Hot Ring Research Articles

Lower hybrid drift instability at the inner edge of the ring current

Excitation of electrostatic waves around and above the lower hybrid frequency at the inner edge of the ring current is investigated. The model consists of cold plasmaspheric ions; hot, dilute, inhomogeneous ring current ions; and cold charge neutralizing electrons. It is shown that in the presence of a sufficiently large density gradient the coupling of the lower hybrid with the drift cyclotron harmonic mode destabilizes the plasma. Unstable interactions also occur at higher cyclotron harmonics when the lower hybrid is replaced by an ion Bernstein mode. Additional power at frequencies above the lower hybrid frequency is attributed to the thermal enhancement by the hot ring current ions, which increases with their density gradient. Particle simulations are conducted, and comparison to AMPTE data is discussed.

Particle simulation of ion heating in the ring current

Heating of heavy ions has been observed in the equatorial magnetosphere in GEOS 1 and 2 and ATS 6 data due to ion cyclotron waves generated by anisotropic hot ring current ions. A one‐dimensional hybrid‐Darwin code has been developed to study ion heating in the ring current. The mechanism for the heating of thermal hydrogen and helium by ion cyclotron waves has been studied previously in particle simulations of a bi‐Maxwellian plasma. Here, a strong instability and heating of thermal ions is investigated in a plasma with a loss cone distribution of hot ions. The linear growth rate calculation and particle simulations are conducted for cases with different loss cones and relative ion densities. The linear instability of the waves, the quasi‐linear heating of cold ions and dependence on the thermal H+/He+ density ratio are analyzed, as well as nonlinear parallel heating of thermal ions. Effects of thermal oxygen and hot oxygen are also studied.

EXPERIMENTAL STUDY ON ECRH TRAPPED ELECTRON BEAM INJECTED INTO THE SIMPLE MIRROR

The experiments on ECRH trapped electron beam injection in various ways have been carried out on a simple mirror-MM-2 device by use of a 15GHz high power gyrotron. The experimental results show that the preionization time of plasma will be greatly reduced for the electron beam injection ahead of the microwave. And because of ECRH trapped electron beam, the parameters of hot electron ring will be improved greatly, and the diamagnetic value increases about 62 percent. The trapping efficiency of electron beam for the increasing rate of diamagnetic is about 30-40 percent. The gas "pressure window" for building a hot electron ring is (4.67-21.3)×10-4 Pa, as the gyrotron output power is about 30kW.

EXPERIMENTAL INVESTIGATION ON PROPERTIES OF E. C. H. PLASMA AND HOT ELECTRON RING

The ECRH experiment has been carried out on a simple mirror-MM-2 device by use of a 15 GHz high power gyrotron. The experimental results showed that the preionization time will be rapidly shorten following raising the pressure of puffed gas. Duing the "C-mode" operation where the gas pressure is higher, the radial profile of plasma density exhibits a saddle shape. The gas "pressure window" for building a hot electron ring is (0.4-1.2)×10-5 Torr, as the gyrotron output is about 30 kW. Simply by using a movable Langmuire probe accompanied with diamagnetic measurment. it has been determined that the hot electron ring radius is 7 cm, the thickness is about 4 cm and the axial boundary of the ring extends from Z= ±10 cm to Z=±20cm, when the central field is 2.95kg. The hot electron temperature is 140 to 170 keV. The average beta value of hot electron ring is (4-5)%. The radial bursts of electrons due to ring instabilities accompanied with the drops of the diamagnetic signal have also been observed.

Hot Electron Ring Formation in ECR Heated Plasma

Energetic particles can be .generated by electron cyclotron resonant heating (ECRH) in tokamak plasma, forming electron ring. The bounce frequency is taken into account in resonance condition. The electron energy is limited by detaching of the adjacent overlapped islands. An analytical criterion for transition is obtained. The critical potential obtained is in good agreement with numerical calculation. Experiment for observing the trapped energetic electrons is suggested.

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.

DISSIPATIVE DRIFT INSTABILITIES IN A HOT ELECTRON PLASMA

Density-gradient-driven dissipative drift instabilities in a hot electron plasma are studied. Dispersion relation (including that of resistivity and viscosity) is derived. Hot electron ring can reduce growth rate of the instability and anomalous transport flux. Stability condition for the drift wave is βh>4ξ/(l + 2ξ). The fluctuation levels and the exciting region of drift mode are measured, and the stabilizing effects of hot electron ring observed. It is found that the experimental results are consistent with the theoretical predictions.

An experimental determination of the hot electron ring geometry in a bumpy torus and its implications for bumpy torus stability

The hot electron rings of the ELMO Bumpy Torus (EBT) [Plasma Physics and Controlled Nuclear Fusion (IAEA, Vienna, 1975), Vol. II, p. 141] are formed by electron-cyclotron resonance heating (ECRH) and have an electron temperature of 350–500 keV. The original intention of these hot electron rings was to provide a local minimum in the magnetic field and, thereby, stabilize the simple interchange and flute modes, which are inherent in a closed field line bumpy torus. To evaluate the electron energy density of the EBT rings and determine if enough stored energy is present to provide a local minimum in the magnetic field, a detailed understanding of the spatial distribution of the rings is imperative. The purpose of this paper is to measure the ring thickness and investigate its implications for bumpy torus stability. The spatial location and radial profile of the hot electron ring is measured with a unique metal ball pellet injector, which injects small metallic balls into the EBT ring plasma. From these measurements the radial extent (or ring thickness) is about 5–7 cm full-width at half-maximum for typical EBT operation, which is much larger than previously expected. These measurements and recent modeling of the EBT plasma indicate that the hot electron ring’s stored energy may not be sufficient to produce a local minimum in the magnetic field.

Harmonic structure of compressional Pc5 pulsations at synchronous orbit

A harmonic structure of compressional Pc5 oscillations during geomagnetically disturbed conditions is found in magnetic field data from the geostationary satellites, GOES 2 and 3. Compressional Pc5 pulsations sometimes show an interesting property that the compressional component oscillates with a frequency twice as high as that of the transverse component. In addition to these second harmonic events, waves with a transitional character between normal Pc5 waves and second harmonic events are also observed. In the normal Pc5 waves, the compressional component changes out of phase with the radial component in the northern equatorial region. In a transitional event, a small hump appears at the maximum phase of the radial component. These Pc5 oscillations with second harmonics dominant in the compressional component were observed mainly at GOES 3 and rarely at GOES 2 in the winter season. This occurrence pattern suggests that compressional Pc5 with harmonic structure is spatially confined to the equatorial region. It is also suggested that the particular modulation dominant in the compressional component reflects a finite amplitude effect in the inhomogeneity of the hot ring current plasma near the magnetic equator.

Solar wind energy transfer regions inside the dayside magnetopause: Accelerated heavy ions as tracers for MHD-processes in the dayside boundary layer

Plasma and magnetic field data from PROGNOZ-7 have revealed that solar wind (magnetosheath) plasma elements may penetrate the dayside magnetopause surface and form high density regions with enhanced cross-field flow in the boundary layer. The injected magnetosheath plasma is observed to have an excess drift velocity as compared to the local boundary layer plasma, comprising both “cold” plasma of terrestrial origin and a hot ring current component. A differential drift between two plasma components can be understood in terms of a momentum transfer process driven by an injected magnetosheath plasma population. The braking action of the injected plasma may be described as a dynamo process where particle kinetic energy is transferred into electromagnetic energy (electric field). The generated electric field will force the local plasma to ε× B -drift , and the dynamo region therefore also constitutes an accelerator region for the local plasma. Whenever energy is dissipated from the energy transfer process (a net current is flowing through a load), there will also be a difference between the induced electric field and the v × B term of the generator plasma. Thus, the local plasma will drift more slowly than the injected generator plasma. We will present observations showing that a relation between the momentum transferred, the injected plasma and the momentum taken up by the local plasma exists. For instance, if the local plasma density is sufficiently high, the differential drift velocity of the injected and local plasma will be small. A large fraction of the excess momentum is then transferred to the local plasma. Conversely, a low local plasma density results in a high velocity difference and a low fraction of local momentum transfer. In our study cases the “cold” plasma component was frequently found to dominate the local magnetospheric plasma density in the boundary layer. Accordingly, this component may have the largest influence on the local momentum transfer process. We will demonstrate that this also seems to be the case. Moreover we show that the accelerated “cold” plasma component may be used as a tracer element reflecting both the momentum and energy transfer and the penetration process in the dayside boundary layer. The high He + percentage of the accelerated “cold” plasma indicates a plasmaspheric origin. Considering the quite high densities of energetic He + found in the boundary layer, the overall low abundance of He + (as compared to e.g. O +) found in the plasma sheet and outer ring current evidently reduces the importance of the dayside boundary layer as a plasma source in the large scale magnetospheric circulation system.

Magnetics Calculations for an ELMO Bumpy Square

Calculations have been carried out to determine the vacuum magnetic parameters, forces, and the use of trim coils in an ELMO Bumpy Square. A configuration having five mirror coils per side and an eight-coil high-field toroidal solenoid corner assembly was studied. Favorable magnetic parameters are achieved in the device. An on-axis mirror ratio of 1.9, a global mirror ratio of 3.6, and excellent centering of plasma pressure contours are achieved. Particle losses are also minimal (<5%). The magnetic forces acting between coils are comparable with those encountered in the EBT-I/S magnet configuration. Circular trim coils were found to be suitable for restoring hot electron ring locations that are displaced when the coil currents are varied for performing magnetic studies or for assessing the effects on the EBS of the global mirror ratio.

Experimental Studies on the Hot Electron Rings in NBT-1M

The scaling characteristics of the high-beta hot-electron rings in NBT-1M were studied experimentally. The hot electron temperature Th and the density nh were measured by the hard X-ray detection system, and were found to have typical values of 220 keV and 3×1010 cm-3, respectively. The stored energy of the hot electron ring, W⊥, scales empirically with the applied microwave power Pµ and the ambient gas pressure PH2 as W⊥ ∝PµPH2-1 in the quiescent T-mode. The dependence of the energy stored in the ring on the gas pressure in the T-mode can be explained by the simple energy balance equation. In T-mode operation, the temperature is independent of the applied microwave power, but the density increases with the power and decreases with the gas pressure.

Simulation studies on stability of EBT

Stability and beta limits of the ELMO Bumpy Torus (EBT) are studied by using a 2 1/2 -D fully relativistic, electromagnetic particle code. A slab model is used which is bounded in the x direction (corresponding to the radial direction) and which is periodic in the y direction (corresponding to the poloidal direction). The imposed magnetic field is in the z direction (the ignorable coordinate) and is a function of x so that the plasma flutes in the absence of an EBT ring. The hot electron ring (layer) is shown to be effective in suppressing the Rayleigh–Taylor instability, when kyρh ≳1, where ρh is the Larmor radius of hot electrons. However, in a system where kyρh &amp;lt;1 for long wavelength modes, the plasma exhibits instability. One possible mode which agrees fairly well with our observations is the low-frequency hot electron interchange instability.

Transport Scaling Studies for EBT Reactor

Transport simulation and modeling studies for the ELMO bumpy Torus (EBT) reactor are carried out by using 0-D and 1-1/2-D transport calculations. The time-dependent 0-D model is used for global analysis whereas the 1-1/2-D radial transport code is used for accurate determination of density, temperature, and ambipolar potential profiles and of the role of these profiles in reactor plasma performance. Analysis with the 1-1/2-D transport code shows that profile effects near the outer edge of the hot electron ring lead to enhanced confinement by a least a factor of 2 to 5 beyond the simple scaling that is obtained from the global analysis. The radial profiles of core plasma density and temperatures (or core pressure) obtained from 1-1/2-D transport calculations are found to be similar to those theoretically required for stability.

Development of Concentric Equipotential Surfaces in Bumpy Torus Plasma

Radial profiles of the plasma space potential are measured in Nagoya Bumpy Torus (NBT-1) by the use of a heavy ion beam probe. Asymmetric potential profiles owing to toroidal drift are observed in high pressure operation (C-mode). As the pressure is decreased, toroidal plasma is effectively heated (T-mode), poloidal precessional frequency overcomes the electron collision frequency and the equipotential surfaces becomes concentric inside the hot electron ring.

EBT stability theory

The theory of unfavorable curvature-driven instabilities is developed for a plasma interacting with a hot electron ring whose drift frequencies are larger than the growth rates predicted from conventional magnetohydrodynamic theory. A Z-pinch model is used to emphasize the radial structure of the problem. Stability criteria are obtained for the five possible modes of instability: The conventional hot electron interchange, a high-frequency hot electron interchange (at frequencies larger than the ion-cyclotron frequency), a magnetic compressional instability, a background pressure-driven interchange, and an interacting pressure-driven interchange. The effect of F.L.R. stabilization on the low-frequency modes (less than the ion-cyclotron frequency) will be discussed.

Stabilization of electrostatic flute mode due to hot electron ring and RF field

The dynamic stabilization of electrostatic flute modes by an RF electric field is studied on the basis of the relatively simple model of a smooth cylinder with artificial gravity and an ambipolar field. It is found that the electrostatic flute modes can be effectively stabilized by the RF electric field together with the hot electron ring.

Effects of an Ambipolar Field on Stability of Flute Modes in a Bumpiless Cylinder

The effect of an ambipolar field on the stability of electrostatic flute modes for a bumpy torus has been studied for both the positive and negative ambipolar fields using a relatively simple model of a bumpiless cylirnder with an artificial gravity. It has been shown that the flute modes are stabilized effectively by the hot electron ring togehter with the rf electric field. The large m number modes ( m denotes the azimuthal mode number) are stabilized by the finite Larmor radius effect and the small m number modes are also stabilized by the reduction of gravitational force due to both the hot electron ring and the rf electric field.

Curvature-driven instabilities in a hot electron plasma: Radial analysis

The theory of curvature-driven instabilities is developed for a plasma interacting with a hot electron ring whose drift frequencies are larger than the growth rates predicted from conventional magnetohydrodynamic theory. A z-pinch model is used to emphasize the radial structure of the problem. Stability criteria are obtained for the five possible modes of instability: the conventional hot electron interchange, a high-frequency hot electron interchange (at frequencies larger than the ion cyclotron frequency), a compressional instability, a background pressure-driven interchange, and an interacting pressure-driven interchange. Numerical plots of the marginal stability boundaries are presented for parameter values corresponding to the EBT-S and EBT-P bumpy torus experiments.

Summary of the Second Workshop on Hot Electron Ring Physics, San Diego, California, December 1–3, 1981

Summary of the Second Workshop on Hot Electron Ring Physics, San Diego, California, December 1–3, 1981