Diurnal distribution of ELF, VLF, and LF noise at high latitudes as observed by Alouette 2

Barrington, R. E.; Hartz, T. R.; Harvey, R. W.

doi:10.1029/ja076i022p05278

Cited by 65 publications

(41 citation statements)

References 24 publications

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“…This requires, with (Bw/B) 3 / 2 > (C/WpeL) 2 , that the wave field exceeds the critical value for trapping over a full period. A more precise rendering of this condition, and its relation to observations, is given in equation (1)(2)(3)(4). Although we will stipulate a third condition below that will uniquely determine a and relate the scale length, L, and wave field, B", this third condition is largely a matter of convenience.…”

Section: (3-8)mentioning

confidence: 99%

“…The terms on the right hand side of eq. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) scale respectively like (dropping the fourth),…”

Section: (3-8)mentioning

confidence: 99%

“…The phase, 0 , in equations (3-1) to (3)(4) gives the phase of a particle with respect to the wave and is expressed as, 0 = 0. + (P + 0, (3-6) where 0 is the particle's gyrophase angle.…”

Section: Lomentioning

confidence: 99%

“…First we neglect the linear damping and the divergence of the group velocity (as higher order in the E"/ expansion as outlined below). The field amplitude is written a, = ETrAeiw, (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) where ET is the field of the triggering wave, so that A is a dimensionless, order unity, slowly varying amplitude. We then scale the velocity to V, = cno/w 1 Note that the slowly varying wave phase W is included with 0, 4 in computing the nonlinear current, so that frequency shifts, bw = -80/Ot , away from the triggering frequency, w = -Oi/ t, are included in the non-linear current.…”

Section: Wkb Wave Equationsmentioning

confidence: 99%

“…pT (1)(2)(3)(4) Here the field strength is given in picotesla, the plasma density in units of 100 cm-3 , and I-shell number in units of 4, as appropriate for conditions near the plasmapause. The factor L/Ln gives the ratio of magnetic to density scale lengths, although the last factor in square brackets is very close to unity, and this is not very important here.…”

Section: S)mentioning

confidence: 99%

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Self‐Consistent Theory of Triggered Whistler Emissions

Molvig¹,

Hilfer²,

Miller³

et al. 1988

J. Geophys. Res.

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A kinetic theory of triggered VLF whistler emissions is given that is capable of predicting from a small scale numerical implementation the observed emission forms, and frequency-time characteristics. The present paper focuses on the theoretical developments and the explanation of the triggering process, complete with a demonstration of the threshold behavior (sometimes known as the dot-dash anomaly) and the generation of specific falling frequency emissions that compare quite favorably to typical observations made in the controlled experiments based in Siple Station, Antarctica. The theory that gives these results is a fully self-consistent nonlinear treatment based on kinetic theory and valid in the asymptotic limit when several trapping periods occur within the interaction region. For a typical set of parameters, I = 4.3, n = 400 cm-3 , and amplitude, BT ~ 1.6 pT, for the input wave magnetic field, one has about seven trapping periods in the triggering signal and would expect good results from the asymptotic limit. In this limit the nonlinear dynamics can be reduced to the determination of the time, r, that the resonant particles are trapped. The nonlinear currents can be expressed in terms of this function, r, by simple integrals over the trapped particles' perpendicular velocities alone. Most of the features of the emission process can be determined analytically and properties, such as the rate of change of frequency, related to magnetospheric parameters. For more quantitative predictions such as amplitude and frequency waveforms, a small numerical code which integrates the nonlinear wave equations is used. The theoretical picture of the triggering mechanism i contains the observed threshold behavior wherein short triggering pulses of nominal amplitude BT ~ 1 pT and 100 ms in duration or less cannot generate an emission, whereas those in the 200 ms range and longer do. Similar sensitivity is found with respect to initial frequency, where in some cases 5.5 kHz signals can trigger, but 5.0 kHz signals cannot.Gains in the range of 20 -30 dB are obtained with initial temporal growth rates in the range 100 -200 dB/sec. The emission process requires an inverted population in the perpendicular velocity distribution function but not necessarily linear instability. A sufficient number of high energy electrons is required that the driven currents can offset convection, but provided this is satisfied, a sufficiently long triggering signal will always generate a self-sustaining emission. Interestingly, however, the self-sustaining emission does not depend on the number of these high energy particles or the details of the velocity distribution function but only on bulk magnetospheric parameters such as magnetic field, gradient scale length, and the plasma density in the plasmapause. Also the marginal signals generated just above the threshold are always fallers as is observed. These features have not been explained by existing theories. Unresolved issues include the mechanism of termination, the generation of ri...

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Section: (3-8)mentioning

confidence: 99%

“…The terms on the right hand side of eq. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) scale respectively like (dropping the fourth),…”

Section: (3-8)mentioning

confidence: 99%

“…The phase, 0 , in equations (3-1) to (3)(4) gives the phase of a particle with respect to the wave and is expressed as, 0 = 0. + (P + 0, (3-6) where 0 is the particle's gyrophase angle.…”

Section: Lomentioning

confidence: 99%

Section: Wkb Wave Equationsmentioning

confidence: 99%

Section: S)mentioning

confidence: 99%

See 3 more Smart Citations

Self‐Consistent Theory of Triggered Whistler Emissions

Molvig¹,

Hilfer²,

Miller³

et al. 1988

J. Geophys. Res.

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A prediction model for the global distribution of whistler chorus wave amplitude developed separately for two latitudinal zones

et al. 2015

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Whistler mode chorus waves are considered to play a central role in accelerating and scattering electrons in the outer radiation belt. While in situ measurements are usually limited to the trajectories of a small number of satellites, rigorous theoretical modeling requires a global distribution of chorus wave characteristics. In the present work, by using a large database of chorus wave observations made on the Time History of Events and Macroscale Interactions during Substorms satellites for about 5 years, we develop prediction models for a global distribution of chorus amplitudes. The development is based on two main components: (a) the temporal dependence of average chorus amplitudes determined by correlating with the preceding solar wind and geomagnetic conditions as represented by the interplanetary magnetic field (IMF) B z and AE index and (b) the determination of spatial distribution pattern of chorus amplitudes, specifically, the profiles in L in all 2 h magnetic local time zones, which are categorized by activity levels of either the IMF B z or AE index. Two separate models are developed: one based only on the IMF B z and the other based only on AE. Both models predict chorus amplitudes for two different latitudinal zones separately: |magnetic latitude (MLAT)| < 10°, and |MLAT| = 10°-25°. The model performance is measured by the coefficient of determination R 2 and the rank-order correlation coefficient (ROCC) between the observations and model prediction results. When tested for a new data interval of~1.5 years, the AE-based model works slightly better than the IMF B z -based model: for the AE-based model, the mean R 2 and ROCC values are~0.46 and~0.78 for |MLAT| < 10°, respectively, and~0.4 and~0.74 for |MLAT| = 10°-25°, respectively; for the IMF B z -based model, the mean R 2 and ROCC values are~0.39 and~0.74 for |MLAT| < 10°, respectively, and~0.33 and~0.70 for |MLAT| = 10°-25°, respectively. We provide all of the model information in the text and supporting information so that the developed chorus models can be used for the existing outer radiation belt electron models.

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Impulsive Ion Injection into the Polar Cusp

Torbert

Carlson

1976

Magnetospheric Particles and Fields

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Diurnal distribution of ELF, VLF, and LF noise at high latitudes as observed by Alouette 2

Cited by 65 publications

References 24 publications

Self‐Consistent Theory of Triggered Whistler Emissions

Self‐Consistent Theory of Triggered Whistler Emissions

A prediction model for the global distribution of whistler chorus wave amplitude developed separately for two latitudinal zones

Impulsive Ion Injection into the Polar Cusp

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