Analytic expression for the energy-transfer rate from photoelectrons to thermal-electrons

Swartz, Wesley E.; Nisbet, John S.; Green, Alex E. S.

doi:10.1029/ja076i034p08425

Cited by 104 publications

(68 citation statements)

References 7 publications

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“…where I e (E, z) is the photoelectron flux at altitude z and energy E and L ee is the electron stopping cross section or loss function [Swartz et al, 1971] L ee E ð Þ ¼ 3:37 Â 10 À12 E 0:94 n 0:03 e E À T* E À 0:53T* 2:36 eV cm 2 ;…”

Section: Appendix A: Electron Heating As a Means To Estimate Neutral mentioning

confidence: 99%

Rise and fall of electron temperatures: Ohmic heating of ionospheric electrons from underdense HF radio wave pumping

et al. 2010

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[1] Here we present electron temperature variations observed with incoherent scatter radar during a European Incoherent Scatter Scientific Association Heating experiment with high-frequency (HF) radio wave transmission at frequencies above the peak ionospheric critical frequency. The electron temperature increased from 2000 K up to 2800 K during the HF transmission periods. During the experiment both pump frequency and polarization were altered between pump pulses. The observed temperature variation is compared with numerical solutions to the electron energy equation with ohmic heating modeling the effect of the radio wave heating of the plasma. Agreement between observations and model is found to be good.

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Section: Appendix A: Electron Heating As a Means To Estimate Neutral mentioning

confidence: 99%

Rise and fall of electron temperatures: Ohmic heating of ionospheric electrons from underdense HF radio wave pumping

et al. 2010

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“…where P (E) is the source function of the high energy electrons, L(E) is the loss function representing a continuous energy loss due to interaction of the streaming electrons with the cold electron gas as given by Swartz et al (1971): Here E is the electron energy in eV, N e is the electron density in cm −3 and T e is the ambient electron temperature in eV. F (E) in Eq.…”

Section: High Energy Tail Of the Thermal Electronsmentioning

confidence: 99%

“…Energy of a secondary electron resulting from the ionizing collision is calculated using the analytical representation (Jackman et al, 1977) of the double differential ionization cross-section measured in a laboratory experiment by Opal et al (1971). Continuous energy loss of the streaming electrons, due to the interaction with the cold electron gas, is determined using the loss function derived by Swartz et al (1971). An electron trajectory (primary and secondary) is traced until the electron exits the upper boundary of the atmosphere or reaches energy of less than 1 eV.…”

Section: The Electron Transport Modelmentioning

confidence: 99%

Modelling of optical emissions enhanced by the HF pumping of the ionospheric F-region

et al. 2012

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Abstract. Strong enhancement of the optical emissions with excitation threshold from 1.96 eV (630.0 nm from O( 1 D)) up to 18.75 eV (427.8 nm from N + 2 (1NG)) have been observed during experiments of the ionosphere modification by high power HF radio waves. Analysis of the optical emission ratios showed clearly that a significant part of the ionospheric electrons have to be accelerated to energies above 30 eV and more in the region where the HF radio wave effectively interacts with the ionospheric plasma. The Monte-Carlo model of electron transport and the optical emission model were used to study the dependence of the optical emission intensity on the acceleration electron parameters. We obtained the following results from analysis of the enhanced intensities of the four optical emissions (630.0, 557.7, 844.6 and 427.8 nm) observed in the EISCAT heating experiment on 10 March 2002. The 630.0 emission with an excitation threshold of 1.96 eV is formed predominately by the thermal electrons, where the accelerated electrons play a minor role in the excitation of this emission. In order to explain the experimentally observed intensity ratios, the accelerated electrons must gain energies of more than 60 eV. For accelerated electrons with a power law energy dependence, the efficiency of the optical emission excitation depends on the exponent defining the shape of the electron spectra. However, an agreement with the observed emission intensities is achieved for exponent values not less than zero. Moreover, increasing the exponent to higher values does not affect the emission intensity ratios.

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“…The tedious evaluation required of the G function, prompted Swartz et al (1971) to make an analytic fit to the energy lorts rate dt for both the classical and quantum mechanical formulas, however, their analytic function best represents the classical formula with the logarithm argument of Eq. A17…”

Section: Etmentioning

confidence: 99%

“…The superscript MT signifies Maxwellian scatterers and tail population scattered particles. Use of the exact energy loss rate d as given by Swartz et al 1971 in Eqs. 8 and 9B provides an accurate evaluation of the heating rate for the MT contribution.…”

Section: Thermal Electron Heating Ratementioning

confidence: 99%

Thermal electron heating rate: A derivation

Hoegy¹

1984

J. Geophys. Res.

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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 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, Q e = Qp + S + Qint, which are respectively: 1) primary electron production term giving the heating from

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Analytic expression for the energy-transfer rate from photoelectrons to thermal-electrons

Cited by 104 publications

References 7 publications

Rise and fall of electron temperatures: Ohmic heating of ionospheric electrons from underdense HF radio wave pumping

Rise and fall of electron temperatures: Ohmic heating of ionospheric electrons from underdense HF radio wave pumping

Modelling of optical emissions enhanced by the HF pumping of the ionospheric F-region

Thermal electron heating rate: A derivation

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