ELMO Bumpy Torus-Scale Research Articles

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.

A comparative measurement of the neutral density and particle confinement time in EBT-S

The neutral density and particle confinement time in the ELMO Bumpy Torus-Scale Experiment (EBT-S) have been determined by two different techniques. These involve a spectroscopic measurement of molecular and atomic hydrogen emissions and a time-decay measurement of a fast-ion population using a diagnostic neutral beam. The results from both diagnostics exhibit identical trends for either estimate, although the absolute values differ by a factor of 2 to 3. The observed variations with fill gas pressure and microwave power from either technique are consistent with measurements of electron density and temperature. In this paper, the measurement techniques are discussed, and the results are compared in the context of consistency with independently observed plasma behaviour.

Stochastic particle diffusion in velocity space for a bumpy torus

Nonadiabatic changes of the magnetic moment μ in the ELMO Bumpy Torus-Scale (EBT-S) have been studied both analytically and numerically. Simple forms of Δ μ and gyrophase change were obtained, permitting the changes in these quantities to be studied using an iteration mapping. The mapping results show stochastic behavior for particles having high energy and low initial μ. Otherwise, superadiabatic motion appears. The stochastic diffusion coefficient for the variation of μ was measured numerically by mapping and was also calculated from quasilinear theory. The results are shown to agree well in the stochastic region. For high-energy particles, the diffusion in μ caused by nonadiabaticity can be comparable to collisional diffusion when stochastic motion occurs for EBT-S.

Electron temperature measurements from induced toroidal current in ELMO Bumpy Torus-Scale

We have carried out measurements on ELMO Bumpy Torus Scale (EBT-S) to estimate the electron temperature of the toroidal plasma by inducing a small (∼2 A) fluctuating (5 Hz) ac toroidal current. The modulating frequency used is low enough to minimize the effects of cavity skin time (∼100 ms) and plasma inductance. We have calculated the temperature from the measured values of the current obtained by use of the Rogowsky loop at various fill pressures at 100 kW with 28-GHz operation. The electron temperature has been estimated to be around 80–90 eV with an error of about 10%–25% in the low T mode, which is in good agreement with the Thomson scattering measurements.

Thomson scattering at plasma densities below 1012 cm−3

Major upgrades in the ruby-laser Thomson scattering system on the microwave-driven ELMO Bumpy Torus-Scale plasma have enabled routine and reliable measurements of the electron temperature and density along a plasma radius. Consisting of both signal-to-noise enhancement techniques and refined data handling procedures, these upgrades allow density determinations down to 2×1011 cm−3. Radial profiles of bulk electron parameters are essentially flat across the core plasma. Evidence is presented for a 1011-cm−3 density suprathermal distribution of electrons, which leads to an understanding of contradictory temperature measurements and of energy flow in the plasma.

Radial structure of curvature-driven instabilities in a hot-electron plasma

A nonlocal analysis of curvature-driven instabilities for a hot-electron ring interacting with a warm background plasma has been made. Four different instability modes characteristic of hot-electron plasmas have been examined: the high-frequency hot-electron interchange (at frequencies larger than the ion-cyclotron frequency), the compressional Alfvén instability, the interacting background pressure-driven interchange, and the conventional hot-electron interchange (at frequencies below the ion-cyclotron frequency). The decoupling condition between core and hot-electron plasmas has also been examined, and its influence on the background and hot-electron interchange stability boundaries has been studied. The assumed equilibrium plasma profiles and resulting radial mode structure differ somewhat from those used in previous local analytic estimates; however, when the analysis is calibrated to the appropriate effective radial wavelength of the nonlocal calculation, reasonable agreement is obtained. Comparison with recent experimental measurements indicates that certain of these modes may play a role in establishing operating boundaries for the ELMO Bumpy Torus-Scale (EBT-S) experiment. The calculations given here indicate the necessity of having core plasma outside the ring to prevent the destabilizing wave resonance of the precessional mode with a cold plasma.

Ion heating and axially evanescent modes in rf experiments on bumpy tori and other toroidal devices

A fluid model including quasilinear heating, collisions, charge exchange, and spatial transport is used to determine the perpendicular wavenumbers and electric fields which can permit appreciable coupling of rf waves to the ions in ELMO Bumpy Torus-Scale (EBT-S) plasmas. The observed significant ion heating at frequencies above the first harmonic ion-cyclotron frequency in EBT-S is consistent with a quasilinear heating model if rf wave amplitudes vary on a spatial scale which is much smaller than the inverse wavenumber for propagating, cold-plasma waves in the WKB approximation. It is shown that axially evanescent modes could account for the necessary, short perpendicular wavelengths. In general, axially evanescent modes could be a powerful means for heating ions at harmonics of the ion-cyclotron frequency. Charge exchange and transport are the dominant loss mechanisms acting on ions and preclude strong collisional coupling of ion tails or minority ion species to the bulk distribution of the majority ion species in EBT-S. This is true even if the applied rf frequency is comparable to the ion-cyclotron frequency of the minority ion species.

Plasma properties in the ELMO bumpy torus

Experiments with 200 kW of applied electron cyclotron heating (ECH) power have demonstrated electron temperatures of about 1 keV in the ELMO Bumpy Torus-Scale (EBT-S) device. Electron densities are in the range of (0.5-1.5)*1018 m-3 and increase as the square root of the applied ECH power. A potential well is present, and its depth in V closely follows the electron temperature expressed in electron volts. Only low charge states of impurities are found, and Zeff approximately=1.0. Data from the electrons can be compared with simple scaling laws when scale lengths are held constant. These comparisons indicate that electron densities, temperatures, and confinement times scale according to neoclassical expectations.

Inhomogeneity effects on wave properties in Elmo Bumpy Torus-Scale

In many plasma-magnetic-field configurations, the ion skin depth is comparable to magnetic field and density-gradient scale lengths and so inhomogeneity must play an important role for wave propagation in the ion-cyclotron range of frequencies. As an example, we consider ion-cyclotron heating in the Elmo Bumpy Torus-Scale (EBT-S) device, where the coupling of infinite and homogeneous fast and slow modes implies that fundamental ion-cyclotron heating can occur even if the waves launched are fast waves (which otherwise do not heat at the fundamental). We also show that singular, weakly damped, two-ion hybrid electrostatic solutions of the cold-plasma dispersion relation which include inhomogeneities are not consistent with the small ion-gyroradius basis for this dispersion relation. This suggests that two-ion hybrid-mode conversion requires an analysis which does not assume small ion-gyroradius and so, if conversion can occur at all in EBT-S, it must be different from that in idealized weakly inhomogeneous slab-geometry plasma models. For shorterwavelength higher-frequency waves in EBT-S and for ion-cyclotron range of frequency waves in larger bumpy tori, like the projected EBT-P (P for proof of principle), inhomogeneity should have a less profound, although not necessarily negligible, impact on wave propagation.

Wave heating models for ion-cyclotron heating in ELMO Bumpy Torus-Scale

Wave heating of the ELMO Bumpy Torus-Scale (EBT-S) experiment in the ion-cyclotron range of frequencies will be strongly influenced by the geometry of the plasma. In particular, the short finite length of the mirror sections means that the electron bounce frequency is of comparable magnitude to the ion-cyclotron frequency. Consequently, the bouncing motion of trapped particles impacts the electron absorption of wave energy. Furthermore, the varying magnetic field strength along magnetic field lines influences the ion-cyclotron absorption of waves because the ion-cyclotron resonance conditions are satisfied only at discrete points along the field lines. Expressions are given for trapped and passing electron absorption as well as ion-cyclotron absorption. A numerical example is also discussed.

Confinement scaling of core plasma electrons in the ELMO Bumpy Torus experiment

Recent high microwave experiments in the ELMO Bumpy Torus-Scale (EBT-S) at power levels through 200 kW cw at 28 GHz cover a broad parameter range (density, temperature, potential well, etc.), the operating window (T-mode) increases with power, and the plasma characteristics change significantly with operating parameters (power and pressure). Because the density profiles are observed to change with these parameters, compasions with zero-dimensional theoretical expectations for the complete data set are not possible. However, it is shown that for controlled power and pressure combinations, scale lengths and eφ/Te are constant and the electron transport in EBT-S scales neoclassically; the power balance (Pμ∼n2/T1/2e ) and particle balance (τE/τp ∼constant) are consistent with neoclassical predictions.