Magnetic Confinement Systems Research Articles

Alfvén mode stability and wave–particle interaction in the JET tokamak: prospects for scenario development and control schemes in burning plasma experiments**Based on an invited talk given at the 8th International Atomic Energy Agency Technical Meeting on Energetic Particles in Magnetic Confinement Systems San Diego, USA, 6–8 October 2003.

We have investigated the effect of different ion cyclotron resonance frequency (ICRF) heating schemes, of error field modes, of the plasma shape and edge magnetic shear, and of the ion ∇B drift direction on the stability of Alfvén eigenmodes (AEs). The use of multi-frequency or 2nd harmonic minority ICRF heating at high plasma density gives rise to a lower fast ion pressure gradient in the plasma core and to a reduced mode activity in the Alfvén frequency range. Externally excited low-amplitude error fields lead to a much larger AE instability threshold, which we attribute to a moderate radial redistribution of the fast ions. The edge plasma shape has a clear stabilizing effect on high-n, radially localized AEs. The damping rate of n = 1 toroidal AEs is a factor 3 higher when the ion ∇B drift is directed towards the divertor. These results represent a useful step towards the extrapolation of current scenarios to the inclusion of fusion-born alpha particles in ITER, with possible application for feedback control schemes for the various ITER operating regimes.

Fast ion absorption of the high harmonic fast wave in the National Spherical Torus Experiment

Ion absorption of the high harmonic fast wave in a spherical torus [Y.-K. M. Peng et al., Nucl. Fusion 26, 769 (1986)] is of critical importance to assessing the viability of the wave as a means of heating and driving current. Analysis of recent National Spherical Torus Experiment [M. Ono et al., Nucl. Fusion 40, 557 (2000)] shots has revealed that under some conditions when neutral beam and rf power are injected into the plasma simultaneously, a fast ion population with energy above the beam injection energy is sustained by the wave. In agreement with modeling, these experiments find the rf-induced fast ion tail strength and neutron rate at lower B-fields to be less enhanced, likely due to a larger β profile, which promotes greater off-axis absorption where the fast ion population is small. Ion loss codes find the increased loss fraction with decreased B insufficient to account for the changes in tail strength, providing further evidence that this is a rf interaction effect. Though greater ion absorption is predicted with lower k∥, surprisingly little variation in the tail was observed, along with a neutron rate enhancement with higher k∥. Data from the neutral particle analyzer, neutron detectors, x-ray crystal spectrometer, and Thomson scattering are presented, along with results from the TRANSP [R. J. Hawryluk, Physics of Plasmas Close to Thermonuclear Conditions 1, 19 (1981); J. P. H. E. Ongena et al., Fusion Technol. 33, 181 (1998)] transport analysis code, ray-tracing codes HPRT [J. Menard et al., Phys. Plasmas 6, 2002 (1999)], and CURRAY [T. K. Mau et al., RF Power in Plasmas: 13th Topical Conference (1999), p. 148], full-wave code AORSA [E. F. Jaeger et al., RF Power in Plasmas: 14th Topical Conference, 2001, p. 369], quasilinear code CQL3D [R. W. Harvey et al., in Proceedings of the IAEA TCM on Advances in Simulation and Modeling of Thermonuclear Plasmas, 1992], and ion loss codes EIGOL [D. S. Darrow et al., in Proceedings of the 6th IAEA TCM on Energetic Particles in Magnetic Confinement Systems, 2000, p. 109] and CONBEAM [J. Egedal et al., Phys. Plasmas 10, 2372 (2003)].

Recent Progress in Magnetic Measurement

This article presents recent progress in magnetic measurements of magnetic confinement systems. “Signal drift” in the integrator for magnetic measurements is one of the major problems for plasma control and the estimation of equilibrium parameters in long-pulse operation. In addition, the durability of sensors such as a magnetic probe, a flux loop, etc., under fusion neutron irradiation environments is also important. The present status of the developments of a long-pulse integrator and a new magnetic sensor are reported.

Studies of fluctuations in the high-temperature plasma of modern stellarators by the microwave scattering technique

Microwave scattering diagnostics are described that allow direct measurements of the turbulent processes in the high-temperature plasma of magnetic confinement systems. The first physical results are presented from fluctuation measurements carried out in 2000–2001 in three stellarators: L-2M (Institute of General Physics, Moscow), LHD (National Institute of Fusion Science, Toki), and TJ-II (CIEMAT, Madrid). Plasma density fluctuations in the axial (heating) regions of the L-2M and LHD stellarators were measured from microwave scattering at the fundamental harmonic of the heating gyrotron radiation. In the TJ-II stellarator, a separate 2-mm microwave source was used to produce a probing beam; the measurements were performed at the middle of the plasma radius. Characteristic features of fluctuations, common for all three devices, are revealed by the methods of statistical and spectral analysis. These features are the wide frequency Fourier and wavelet spectra, autocorrelation functions with slowly decreasing tails, and non-Gaussian probability distributions of the magnitudes and the increments in the magnitude of fluctuations. Observations showed the high level of coherence between turbulent fluctuations in the central region and at the edge of the L-2M plasma. The drift-dissipative instability and the instability driven by trapped electrons are examined as possible sources of turbulence in a high-temperature plasma.

Relaxation of plasma rotation in toroidal magnetic confinement systems

A study is made of the relaxation of plasma rotation in nonaxisymmetric toroidal magnetic confinement systems, such as stellarators and rippled tokamaks. In this way, a solution to the drift kinetic equation is obtained that explicitly takes into account the time dependence of the distribution function, and expressions for the diffusive particle fluxes and longitudinal viscosity are derived that make it possible to write a closed set of equations describing the time evolution of the ambipolar electric field E and the longitudinal (with respect to the magnetic field) plasma velocity U0. Solutions found to the set of evolutionary equations imply that the relaxation of these two parameters to their steady-state values occurs in the form of damped oscillations whose frequency is about 2vT/R (where vT is the ion thermal velocity and R is the major plasma radius) and whose damping rate depends on the ion-ion collision frequency and on the magnetic field parameters. In particular, it is shown that, for tokamaks with a slightly rippled longitudinal magnetic field, the frequency of oscillations in the range q>2 (where q is the safety factor) is, as a rule, much higher than the damping rate. For stellarators, this turns out to be true only of the central plasma region, where the helical ripple amplitude ɛ of the magnetic field is much smaller than the toroidal ripple amplitude δ=r/R.

Pulsed time-of-flight refractometry measurements of the electron density in the T-11M tokamak

A new method for measuring the plasma density in magnetic confinement systems—pulsed time-of-flight refractometry—is developed and tested experimentally in the T-11M tokamak. The method is based on the measurements of the time delay of short (with a duration of several nanoseconds) microwave pulses propagating through the plasma. When the probing frequency is much higher than the plasma frequency, the measured delay in the propagation time is proportional to the line-averaged electron density regardless of the density profile. A key problem in such measurements is the short time delay of the pulse in the plasma (∼1 ns or less for small devices) and, consequently, low accuracy of the measurements of the average density. Various methods for improving the accuracy of such measurements are proposed and implemented in the T-11M experiments. The measurements of the line-averaged density in the T-11M tokamak in the low-density plasma regime are performed. The results obtained agree satisfactorily with interferometric data. The measurement errors are analyzed, and the possibility of using this technique to measure the electron density profile and the position of the plasma column is discussed.

Conference Summary: Energetic particles in magnetic confinement systems

Report on the 7th IAEA Technical Committee Meeting held at the Scandic Hotel Opalen, Gothenburg, Sweden, 8-11 October 2001

Physical nature of the electric current produced by the asymmetry of particle motion in toroidal magnetic confinement systems

A new type of longitudinal electric current is revealed by analyzing the drift trajectories of charged particles in a tokamak—the current that may be referred to as the asymmetry current because it is associated with the asymmetry of the boundary between trapped and transit particles in phase space. The generation of this current is explained by the fact that the motions of the particles that cross the magnetic surface at a given point in opposite directions are qualitatively different. The asymmetry current results from the toroidal variations of the magnetic field and is maintained by the radial momentum flux of transit particles. The contribution of the particles of different species to the asymmetry current density is proportional to their pressure, is independent of the gradients of the plasma parameters, is maximum at the magnetic axis, and decreases toward the plasma periphery. In contrast to standard neoclassical theory, the asymmetry current can be found only from exact particle trajectories. The asymmetry current is calculated for tokamaks with differently shaped magnetic surfaces and for a model stellarator. By exploiting the newly revealed asymmetry current, together with the bootstrap current, it may be possible to substantially simplify the problem of creating a tokamak reactor.

Some theoretical problems of the toroidal plasma equilibrium

Two problems of toroidal magnetic plasma confinement systems are considered. The first one is connected with advanced helical systems. The peculiarity of geometry of these stellarator systems with the improved confinement is discussed. Some additional ways for further optimization are marked too. The second problem is concerned with the island structure in toroidal systems. From the very beginning, the theoretical research on plasma equilibrium in stellarators was based mainly on the assumption that the toroidal magnetic surfaces are nested. It means that there is a unique magnetic axis which serves as the edge of the azimuthal coordinate surface θ = const. To avoid the difficulties with such a coordinate in the case of many magnetic axes that result from islands, the tokamak-like representation of the magnetic field B which does not use the coordinate θ is proposed.

Plasma convection near the threshold for MHD instability in nonparaxial magnetic confinement systems

Using a highly nonparaxial magnetic confinement system with an internal levitated ring as an example, it is shown that, in a plasma near the threshold for ideal MHD instability, the external heating and the original local dissipative processes may give rise to and maintain self-consistent nonlinear MHD convection, which leads to an essentially nonlocal, enhanced heat transport. A closed set of equations is derived that makes it possible to describe such convective processes in a weakly dissipative plasma with β∼1. Numerical simulations carried out with a specially devised computer code demonstrate that the quasisteady regime of nonlinear convection actually exists and that the marginally stable profile of the plasma pressure is maintained. A large amount of data on the structure of the nascent convective flows is obtained and analyzed.

Electromagnetic oscillations near the critical surface in a magnetized plasma

It is shown that, in a plasma whose density varies across the magnetic field lines, electromagnetic oscillations that are localized near the critical surface can exist. Such oscillations can be excited spontaneously in a nonequilibrium plasma of closed magnetic confinement systems.

Advanced Particle Simulation of Open-Field Plasmas in Magnetic Confinement Systems

Particle simulation of open-field plasmas in magnetic confinement systems is required to validate various physics models introduced to fluid simulations. An advanced particle simulation code PARASOL was developed, in which a binary collision model is incorporated to an electrostatic particle-in-cell (PIC) method. The simulation model is described in detail. Boundary conditions at the sheath entrance obtained by PARASOL simulations are shown. Effects of E×B drift, diffusive loss, and radiative cooling are studied. Heat transport along magnetic field is also investigated.

Summary of Workshop on Future Directions in Theory of 3D Magnetic Confinement Systems

A workshop on Future Directions in Theory of 3D Magnetic Confinement Systems was held in Oak Ridge, Tennessee on January 7–9, 2002. The broad objectives of the workshop were: to have a scientific exchange on issues and opportunities for theory of 3D confinement systems and to identify crucial issues not presently being adequately addressed; to provide a forum for the experimental programs to communicate needs and priorities to the theory community; to draw in researchers not traditionally associated with stellarators; and, finally, to stimulate the formation of collaborations and possible new initiatives. The workshop was organized around seven topical sessions: input from experimental programs, MHD, confinement, modeling and diagnostics, wave propagation and RF applications, optimization, and edge physics modeling. The workshop attracted a wide cross section of U.S. fusion researchers, totaling 38 attendees from four laboratories and seven universities.

Electrostatic plasma turbulence and spitzer longitudinal conductivity in tokamaks

An analysis has revealed that there may be three radically different steady states of a tokamak plasma: (i) discharges in which the electron and ion transport can be described by neoclassical theory; (ii) discharges with the Spitzer longitudinal conductivity, neoclassical ion transport, and “anomalous” electron transport; and (iii) discharges in which the electron transport and ion transport are both “anomalous.” The dimensionless parameters responsible for the occurrence of the three types of discharges are determined. In accordance with the criteria derived for the achievement of different steady states, discharges of the second type are most typical of modern tokamaks and discharges of the third type can occur only if the turbulence is sufficiently strong. Discharges of the first type cannot occur in the range of the working parameters of present-day tokamaks and future tokamak reactors, but they can be ignited in a large class of magnetic confinement systems. The physical reason for the onset of different types of discharges is associated with the fact that turbulent fluctuations play very different roles in the dynamics of the ion and electron components of a finite-size magnetized plasma. The question of the self-consistency between the profiles is considered. A law is derived according to which the thermal diffusivity increases toward the plasma edge.

Energetic particles in magnetic confinement systems

Report on the 6th IAEA Technical Committee Meeting held at Naka-machi, Naka-gun, Ibaraki, Japan 12-14 October 1999

Anderson-localized ballooning modes in general toroidal plasmas

Ballooning instabilities are investigated in three-dimensional magnetic toroidal plasma confinement systems with low global magnetic shear. The lack of any continuous symmetry in the plasma equilibrium can lead to these modes being localized along the field lines by a process similar to Anderson localization. This produces a multibranched local eigenvalue dependence, where each branch corresponds to a different unit cell of the extended covering space in which the eigenfunction peak resides. These phenomena are illustrated numerically for the three-field-period heliac H-1 [S. M. Hamberger et al., Fusion Technol. 17, 123 (1990)], and contrasted with an axisymmetric s-α tokamak model. The localization allows a perturbative expansion about zero shear, enabling the effects of shear to be investigated.

Three-dimensional reduced drift kinetic equation for neoclassical transport of helical plasmas in the ultralow collisionality regime

Based on the original five-dimensional drift kinetic equation, a three-dimensional reduced drift kinetic equation has been obtained to describe the neoclassical transport of helical plasmas in the ultralow collisionality regime, where the collision frequency is much lower than the poloidal bounce frequency of the superbanana particles. The reduced drift kinetic equation describes the evolution of the distribution function in terms of three constants of motion as independent variables. This reduced drift kinetic equation is suitable for studying the collisional transport of fast ions in helical magnetic confinement systems, since it includes the effects of finite superbanana width and finite aspect ratio, and it includes the collisional slowing-down and energy-scattering terms in addition to the pitch-angle-scattering term.

Prospects for attractive fusion power systems

As one of the alternative sources of energy for the future, fusion power must demonstrate that it can be a safe, clean and economically attractive option in a diverse and competitive energy marketplace. Conceptual power-plant design studies for both magnetic– and inertial–confinement approaches allows one to translate commercial requirements into design features that must be met if fusion is to play a role in the world9s energy mix. As a new technology in the energy marketplace, fusion must have advantages to offset the inherent technical risk of a new technology in order to be accepted. Fusion electricity should have a competitive cost and fusion power plants should achieve a high degree of availability and reliability. Realization of the full safety and environmental potential of fusion will help fusion to achieve a large advantage over other sources of electricity. Progress in the physics of the magnetic fusion power plant, technology and design is described for tokamaks and alternative magnetic–confinement systems. Recent research in this area shows that potential safety and environmental attributes of fusion can be realized by using low–activation material and care in design. The projected economic prospects show that fusion will be capital intensive and the trends are towards higher power density and higher–performance systems in order to enhance the economic competitiveness of fusion. In addition, alternative confinement approaches may offer substantial economic and operational benefits, although their physics basis is much less developed. Fusion power technologies are far less advanced than plasma technologies, since the latter have evolved in conjunction with large fusion experiments. And yet the design, material choices and performance of plasma–facing and nuclear components are the dominant factors in arriving at an attractive power plant. Fusion power technologies are reviewed, and the R and D needed will be assessed in the context of the world9s existing programmes.

The physics of spherical confinement systems

Spherical torus magnetic confinement systems, covering spheromaks and spherical tokamaks (STs), are reviewed. As well as being potentially very important for fusion, spherical tori research is enhancing our understanding of magnetic confinement systems with wider applications than fusion research. The studies contribute to the conventional tokamak, for example, ITER via a range of scalings, as well as to our understanding of `quiescent' plasmas and those subject to `turbulent magnetohydrodynamic (MHD) relaxation'. The theoretical and experimental properties are described, showing how these vary with configuration and contrasting them with the conventional aspect ratio tokamak. Topics covered include equilibrium, refuelling, helicity injection, influence of trapped particle fraction, plasma heating, confinement, stability (including pressure limits and energetic particle instabilities) and disruption resilience.

Mirror-Based Fusion: Some Possible New Directions

This paper examines some possible areas for the study of new approaches to fusion research, ones that employ magnetic confinement systems based on open-ended field topology and employing the magnetic mirror principle. In the spirit of encouraging a wider look at possibilities, some unconventional approaches are suggested. These approaches, involving long linear systems having ion injectors and direct converters at their ends, attempt to exploit some inherent advantages of open-ended systems for fusion. The results of analysis, calculations and preliminary cost estimates for long linear systems of this type that utilize the magnetic mirror effect to achieve their operating regimes will be presented. The approaches suggested, when examined in greater depth, may not stand the test of time, but they might encourage thinking in new areas.