alpha particle motion and a non-linear delta f scheme is employed to calculate the wave-particle energy exchange. For a single TAE mode, the particle radial excursion is much less than the spacing between the resonances produced by the poloidal harmonics for International Thermonuclear Experimental Reactor parameters. Modification of the particle distribution leading to mode saturation is observed. A TAE is found in some cases to cause loss through induced ripple trapping

New numerical simulations are presented on the self-consistent dynamics of energetic particles and a set of unstable discrete shear Alfven modes in a. tokamak. The code developed for these simulations has been previously tested in simulations of the bump-on-tail instability model. The code has a Hamiltonian structure for the mode-particle coupling, with the superimposed wave damping, particle source and classical relaxation processes. In the alpha-particle-Alfven-wave problem, we observe a transition from a single mode saturation to mode overlap and global quasi-linear diffusion, which is qualitatively similar to that observed in the bump-on-tail model. A considerable enhancement in the wave energy due to the resonance overlap is demonstrated. The effect of global diffusion on the energetic particle losses is also demonstrated

The growth rate of toroidal Alfven eigenmodes (TAEs) driven unstable by resonant coupling of energetic charged particles is evaluated in the `ballooning` limit over a wide range of parameters. All damping effects are ignored. Variations in orbit width, aspect ratio and the ratio of Alfven velocity to energetic particle `birth` velocity are explored. The relative contribution of passing and trapped particles, and finite Larmor radius effects, are also examined. The phase space location of resonant particles that interact strongly with the modes is described. The accuracy of the analytic results with respect to growth rate magnitude and parametric dependence is investigated by comparison with numerical results

Ion cyclotron emission (ICE) has been observed from neutral beam heated TFTR, and JET tritium experiments at sequential cyclotron harmonics of both fusion products and beam ions. The emission originates from the outer midplane plasma, where fusion products and beam ions are likely to have a drifting ring-type velocity-space distribution that is anisotropic and sharply peaked. Fusion product driven ICE in both TFTR and JET can be attributed to the magnetoacoustic cyclotron instability, which involves the excitation of obliquely propagating waves on the fast Alfven/ion Bernstein branch at cyclotron harmonics of the fusion products. Differences between ICE observations in JET and TFTR appear to reflect the sensitivity of the instability growth rate to the ratio v_birth/c_A where v_birth is the fusion product birth speed and c_A is the local Alfven speed for fusion products in the outer midplane edge of TFTR supershots, v_birth < c_A for alpha particles in the outer midplane edge of JET, the opposite inequality applies. If sub-Alfvenic fusion products are isotropic or have undergone even a moderate degree of thermalization, the magnetoacoustic instability cannot occur. In contrast, the super-Alfvenic alpha particles that are present in the outer midplane of JET can drive the magnetoacoustic cyclotron instability even if they are isotropic or have a relatively broad distribution of speeds. These conclusions may account for the observation that fusion product driven ICE in JET persists for longer than fusion product driven ICE in TFTR. Moreover, the time evolution of the maximum growth rate, obtained using the Sigmar model for the alpha particle distribution and TFTR data for the fusion product source rate, closely follows the observed time evolution of the ICE amplitude in TFTR supershot discharges. Other observed features of fusion product driven ICE that match the linear instability include the scaling with fusion product density, doublet splitting of spectral peaks, the relative strength of certain harmonics and source localization. A separate mechanism is proposed for the excitation of beam driven ICE in TFTR: electrostatic ion cyclotron harmonic waves, supported by strongly sub-Alfvénic beam ions, can be destabilized by a low concentration of such ions with a very narrow spread of velocities in the parallel direction. Sufficiently narrow distributions are likely to exist in the edge plasma, close to the point of beam injection.

Two-dimensional solutions of compressional Alfven eigenmodes (CAEs) are studied in the cold plasma approximation. For finite inverse aspect ratio tokamak plasmas the two-dimensional eigenmode envelope is localized at the low magnetic field side with the radial and poloidal localization on the order of a/ square root m and a/⁴ square root m, respectively, where m is the dominant poloidal mode number. Charged fusion product driven Alfven cyclotron instability (ACI) of the compressional Alfven eigenmodes provides the explanation for the ion cyclotron emission (ICE) spectrum observed in tokamak experiments. The ACI is excited by fast charged fusion products via Doppler shifted cyclotron wave-particle resonances. The ion cyclotron and electron Landau dampings and fast particle instability drive are calculated perturbatively for deuterium-deuterium (DD) and deuterium-tritium (DT) plasmas. Near the plasma edge at the low field side the velocity distribution function of charged fusion products is localized in both pitch angle and velocity. The poloidal localization of the eigenmode enhances the ACI growth rates by a factor of square root m in comparison with the previous results without poloidal envelope. The thermal ion cyclotron damping determines that only modes with eigenfrequencies at multiples of the edge cyclotron frequency of the background ions can be easily excited and form an ICE spectrum similar to the experimental observations. Theoretical understanding is given for the results of TFTR DD and DT experiments with v_{alpha 0}/v_A approximately=1 and JET experiments with v_{alpha 0}/v_A>1

The complete channelling of energy from alpha particles is likely to be realized only through the excitation of a variety of waves, rather than by one wave alone. While one wave constrains more firmly the direction of the energy transfer, the necessary wave characteristics are far more easily achieved through a combination of waves, even at the expense of less restrictive motion of the alpha particles

The plasma potential energy delta W_tot associated with m=1 internal kink displacements is calculated for JET equilibria, taking into account the presence of alpha particles and ions heated by ion cyclotron resonance frequency (ICRF) waves. In the latter case the heated ion distribution is modelled as a simple function of ICRF parameters, which is consistent with numerical Fokker-Planck calculations. It is likely that the kink energy is an important parameter in determining the properties of sawtooth oscillations: in the ideal limit, positive values of delta W_tot indicate that kink displacements are stable. Alpha particles give rise to a stabilizing kinetic term in delta W_tot, but also exert a destabilizing influence owing to their effect on the Shafranov shift. The alpha particle contribution to delta W_tot is found to be destabilizing when the central value of the safety factor q₀=0.75, but stabilizing when q₀=0.9. The effect of ICRF heated minority ions can be calculated in terms of fluid and kinetic corrections to delta W_tot. Both trapped and passing ICRF heated ions play a significant stabilizing role. Complete stabilization of the ideal kink mode, due to either alpha particles or ICRF heated ions, is most easily achieved if q₀ lies close to unity or if the radius of the q=1 surface is small

A gyrobroadening process causing the perpendicular energy of fast ions to be broadened by cyclotron instabilities due to the relativistic mass variation of the fast ions in a magnetized plasma is reported. At low cyclotron harmonics, a two-gyro-stream instability can be excited with the involvement of thermal ions if the condition l_fw_cf < w < l_sw_cs is satisfied. The fast ions can be anomalously thermalized. Their lost energy goes to bulk ion heating. While the fusion produced protons can satisfy the condition, the alphas cannot. The low harmonics are linearly stable for the alphas. Therefore, for low harmonics one has to inject waves to affect the alpha dynamics. However, the alphas can excite high harmonic cyclotron waves in the lower hybrid regime, in which thermal ions respond as cold plasma. The interaction becomes selective. Only alphas with high pitch angle are involved. The implications of this process for fusion ignition and fast ion confinement are assessed