Table of contents

Using the total power balance of an ignited tokamask plasma as a guideline, a range of alpha driven effects is surveyed regarding their impact on achieving and maintaining fusion burn. Specific examples of MHD and kinetic modes and multi species transport dynamics are discussed, including the possible interaction of these categories of effects. This power balance approach rather than a straightforward enumeration of possible effects serves to reveal their non-linear dependence and the ensuing fragility of our undestanding of the approach to and maintenance of ignition. Specific examples are given of the interaction between α-power driven sawtoothing and ideal MHD stability, and direct α-effects on MHD modes including kinetic corrections. Anomalous ion heat transport and central impurity peaking mechanisms and anomalous and collisional α-transport including the ambipolar electric field are discussed.

Issues related to the presence of fusion α-particles which are of importance for the design of a tokamak reactor are listed and shortly discussed. It is concluded that these issues, although to a large extent directly connected with the general problems of tokamak physics, require more attention to provide the information needed for designing a tokamak reactor.

Fusion product alpha populations can significantly influence tokamak stability due to coupling between the trapped alpha precessional drift and the kinetic ballooning mode frequency. This effect is of particular importance in parameter regimes where the alpha pressure gradient begins to constitute a sizeable fraction of the thermal plasma pressure gradient. Careful, quantitative evaluations of these effects are necessary in burning plasma devices such as the Tokamak Fusion Test Reactor and the Joint European Torus, and we have continued systematic development of such a kinetic stability model. In this model we have considered a range of different forms of the alpha distribution function and the tokamak equilibrium. Both Maxwellian and slowing-down models have been used for the alpha energy dependence while deeply trapped and, more recently, isotropic pitch angle dependences have been examined. In the latter case the drift reversal of the not so deeply trapped alphas is an important new feature not included in the deeply trapped model. The tokamak equilibrium was initially described using the nearly concentric circular flux surface model as well as more realistic analytic and numerical calculations that include the higher order poloidal harmonics of the equilibrium. An improved analytic model gives especially close agreement with the finite β numerical equilibrium. Detailed comparisons of these various models are presented. Our results indicate that alpha populations can significantly deteriorate the first stability window for ballooning modes as the alpha pressure gradient is increased and as the background electron temperature is raised (for the slowing-down model) or, equivalently, the ratio of alpha to background temperature is lowered (for the Maxwellian model). A related effect is the observed destabiliation with increased aspect ratio (_p^-1 = R₀/r_p where r_p is the local pressure gradient scale length). These scalings are consistent with an interaction between the ballooning mode frequency and the alpha precessional drift at energies involving increasingly larger fractions of the alpha distribution. Such regimes will characterize the central regions of burning tokamak devices and should be observable for the projected ranges alpha pressure and background temperature.

The interaction of alpha particles with low-frequency fast magnetosonic and Alfvén waves in toroidal configuration is studied. The interaction of alpha particles with high-frequency one-dimensional magnetosonic solitons and low-frequency two-dimensional drift vortices in the approximation of the straight uniform magnetic field is examined. It is shown that as a result of these interactions the amplification of above structures of plasma takes place, which can lead to the complementary diffusion of plasma particles and losses of heat.

A short review of modern transport concepts for high energy alpha particles in tokamaks is presented. A theory of the collisional diffusion of alpha particles in tokamaks in the presence of a weak toroidal field ripple is developed. The neoclassical transport processes of alpha particles in the plasma central region including the magnetic axis are analyzed.

It is shown that global Alfvén modes can be excited by fusion produced trapped alpha particles due to resonance with the precession drift. The order of magnitude of the transport has been estimated.

Several aspects of energetic alpha behavior in a burning fusion plasma are considered. Alpha losses during slowing down and alpha-induced plasma rotation are discussed as the basis for important measurements. Potential kinetic instabilities (alpha-driven Alfvén waves in both toroidal and mirror systems) are considered from the point of view of threshold requirements. The possibility that other synergistic effects (e.g., orbit drift and shear Alfvén wave driven transport) might trigger these instabilities is also noted.

A major premise in the operation of Tandem Mirror reactors is that the fusion reactions take place in the central cell only. The alpha particles generated by the Deuterium-Tritium (DT) fusions, along with other ions, will however pass from the central cell to the thermal barriers and return to the central cell as a result of reflection by the potential hills that exist on the plugs' side of these barriers. This streaming motion gives rise to electrostatic and electromagnetic instabilities which could detract from the barrier's function as a thermal insulator. The number density and streaming velocity of these passing particles are dictated by the electrostatic potential variation and the magnetic field structure in these regions. It is shown that, in the absence of alphas, barriers with deep potential depression are less susceptible to electrostatic instabilities while particularly vulnerable to unstable electromagnetic modes. In the presence of alphas, especially the fast alphas whose mean energy is significantly larger than the barrier potentials they see, (which is twice as high as that seen by the ions) both types of modes become unstable.

The use of relativistic electron rings to stabilize plasmas against the interchange modes has been utilized in such devices as the Elmo Bumpy Torus (EBT) and the plugs of a Tandem Mirror device (STM). In the EBT case enhanced stability is reflected in higher betas (ratio of plasma to magnetic field pressures), while in the Tandem Mirror case symmetry in the plug magnetic geometry results in reduced particle diffusion across the magnetic field in the central cell. Regardless of the application, the question arises as to what effect would alpha particles generated by the Deuterium-Tritium (DT) reactions have on the stability of such ring-stabilized devices. In this paper the macroscopic stability of such systems is reexamined in order to assess the effect of alphas on the background interchange mode, the interacting interchange mode, and the high frequency compressional Alfvén and coupled modes. A fluid description is used for the background plasma while a kinetic treatment is utilized for the hot electron species and alpha particles. It is shown that the Alphas tend to mildly destabilize the interacting interchange while stabilizing the background interchange due to their sizable Larmor radii. The destabilization is most pronounced at high alpha energies i.e., at birth, and near complete recovery of stability is achieved as these particles approach thermalization with the background ions. It is also shown that the alphas completely stabilize the high frequency modes.

The calculation of the single alpha particle orbit in a background of thermalized plasma is fundamentally transparent and leads often to a simple physical interpretation. However, for certain tasks, like those including also statistics on random events, these calculations can be excessively time consuming, even for large computers. These tasks are best suited for calculations including statistical operators which, however, often require the simplification of the model, leaving off for example, the space dependence of the plasma parameters. As the fast fusion products have relatively large Larmor radii and their guiding centers may have large excursions in a possibly inhomogeneous plasma, such a simplification may produce misleading results. Therefore, it may be necessary to turn back to orbit calculations. In this paper, we will give the results of several cases at the frontier between orbit and statistical operator calculations:

(1) The burn up of fusion produced tritium in the ohmic FT (theory and experiment).

(2) The hot spots of ³He wall loading due to magnetic ripple (computational study).

(3) Slow down of α with ripple resonance (computational study).

The Compact Ignition Tokamak (CIT) is a proposed modest-size ignition experiment designed to study the physics of alpha particle heating. The basic concept is to achieve ignition in a modest-size minimum cost experiment by using a high plasma density to achieve nτ_E ∼ 2 × 10²⁰s/m³ required for ignition. The high density requires a high toroidal field (10 T). The high toroidal field allows a large plasma current (10 MA) which provides a high level of ohmic heating, improves the energy confinement, and allows a relatively high beta (∼ 6%). The present CIT design also has a high degree of elongation (κ ∼ 1.8) to aid in producing the large plasma current. A double null poloidal divertor and pellet injection are part of the design to provide impurity and particle control, improve the confinement, and provide flexibility for improving the plasma profiles. Auxiliary heating is expected to be necessary to achieve ignition, and 10-20 MW of ICRF is to be provided.

The different schemes for burn temperature control in tokamaks are reviewed with respect to stability, compatibility with other system components, impact on cost, viability of the underlying physics and validity of the models used for the theoretical description. Open problems of burn temperature control and additional R- and D-needs are discussed.

The numerical calculations of the longitudinal motion in multi-mirror reactor have shown that the energy contribution of α-particles has substantial influence on the gain factor (the given off thermonuclear energy/ the initial imparted energy) in the temperature region 5-7 keV. The numerical technique has been developed that takes into account the radial distribution of α-particles caused by their drag on electrons. This effect is substantial for ϱ_α/R ⩾ 1/2 (where ϱ_α is α-particles gyro radius, R is a plasma radius), e.g. for Gas-Dynamic trap. In a Tandem-Mirror reactor some part of fusion α-particles have the probability to slow down to the plasma energy, that can lead to the `poisoning' of the reactor by the thermonuclear reaction products. The fusion α-particles can have a strong effect on accumulation of impurities with z ⩽ 15 and thermal α-particles in TMR.

TFTR is expected to produce approximately 5 MW of alpha heating during the D/T Q ≈ 1 phase of operation in 1989–1990. At that point the collective confinement properties and the heating effects of alpha particles become accessible to study for the first time. This paper outlines the potential performance of TFTR with respect to alpha particle production, the diagnostics which will be available for alpha particle measurements, and the physics issues which can be studied both before and during D/T operation.

The prospects for alpha particle heating in JET are discussed. A computational model is developed to represent adequately the neutron yield from JET plasmas heated by neutral beam injection. This neutral beam model, augmented by a simple plasma model, is then used to determine the neutron yields and fusion Q-values anticipated for different heating schemes in future operation of JET with tritium. The relative importance of beam-thermal and thermal-thermal reactions is pointed out and the dependence of the results on, for example, plasma density, temperature, energy confinement and purity is shown. Full 1½-D transport code calculations, based on models developed for ohmic, ICRF and NBI heated JET discharges, are used also to provide a power scan for JET operation in tritium in the low density, high ion temperature regime. The results are shown to be in good agreement with the estimates made using the simple plasma model and indicate that, based on present knowledge, a fusion Q-value in the plasma centre above unity should be achieved in JET.

A new type of computational tool under development, employing techniques of symbolic computation and artificial intelligence to automate as far as possible the research activities of a human plasma theorist, is described. Its present and potential uses are illustrated using the area of the theory of alpha particle effects in fusion plasmas as a sample domain.

Several diagnostic methods are possible for measuring the spatial and energy distributions of alpha particles in three different contexts: the fast confined alpha particles in the fusion plasma, the thermalized alphas (the He "ash") and the alpha particles escaping from the plasma. Many phenomena, such as single and double charge exchange from neutral beams to the alpha particles, damping of lower hybrid waves, emission at ion cyclotron harmonics, γ-ray emission from nuclear reactions with the alpha particles, and small-angle laser scattering as well as escaping alphas, are involved in the different proposals for determining the phase space distribution of the fusion-produced alpha particles in burning D-T plasmas. The necessary developmental effort is greatly influenced by the high neutron and x-ray backgrounds.

For the purpose of diagnosing alpha particle confinement and velocity distributions in fusion plasmas we consider several (α, n) and (α, γ) reactions with impurities or introduced elements.

Reaction rates and energy spectra of emerging particles under different conditions are discussed particularly with respect to potential measurements in the severe high neutron- and gamma background, originating from fusion reactions. The reactions considered will possibly provide information about total alpha particle confinement and velocity distribution particularly in the high energy range.

Energy spectra of the emerging neutrons and gammas for different alpha particle distributions are calculated and possible pieces of information are discussed.

Finally, we conclude that due to the nature of alpha particles one needs to utilize several reactions and also different kinds of diagnostics to fully explore confinement and velocity distribution of the alpha particles.

The measurement of the pitch angle distribution of energetic alphas escaping from a burning plasma represents a key next step diagnostics problem. A unique wall detector design is proposed here which uses a combination of curved collimation, thin scintillator and a fast multi-channel signal processing unit to allow detection of 10^-5 alphas per fusion neutron despite the intensive background radiation field involved. An analysis of the shielding of this radiation hardened detector system is presented.

Study of fusion reaction products emitted from deuterium plasmas provides information on the confinement and slowing down of fast charged particles. The information gained through these studies has a bearing on the confinement of α-particles and may contribute to predictions concerning the α-particle heating in deuterium-tritium plasmas.

Proton spectra have recently been measured at JET from the reaction d + ³He → p + α at energies around E_p = 14.6 MeV. ³He was introduced by gas puff (for ICRF minority heating) but is otherwise always present as a product of the reaction d + d → ³He + n. The instrument and some of the results obtained are described.

Neutrons of about 14.0 MeV from the reaction t' + d → α + n (where the 1.0 MeV tritons t' come from d + d → p + t') can be studied given a spectrometer of high efficiency ( ⪆ 0.2 cm²) and low sensitivity to 2.5 MeV neutrons. A proposed spectrometer design and its envisaged diagnostic capabilities are discussed.

Besides studying the fast ions in the plasma through their fusion burn up products, atomic "burn up" is suggested as another possibility; i.e. the radiative recombination e + t → γ + t⁰ of fast tritons and measurement of their velocity distribution as represented in the neutral t⁰ emission.

A comparison is made of limitations and capabilities between charged particle, neutron and neutral t⁰ measurements for purpose of studying the fast ion physics and of diagnosing the plasma.

A proton spectrometer has been installed and operated on JET with the objective of measuring the energy spectrum of 15 MeV protons produced in ³He-d reactions under conditions of ICRF heating. The proton emission is observed to be briefly but strongly enhanced at the moment of a sawtooth collapse. A convincing explanation is proposed for the proton energy spectrum recorded between sawtooth collapses. The interpretation of the spectra recorded at the collapse itself is more contentious, nevertheless it is clear that a momentary radial drift for the energetic particles is required as well as a significant alteration in pitch angle.

The balance in between particle diffusion, reaction processes and particle injection from external sources of tritium and deuterium in a burning fusion plasma is studied analytically by means of coupled model equations. The diffusion processes are described by scaling terms approximating the associated diffusion operators in the coupled reaction-diffusion equations. From the results obtained for the particle densities the associated expressions describing the alpha particle production are constructed for simultaneous beam-thermal and thermal-thermal reactions.