ELMO Bumpy Torus Research Articles

An Overview of Tokamak Alternatives in the US Fusion Program with the Aim of Fostering Concept Innovation

The US fusion program has operated for just over 50 years, during which time the tokamak has emerged as the most promising vehicle for a burning plasma experiment. However, many other concepts have been built and investigated as alternatives (and possible improvements) to the tokamak, perhaps to make energy from fusion an economic reality sooner. This Paper is an overview of the conventional alternatives to the tokamak and a set of those that are not so conventional with the aim of fostering concept innovation. Usually the devices are grouped into magnetic, inertial, electrostatic, or other categories, with sub-categories. Here, the groupings of conventional- and non-conventional-alternatives are used too. The conventional alternatives are those devices that have been adopted as serious alternatives, and for which many references are immediately available (e.g. rfp, mirror, stellarator, spheromak, laser ICF, etc). The non-conventional alternatives comprise approaches that are not being currently investigated or are worth consideration. In this grouping lie ideas like impact fusion, muon catalyzed fusion, and many historical ones (like the Elmo Bumpy Torus). Several examples of the physics of non-conventional alternatives are presented in summary form as examples of skunkworks in the hope that others will take up the challenge of concept innovation.

A heavy ion beam probe for the Madison Symmetric Torus

A heavy ion beam probe (HIBP) is being developed for application on the Madison Symmetric Torus (MST). It will be used to make measurements of the plasma space potential Φ(r), fluctuations in potential Φ̃(r), the electron density ne(r), fluctuating electron density ñe(r), and radial electric field Er(r) from the core to the edge region of the plasma in MST. While information on these quantities can and has been obtained with probes inserted in the surface region, none of the above measurements have been made in the core of a hot reversed field pinch. Measurements of Φ(r), Er(r), and ne(r) have been well established in previous HIBP systems on tokamaks such as Impurities Studies Experiment, Texas Experimental Tokamak (TEXT), and TEXT Upgrade, stellarators such as Advanced Toroidal Facility and Compact Helical System and Bumpy Tori such as Elmo Bumpy Torus and Nagoya Bumpy Torus. Less well developed in terms of HIBP measurements are equilibrium and fluctuating magnetic fields. Because the confining field on MST is determined by plasma conditions, some effort has been made in the design of the MST beam probe to make it possible to characterize B before, during, and after the plasma discharge.

Parametric decay instability of an upper-hybrid wave in a two-temperature plasma

Parametric decay of an upper-hybrid pump into another upper-hybrid wave and a low-frequency lower-hybrid mode is considered in a two-electron temperature plasma. Expressions for the nonlinear dispersion relation and growth rate are obtained. It is found that the growth rate is quite sensitive to the hot-electron temperature and the density ratio of the hot and the cold components only when the side-band frequency is close to the second or third harmonic of the cyclotron frequency. The relevance of our investigation to Q machines and the ELMO bumpy torus is pointed out.

Temperature and density measurements in a non-axisymmetric, continuously operating fusion experiment using a heavy ion beam probe

Two-dimensional electron temperature and density data have been obtained in the midplane of the non-axisymmetric magnetic confinement device ELMO Bumpy Torus (EBT) through the use of a heavy ion beam probe. This beam probe differs from others operated on toroidal or open magnetic geometries in its combination of complete computer control with the steady-state nature of EBT which allows, under normal operating conditions, for extensive calibration of the system in situ, minimizing both alignment and acquisition errors, along with the use of synchronous detection to dramatically improve the quality of the detected signal over what is typically possible in fast pulse devices. These techniques are important and applicable to long pulse devices where the beam probe may be an ideal diagnostic to measure, for example, parameters of the edge plasma. While the EBT beam probe was implemented to obtain profiles of plasma space potential, we have found that it can also be used effectively to measure the temperature and density profiles in the midplane between magnetic field coils. The data obtained support the contention that the formation of a hollow temperature profile in the T-Mode sufficiently inverts the plasma pressure such that stability of the core plasma would be expected even without diamagnetic effects from the hot electron rings which have previously been considered essential.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A short history of heavy ion beam probing

The author describes some aspects of research on controlled thermonuclear fusion as an energy source, starting in the late 1950s. There was a need for new diagnostic techniques for studying high temperature plasmas. The author proposed a diagnostic for measuring plasma density by probing a deuterium plasma with a deuterium beam and measuring the proton production from the D-D nuclear reaction. By the mid 1960s, it was possible to do so. After carrying out a D-D measurement, the author suggested switching over to an H/sub 2//sup +/ beam and looking for an H/sup +/ signal. The H+ was loud and clear and that was the last of the nuclear measurements. One of the first things done using the molecular break-up of the H/sub 2//sup +/ to measure the density of the hollow cathode arc plasma was a study of a coherent instability. The frequency response wasn't sufficient to measure the instability directly, so a Langmuir probe was used to detect the instability. The Langmuir probe gave a signal from a fixed spatial location but the beam probe signal was swept across the plasma giving 2D spatial resolution. This was the first detailed mapping of a plasma instability. Attempts to apply the ion beam probe to measuring the plasma current density in the ST Tokamak are described. Heavy ion beam probing measurements using hollow cathode arcs as target plasmas made it possible to measure T/sub e/ at low temperatures and to identify space potential fluctuations. Installation of a beam probe on the Laser Initiated Target Experiment are described, along with work on the ELMO Bumpy Torus, the VERSATOR Tokamak, TMX, TEXT, ISX-B, the Ergodic Magnetic Limiter and ATF.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modulational and filamentation instabilities in ELMO bumpy torus

An analytical investigation of modulational and filamentation instabilities of an upper-hybrid wave due to electron-acoustic density perturbations in a two-electron temperature plasma has been made. A hydrodynamical model of the plasma is used. Nonlinear dispersion relation and growth rates are calculated. As an application of the investigation, the variation of the growth rate with the concentration ratio of hot to cold electrons, temperature ratio (Tc/Th) and magnetic field for typical parameters of laser-plasma interaction in ELMO bumpy torus is studied and is shown graphically.

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Parametric decay in a two-electron-temperature plasma

Nonlinear decay of an ordinary electromagnetic pump wave into an electro-acoustic wave and an upper-hybrid wave in a two-electron-temperature plasma has been investigated analytically. In contrast with the work of Sharma, Ramamurthy &amp; Yu (1984), it is found that the decay can take place in the absence of the restrictive condition Ti ≫ Te and the plasma be magnetized. Using a hydrodynamical model of the plasma, the nonlinear dispersion relation and growth rate are obtained. A comparison of the present investigation is made with earlier work, and its possible application to the ELMO bumpy torus is discussed.

Drift loss transport driven by radiofrequency heating

Synergetic effects involving transport and radiofrequency (RF) heating in fusion confinement devices are important if regions of phase space that contain poorly confined particles are populated by the use of auxiliary heating. Such poorly confined particles include ripple trapped particles in tokamaks and stellarators or transitional and high energy passing particles in bumpy tori. A two-dimensional, steady state Fokker-Planck code has been developed to study the interaction of these processes and it has been used to model the Elmo Bumpy Torus (EBT). Accurate modelling of the RF absorption profile in real space is shown to be of critical importance for the simulation of EBT, and a comparison of the results of the model with experimental data shows very good agreement. Extension of the model to closed-field-line configurations with straight ‘bumpy’ sections connected with high magnetic field corners shows reduced synergetic effects and greatly improved performance compared with bumpy tori.

Summary of ELMO Bumpy Torus (EBT-S) experiments from 1982 to 1984

Experiments were conducted in the ELMO Bumpy Torus (EBT) from 1973 until 1984. A number of papers have been published concerning various aspects of experiments during the final two years of operation. The paper summarizes the final experimental conclusions and discusses those issues which remain unresolved. The main conclusions are as follows: (1) measurements of the width of the hot electron rings showed them to be wider than previously suspected, diluting their diamagnetism and negating their ability to locally reverse the magnetic field gradient; (2) two-dimensional plots of the plasma potential revealed open potential contours in the C-mode and closed potential contours near the plasma centre in the T-mode; (3) an in–out asymmetry in the plasma potential was always observed, giving rise to electric fields which drove convective plasma loss.

Far-infrared scattering experiment on a bumpy torus

A far-infrared scattering experiment was installed on the ELMO bumpy torus experiment at Oak Ridge National Laboratory [Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Vienna, 1975), Vol. II, p. 141]. The design allowed for coupled scanning of spatial and wave vector parameters while recording the frequency spectrum. Coherent waves and incoherent density fluctuations were observed for varying plasma conditions. Also, coherent waves were recorded in conjunction with ion cyclotron heating fast wave heating experiments, which demonstrated fast wave penetration into the plasma and ion-Bernstein wave conversion between harmonic zones.

Electron bounce resonance heating by r.f. waves in a bumpy cylinder

In bumpy cylinder geometry, electrons are classified into trapped and passing particles. The interaction between a wave near the electron bounce frequency and the electrons is studied both numerically and analytically. It is shown that coupling of the waves to the electron bounce motion parallel to the magnetic field can lead to heating of those electrons near the passing/trapped boundary in velocity space. The stochastic threshold condition is eE0k0/m omega b2 approximately=0.1, which is an order lower than the quadratic magnetic well results. For this mechanism, the wave energy density required to induce stochastic heating in the ELMO Bumpy Torus (EBT) by radio frequency (in the frequency range of ion cyclotron resonance heating) is about an order of magnitude more than that estimated on the basis of cold plasma wave theory. However, it is suggested that the bounce resonance can enhance the electron cyclotron resonance heating efficiency in an EBT-like heating scheme.

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Convective contributions to local power loss in a bumpy torus

Power flow in the ELMO Bumpy Torus [Plasma Physics and Controlled Nuclear Fusion Research, 1974, Tokyo (IAEA, Vienna, 1975), Vol. 2, p. 141; Plasma Phys. 25, 597 (1983)] was investigated by measuring the power received by a limiter. This power was found to be a small fraction of the gyrotron output power (in one case, 13 out of 100 kW). To investigate the reason for the small fraction that appeared on the limiter, power was selectively removed from various cavities, including the cavity containing the limiter. These experiments have demonstrated that the majority of the power is lost locally. Observations of the potential structure demonstrate that asymmetric potential contours are present that can lead to enhanced plasma loss.

Coupled model of wave damping, quasilinear heating, and radial transport applied to bumpy tori.

A simple Fokker-Planck model of rf heating is presented which includes quasilinear velocity diffusion, collisions, and particle transport by radial collisional diffusion and direct-drift losses. In addition, the influence of the incident-wave electric-field spatial profile on the velocity-space structure of the quasilinear operator and, in turn, the effect of the nonlinear distribution function on the wave field are included. Application is made to electron-cyclotron heating in the Elmo bumpy torus.

Monte Carlo estimates of particle and energy confinement times in a bumpy torus and a bumpy square with poloidal electric fields

Since significant poloidal structure in the electrostatic potential in Elmo Bumpy Torus (EBT) has been observed experimentally [Phys. Fluids 28, 2848 (1985)] and predicted theoretically (C. L. Hedrick, submitted to Phys. Fluids), a Monte Carlo calculation has been used to make estimates of the particle and energy confinement times in EBT with varying degrees of asymmetry in the electric field. The code is applicable to the bulk ion population and the ‘‘cool’’ electron population in EBT, but not to the intermediate-energy electrons believed to be responsible for the formation of the potential. A similar calculation is possible for an alternate magnetic field configuration known as a bumpy square, which is expected to have more symmetric potential profiles because of much better centering of the particle orbits. The calculations indicate that the confinement time in a bumpy square would be two to three orders of magnitude better than in EBT.

Poloidally asymmetric electrostatic potentials in closed line bumpy toroids

Here an analytic expression is developed for the poloidal asymmetry in the electrostatic potential observed experimentally in the T mode of operation in the Elmo Bumpy Torus (EBT) [Phys. Fluids 28, 2848 (1985)]. A multiple fluid treatment for the ‘‘cool,’’ ‘‘warm,’’ and ‘‘hot’’ electrons is used. The central idea is that the ‘‘warm’’ electrons dominate both the radial and poloidal structure of the electrostatic potential in the T mode of operation. The expression for the poloidal asymmetry in the electrostatic potential, which agrees reasonably well with experiment, is also applied to a modification of the EBT magnetic configuration. It is found that a substantial reduction in the asymmetry of the electrostatic potential below that of the Elmo Bumpy Torus is possible in the modification of the EBT magnetic configuration.

Effect of electric fields and fluctuations on confinement in a bumpy torus

In order to understand the relationships between confinement and space potential (electric field) and between confinement and density fluctuations, plasma parameters in the ELMO Bumpy Torus Scale (EBT-S)[in Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Tokyo, 1974), Vol. 2, p. 141; Plasma Phys. 25, 597 (1983)] have been measured systematically for a wide range of operating conditions. Present EBT plasma parameters do not show a strong dependence on the potential profile, but rather exhibit a correlation with the fluctuations. The plasma pressure profile is found to be consistent with the profile anticipated on the basis of the flute stability criterion for a marginally stable plasma. For a heating power of 100 kW, the stored energy density is found to be restricted to the range between 4.5×1013 eV-cm−3 and 7×1013 eV-cm−3. The lower limit remains constant regardless of heating power and pertains to plasmas lacking an equilibrium and/or stability. The upper limit increases with heating power and is found to result from the onset of instabilities. In between the two limits is a plasma that is in an equilibrium state and is marginally stable. Operational trajectories exist that take the EBT plasma from one limit to the other.

The Role of Alpha Particles in the Dynamics of Ring-Stabilized Devices

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.