Electron Heating Rate Research Articles

Inelastic scattering effects on photoelectron spectra and ionospheric electron temperature

Three sets of inelastic scattering cross sections have been used by various investigators in energy degradation computations of photoelectrons. The effects of the three sets upon photoelectron spectra in the ionosphere, electron heating rates and temperature, and dayglow emissions are examined for solar minimum and solar maximum conditions. Comparison of individual cross sections shows large differences among the three sets but the overall inelastic scattering, summed over states and species is sufficiently similar such that the effect on the electron heating rate and temperature is only minor. Photoelectron spectra differ in details at energies below about 20 eV. The major difference is found in the excitation and emission rates of some features in the dayglow spectrum.

Turbulent resistive heating of solar coronal arches

The possibility that coronal heating occurs by means of anomalous Joule heating by electrostatic ion cyclotron waves is examined, with consideration given to currents running from foot of a loop to the other. It is assumed that self-fields generated by the currents are absent and currents follow the direction of the magnetic field, allowing the plasma cylinder to expand radially. Ion and electron heating rates are defined within the cylinder, together with longitudinal conduction and convection, radiation and cross-field transport, all in terms of Coulomb and turbulent effects. The dominant force is identified as electrostatic ion cyclotron instability, while ion acoustic modes remain stable. Rapid heating from an initial temperature of 10 eV to 100-1000 eV levels is calculated, with plasma reaching and maintaining a temperature in the 100 eV range. Strong heating is also possible according to the turbulent Ohm's law and by resistive heating.

Heating of thermal ionospheric electrons by suprathermal electrons

Several investigators have computed ionospheric electron heating rates in the past using an incorrect term in the expression for the energy transfer from the suprathermal to the thermal electrons derived by Mantas [1975]. This incorrect formulation was also based on an electron energy loss rate inversely proportional to the suprathermal electron energy, limiting its application to energies above about 2‐3 eV. Since the proper low‐energy cutoff is the cross‐over energy at which the thermal electron intensity equals the suprathermal one, a considerable portion of the ambient electron heating may take place below 2‐3 eV, depending on the ionospheric conditions. Mantas [1981] has amended these inadequacies, but has not explored their geophysical consequences. Comparing electron heating rates and electron temperatures computed by the incorrect approach with identical computations based on the proper energy transfer term, energy loss rate and cross‐over energy, we find that the previous approach leads to a substantial underestimate of the ambient electron heating rate as well as the resulting ionospheric electron temperature. This underestimate is more pronounced for solar minimum than for solar maximum conditions as could be anticipated since the elevated electron densities and temperatures at solar maximum lead to a higher cross‐over energy and thus a lesser impact of the inadequacies in previous treatments.

Rate of electron heating in a multidipole plasma

The rate of increase in electron temperature in a multidipole device due to the interaction of a group of test electrons with an argon plasma is determined.

Electron temperatures in the Jovian ionosphere

The daytime electron temperature profile of the Jovian ionosphere was calculated, taking into account the effects of thermal conduction and heat inflow from the plasmasphere. The photoelectron fluxes and electron heating rates were determined by using the two-stream approach of Banks and Nagy (1970) and Nagy and Banks (1970). The calculated electron temperatures were found to follow the neutral temperature up to an altitude slightly above the electron density peak, while at higher altitudes they were significantly enhanced above the assumed neutral temperature value.

Gas breakdown at cyclotron resonance with a submillimeter laser

A pulsed 496-μm CH3F laser is used to produce gas breakdown in He at pressures between 1 and 300 Torr in an intense longitudinal magnetic field. Breakdown is detected by the observation of visible light when the electron cyclotron frequency (eB/m) equals the laser frequency, which occurs at B=216 kG for λ=496 μm. At the lowest helium pressures and near cyclotron resonance, the focused laser intensity of 40 kW/cm2 gives rise to very large electron heating rates, well beyond the limit of validity of conventional equilibrium breakdown theory. The observed result is an intensity-dependent resonant linewidth, much larger than predicted by equilibrium theories.

Parametric instabilities and plasma heating in an inhomogeneous plasma

Experimental studies of plasma heating due to microwave irradiation of the magnetically confined plasma column in the Princeton L-3 device is presented. X-band (10.4 GHz) microwave power, both in the ordinary and the extraordinary modes of propagation, is used in these experiments. Plasma heating is observed to occur simultaneously with the occurrence of parametric decay instabilities. The mode structure of the pump wave and the decay ion wave dispersion have been measured with high frequency probes. Detailed measurements of electron heating rates are presented and compared with collisional heating rates. In addition, production of suprathermal electrons and ions is also observed and measured. A comparison is made with recent laser-pellet interaction experiments.

Electron heating resulting from interhemispherical transport of photoelectrons

Ambient electron heating rates along several magnetic field lines have been determined for subsequent studies of electron and ion temperatures. Use is made of the modified diffusion method for computing the heating of the ambient plasma, and the escape fluxes from both hemispheres are coupled by self-consistent upper boundary conditions supplied by interhemispheric fluxes degraded in energy along the magnetic field tubes. Heating rates and fluxes are presented for several low L-shells appropriate for noon solstice conditions when both hemispheres are illuminated. The opacity of the field tubes as a function of L is expected to go through a minimum due to the transition from large collective effects of coulomb small angle scattering and energy loss for high L-shells, to a domination by neutral scattering all along the field lines of low L-shells.

Electron heating rates in the E and lower F regions

Electron temperatures and electron densities measured on four rocket flights have been used to deduce electron heating rates in the E and lower F regions. Above 150 km heating rates at midday are found to be in good agreement with calculated values. Anomalies are found in heating rates at sunrise which are attributed to a source, such as joule heating, which does not produce ionization.

Theory of enhanced ion and electron heating, and dissipation, due to ion acoustic turbulence

A calculation is made of the enhanced ion heating rate ν+, electron heating rate ν−, and dissipation, produced by ion acoustic turbulence. The effects of turbulence on ion motions are accounted for. It is found that ν+ ≳ ν− for some experiments, leading to a decreasing ratio of electron to ion temperatures and cessation of heating. It is also shown that ν+ ∝ m+−1/2 (ion mass).

Theory of Anomalous Resistivity and Turbulent Heating in Plasmas

General expressions for the d.c. resistivity and the heating rates of the electrons and the ions are obtained in terms of the spectral functions of particle correlation functions; the results are rigorous and applicable to both quiescent and turbulent plasmas. The method of analysis is based on the moment calculations of the first equations of the Bogo-liubov-Born-Green-Kirkwood-Yvon hierarchy for a multicomponent plasma. Definite predictions are made on the relative magnitudes of the electron and ion heating rates when the nature of the turbulent fluctuations is known. Some of the well-known formulas for the anomalous resistivity are obtained as specific cases of the present calculation. It is shown that a consideration of the critical fluctuations alone cannot account for the anomalous resistivity in a turbulent plasma.

Effect of excited states of atomic oxygen ions on the reaction rates and thermal balance in the F-region

A recent paper by Rutherford and Vroom (1971) showed that the charge transfer reaction of the metastable O +( 2D) with N 2 was significantly faster than the ground state, O +( 4S), reaction. Similarly, Stebbings et al. (1966) showed that the charge transfer with O 2 was at least an order of magnitude greater for the excited O +( 2D) than the ground state atomic oxygen ion. Thus a substantial portion of the atomic oxygen ions in the O +( 2D) state will provide an important source of N 2 + and O 2 + which will have the effect of increasing the electron-ion recombination rate. The excited states of atomic oxygen ions can also undergo de-excitation by means of radiative transitions or collisional electron deactivation. The electron deactivation provides the electrons with several eV of energy for each collision, and thus provides a highly efficient heating source for the ambient electrons. This paper presents the reaction rates for the metastable states of O + and other relevant data needed to calculate the electron-ion recombination rate and the ambient electron heating rate. A comparison is made to indicate how much effect the excited states of O + have on these two processes in the F-region.

Revised calculations ofFregion ambient electron heating by photoelectrons

Photoelectron energy degradation calculations have been performed with the improved analytic expression for the photoelectron to ambient electron energy transfer rate given by Swartz et al. (1971). On the basis of these calculations, two curves for the mean energy transferred per photoelectron to the ambient electrons are given as functions of the electron-neutral density ratio. One curve is based on the primary-photoelectron production rate, and the other on the total production rate. When the electron-neutral density ratio falls between 10−6 and 10−3, these curves provide good estimates of the electron heating rates over a wide range of F region conditions. The large differences between the energy transfer rate coefficients used in these calculations and the Butler and Buckingham (1962) form used in most previous investigations do not result in a major modification of the ambient electron heating rate.

Time-dependent behaviour of a stable auroral red arc excited by an electric field

We examine the electric field hypothesis as a possible explanation of a stable auroral red arc. An electric field perpendicular to the geomagnetic field in the ionosphere heats the ambient F-region electrons and ions. Given large enough electric fields, the electrons can be heated sufficiently to excite the OI ( 1 D) term of atomic oxygen by electron impact, giving rise to the λ6300 emission characteristic of the red arc. The electron and ion heating rates are determined by the relative drift between the plasma and neutral gas. The electric field, acting through ion drag, accelerates the neutral gas in a time scale small compared to the observed lifetime of the arc. If the electron density within the red arc is high, the relative drift between the plasma and neutral gas is significantly reduced and the red arc excitation is effectively shut off because of the consequent lower electron and ion heating rates. For low electron densities, the electric field strength necessary to excite the red arc is far greater than any fields which have been observed. For all electron densities between these two extremes, the calculated features of a red arc excited by a perpendicular electric field cannot be made consistent with both satellite observations of electron temperature and ground-based observations of λ6300 emission. We conclude that it is not possible for a perpendicular electric field to excite a red arc such as observed, and thus support the contention that conduction of heat in the electron gas from the magnetosphere alone is sufficient to excite and maintain the stable auroral red arc.

The electron heating rate and ion chemistry in the thermosphere above Wallops Island during the solar eclipse of 7 March 1970

An identical pair of thermosphere probes measured the N 2 concentration and temperature, the ion composition and concentrations and the electron temperature up to 290 km about 30 min and 5 min before totality during the 7 March 1970 eclipse at Wallops Island. The rockets travelled similar trajectories thus permitting the purely temporal changes between nights to be resolved. The neutral temperature and N 2 concentration changed little but the electron temperature decreased by as much as 20 per cent in the lower F-region. The ion concentration decreased by about 30 per cent in the F-region and about 50 per cent in the E-region, with little change in relative ion composition. The electron cooling rates decreased by a factor of 6 in the lower F-region, approximately in proportion to the change in visible solar disc. A smaller than expected decrease in the cooling rate below 150 km between the two flights indicates a hardening of the solar spectrum and suggests a significant heat contribution from the solar corona near totality. The ion composition measurements were consistent with solutions of the ion continuity equations. A proper fit required a factor of three enhancement of the flux below 200 Å, an amount also consistent with the electron heat balance analysis. Reactions involving the minor ions N + and N 2 + were found to be important for the ion chemistry of the major ions O 2 + and NO +, especially at the time of eclipse. The negligible response of the neutral atmosphere to the eclipse is reasonable considering the long time constants for the conductive and convective transport processes and the local nature of the disturbance.

Turbulent Heating in Computer Simulations of the Modified Plasma Two-Stream Instability

Computer simulations of the fluidlike modified two-stream instability, driven by relative electron-ion drifts across a magnetic field, show strong anomalous plasma heating. The electron and ion heating rates are comparable and result in ion thermal speeds which approach the relative drift speed within a few ion plasma periods.

Experiment in Stochastic Heating

A collisionless plasma in a magnetic mirror is heated by a random electric field, acting transverse to the magnetic field. Heating occurs when the noise spectrum spans the band of electron cyclotron frequencies existing in the mirror. The electron heating rate, 1.0 × 105 〈E2(V/cm)2〉 eV/sec, is in reasonable agreement with the value predicted by a simplified theoretical analysis.

Stochastic heating experiment

A collisionless plasma in a magnetic mirror is heated by an externally applied random electric field acting transverse to the magnetic field direction. The electron heating rate is found to be 1.0 × 10 5 E 2 eV/s, in good agreement (within a factor of two) with the value predicted by a theoretical analysis.

Stochastic Electron Heating and Hydromagnetic Wave Damping

Physical processes involved in collisionless damping of the fast hydromagnetic mode are investigated by considering the stochastic heating of electrons by a random spectrum of fast waves. We take as a model a weakly damped fast wave, propagating in a direction such that the damping is mainly due to electron heating; allowance is made for the possibility of a small component of electric field parallel to the unperturbed field. To estimate the damping we consider an ensemble of electrons accelerated (1) by magnetic-moment magnetic-field-gradient interaction and (2) by the parallel electric field. Electron heating is calculated from a Fokker—Planck type of equation; the damping decrement is obtained by equating the electron heating rate to the wave energy loss rate, and agrees with the damping decrement obtained from the appropriate asymptotic limit of the general dispersion relation. Some general aspects of this method for obtaining wave-damping decrements are discussed.

Experimental Study of Collision-Free Shock Waves and Anomalous Electron Heating

Cylindrically converging magnetic compression waves have been observed propagating into a low density hydrogen plasma (ne = 3 × 1014, kTe = 1.4 eV) in a fast theta pinch discharge with the compressing field and initial field both parallel and antiparallel. For parallel fields, the waves are nonstationary in this experiment and cylindrical convergence effects cannot be ruled out. The thickness of the transition is greater than 1 cm which is less than the ion gyroradius and the ion mean free path for ions travelling with the wave front across the initial magnetic field. The electron heating rate (≃10 eV/nsec) and the transition thickness are both greater than one would expect for resistive heating with the Spitzer-Härm resistivity. In the case where the compressing field and the initial field are antiparallel, a wave flow develops which appears to be an almost plane and nearly stationary collision-free shock. For an initial field of −450 G the Alfvén Mach number is estimated between 4 and 9. The magnetic transition has a slowly rising front part (>1 cm) followed by a faster rising part (l ≃ 3 mm).