Studies of the impurity pellet ablation in the high-temperature plasma of magnetic confinement devices

The ablation of impurity pellets in tokamak and stellarator plasmas is investigated. Different mechanisms for shielding the heat fluxes from the surrounding plasma to the pellet surface are discussed. A model for impurity pellet ablation is developed that can account for both neutral and electrostatic shielding. It is shown that the experimental values of the impurity pellet ablation rate are well described by the neutral gas shielding model over a wide range of plasma temperatures and densities. Taking into account the electrostatic shielding leads to worse agreement between the predictions of the model and the experimental data; this result still remains unclear. Scaling laws are obtained that allow one to estimate the local ablation rate of impurity pellets made of various materials over a wide range of plasma parameters in the neutral gas shielding model.     

Study of L-H transition triggered by pellet injection based on a power threshold model

Simulations of ITER plasma during an L-H transition triggered by pellet injection are carried out using the 1.5D BALDUR integrated predictive modeling code. In these simulations, plasma core transport is predicted using a combination of the Multimode (MMM95) turbulent transport model and neoclassical transport (NCLASS) model. The pellet ablation behavior is described using the neutral gas shielding pellet model with the grad-B drift effect also included. Because of the increase of the plasma density and the reduction of the temperature, the plasma self-heating powers (ohmic heating and alpha heating) increase, whereas the plasma energy loss (through radiation) decreases. As a result, the total power across the separatrix increases. On the other hand, the L-H power threshold decreases. With all the changes of heating, an L-H transition can be induced even though the auxiliary heating is not enough for the L-H transition before pellet injection. It is also found that the L-H transition triggered by pellet injection depends sensitively on the pellet radius, but only moderately on the pellet velocity.     

Simulations of plasma behavior during pellet injection in ITER

Plasma behavior during pellet injection in ITER is investigated using a 1.5D BALDUR integrated predictive modeling code. In these simulations, the pellet ablation is described using the neutral gas shielding (NGS) model developed by Parks and Turnbull [Phys. Fluids 21, 1735 (1978)]. The NGS pellet ablation model that includes the ?B drift effect is coupled with a plasma core transport model, which is a combination of an MMM95 anomalous transport model and an NCLASS neoclassical transport model. The combination of core transport models, together with pellet model, is used to simulate the time evolution of plasma current, ion and electron temperatures, and density profiles for ITER standard type-I ELMy H-mode discharges during the pellet injection. It is found that the injection of pellet can result in either enhancement or degradation of plasma performance. The ?B drift effect on the pellet deposition is very strong in ITER. The plasma density with high field side pellets, which favorable with the ?B drift effect, is much higher and pellet can penetrate much deeper than that with low field side pellets.     

Impacts of pellets injected from the low-field side on plasma in ITER

Impacts of pellets injected from the low-field side (LFS) on plasma in ITER are investigated using the 1.5D BALDUR integrated predictive modeling code. In these simulations, the pellet ablation is described using the neutral gas shielding (NGS) model. The pellet ablation model is coupled with the plasma core transport model, which is a combination of the MMM95 anomalous transport model and NCLASS neoclassical transport model. The boundary conditions are assumed to be at the top of the pedestal, in which the pedestal parameters are predicted using a pedestal model based on the theoretical-based pedestal width scaling (either magnetic and flow shear stabilization width scaling, or flow shear stabilization width scaling, or normalized poloidal pressure width scaling) and the infinite-n ballooning mode pressure gradient limit. These pedestal models depend sensitively on the density at the top of the pedestal, which can be strongly influenced by the injection of pellets. The combination of the MMM95 and NCLASS models, together with the pedestal and NGS models, is used to simulate the time evolution of the plasma current, ion and electron temperatures, and density profiles for ITER standard type-I ELMy H-mode discharges during the injection of LFS pellets. It is found that the injection of pellets results in a complicated plasma scenario, especially in the outer region of the plasma and the plasma conditions at the boundary in which the pellet has an impact on increasing the plasma edge density, but reducing the plasma edge temperature. The LFS pellet has a stronger impact on the edge as compared to the center. For fusion performance, the pellet can result in either enhancement or degradation, depending sensitively on the pellet parameters; such as the pellet size, pellet velocity, and pellet frequency. For example, when a series of deuterium pellets with a size of 0.5 cm, velocity of 1 km/s, and frequency of 2 Hz are injected into the ITER plasma from the LFS, the plasma performance, evaluated in terms of Q _fusion, can increase to 72% of that before the use of pellets. It is also found that the injection of pellets results in an increase in the ion and electron densities, but does not enhance the central plasma density. On the other hand, it results in the formation of another peak of the plasma density in the outer region near the plasma edge. The formation of the density peak results in the reduction of plasma transports near the edge by decreasing the contributions of ion-temperature-gradient and trapped electron modes, as well as kinetic ballooning modes.     

Studies of the structure of C pellet ablation clouds in W7-AS

The structure of the ablation clouds surrounding carbon pellets injected into the ECR-heated Wendelstein 7-AS plasma has been studied. Snapshot and integrated photographs obtained in the spectral ranges containing the CII (720 ± 5 nm and 723 ± 1 nm) and CIII (770 ± 5 nm) spectral lines were analyzed over a wide range of the bulk plasma parameters. It is found that the cloud luminosity profile along the magnetic field is exponential with either one or two characteristic decay lengths of about a few millimeters and a few centimeters. The smaller length corresponds to the zone closer to the pellet. There is good agreement between the characteristic decay lengths deduced from snapshot and integrated photographs. The characteristic decay lengths were obtained along the entire pellet trajectory and were found to change weakly in the central region and to grow at the plasma periphery (generally, in inverse proportion to the plasma electron density). In the central region, the characteristic decay lengths are about a few millimeters and 1 cm. They depend weakly on the bulk plasma temperature and decrease with increasing bulk plasma density. These lengths agree fairly well with estimates of the ionization length of carbon ions into the C²⁺, C³⁺, and C⁴⁺ charge states, respectively, assuming that ionization is provided by the hot electrons of the bulk plasma and that the cloud expands with the ion-acoustic velocity at a temperature of ～1 eV. The results obtained prove that the cloud structure in the vicinity of the pellet is mainly determined by the bulk plasma electrons.     

Theory of the acoustic instability and behavior of the phase velocity of acoustic waves in a weakly ionized plasma

The amplification of acoustic waves due to the transfer of thermal energy from electrons to the neutral component of a glow discharge plasma is studied theoretically. It is shown that, in order for acoustic instability (sound amplification) to occur, the amount of energy transferred should exceed the threshold energy, which depends on the plasma parameters and the acoustic wave frequency. The energy balance equation for an electron gas in the positive column of a glow discharge is analyzed for conditions typical of experiments in which acoustic wave amplification has been observed. Based on this analysis, one can affirm that, first, the energy transferred to neutral gas in elastic electron-atom collisions is substantially lower than the threshold energy for acoustic wave amplification and, second, that the energy transferred from electrons to neutral gas in inelastic collisions is much higher than that transferred in elastic collisions and thus may exceed the threshold energy. It is also shown that, for amplification to occur, there should exist some heat dissipation mechanism more efficient than gas heat conduction. It is suggested that this may be convective radial mixing within a positive column due to acoustic streaming in the field of an acoustic wave. The features of the phase velocity of sound waves in the presence of acoustic instability are investigated.     

The critical electric field in heated SF<Subscript>6</Subscript>

The critical electric field at which the ionization rate is equal to the rate of electron attachment to neutral particles in heated sulfur hexafluoride (SF₆) is calculated by numerically solving the Boltzmann equation for electrons. It is shown that the main causes of a decrease in the critical field with increasing gas temperature are the change in the electron energy distribution due to gas dissociation and the reduction in the rate of electron attachment to neutral particles. The calculated results are in qualitative agreement with the available experimental data.     

Model for calculating low-current moderate-pressure RF discharges with photon-driven secondary electron photoemission from the electrode surface

A model is developed for calculating a low-current moderate-pressure RF discharge with allowance for an electron cloud that is formed by electrons produced during the preceding periods of the RF field and fills the electrode sheath at regular intervals in accordance with the phase of the RF voltage applied to the electrodes. The cloud arises due to a phase shift of π/2 between the voltage across the sheath and that across the column of a low-current RF discharge plasma. The photon generation mechanism is as follows: as the cloud electrons fill the sheath, they acquire energy in superelastic collisions with metastables produced by the sheath electrons during the preceding periods of the RF field and then excite the metastable states to emitting levels. The discharge sheath forms due to the overlap of the secondary electron avalanches triggered by electron photoemission from the electrode surface. The parameters of the sheath in a low-current RF discharge are determined by the conditions under which the electron photoemission current in the sheath is self-sustaining, but the capacitive susceptance of the sheath is substantially higher than its active electrical conductance. The results of calculations are compared with the experimental data.     

Potential of a test charge in a dust-electron plasma

The potential of a slowly moving test charge in a positive-dust-electron plasma is calculated taking into account dust grain charge fluctuations, as well as collisions between neutral atoms and electrons and dust grains. The results should be useful for understanding the shielding in a dusty plasma sheath with levitated grains.     

Laser-generated plasmas at INFN-LNS

Hot plasmas can be generated by fast and intense laser pulses ablating solids placed in vacuum. A Nd:Yag laser operating at the fundamental and second harmonics with 9-ns pulses (maximum energy of 900 mJ) focused on metallic surfaces produces high ablation yields of the order of μg/pulse and dense plasma that expands adiabatically at supersonic velocity along the normal to the target surface. The plasma emits neutral and charged particles. Charge states up to 10+ have been measured in heavy elements ablated with intensities of the order of 10¹⁰ W/cm². The ion temperature of the plasma is evaluated from the ion energy distributions measured with an ion energy analyzer. The electron temperature is measured through Faraday cups placed at the end of long drift tubes by using time-of-flight technique. The neutral temperature is measured with a special mass quadrupole spectrometer placed along the normal to the target surface. The plasma temperature increases with the laser pulse intensity. The ion temperature reaches values of the order of 400 eV, the electron temperature is of the order of 1 keV for hot electrons and 0.1 eV for thermal electrons, and the neutral temperature is of the order of 200 eV. The experimental apparatus, the diagnostic techniques, and the procedures for the plasma temperature characterization will be presented and discussed in detail. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 6, pp. 558–564. The text was submitted by the authors in English.     

Spatial distribution of the RF power absorbed in a helicon plasma source

The spatial distributions of the RF power absorbed by plasma electrons in an ion source operating in the helicon mode (ω _ci < ω < ω _ce < ω _pe ) are studied numerically by using a simplified model of an RF plasma source in an external uniform magnetic field. The parameters of the source used in numerical simulations are determined by the necessity of the simultaneous excitation of two types of waves, helicons and Trivelpiece-Gould modes, for which the corresponding transparency diagrams are used. The numerical simulations are carried out for two values of the working gas (helium) pressure and two values of the discharge chamber length under the assumption that symmetric modes are excited. The parameters of the source correspond to those of the injector of the nuclear scanning microprobe operating at the Institute of Applied Physics, National Academy of Sciences of Ukraine. It is assumed that the mechanism of RF power absorption is based on the acceleration of plasma electrons in the field of a Trivelpiece-Gould mode, which is interrupted by pair collisions of plasma electrons with neutral atoms and ions of the working gas. The simulation results show that the total absorbed RF power at a fixed plasma density depends in a resonant manner on the magnetic field. The resonance is found to become smoother with increasing working gas pressure. The distributions of the absorbed RF power in the discharge chamber are presented. The achievable density of the extracted current is estimated using the Bohm criterion.     

Low-current medium-pressure RF discharge with electron photoemission in the electrode sheath and penetration of the sheath electrons into the discharge column

A model is developed for simulating a low-current moderate-pressure RF discharge with allowance for such characteristic discharge properties as the existence of two sheaths near both electrodes throughout the RF field period; the formation of an electron cloud at the sheath boundary that periodically fills the sheath and leaves it, depending on the phase of the applied RF voltage; the production by the sheath electrons of metastable gas particles that interact with the cloud electrons during subsequent field periods, followed by the excitation of metastable states to the emitting levels; the formation of a sheath in a low-current RF discharge due to the overlap of the secondary electron avalanches triggered by electron photoemission from the electrode surface; and the conditions under which the sheath electrons penetrate into the positive column and accumulate there, which makes, thereby making a low-current RF discharge similar to a non-self-sustained discharge. The parameters of the sheath in a low-current RF discharge are determined by the conditions under which the electron photoemission current from the electrode surface in the sheath is self-sustaining and, like the parameters of the positive discharge column, depend on the sort of gas, the gas pressure, the frequency of the applied RF field, and the interelectrode distance. The results of calculating the parameters of the sheath and column of a low-current RF discharge for nitrogen and helium at different pressures, as well as for different field frequencies and interelectrode distances, are presented and are compared with the experimental data.     

A modeling study of anaerobic biofilm systems: I. Detailed biofilm modeling

A detailed model acetate-utilizing methanogenic biofilms accounting for the diffusion of neutral and ionic species, chemical equilibrium, electroneutrality, gas production within the biofilm, pH-dependent Monod kinetics, and the presence of a concentration boundary layer is presented. The model qualitatively fits the pH profiles that are reported for acetate-utilizing methanogenic aggregates. A sensitivity analysis on the biological parameters showed that the flux of acetate is sensitive to the maximum utilization rate, half-saturation constant, and biofilm density for the bulk conditions investigated. Criteria when traditional biofilm models can be used to predict the flux of acetate into the biofilm are established. If the maximum pH change predicted using a hypothetical system is within +/-0.05, the traditional model predicts the flux to within +/-5% of the value calculated with the model developed in this study. (c) 1995 John Wiley & Sons, Inc.     

Estimation of the electron density and radiative energy losses in a calcium plasma source based on an electron cyclotron resonance discharge

The parameters of a calcium plasma source based on an electron cyclotron resonance (ECR) discharge were calculated. The analysis was performed as applied to an ion cyclotron resonance system designed for separation of calcium isotopes. The plasma electrons in the source were heated by gyrotron microwave radiation in the zone of the inhomogeneous magnetic field. It was assumed that, in such a combined trap, the energy of the extraordinary microwave propagating from the high-field side was initially transferred to a small group of resonance electrons. As a result, two electron components with different transverse temperatures—the hot resonance component and the cold nonresonance component—were created in the plasma. The longitudinal temperatures of both components were assumed to be equal. The entire discharge space was divided into a narrow ECR zone, where resonance electrons acquired transverse energy, and the region of the discharge itself, where the gas was ionized. The transverse energy of resonance electrons was calculated by solving the equations for electron motion in an inhomogeneous magnetic field. Using the law of energy conservation and the balance condition for the number of hot electrons entering the discharge zone and cooled due to ionization and elastic collisions, the density of hot electrons was estimated and the dependence of the longitudinal temperature T _e∥ of the main (cold) electron component on the energy fraction β lost for radiation was obtained.     

Development of the concept of charge-exchange recombination spectroscopy for ITER

Charge-exchange recombination spectroscopy under ITER conditions is numerically simulated using the DINA code. The code allows one to calculate the attenuation of neutral beams in plasma, the intensity of atomic emission and emission from the ions produced by charge exchange with the neutral beam, and the intensity ratio between the emission related to charge exchange and the background continuum plasma emission. The cross sections for atom-ion interactions in plasma are calculated, and the excitation rates of spectral transitions in hydrogen-like impurity ions are determined. The measurement scheme and the main parameters of the spectrometer proposed for charge-exchange recombination diagnostics in ITER are described.     

Resonance microwave volume plasma source

A conceptual design of a microwave gas-discharge plasma source is described. The possibility is considered of creating conditions under which microwave energy in the plasma resonance region would be efficiently converted into the energy of thermal and accelerated (fast) electrons. Results are presented from interferometric and probe measurements of the plasma density in a coaxial microwave plasmatron, as well as the data from probe measurements of the plasma potential and electron temperature. The dynamics of plasma radiation was recorded using a streak camera and a collimated photomultiplier. The experimental results indicate that, at relatively low pressures of the working gas, the nonlinear interaction between the microwave field and the inhomogeneous plasma in the resonance region of the plasmatron substantially affects the parameters of the ionized gas in the reactor volume.     

Kinetic study of the linear stage of thermocurrent instability in the framework of the Boltzmann equation for a model gas

The linear stage of thermocurrent instability is investigated for a model gas in which the integral of inelastic collisions of electrons with gas particles has a divergent form and the frequencies of elastic and inelastic collisions are independent of the electron velocity. The proposed approach consists in the reduction of the Boltzmann equation for electrons in an inhomogeneous plasma to a set of equations for the moments of the electron velocity distribution function. The instability growth rate and the wave phase velocity as functions of the perturbation wavenumber are calculated, the maximum growth rate and the corresponding wavenumber are determined, and the dependence of these quantities on the degree of plasma quasineutrality is examined. It is demonstrated that the model satisfactorily (both qualitatively and quantitatively) describes the linear stage of thermocurrent instability in helium.     

Distribution Function of Relativistic Electrons Produced by the Tunneling Ionization of a Gas by an Intense Electromagnetic Wave

The distribution function of the relativistic electrons produced in the interaction between an intense electromagnetic wave and a neutral gas is derived and is shown to be nonequilibrium and anisotropic. The drift plasma current is calculated, and the applicability conditions for the results obtained are determined.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Investigations of high-energy electrons of the microwave discharge plasma at configuration of the “Magnetor” Bi-dipole magnetic confinement system by X-ray radiation analyses

The results of the investigations of a group of fast electrons in a microwave discharge plasma in the “Magnetor” magnetic trap are presented. The data on the presence and location of this group of electrons is important for estimating the total plasma pressure taking the previous probe measurements into account. Fast electrons are found to be localized within the magnetic separatrix in the region of confinement of the main plasma. The maximal energy of fast electrons is higher than 25 keV.