Electron Heating Rate Research Articles

Electron kinetics and non-Joule heating in near-collisionless inductively coupled plasmas

Electron kinetics in an inductively coupled plasma sustained by a coaxial solenoidal coil is studied for the near-collisionless regime when the electron mean free path is large compared to the tube radius. Emphasis is placed on the influence of the oscillatory magnetic field induced by the coil current and the finite dimension of the plasma on electron heating and formation of the electron distribution function (EDF). A nonlocal approach to the solution of the Boltzmann equation is developed for the near-collisionless regime when the traditional two-term Legendre expansion for the EDF is not applicable. Dynamic Monte Carlo (DMC) simulations are performed to calculate the EDF and electron heating rate in argon in the pressure range 0.3--10 mTorr and driving frequency range 2--40 MHz, for given distributions of electromagnetic fields. The wall potential ${\mathrm{\ensuremath{\varphi}}}_{\mathrm{w}}$ in DMC simulations is found self-consistently with the EDF. Simulation results indicate that the EDF of trapped electrons with total energy \ensuremath{\varepsilon}${\mathrm{\ensuremath{\varphi}}}_{\mathrm{w}}$ is almost isotropic and is a function solely of \ensuremath{\varepsilon}, while the EDF of untrapped electrons with \ensuremath{\varepsilon}ge${\mathrm{\ensuremath{\varphi}}}_{\mathrm{w}}$ is notably anisotropic and depends on the radial position. These results are in agreement with theoretical analysis.

Self-similar electron distributions in a non-uniform plasma embedded in a high-frequency electromagnetic field

New self-similar distributions functions (EDF's) in a non-uniform plasma embedded in a non-uniform high frequency electromagnetic field are reported. The dependences of the EDF's on the degree of density non-uniformity, on the rate of electron heating due to inverse bremsstrahlung absorption of high frequency field, and on the value of the electric current in a plasma are established. It is shown how the EDF modifications influence the energy absorption of the electromagnetic field and the electron heat transfer. The self-consistent states of the plasma and the electromagnetic field in which the self-similar electron distributions take place are described.

Nonlinear expansion and heating of a nonneutral electron plasma due to elastic collisions with background neutral gas

This paper investigates theoretically the heating and nonlinear expansion of a nonneutral electron plasma due to elastic collisions with constant collision frequency νen between the plasma electrons and a background neutral gas. The model treats the electrons as a strongly magnetized fluid (ωpe2/ωce2≪1) immersed in a uniform magnetic field B0êz. The model also assumes an axisymmetric plasma column (∂/∂θ=0) with negligible axial variation (∂/∂z=0), and that the process of heat conduction is sufficiently fast that the electrons have relaxed through electron-electron collisions to a quasi-equilibrium state with scalar pressure P(r,t)=n(r,t)T, and isothermal temperature T. Assuming that the electrons undergo elastic collisions with infinitely massive background gas atoms, global energy conservation is used to calculate the electron heating rate, dT(t)/dt, as the plasma column expands on a time scale τdiff∼(ωpe2νen/ωce2 )−1, and the electrostatic potential energy decreases. Coupled dynamical equations that describe the nonlinear evolution of the mean-square column radius r20(t) and electron temperature T(t) are derived and solved numerically.

Computational studies for a multiple-frequency electron cyclotron resonance ion source (abstract)

The number density of electrons, the energy (electron temperature), and energy distribution are three of the fundamental properties which govern the performance of electron cyclotron resonance (ECR) ion sources in terms of their capability to produce high charge state ions. The maximum electron energy is affected by several processes including the ability of the plasma to absorb power. In principle, the performances of an ECR ion source can be realized by increasing the physical size of the ECR zone in relation to the total plasma volume. The ECR zones can be increased either in the spatial or frequency domains in any ECR ion source based on B-minimum plasma confinement principles. The former technique requires the design of a carefully tailored magnetic field geometry so that the central region of the plasma volume is a large, uniformly distributed plasma volume which surrounds the axis of symmetry, as proposed in Ref. . Present art forms of the ECR source utilize single frequency microwave power supplies to maintain the plasma discharge; because the magnetic field distribution continually changes in this source design, the ECR zones are relegated to thin ‘‘surfaces’’ which surround the axis of symmetry. As a consequence of the small ECR zone in relation to the total plasma volume, the probability for stochastic heating of the electrons is quite low, thereby compromising the source performance. This handicap can be overcome by use of broadband, multiple frequency microwave power as evidenced by the enhanced performances of the CAPRICE and AECR ion sources when two frequency microwave power was utilized. We have used particle-in-cell codes to simulate the magnetic field distributions in these sources and to demonstrate the advantages of using multiple, discrete frequencies over single frequencies to power conventional ECR ion sources. The electron heating rates are found to scale directly in proportion to the resonant plasma ‘‘volume.’’

Joule heating by ac electric fields in the ionosphere of Venus

It is shown that Joule heating from electron collision damping of ac electric fields could be a significant source of energy for electrons in the Venus ionosphere if they occur naturally on a large scale. On the assumption that the fields are due to electromagnetic waves on a planetary scale, we calculate heating rates implied by observations on the day side and compare them with the profiles of photoelectron heating rates used by modelers. It is found that sufficient amplitudes have been measured on Pioneer Venus Orbiter in the frequency channels of 730 and 100 Hz to cause greater local electron heating rates than that due to photoelectrons, up to 3 orders of magnitude in some cases. Nightside heating rates at low altitudes for the 100‐Hz signal would cause great heating of the ionosphere and thermosphère, airglow, and aurora. The difficulties produced by these findings would be relieved if the electric field disturbances were closely confined to the spacecraft or at least were much less than planetary in scale.

Modeling of O+ ions in the plasmasphere

Heavy ion (O+, O++, and N+) density enhancements in the outer plasmasphere have been observed using the retarding ion mass spectrometer instrument on the DE 1 satellite. These are seen at L shells from 2 to 5, with most occurrences in the L = 3 to 4 region; the maximum L shell at which these enhancements occur varies inversely with Dst. It is also known that enhancements of O+ and O++ overlie ionospheric electron temperature peaks. It is thought that these enhancements are related to heating of plasmaspheric particles through interactions with ring current ions. This was investigated using a time‐dependent one‐stream hydrodynamic model for plasmaspheric flows, in which the model flux tube is connected to the ionosphere. The model simultaneously solves the coupled continuity, momentum, and energy equations of a two‐ion (H+ and O+) quasi‐neutral, currentless plasma. This model is fully interhemispheric and diffusive equilibrium is not assumed; it includes a corotating tilted dipole magnetic field and neutral winds. First, diurnally reproducible results were found assuming only photoelectron heating of thermal electrons. For this case the modeled equatorial O+ density was below 1 cm−3 throughout the day. The O+ results also show significant diurnal variability, with standing shocks developing when production stops and O+ flows downward under the influence of gravity. Numerical tests were done with different levels of electron heating in the plasmasphere; these show that the equatorial O+ density is highly dependent on the assumed electron heating rates. Over the range of integrated plasmaspheric electron heating (along the flux tube) from 8.7 to 280×109 eV/s, the equatorial O+ density goes like the heating raised to the power 2.3.

The role of ring current nose events in producing stable auroral red arc intensifications during the main phase: Observations during the September 19‐24, 1984, Equinox Transition Study

An examination of stable auroral red (SAR) arc emissions over the last solar cycle (Slater and Kleckner, 1989) indicates that the strongest emissions, during the lifetime of a particular SAR arc, often occur in association with the main phase of the magnetic storm. Previous observations of thermal and energetic particle populations at high and low altitudes on SAR arc field lines by Kozyra et al. (1987a) indicate that the energy source for these emissions is the O+ in the ring current. The O+ content of the ring current increases with increasing magnetic activity reaching its maximum percentage contribution near minimum Dst for a particular storm. This variation in the O+ content of the ring current is inconsistent with an early main phase enhancement of SAR arc emissions. To investigate the source of main phase enhancements in SAR arc emissions, a study of the September 19‐24, 1984, magnetic storm period during which SAR arc emissions were observed by the ground‐based mobile automatic scanning photometer network in both the main and recovery phases is presented. The emissions associated with the main phase (∼ 400 R) were an order of magnitude greater than those associated with the recovery phase (tens of R). Energetic particle measurements from the DE 1 and AMPTH spacecraft, on field lines that map to the SAR arc position at low altitude, were examined to determine if differences in the energy sources during these time periods were evident. In agreement with previous work, ring current O+ supplied the bulk of the electron heating during storm recovery phase as a result of Coulomb collisions of O+ with the plasmaspheric electrons; contributions by ring current H+ were negligible. A new result of the present work is that an enhancement of the 15‐25 keV H+ component of the ring current during the main phase of the September 19 magnetic storm was responsible for an approximately one order of magnitude increase in the electron heating rate and SAR arc emissions during the main phase compared to the recovery phase. The increase in the H+ flux occurred in association with a ring current “nose event”, a front of ions injected into the inner magnetosphere in response to a discontinuous change in the cross‐tail electric field. The association between nose events and intensifications of SAR arc emissions in the main phase has not previously been explored but is a natural consequence of the injection of significant fluxes of relatively low‐energy ring current ions earthward of the plasmapause during early storm time ring current formation.

Ultrafast field-dependent response of bandedge photogenerated electrons in quantum-well structures

The authors analyze the field-dependent femtosecond dynamics of bandedge photogenerated electrons undergoing parallel transport in quantum-well structures. The intracollisional field effect, breakdown of the Fermi golden rule, quantization of the phonon modes, and transient charge variations are all comprehensively included. The electron heating rates at zero fields are in agreement with experiments. The results are indicative of an adequate description of the electron-phonon interaction in two-dimensional systems. At high fields, an energy overshoot structure in keeping with recently observed data was observed without any real-space transfer. >

Global Characteristics of Field-Aligned Acceleration Processes Associated with Auroral Arcs.

To study the global characteristics of field-aligned acceleration processes associated with auroral arcs, we have analyzed the particle and aurora image data obtained from the DMSP-F6 and -F7 satellites. The intensities of auroral emissions for 5577-Å, 6300-Å and N2 (1PG) have been calculated using the observed electron fluxes and the two-stream electron transport code to show that the fluxes of precipitating electrons are sufficient to produce visible auroral arcs. Then, the density and thermal energy of these electron fluxes at magnetospheric altitude have been estimated by fitting the accelerated Maxwellian distribution function to the observed electron energy spectra and by evaluating the effect of electron heating during the acceleration. We have obtained global distributions of the field-aligned potential difference, magnetospheric electron density and thermal energy, electron heating rate during the acceleration and auroral emission intensities for magnetic quiet and active periods, respectively. It is found that the field-aligned potential difference increases as magnetospheric electron density and adiabatic field-aligned conductivity decrease, suggesting the constant-current generator for the magnetosphere-ionosphere current circuit. The magnetospheric source electrons of dayside arcs are characterized by high density and low thermal energy, particularly in the quiet period. It is suggested that accelerated electron precipitation events observed on the lower latitude side of the cusp region are connected to the LLBL, while those observed on the higher latitude side of the cusp region are connected to the plasma mantle. In the quiet period, the region of latter events expands to higher latitude region associated with the expansion of the plasma mantle into the magnetospheric lobe region. The nightside events which show low electron density and high thermal energy at the magnetospheric source region appear to have originated from the plasma sheet region. The morning side events are a mixture of high density events and low density events. We consider that the former events have a source in the LLBL or the plasma mantle, while the latter events have a source in the plasma sheet which expands to the tail flank region. These different characteristics of magnetospheric source electrons for different magnetic local time and magnetic latitude seem to produce the variety of auroral arcs on global scale.

Rocket observation of the magnetosphere‐ionosphere coupling processes in quiet and active arcs

Magnetosphere‐ionosphere coupling processes in inverted‐V electron precipitation regions have been investigated using particle and magnetic field data obtained from two antarctic sounding rockets S‐310JA‐11, and S‐310JA‐12, launched into quiet and active auroral arcs, respectively. These data have suggested the presence of a linear relation between field‐aligned current and field‐aligned potential difference, i.e., j∥ = KV∥, given by Fridman and Lemaire [1980] and Lyons [1980]. The density n and thermal energy E0 of primary electrons have been obtained by fitting accelerated Maxwellian distribution functions to the observed electron energy spectra. It is found that the thermal energy E0 is larger inside the arcs than outside the arcs for both the quiet and active arcs observed, suggesting that precipitating electrons are heated during the field‐aligned acceleration. In contrast, the electron density n is enhanced outside the arcs for the quiet arc event, while it is enhanced inside the arcs for the active arc event. From an investigation of the relation between E0 and V∥ and also the relation between E0 and j∥, it is suggested that the heating occurs effectively when the current intensity exceeds a certain threshold and that the electron heating rate is 5–40% of the energy gain due to the field‐aligned acceleration. Assuming that, this heating is due to Joule heating through anomalous resistivity, it is also suggested that the total anomalous resistivity along the magnetic field line decreases with an increase of K.

Effects of collisional processes on the Critical Velocity Hypothesis

Plasma production in a gas release from a body moving in low Earth orbit may occur via Alfven's critical ionization velocity (CIV) process. The effects of the collisional processes of charge exchange and elastic collisions of neutrals with ions and electrons are examined by numerical simulations of a plasma with a beam of fast neutral molecules. The rate of electron heating via plasma interactions increases as the fraction of ions in the fast beam increases. When the initial beam fraction is 0.005, increasing the neutral number density nN (for nN < 1012 cm−3) increases the number of excitations and ionizations by electrons. This increased electron heating results from ambient charge exchange collisions increasing the fraction of beam ions. When the initial beam fraction is 0.5, the number of ionizations and excitations is shown to go through a maximum as nN increases. The initial increase is the result of the shorter collision times for the fast electrons, and the later decrease is the result of elastic collisions that disrupt the electron heating. In the higher density regime, the lower energy process of excitation is favored over ionization. Resonant charge exchange is an important process in maintaining the energy of the fast ion beam, and it lowers the threshold velocity for the CIV process.

Computer simulation of Alfvén wave heating

A particle simulation study of shear Alfvén wave resonance heating is presented. A particle simulation model has been developed for this application that incorporates Darwin’s formulation of the electromagnetic fields with a guiding center approximation for electron motion perpendicular to the ambient magnetic field. With this model, several cases of Alfvén wave heating are examined in both uniform and nonuniform simulation systems in a two-dimensional slab. When the antenna parameters match the shear Alfvén resonance condition, the simulation plasmas in the homogeneous cases react strongly with the driven wave. For the inhomogeneous case studies, the kinetic Alfvén wave develops in the vicinity of the shear Alfvén resonance region. The electrons kinetically react with the wave through a collisionless process. The electron velocity distribution function flattens about the parallel phase velocity of the wave with accompanying changes in the spatial structure of the wave. The electron heating rate is in good agreement with the Landau damping model. A substantial electron current is also generated parallel to the applied magnetic field. The ions gain energy by oscillating in the wave electric fields.

Excitation of kinetic Alfvén waves by resonant mode conversion and longitudinal heating of magnetized plasmas

Simulation of the kinetic Alfvén wave is performed using a two-and-one-half-dimensional (2 (1)/(2) -D) macroscale particle [magnetohydrodynamic (MHD) scale kinetic] simulation code. An oscillating antenna current is applied in one of the boundary regions to launch MHD perturbations into an inhomogeneous plasma in which a sheared magnetic field is present. It is shown that the applied perturbation is mode converted into the kinetic Alfvén wave at the Alfvén resonance layers, resulting in resonant heating of both the ions and electrons. When the plasma beta is relatively low, only the electrons are heated along the ambient magnetic field. The electron heating rate is found to be scaled as dTe∥/dt∝β1/2e 〈δB2y〉, where βe is the electron beta and 〈δB2y〉 is the wave magnetic field intensity. In contrast, ion heating occurs when the ion beta is close to unity and the temperature ratio satisfies Te/Ti>1. Besides plasma heating, it is found that the plasma particles are accelerated along the ambient magnetic field in the direction of the wave propagation through Landau resonance with the kinetic Alfvén wave.

A new model of cometary ionospheres

The coupled continuity, momentum, and energy equations were solved for ionospheric conditions appropriate for comet Halley at 1 AU. The numerical scheme used is such that any shock transition appears naturally in the solution and no a priori assumptions are necessary. Solutions were obtained for a number of different assumptions concerning electron heating rates, but all showed that the electron temperatures increase rapidly and significantly at a distance from the nucleus where collisional electron‐neutral cooling becomes unimportant. This temperature increase is accompanied by a sharp increase in both the plasma pressure and its associated polarization electric field, causing the supersonic plasma flow to go subsonic. It is not clear at this time whether or not this sonic transition is accompanied by a shock.

The role of ring current O+ in the formation of stable auroral red arcs

Coulomb collisions between ring current protons and thermal electrons were first proposed by Cole (1965) as the energy source for stable auroral red (SAR) arcs. Recent observations have shown that the ring current and magnetospheric plasma contain significant amounts of heavy ions (Johnson et al., 1977; Young et al., 1977; Geiss et al., 1978; and others). In fact, the ring current is often dominated by heavy ions at those energies (E ≤ 17 keV) important for Coulomb collisions on SAR arc field lines (Kozyra et al., 1986a). Observations (during four SAR arcs in 1981) of thermal and energetic ion populations by the Dynamics Explorer 1 satellite in the magnetospheric energy source region and nearly simultaneous Langmuir probe measurements of enhanced electron temperatures by Dynamics Explorer 2 within the SAR arc at F region heights have allowed us to examine the role of heavy ions in the formation of SAR arcs. We find that (1) sufficient energy is transferred to the electron gas at high altitudes via Coulomb collisions between the observed ring current ions and thermal electrons to support the enhanced (SAR arc) F region electron temperatures measured on these field lines, (2) the latitudinal variation in the electron heating rates calculated using observed ion populations is consistent with the observed variation in electron temperature across the SAR arc, and (3) in all cases, ring current O+ is the major source of energy for the SAR arcs. This implies a relationship between the heavy ion content of the magnetospheric plasma and the occurrence frequency and intensity of SAR arcs.

STUDY ON HEAT TRANSPORT IN TOKAMAK PLASMA FROM SOFT X-RAY SAWTOOTH OSCILLATION

Soft X-ray emission and its fluctuation in CT-6B tokamak are detected by using a Au(Si) surface barrier detectors array. The empirical scaling law for soft X-ray sawtooth oscillation in the center of plasma during internal disruption period is given in this paper. The electron thermal transport phenomena, such as electron heating rate, electron energy balance, electron energy confinement time, current density distribution, and electron temperature in the center of plasma during internal disruption are studied from soft X-ray sawtooth oscillation observations.

Thermal electron quenching of N( 2D): Consequences for the ionospheric photoelectron flux and the thermal electron temperature

This paper examines the effects of quenching of N( 2D) by thermal electrons on the ionospheric photoelectron flux and on the thermal electron heating rate. It is shown that the 2.5 eV electrons produced by electron quenching of N( 2D) can account for the differences between theoretical and experimental 0–3 eV photoelectron fluxes above 200 km altitude. In addition, the heat transferred to the thermal electron gas amounts to 70% of the photoelectron local heating rate at 250 km altitude. The effect of the extra heating is to increase the electron temperature by approximately 200 K at 250 km.

Optimization of energetic electron energy degradation calculations

The optimization of the energy degradation and reapportionment computer algorithms within theoretical computations of the effects and behavior of photoelectrons and other energetic electrons is established within a framework of discrete losses resulting from inelastic collisions with a neutral gas and interactions with the ambient electron gas. The basic method described guarantees energy conservation, while allowing large increases in the energy cell sizes with increasing energy with minimal distortion of the total excitation rates of neutrals and heating of the ambient electrons over what would otherwise be possible. When energy resolution of the spectra can be sacrified, extensions to very large energies are economically feasible using approximately seven cells per decade of energy without significant distortions in the energy reapportionment to other species. The emphasis is not on what particular set of cross sections should be used but rather on how to adapt the energy degradation procedure and the energy grid to the characteristics of the cross sections over the energy range of interest. For example, accurate determination of the ambient electron heating rate in terrestrial applications requires fairly small energy cells at low energies (usually less than 0.2 eV wide below 10 eV), while secondary ionization rates and most neutral excitation rates place no severe limitations on the energy cell sizes. Cell widths much larger than the excitation thresholds are possible and can be large fractions of the mean cell energy. At energies above 30 eV, cell widths that are up to 40% of the mean cell energy appear adequate for some applications not requiring high spectral resolution.

Heat balance of the ionosphere: Implications for the international reference ionosphere

Theoretical considerations can be helpful tools in modelling ionospheric parameters in regions and for times where not enough experimental data are available. Our study asks whether results of heat balance calculations should be introduced to supplement the data base for the International Reference Ionosphere (IRI). We discuss the present status of our theoretical understanding and examine the influence of the following unresolved or neglected terms: (1) electron heating rate, (2) electron cooling by fine structure excitation of atomic oxygen, and (3) height-dependent Coulomb Logarithm. The ambiguity introduced by (1)–(3) leads up to 30% uncertainty in the electron temperature of the lower thermosphere. The electron temperature in the upper ionosphere is largely determined by heat conduction from above and depends critically on the conditions assumed at the boundary between ionosphere and plasmasphere.

Thermal electron heating rate: A derivation

The thermal electron heating rate, Qe, is an important heat source term in the ionospheric electron energy balance equation, representing heating by photoelectrons or by precipitating higher energy electrons. A formula for the thermal electron heating rate is derived from the kinetic equation by using the electron‐electron collision operator as given by the unified theory of Kihara and Aono. This collision operator includes collective interactions to produce a finite collision operator with an exact Coulomb logarithm term. The derived heating rate Qe is the sum of three terms, Qe = Qp + S + Qint, which are, respectively, (1) primary electron production term giving the heating from newly created electrons that have not yet suffered collisions with the ambient electrons, (2) a heating term evaluated on the energy surface meυ²/2 = ET at the transition between Maxwellian and tail electrons at ET, and (3) the integral term representing heating of Maxwellian electrons by energetic tail electrons at all energies > ET. Published ionospheric electron temperature studies have used only the integral term Qint with differing lower integration limits. There can be a significant numerical difference between Qe and Qint. Use of the incomplete heating rate could lead to erroneous conclusions regarding electron heat balance, since Qe is greater than Qint by as much as a factor of 2. The sensitivity of the heating rate to the method of calculating the energetic (tail) electron distribution function by using either a linear or a quadratic collision operator is demonstrated. Choice of the transition energy, ET, between the thermal (Maxwellian) population and the energetic tail electrons significantly affects the magnitude of the individual heating rate terms. The net heating rate Qe is less sensitive to the value of ET than are the individual terms.