Showing papers in "Nuclear Fusion in 1987"

Plasma Physics and Controlled Nuclear Fusion Research

Abstract: FIRST EXPERIMENTS IN JET. Results obtained from JET since June 1983 are described which show that this large tokamak behaves in a similar manner to smaller tokamaks, but with correspondingly improved plasma parameters. Long-duration hydrogen and deuterium plasmas (>10 s) have been obtained with electron temperatures reaching > 4 keV for power dissipations < 3 MW and with * Euratom-IPP Association, Institut fur Plasmaphysik, Garching, Federal Republic of Germany. ** Euratom-ENEA Association, Centro di Frascati, Italy. *** Euratom-UKAEA Association, Culham Laboratory, Abingdon, Oxfordshire, United Kingdom. **** University of Dusseldorf, Dusseldorf, Federal Republic of Germany. + Euratom-Ris0 Association, Ris National Laboratory, Roskilde, Denmark. ++ Euratom-CNR Association, Istituto di Física del Plasma, Milan, Italy. +++ Imperial College of Science and Technology, University of London, London, United Kingdom. ++++ Euratom-FOM Association, FOM Instituut voor Plasmafysica,. Nieuwegein, Netherlands. ® Euratom-Suisse Association, Centre de Recherches en Physique des Plasmas, Lausanne, Switzerland.

Solution of stellarator boundary value problems with external currents

Abstract: Neumann boundary value problems are solved for stellarator fields generated by external currents. The method can be applied to the construction of external coil configurations of stellarators and to studies of the properties of vacuum fields. A computer code, NESCOIL, has been developed and applied to the Helias and ATF stellarator configurations.

The magnetic mirror approach to fusion

Abstract: The magnetic mirror approach to fusion is reviewed in depth. Starting with a brief chronological history of the development of the basic mirror concept, its subsequent evolution into the tandem mirror, the field reversed mirror and other variants is described. Also discussed are the many-faceted aspects of mirror theory, including adiabatic invariants, MHD equilibrium and stability, collisional processes, transport theory and micro-instability theory. The review concludes with an updating of experimental results, a discussion of mirror-related technology, including neutral beam injection and direct conversion, and a brief description of design studies of mirror fusion power plants.

Fully toroidal ion temperature gradient driven drift modes

Abstract: A simple quadratic dispersion relation is derived for electrostatic ion temperature gradient driven modes without expansion in the inverse aspect ratio. It is also shown that these modes experience the local curvature only on the outside of the magnetic surface.

Ideal MHD stability properties of pressure driven modes in low shear tokamaks

Abstract: The role of shear in determining the ideal MHD stability properties of tokamaks is discussed. In particular, the effects of low shear within the plasma upon pressure driven modes are assessed. The standard ballooning theory is shown to break down as the shear is reduced, and the growth rate is shown to be an oscillatory function of n, the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure profile and the safety factor profile. When the shear is sufficiently weak, the oscillations can result in bands of unstable n-values, which are present even when the standard ballooning theory predicts complete stability. These instabilities are named 'infernal modes'. The occurrence of these instabilities at integer n is shown to be a sensitive function of the q-axis, raising the possibility of a sharp onset as the plasma parameters evolve.

Tokamak transport code simulations with drift wave models

Abstract: Simple models for the dissipative trapped electron, circulating electron and toroidal ion temperature gradient drift modes, together with the effect of low-m tearing mode islands, are incorporated into a standard tokamak transport code to study anomalous energy transport in tokamaks, primarily in the Doublet HI tokamak. In simulations of Doublet III in the Ohmic regime, low density neo-Alcator scaling is obtained. At high density the ion temperature gradient mode contributes strongly to the saturation of the energy confinement time. In the beam heating regime, the model predicts that the energy confinement time has weak density and magnetic field dependence, degradation with power and favourable current scaling. The generality of the drift wave model is further tested by simulating smaller tokamaks (ISX-A, Alcator A, Alcator C) as well as the largest tokamak, JET.

Characterization of tokamak edge turbulence by far-infrared laser scattering and Langmuir probes

Abstract: The spectra, magnitude and spatial distribution of low-frequency (ω ωci) density fluctuation have been measured by two independent experimental methods in the edge plasma of the TEXT tokamak. Good agreement between far-infrared laser scattering and Langmuir probe measurements has been achieved and the strengths of each technique are evaluated. Langmuir probes are used to directly determine the particle flux induced by edge fluctuations (Γ ∝ n×B) and collective Thomson scattering permits an extension of these observations to the plasma interior. Results are presented for typical discharge conditions in a tokamak.

Fast ion kinetics and fusion reaction mechanism in the plasma focus

Abstract: In a generalized beam-target model, the Gyrating Particle Model (GPM), the strong suprathermal fusion production of both dynamic phases of the plasma focus POSEIDON (W0 = 280 kJ, U0 = 60 kV, Mather type) is considered to be due to the fast accelerated deuterons gyrating in pinch structures. The results of this new model are compared with spectrally and spatially resolved measurements of fusion protons and accelerated deuterons, to give evidence of the validity of this generalized beam-target model for both phases. Statements are obtained on the number and distribution function of accelerated deuterons, necessary to explain the observed fusion yield.

The spectrum, spatial distribution and scaling of microturbulence in the TEXT tokamak

Abstract: Strong asymmetries in the spectrum and magnitude of low frequency (? ? ?ci) density fluctuations in the Texas Experimental Tokamak (TEXT) are described. Microturbulence is investigated under a variety of plasma parameters and a comparison with mixing length theory is made. Broadband fluctuations (??/? ? 1, ?k/k? ? 1.5, propagating in the electron diamagnetic drift direction) are observed throughout the plasma cross-section, but they peak at the limiter and possess a strong up-down asymmetry which inverts with reversal of plasma current direction. The spatial distribution of these fluctuations can be dramatically altered by the introduction of a point limiter. Inside the magnetic axis, a large-magnitude quasi-coherent fluctuation (??/? ? 0.2, ?k/k? ? 0.7, propagating in the electron diamagnetic drift direction) is seen to dominate the ubiquitous broadband microturbulence. This type of fluctuation peaks on the midplane. For high density discharges, a distinct ion mode (density fluctuations propagating in the ion diamagnetic drift direction) is observed in the microturbulence spectra. Onset of the ion feature occurs at plasma densities where a clear saturation is evident in the global energy confinement time.

Global particle confinement in the Texas Experimental Tokamak

Abstract: Particle transport in an ohmically heated tokamak plasma was investigated in the Texas Experimental Tokamak (TEXT). Spectroscopic measurements of the electron source were used with electron density measurements to derive particle confinement times from the continuity equation. Scalings were developed for particle confinement time with electron density, plasma current, toroidal field, and plasma positioning. Simultaneous measurement of electrostatic fluctuations with Langmuir probes may suggest a correlation between edge particle transport in TEXT and electrostatic turbulence. In addition, two major features of transport were isolated. First, transport is poloidally asymmetric at least in the plasma edge. Secondly, in some cases, the particle confinement scalings are closely associated with the scalings for recycling at particular surfaces. Similarities of the TEXT global particle confinement time scalings to those observed in other tokamaks may allow the conclusions of this work to be extended to other devices.

Poloidal asymmetries in the scrape-off layer plasma of the Alcator C tokamak

Abstract: Large poloidal asymmetries in density, electron temperature, radial density e-folding length and floating potential have been measured in the plasma existing between the limiter radius and the wall of the Alcator C tokamak. Typically, variations in density by factors of about 4–20 and variations in radial density e-folding length by factors of about 3–8 are recorded in discharges which are bounded by poloidally symmetric ring limiters. These poloidal asymmetries show that pressure is a function of poloidal angle on open magnetic flux surfaces in this region of the plasma. Observations of toroidally symmetric MARFE phenomena further imply that density and perhaps pressure are also a function of poloidal angle on closed flux surfaces existing just inside the limiter radius. The magnitude of these poloidal asymmetries and their dependence on poloidal angle persists independent of machine parameters (central plasma density, plasma current, toroidal field, MARFE versus non-MARFE discharges). Analysis of the data indicates that these asymmetries are caused by poloidal variations in perpendicular particle and heat transport in both the main plasma and the scrape-off layer. A number of possible asymmetric perpendicular transport processes in the scrape-off layer plasma are examined, including diffusion and × plasma convection.

Tokamak heat transport – a study of heat pulse propagation in JET

Abstract: The propagation of heat pulses originating from sawtooth activity in JET has been investigated in a series of limiter discharges with the following parameters: plasma current, Ip 3 MA, toroidal magnetic field, BT 3 T and elongation, κ = 1.45. The auxiliary power was varied such that the total power ranged from 2 to 13.5 MW. Electron temperature perturbations in a 20 cm region around a minor radius of r = (2/3)a were recorded with high time resolution, using a 12 channel electron cyclotron emission polychromator. From these measurements the electron heat diffusivity was derived. Over the whole range of powers considered, was found to be independent of power and to lie in the range of 2.5 ± 0.5 m2s−1. The quantity is compared to as derived from global power balance analysis. For Ohmic heating, the latter is lower than by a factor of 2.5. For increasing auxiliary power, approaches . A model for the dependence of the local χe n the temperature gradient is presented; it permits a unified description of the heat pulse behaviour, the deterioration of confinement and a certain degree of profile consistency. The model does not invoke non-local parameters such as the total power input. It is shown that the present heat pulse data, subject to this interpretation, contradict the τE scaling laws of the typical form τE ∝ P−0.5.

Direct drive cryogenic ICF capsules employing D-T wetted foam

Abstract: One roadblock to ICF (inertial confinement fusion) power production has been the difficulty of formation of thick, uniform cryogenic spherical shells of D-T at an acceptable cost and repetition rate. A new approach to this problem is proposed: the use of a small pore size, open cell, rigid foam structure as a sponge to precisely define the layer contours and to stabilize the liquid against gravitational slumping.

Modelling of temperature profiles and transport scaling in auxiliary heated tokamaks

Abstract: The temperature profiles produced by various heating profiles are calculated from local heat transport models. The models take the heat flux to be the sum of heat diffusion and a non-diffusive heat flow, consistent with local measurements of heat transport. Two models are developed analytically in detail: (i) a heat pinch or excess temperature gradient model with constant coefficients; and (ii) a non-linear heat diffusion coefficient (χ) model. Both models predict weak (≲20%) temperature profile responses to physically relevant changes in the heat deposition profile – primarily because the temperature profile is a double integral of the heating profile. The model predictions are shown to agree with JET data for a variety of heating profiles ranging from peaked on-axis through approximately flat (NBI at high density) to localized off-axis (ICRH). The modest temperature profile responses that result from the models clarify why temperature profiles in many tokamaks are often characterized as exhibiting a high degree of 'profile consistency'. Global transport scaling laws are also derived from the two models. The non-linear model with χ ∝ dT/dr produces a non-linear energy confinement time (L-mode) scaling with input power, . The constant heat pinch or excess temperature gradient model leads to the offset linear law for the total stored energy W with Pin, W = τinc Pin + W(0), which describes JET auxiliary heating data quite well. It also provides definitions for the incremental energy confinement time , the heating effectiveness η, and the energy offset W(0). Considering both the temperature profile responses and the global transport scaling, the constant heat pinch or excess temperature gradient model is found to best characterize the present JET data. Finally, new methods are proposed for interpreting auxiliary heating data in terms of these local transport models.

Magnetic separatrix experiments in JET

Abstract: Magnetic separatrix configurations have been produced in JET for plasma currents of up to 3 MA. Experimental results obtained with these configurations show that some features can be achieved that are common to divertor tokamaks. In Ohmic discharges, high recycling regimes can be produced. In neutral beam heated discharges, substantial improvement of the energy confinement time is achieved together with the characteristic signatures of an H-mode. These characteristics include improved particle confinement, flatter density profile, and an increase in electron temperature especially at the edge, leading to a characteristic pedestal feature. At higher neutral beam power, higher plasma densities are reached, with deterioration of beam penetration and strong radiation losses in the outer region of the plasma. The global energy confinement time in the H-mode is observed to degrade with additional power. However, results of radial power balance analysis suggest that in the central region, where the radiation is not important, the degradation of confinement is small.

Hot particle stabilization of ballooning modes in tokamaks

Abstract: The concept of energetic particle stabilization of ballooning modes in tokamaks is extended by considering numerically generated finite aspect ratio equilibria and attempting to simultaneously stabilize all flux surfaces against ballooning modes by suitable choice of a hot particle anisotropic pressure. To achieve access to the second stability regime at as low a beta value as possible, tokamaks with circular cross-section and an aspect ratio of ten are considered. Global stabilization of ballooning modes is demonstrated, even though the drift reversal constraint requires careful tailoring of the anisotropic pressure profile. A prescription for determining the optimum anisotropic pressure profiles for any equilibrium is provided.

Non-linear coupling effects on the relaxation process in the reversed field pinch

Abstract: The relaxation process in the reversed field pinch has been studied extensively with three-dimensional magnetohydrodynamic simulations. It is found that the non-linear coupling between multiple helicity modes plays a leading role in the relaxation process. Specifically, the (m; n)=(0; 1) island is excited as a result of non-linear coupling between the linearly unstable m=l modes, with a toroidal mode number difference of one. The m=0 island is then subject to axisymmetric non-linear reconnection whereby reversed flux is effectively generated in the outer region. It should be noted that although the axisymmetric non-linear reconnection of m=0 island is the dominant relaxation process, helical non-linear reconnection of linearly unstable m=l modes also plays some role in the relaxation of the whole system. It is also found that through this multiple helicity relaxation process, Taylor's minimum energy state is realized. The simulation results are generally consistent with experimental observations in the sustainment phase. This indicates that the multiple helicity relaxation process is of fundamental importance in the maintenance of the reversed field during the sustainment phase as well as in the self-reversal during the set-up phase. The relation between relaxation and aspect ratio has also been examined and it is found that the relaxation process is not strongly affected by the aspect ratio.

An algorithm for the calculation of three-dimensional ICRF fields in tokamak geometry

Abstract: A computational scheme is developed which permits tractable calculation of three-dimensional full-wave solutions to the Vlasov-Maxwell equations under typical ion cyclotron range of frequencies (ICRF) experimental conditions. The method is unique in that power deposition to the plasma is determined via the anti-Hermitian part of a truncated warm plasma dielectric operator, rather than as the result of an assumed phenomenological collision frequency. The resulting computer code allows arbitrary variation of density, temperature, magnetic field and minority concentration in the poloidal plane by performing a convolution of poloidal modes to produce a coupled system of differential equations in the radial variable. By assuming no inhomogeneity along the toroidal axis, an inverse transform over k|| is performed, yielding the global three-dimensional fast wave field solutions. The application of the code to TFTR-like plasmas shows a mild resonance structure in antenna loading related to the changing number of wavelengths between the antenna and the resonance layer.

Transport simulations of Ohmic TFTR experiments with microinstability based, profile consistent models for electron and ion thermal transport

Abstract: Transport simulations of ohmically heated TFTR experiments with recently developed microinstability based, profile consistent models for the anomalous thermal diffusivities, χe and χi, give good agreement with experimental data. The steady state temperature profiles and the total energy confinement times, τE, were found to agree for each of the Ohmic TFTR experiments simulated, including three high radiation cases and two plasmas fuelled by pellet injection. Both collisional and collisionless models are tested. The trapped electron drift wave microinstability model results are consistent with the thermal confinement of large plasma Ohmic experiments on TFTR. It is also found that transport due to the profile consistent model based on toroidal ion temperature gradient (ηi) mode transport can cause saturation in τE at the highest densities comparable to that observed on TFTR and equivalent to a neoclassical anomaly factor of three. Predictions based on stabilized ηi mode driven ion transport are found to be in agreement with the enhanced global energy confinement times for pellet fuelled plasmas.

Conditioning of the graphite bumper limiter for enhanced confinement discharges in TFTR

Abstract: A strong pumping effect was observed with plasma operation on the toroidal graphite bumper limiter in TFTR. The pumping effect was induced by conditioning the limiter with a short series (10-20) of low density deuterium or helium initiated discharges. The decay constant for gas fuelled Ohmic discharges was reduced from before conditioning to a minimum of after conditioning, which corresponds to a reduction in the global recycling coefficient from about 100% to less than 50%. Coincident with the low recycling conditions, low current neutral beam fuelled discharges showed global energy confinement times which were enhanced by a factor of two over the values obtained with an unconditioned limiter. Two models are proposed for the observed pumping effects: (1) a depletion model, based on pumping of hydrogenic species in the near-surface region of the limiter after depletion of the normally saturated surface layer by (carbon and helium) ion induced desorption; and (2) a co-deposition model, based on adsorption of hydrogenic species in carbon films formed by material sputtered from the limiter during conditioning.

Observation of hot electrons produced by second harmonic electron cyclotron heating in the axisymmetric tandem mirror GAMMA 10

Abstract: Microwave power, PECH ≤ 140 kW, has been injected at 28 GHz into the axisymmetric plug/barrier cell in the axisymmetrized tandem mirror GAMMA 10. As observed by soft X-ray measurements, the microwaves generate a hot (50-60 keV) electron population, radially peaked on the magnetic axis, which results in the formation of a thermal barrier. The production mechanism of these hot electrons is found to be second harmonic electron cyclotron heating (ECH), corrected for the effects of the relativistic mass variation and the Doppler shift. This mechanism also explains the first experimental observation of a saturation of the single-component hot electron temperature Teh as being caused by the finite width of the incident microwave lobe. The dependence of the plasma parameters on the filling gas pressure, the plasma density and the ECH power is studied. It is found that the heating process can be interpreted as a competition between electron acceleration by the incident wave, electron deceleration by collisions, and the mirror trapping efficiency of the source electrons for hot electrons. The axial profile of the soft X-rays is investigated in relation to the mechanism of the second harmonic ECH. The heating process is discussed in terms of the electron pitch angle and the magnetic field intensity.

Self-sustained oscillations in the divertor plasma

Abstract: A simple analytical model for a high recycling edge plasma, which relies on the presence of a small parameter – the ratio of the particle flows crossing the magnetic field to those impinging on the target – is proposed. The concept of a one-dimensional steady state (OSS) is introduced as a zero approximation in the small parameter. The mean number density of the particles – ions plus neutrals – in the magnetic flux tube is chosen as the most representative and convenient parameter of the problem. The OSS is shown to be ambiguous in a certain range for sufficiently high values of the energy flow entering the scrape-off layer from the bulk plasma. This ambiguity is confirmed by 1-D calculations. An equation describing quasi-steady variations in OSS is derived, and a mechanism of exciting self-sustained oscillations is developed. These oscillations are related to peculiarities of the neutral gas transport in the edge plasma and to the ambiguity of the OSS. The results of a 2-D simulation of the edge plasma oscillations are found to be in a good agreement with this mechanism, which might be responsible for the edge localized oscillations observed in H-mode divertor experiments.

Initial results from the Coaxial Slow Source FRC device

Abstract: The Coaxial Slow Source (CSS) is a device in which 'annular' FRCs, i.e. small aspect ratio, highly elongated plasmas with poloidal fields only, are formed in the annular space between concentric coils carrying toroidal currents. The device is constructed so that the plasma can be translated into a simple cylindrical chamber and re-formed as a true FRC. The goal of the investigation is to form FRCs on slow (diffusive) time-scales and at low voltage. Initial operation shows that the desired configurations are formed over a wide range of coil voltages and fill pressures. The radial plasma position can be controlled. Configuration lifetimes are 30-60 μs, with flux lifetimes of 15-20 μs. Flux is built up over 25 μs, at loop voltages of 1-2 kV, in comparison with 2.5 μs and 100 kV for comparably sized field reversed theta pinches conventionally employed for FRC generation.

Cross-effect on electron cyclotron and lower hybrid current drive in tokamak plasmas

Abstract: 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.

Stable AC tokamak discharges in the STOR-1M device

Abstract: Stable and clean AC tokamak discharges have been achieved in the STOR-1M device. The plasma current is reversed from +4.1 kA to −4.0 kA within 1.9 ms. During the reversal, no disruptive behaviour is observed, the loop voltage changes smoothly from +1 V to −5 V without any spike, and impurities are not released. An electron density of (2–4) × 1012 cm−3 is maintained during current reversal. The possibility of continuous tokamak operation with a low frequency alternating plasma current is discussed.

Stabilization of MHD modes in an axisymmetric plasma column through the use of a magnetic divertor

Abstract: The introduction of a magnetic limiter is proposed for stabilization of MHD interchange modes in the central cell of a tandem mirror. The magnetic limiter creates a ring null in the magnetic field, and electrons which enter the null can stream azimuthally and thereby 'short-circuit' m = 1 fluctuations. This disallows a rigid m = 1 response and introduces finite Larmor radius stabilization effects in much the same way as they appear for higher azimuthal modes. Some pressure gradient can be maintained on the separatrix flux surface by locating the null on a local magnetic maximum. This scheme introduces the possibility of a fully axisymmetric tandem mirror.

First results from the LIDAR Thomson Scattering System on JET

Abstract: The LIDAR Thomson Scattering System on the JET tokamak is described. Backscattering geometry and the time of flight method are employed to measure profiles along the major radius in the equatorial plane. First electron temperature profiles with a spatial resolution of better than 15 cm obtained with this new diagnostic technique are presented.

ICRF fundamental minority heating in inhomogeneous tokamak plasmas

Abstract: A theoretical model for the investigation of the ICRF fundamental minority plasma heating scheme in tokamak configurations is developed. The wave differential operator is obtained by including in a selfconsistent manner the effects of strong wave damping, linear mode conversion and a one-dimensional non-uniform equilibrium configuration. It is found that the use of a self-consistent equilibrium distribution function yields important modifications of the ICRF wave differential operator applicable to this heating regime. In particular, the paper presents a set of new terms which are resonant at the fundamental cyclotron frequency and which ensure the self-adjointness of the resulting wave operator in the limit k|| → 0. A numerical scheme is developed with which solutions for the ICRF electromagnetic field and the corresponding power deposition and energy flux profiles can be obtained. An extensive parametric study is carried out for a range of wave and plasma parameters illustrative of current and proposed JET operating regimes. The results are considerably different from those obtained using a WKB fast wave model. In particular, the 'full wave' model presented in this paper yields a percentage for the wave power absorbed by the ionic species which is much larger than the one predicted by the WKB theory. The model presented also shows that the majority species can absorb a much higher proportion of the incident wave power than previously reported. Finally, the results obtained for JET indicate that in the case of low magnetic field incidence a sizeable percentage of the launched wave energy can be reflected on the fast wave branch for values of k|| ≤ 6 m−1 and that at higher plasma temperatures electron heating becomes appreciable.

Impact of electron trapping on RF current drive in tokamaks

Abstract: Radiofrequency current drive in tokamak plasmas in the presence of trapped electrons is investigated. The appropriate response function, allowing the current drive efficiency, J/P, to be expressed by a simple analytical formula, is evaluated. It is shown that a significant degradation of the current generated away from the plasma axis is to be expected for methods relying on perpendicular diffusion only, even for appreciably high resonant parallel velocities.

Profile consistency on TFTR

Abstract: Electron heat transport on TFTR and other tokamaks is several orders of magnitude larger than neoclassical calculations predict. Despite considerable effort, there is still no clear theoretical understanding of this anomalous transport. The electron temperature profile, Te(r), has shown a marked consistency on many machines for a wide range of plasma parameters and heating profiles. This could be an important clue as to the process responsible for this enhanced thermal transport. In the first section of the paper the result is presented that TFTR electron temperature profile shapes are even more constrained than previous models of profile consistency suggested. The profile shapes, Te(r)/Te(a/2), are found to be invariant (for r > 0.4 a) for a wide range of parameters, including q(a). In the second section, an experiment is discussed which uses a fast current ramp to transiently decouple the current density profile, J(r), and the Te(r) profiles. From this experiment, it has been determined that the J(r) profile can be strongly modified with no measurable effect on the electron temperature profile shape. Thus, while the electron temperature profile is apparently constrained, the current profile is not.