Propagation and Group Velocity in a Warm Magnetoplasma

Aubry, M. P.; Bitoun, J.; Graff, Ph.

doi:10.1029/rs005i003p00635

Cited by 27 publications

(23 citation statements)

References 7 publications

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“…Subscripts “0” refer to cold plasma parameters and subscripts “1” refer to warm plasma parameters. The parameter q T = k B T j / m j c 2 accounts for the effect of temperature, where k B is Boltzmann's constant, T j and m j are respectively the temperature in Kelvin and mass of the j th plasma species, and c is the speed of light [ Sitenko and Stepanov , ; Aubry et al , ; Fang and Andrews , ]. A 0 , B 0 , and C 0 are defined by the cold plasma dielectric tensor, K 0 :

K^{0} = ([], \begin{matrix} arrayleft \\ 1 - \sum_{j} \frac{X}{1 - Y^{2}} & \sum_{j} \frac{iXY}{1 - Y^{2}} & 0 \\ \sum_{j} \frac{- iXY}{1 - Y^{2}} & 1 - \sum_{j} \frac{X}{1 - Y^{2}} & 0 \\ 0 & 0 & 1 - X \end{matrix})

where

X = ω_{pj}^{2} / ω^{2}

, Y = ω c j / ω ,

ω_{pj} = q_{j}^{2} N_{j} / ϵ_{0} m_{j}

, and ω c j = q j B 0 / m j are respectively the plasma and cyclotron frequency of the j th plasma species, q j , N j , and m j are the corresponding charge, density, and mass, B 0 is the magnitude of the ambient magnetic field, ϵ 0 is the permittivity of free space, ω is the angular wave frequency, and

i = \sqrt{- 1}

.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…We can add a linear temperature correction to K 0 above: K = K 0 + τ K 1 , where K is the total dielectric tensor, K 1 is the warm plasma correction, and τ = q T μ 2 . The components of K 1 are given in Aubry et al []

\begin{matrix} alignleft \\ align-1 K_{11}^{1} & align-2 = \sum_{j} [\frac{- X}{1 - Y^{2}} (\frac{3 \overset{2}{\sin} ψ}{1 - 4 Y^{2}} + \frac{1 + 3 Y^{2}}{{(1 - Y^{2})}^{2}} \overset{2}{\cos} ψ)] \end{matrix}

\begin{matrix} alignleft \\ align-1 & align-2 \\ align-1 K_{22}^{1} & align-2 = \sum_{j} [\frac{- X}{1 - Y^{2}} (\frac{1 + 8 Y^{2}}{1 - 4 Y^{2}} \overset{2}{\sin} ψ + \frac{1 + 3 Y^{2}}{{(1 - Y^{2})}^{2}} \overset{2}{\cos} ψ)] \end{matrix}

\begin{matrix} alignleft \\ align-1 & align-2 \\ align-1 K_{33}^{1} & align-2 = \sum_{j} [- X (3 \overset{2}{\cos} ψ + \frac{\overset{2}{\sin} ψ}{1 - Y^{2}})] \end{matrix}

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Here we include finite particle temperature and investigate how this affects the conclusions of Kulkarni et al [2006] and Kulkarni et al [2008] that we hereafter refer to as Paper I and Paper II, respectively. To do so, we extend previous work [Sitenko and Stepanov, 1957;Buneman, 1961;Aubry et al, 1970] to include the effects of positive ions in a fully adiabatic warm plasma theory and calculate relevant refractive index surfaces.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The effect of electron and ion temperature on the refractive index surface of 1–10 kHz whistler mode waves in the inner magnetosphere

et al. 2015

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Whistler mode waves in the magnetosphere play an important role in the energy dynamics of the Earth's radiation belts. Previous theoretical work has been extended to include ions in the fully adiabatic warm plasma theory. Using a finite electron and ion temperature of 1 eV, refractive index surfaces are calculated for 1–10 kHz whistler mode waves in the inner magnetosphere (L ≲ 2.5). For the frequencies of interest, a finite ion temperature is found to have a greater effect on the refractive index surface than the electron temperature and the primary effect is to close an otherwise open refractive index surface. Including a finite ion temperature is especially important when the wave frequency is just above the local lower hybrid resonance frequency. For wave frequencies more than ∼1 kHz above the local lower hybrid resonance frequency, including the ion temperature has a negligible effect on the refractive index surface calculation. The results are used to assess previous conclusions on whether in situ whistler mode sources can be realistically used to precipitate energetic electrons. It is found that the number of in situ sources needed to illuminate the inner plasmasphere (L≲2.5) with whistler mode energy may be greater than previously predicted.

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K^{0} = ([], \begin{matrix} arrayleft \\ 1 - \sum_{j} \frac{X}{1 - Y^{2}} & \sum_{j} \frac{iXY}{1 - Y^{2}} & 0 \\ \sum_{j} \frac{- iXY}{1 - Y^{2}} & 1 - \sum_{j} \frac{X}{1 - Y^{2}} & 0 \\ 0 & 0 & 1 - X \end{matrix})

where

X = ω_{pj}^{2} / ω^{2}

, Y = ω c j / ω ,

ω_{pj} = q_{j}^{2} N_{j} / ϵ_{0} m_{j}

i = \sqrt{- 1}

.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

\begin{matrix} alignleft \\ align-1 K_{11}^{1} & align-2 = \sum_{j} [\frac{- X}{1 - Y^{2}} (\frac{3 \overset{2}{\sin} ψ}{1 - 4 Y^{2}} + \frac{1 + 3 Y^{2}}{{(1 - Y^{2})}^{2}} \overset{2}{\cos} ψ)] \end{matrix}

\begin{matrix} alignleft \\ align-1 & align-2 \\ align-1 K_{22}^{1} & align-2 = \sum_{j} [\frac{- X}{1 - Y^{2}} (\frac{1 + 8 Y^{2}}{1 - 4 Y^{2}} \overset{2}{\sin} ψ + \frac{1 + 3 Y^{2}}{{(1 - Y^{2})}^{2}} \overset{2}{\cos} ψ)] \end{matrix}

\begin{matrix} alignleft \\ align-1 & align-2 \\ align-1 K_{33}^{1} & align-2 = \sum_{j} [- X (3 \overset{2}{\cos} ψ + \frac{\overset{2}{\sin} ψ}{1 - Y^{2}})] \end{matrix}

…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The effect of electron and ion temperature on the refractive index surface of 1–10 kHz whistler mode waves in the inner magnetosphere

et al. 2015

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“…In addition to the usual electromagnetic-wave echoes, many other responses, called resonances, are observed by topside sounders. The most frequent and predictable of these are long, nearly continuous signals that occur when the operating frequency is close to either the plasma frequency, upper hybrid frequency, or harmonics of the electroncyclotron frequency of the ambient plasma [Lockwood, 1963;Calvert and Goe, 1963].Resonances at the plasma frequency and the upper hybrid frequency have recently been explained as electrostatic-wave echoes [McAfee, 1968[McAfee, , 1969a[McAfee, , 1969bFejer and Yu, 1970;Aubry, Bitoun, and Graff, 1970]. In this model, electrostatic waves launched obliquely at frequencies within several kilohertz of the plasma frequency or upper hybrid frequency propagate short distances from the spacecraft, are reflected, and return to it, producing a signal at a…”

mentioning

confidence: 99%

“…Resonances at the plasma frequency and the upper hybrid frequency have recently been explained as electrostatic-wave echoes [McAfee, 1968[McAfee, , 1969a[McAfee, , 1969bFejer and Yu, 1970;Aubry, Bitoun, and Graff, 1970]. In this model, electrostatic waves launched obliquely at frequencies within several kilohertz of the plasma frequency or upper hybrid frequency propagate short distances from the spacecraft, are reflected, and return to it, producing a signal at a…”

mentioning

confidence: 99%

Electron temperature from topside plasma resonance observations

Warnock¹,

McAfee²,

Thompson³

1970

J. Geophys. Res.

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The resonance observed by topside sounders near the plasma frequency is due to oblique electrostatic‐wave echoes. Under certain conditions, two simultaneous echoes of slightly different frequencies occur and produce a beat pattern. The good agreement between the observed and theoretical beat patterns is good support for the theory. Furthermore, this beat pattern depends on electron temperature, and provides a new method of measuring it. The possibility of continuous and accurate electron temperature measurement suggests sounder experiments designed to observe the individual electrostatic‐wave echoes.

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Magnetospheric whistler mode ray tracing in a warm background plasma with finite electron and ion temperature

Maxworth

Gołkowski

2017

JGR Space Physics

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Whistler mode waves play a major role in the energy dynamics of the Earth's magnetosphere. Numerical ray tracing has been used for many years to determine the propagation trajectories of whistler mode waves from various sources, both natural and anthropogenic. Previous work has been under the ideal cold plasma assumption even though temperatures of the background ions and electrons are in the range of several eV. We perform numerical ray tracing with the inclusion of finite electron and ion temperatures to more accurately model the plasma environment of the Earth's magnetosphere. Finite temperature effects are found to play a significant role in the whistler mode refractive index surface only when the wave frequency is near the lower hybrid resonance frequency and the wave normal angle is oblique. In such cases, the primary effect on whistler mode propagation is to lower the refractive index magnitude and increase the group velocity with slight modifications to the ray trajectories. Landau damping is shown to increase slightly with the inclusion of finite temperature.

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Propagation and Group Velocity in a Warm Magnetoplasma

Cited by 27 publications

References 7 publications

The effect of electron and ion temperature on the refractive index surface of 1–10 kHz whistler mode waves in the inner magnetosphere

The effect of electron and ion temperature on the refractive index surface of 1–10 kHz whistler mode waves in the inner magnetosphere

Electron temperature from topside plasma resonance observations

Magnetospheric whistler mode ray tracing in a warm background plasma with finite electron and ion temperature

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