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Stability of a pure electron plasma in cylindrical geometry Progress report
Stability of cylindrical cold plasma consisting of electrons
Particle simulations of mode conversion between slow mode and fast mode in lower hybrid range of frequencies
The propagation and mode conversion of lower hybrid waves in an inhomogeneous plasma are investigated by using the nonlinear δf algorithm in a two-dimensional particle-in-cell simulation code based on the gyrokinetic electron and fully kinetic ion (GeFi) scheme [Lin et al., Plasma Phys. Controlled Fusion 47, 657 (2005)]. The characteristics of the simulated waves, such as wavelength, frequency, phase, and group velocities, agree well with the linear theoretical analysis. It is shown that a significant reflection component emerges in the conversion process between the slow mode and the fast mode when the scale length of the density variation is comparable to the local wavelength. The dependences of the reflection coefficient on the scale length of the density variation are compared with the results based on the linear full wave model for cold plasmas. It is indicated that the mode conversion for the waves with a frequency of 2.45 GHz (ω ∼ 3ω{sub LH}, where ω{sub LH} represents the lower hybrid resonance) and within Tokamak relevant amplitudes can be well described in the linear scheme. As the frequency decreases, the modification due to the nonlinear term becomes important. For the low-frequency waves (ω ∼ 1.3ω{sub LH}), the generations of the high harmonic modes and sidebands through nonlinear mode-mode coupling provide new power channels and thus could reduce the reflection significantly.
Study of the absorption coefficient of alpha particles to lower hybrid waves in tokamak
Part of the energy of the Lower Hybrid (LH) waves may be absorbed by the α particles via the so-called perpendicular landau damping mechanism, which depends on various parameters of fusion reactors and the LH waves. In this article, we calculate the absorption coefficient γ{sub α} of LH waves due to α particles. Results show that, the γ{sub α} increases with the parallel refraction index n{sub ∥} while deceases with increasing the frequency of LH waves ω{sub LH} over a wide range. Higher background plasma temperature and toroidal magnetic field will increase the absorption, and there is a peak value of γ{sub α} when n{sub e}≈8×10{sup 19}m{sup −3} for ITER-like scenario. The thermal corrections to the cold plasma dispersion relation will change the damping rate to a certain extent under some specific conditions. We have also evaluated the fraction of LH power absorbed by the alpha particles, η ≈ 0.47% and 4.1% for an LH frequency of 5 GHz and 3.7 GHz respectively for ITER-like scenario. This work gives the effective reference for the choice of parameters of future fusion reactors.
Electron beam generated whistler emissions in a laboratory plasma
Naturally occurring whistler mode emissions in the magnetosphere, are important since they are responsible for the acceleration of outer radiation belt electrons to relativistic energies and also for the scattering loss of these electrons into the atmosphere. Recently, we reported on the first laboratory experiment where whistler waves exhibiting fast frequency chirping have been artificially produced [1]. A beam of energetic electrons is launched into a cold plasma and excites both chirping whistler waves and broadband waves. Here we extend our previous analysis by comparing the properties of the broadband waves with linear theory.
The Earth's Plasmasphere
The Earth's plasmasphere is an inner part of the magneteosphere. It is located just outside the upper ionosphere located in Earth's atmosphere. It is a region of dense, cold plasma that surrounds the Earth. Although plasma is found throughout the magnetosphere, the plasmasphere usually contains the coldest plasma. Here's how it works: The upper reaches of our planet's atmosphere are exposed to ultraviolet light from the Sun, and they are ionized with electrons that are freed from neutral atmospheric particles. The results are electrically charged negative and positive particles. The negative particles are electrons, and the positive particles are now called ions (formerly atoms and molecules). If the density of these particles is low enough, this electrically charged gas behaves differently than it would if it were neutral. Now this gas is called plasma. The atmospheric gas density becomes low enough to support the conditions for a plasma around earth at about 90 kilometers above Earth's surface. The electrons in plasma gain more energy, and they are very low in mass. They move along Earth's magnetic field lines and their increased energy is enough to escape Earth's gravity. Because electrons are very light, they don't have to gain too much kinetic energy from the Sun's ultraviolet light before gravity loses its grip on them. Gravity is not all that holds them back, however. As more and more electrons begin to escape outward, they leave behind a growing net positive electric charge in the ionosphere and create a growing net negative electric charge above the ionosphere; an electric field begins to develop (the Pannekoek-Rosseland E-field). Thus, these different interacting charges result in a positively charged ionosphere and negatively charged region of space above it. Very quickly this resulting electric field opposed upward movement of the electrons out of the ionosphere. The electrons still have this increased energy, however, so the electric field doesn't just go away. Instead the ions react to the electric field and are attracted to it. They begin to move upward out of the ionosphere too. Since all this happens on a small scale, it simply looks like the electrons and ions move out of the ionosphere together. Ultimately the effect is that the lighter ions of hydrogen, helium and oxygen are able to escape from the ionosphere. For a planet like Earth with a strong planetary magnetic field, these outward moving particles remain trapped near the planet unless other processes further draw them away and into interplanetary space. As is always the case with nature, there is much more story to tell about this "upwardly mobile" plasma and these other processes. Over only a short time period of hours and days this escaping plasma can, in some places, build up in concentration until an equilibrium is reached where as much plasma flows inward into the ionosphere as flows outward. This "donut shaped" region of cold (about 1 electron volt in energy) plasma encircling the planet is called the plasmasphere. Because of space weather storms (kind of a generic phrase for those other processes) this cold and dense plasmaspheric plasma can actually end up all over the place. Generally, that region of space where plasma from the ionosphere has the time to build up to become identified as the plasmasphere rotates or nearly rotates with the Earth. That region shrinks in size with increased space weather activity and expands or refills during times of inactivity. As it shrinks with increasing activity, some of the plasmasphere is drawn away from its main body (plasmaspheric erosion) in the sunward direction toward the boundary in space between that region dominated by Earth's magnetic field and the much larger region dominated by the Sun's magnetic field. The region dominated by Earth's magnetic field is called the magnetosphere. The larger Sun dominated region is called the heliosphere.
Simulations of ICRF Heating for SPARC during First Campaign and Primary Reference-Like Discharge using the Stix Code
High magnetic field tokamaks, like SPARC, rely on ion cyclotron radio frequency heating (ICRF) to reach fusion relevant temperatures. The SPARC tokamak will have 14 ICRF antennas in 7 toroidal locations delivering > 20 MW of power to the plasma. New capabilities with the full wave cold plasma solver, Stix, now allow for resolving the wave-particle resonances using lower order thermal corrections to capture core absorption of Landau damping and ion resonances in devices like SPARC. Favorable comparisons to the TORIC codes give confidence in the single pass absorption of this model to accurately capture the strength of edge interactions of the RF. Using this new dielectric formulation in the Stix code, simulations of the 2D poloidal cross section of SPARC are completed for the first campaign and primary reference-like discharges (PRD-like). A scan of the minority ion concentrations of helium-3 is performed and shows the expected behavior that as the helium-3 decreases the amount of single pass absorption also decreases which is seen in both scenarios. Additionally, both scenarios show only slight differences in single-pass absorption for the range of 3% to 5% helium-3 allowing for more flexibility in experiments. This study also highlights the differences between the first campaign and PRD-like with the first campaign discharges showing much more multi-pass absorption and an effect of confining the wave to a smaller portion of the cross-section due to the fast wave cut-off. This latter result suggests that far-field sheath rectification at the high-field side would be minimal for the first campaign scenario.
Nonlinear wave interaction in a plasma column
Two particular cases of nonlinear wave interaction in a plasma column were investigated. The frequencies of the waves were on the order of magnitude of the electron plasma frequency, and ion motion was neglected. The nonlinear coupling of slow waves on a plasma column was studied by means of cold plasma theory, and the case of a plasma column surrounded by an infinite dielectric in the absence of a magnetic field was also examined. Nonlinear scattering from a plasma column in an electromagnetic field having it's magnetic field parallel to the axis of the column was investigated. Some experimental results on mode conversion in the presence of loss are presented along with some observations of nonlinear scattering, The effect of the earth's magnetic field and of discharge symmetry on the radiation pattern are discussed.
Lower hybrid emission diagnostics on the NASA Lewis bumpy torus
The feasibility of using RF emission near the lower hybrid frequency of the NASA Lewis Bumpy Torus plasma for diagnostic purposes is examined. The emission is detected using a spectrum analyzer and a 50 omega miniature coaxial antenna that is sensitive to the polarization of the incoming signal. The frequency shift of the lower hybrid emission peak is monitored as a function of the background pressure, electrode voltage, electrode ring configuration and the strength of the toroidal dc magnetic field. Simultaneous measurements of the average plasma density are made with a polarization diplexing microwave interferometer. Data derived from the experiment are discussed with reference to the following: (1) the strength of the dc magnetic field in the emitting region; (2) comparison of the lower hybrid plasma density with the average plasma density; and (3) validity of the cold plasma lower hybrid resonance formula in the high density operating regime of the bumpy torus plasma.
Electric fields and double layers in plasmas
Various mechanisms for driving double layers in plasmas are briefly described, including applied potential drops, currents, contact potentials, and plasma expansions. Some dynamical features of the double layers are discussed. These features, as seen in simulations, laboratory experiments, and theory, indicate that double layers and the currents through them undergo slow oscillations which are determined by the ion transit time across an effective length of the system in which double layers form. It is shown that a localized potential dip forms at the low potential end of a double layer, which interrupts the electron current through it according to the Langmuir criterion, whenever the ion flux into the double is disrupted. The generation of electric fields perpendicular to the ambient magnetic field by contact potentials is also discussed. Two different situations were considered; in one, a low-density hot plasma is sandwiched between high-density cold plasmas, while in the other a high-density current sheet permeates a low-density background plasma. Perpendicular electric fields develop near the contact surfaces. In the case of the current sheet, the creation of parallel electric fields and the formation of double layers are also discussed when the current sheet thickness is varied. Finally, the generation of electric fields and double layers in an expanding plasma is discussed.
Coagulation of dust particles in a plasma
The electrostatic charge of small dust grains in a plasma in which the temperature varies in time is discussed, pointing out that secondary electron emission might introduce charge separation. If the sign of the charge on small grains is opposite to that on big ones, enhanced coagulation can occur which will affect the size distribution of grains in a plasma. Two scenarios where this process might be relevant are considered: a hot plasma environment with temperature fluctuations and a cold plasma environment with transient heating events. The importance of the enhanced coagulation is uncertain, because the plasma parameters in grain-producing environments such as a molecular cloud or a protoplanetary disk are not known. It is possible, however, that this process is the most efficient mechanism for the growth of grains in the size range of 0.1-500 microns.
Effects of ion abundances on electromagnetic ion cyclotron wave growth rate in the vicinity of the plasmapause
Electromagnetic ion cyclotron (EMIC) waves in multi-ion species plasmas propagate in branches. Except for the branch corresponding to the heaviest ion species, which has only a resonance at its gyrofrequency, these branches are bounded below by a cutoff frequency and above by a resonant gyrofrequency. The condition for wave growth is determined by the thermal anisotropies of each ion species, j, which sets an upper bound, ω{sub j}{sup ∗}, on the wave frequency below which that ion species contributes positively to the growth rate. It follows that the relative positions of the cutoffs and the critical frequencies ω{sub j}{sup ∗} play a crucial role in determining whether a particular wave branch will be unstable. The effect of the magnetospheric ion abundances on the growth rate of each branch of the EMIC instability in a model where all the ion species have kappa velocity distributions is investigated by appealing to the above ideas. Using the variation of the cutoff frequencies predicted by cold plasma theory as a guide, optimal ion abundances that maximise the EMIC instability growth rate are sought. When the ring current is comprised predominantly of H{sup +} ions, all branches of the EMIC wave are destabilised, with the proton branch having the maximum growth rate. When the O{sup +} ion abundance in the ring current is increased, a decrease in the growth rate of the proton branch and cyclotron damping of the helium branch are observed. The oxygen branch, on the other hand, experiences an increase in the maximum growth rate with an increase in the O{sup +} ion abundance. When the ring current is comprised predominantly of He{sup +} ions, only the helium and oxygen branches of the EMIC wave are destabilised, with the helium branch having the maximum growth rate.
The Critical Need for Innovations in Instruments and Techniques to Enable In-Situ Cold Ion and Cold Electron Measurements within the Magnetosphere
Relatively few studies have focused on the cold plasma populations of the magnetosphere due to difficulties associated with obtaining measurements. The cold particle populations are defined here as those with total energy approximately <100 eV which is an energy range for which measurements are difficult (regardless of species), but which often make up the bulk of the plasma density. These populations have known and suspected impacts on the structure and dynamics of the magnetosphere. Unfortunately, the lack of accurate measurements of the cold ion and cold electron populations through the magnetosphere makes closure of these science questions extremely difficult if not impossible. In a complex system of interconnected parts like the Earth’s magnetosphere, a lack of understanding of one part of the system (the cold electron and ion populations) is disabling. Hence, until cold electron and cold ion measurements are obtained robustly with every mission, the magnetospheric plasma environment cannot be completely understood. This will require innovations in plasma spectrometers and associated techniques required to obtain high-fidelity in-situ measurements of the cold ion and cold electron populations in the magnetosphere. This paper seeks to review the instruments and techniques that have been used to date and present possible options for future missions.
A review of instrument techniques to measure magnetospheric cold electrons and ions
A review of the instruments and techniques to directly measure the full distributions of the cold-ion and cold-electron populations in the magnetosphere is presented. Relatively few studies have focused on the cold plasma populations of the magnetosphere due to difficulties associated with obtaining measurements. The cold particle populations are defined here as those with total energy approximately <100 eV which is an energy range for which measurements are difficult (regardless of species), but which often make up the bulk of the plasma density. These populations have known and suspected impacts on the structure and dynamics of the magnetosphere but to date have not yet been measured adequately. The lack of accurate measurements cold ion and electron populations through the magnetosphere makes closure of these science questions extremely difficult if not impossible. Reaching closure will require innovations in plasma spectrometers and associated techniques required to obtain high-fidelity measurements of the cold ion and electron populations in the magnetosphere. This paper seeks to review the instruments and techniques that have been used to date and present possible options for future missions.
Towards identifying the mechanisms underlying field-aligned edge-loss of HHFW power on NSTX
Fast-wave heating will be a major heating scheme on ITER, as it can heat ions directly and is relatively unaffected by the large machine size unlike neutral beams. However, fast-wave interactions with the plasma edge can lead to deleterious effects such as, in the case of the high-harmonic fast-wave (HHFW) system on NSTX, large losses of fast-wave power in the scrape off layer (SOL) under certain conditions. In such scenarios, a large fraction of the lost HHFW power is deposited on the upper and lower divertors in bright spiral shapes. The responsible mechanism(s) has not yet been identified but may include fast-wave propagation in the scrape off layer, parametric decay instability, and RF currents driven by the antenna reactive fields. Understanding and mitigating these losses is important not only for improving the heating and current-drive on NSTX-Upgrade but also for understanding fast-wave propagation across the SOL in any fast-wave system. This talk summarizes experimental results demonstrating that the flow of lost HHFW power to the divertor regions largely follows the open SOL magnetic field lines. This lost power flux is relatively large close to both the antenna and the last closed flux surface with a reduced level in between, so the loss mechanism cannot be localized to the antenna. At the same time, significant losses also occur along field lines connected to the inboard edge of the bottom antenna plate. The power lost within the spirals is roughly estimated, showing that these field-aligned losses to the divertor are significant but may not account for the total HHFW loss. To elucidate the role of the onset layer for perpendicular fast-wave propagation with regards to fast-wave propagation in the SOL, a cylindrical cold-plasma model is being developed. This model, in addition to advanced RF codes such as TORIC and AORSA, is aimed at identifying the underlying mechanism(s) behind these SOL losses, to minimize their effects in NSTX-U, and to predict their importance in ITER.
Spatial profile of argon (1s 5 ) metastables in an electron beam generated plasma
Electron beams with an applied magnetic field generate a secondary cold plasma with a selective chemical composition, featuring low-energy ions and metastable species in the discharge periphery, ideal for low-damage plasma treatment of material substrates. In this work, we studied the plasma generated by an e-beam using a 4 kV voltage in a pure argon gas environment under a magnetic field of 150 G and in the pressure range of 25–90 mTorr. We measured the absolute spatial density profile of argon (1 s 5 ) metastables in an electron beam generated plasma by laser-induced fluorescence and found it to be of the order of 10 16 m −3 . The electron temperature and the electron density measured by a Langmuir probe were of the order of 10 16 m −3 and less than an eV respectively. Electron-impact quenching was identified as a significant loss mechanism for the Ar(1s 5 ) state, leading to the saturation of the metastable density at higher pressures. Outside the primary ionization region, the spatial distribution of argon metastables followed a linear diffusion profile, indicating negligible additional production in those regions.
Effect of the motion of a strongly magnetized plasma on the emission of radiation by a finite dipole.
Magnetized cold plasma motion effect on electromagnetic wave propagation and radiation