Abstract
Abstract. The VLF-wave frequency modulation efficiency as a function of magnetosphere plasma parameters under the weak pitch-angle diffusion regime is studied. The study is based on the VLF growth-rate modulation both in the magnetosphere equatorial plane and after integrating along the magnetic field line. It is shown that for the typical quiet magnetosphere plasma parameters the relative shift of the maximum intensity frequency ∆ωm/ωm is approximately equal to relative disturbance of the magnetic field in the magnetosphere equatorial plane, but may exceed it when both electron temperature anisotropy and the parameter αβ∥are small; here α is the total-to-warm electron content ratio and β∥ is the electron parallel beta. It is also shown that relative shift of the maximum intensity frequency ∆ωm/ωm after integrating along the field line is not less than 50% from its value at the equatorial plane, which allows the use of the equatorial-plasma-parameter data to estimate the VLF frequency modulation on the ground. The upper cut-off frequency modulation is considered as well. The calculated theoretical sonagrams show that this frequency modulation may be related to the non-dispersive and to the "inverted-V'' structures of QP hiss.
Highlights
Frequency modulation in VLF range is closely associated with the observed intensity variations; it is most common for so-called quasi-periodic (QP) emissions observed outside the plasmapause (Sato et al, 1974; Likhter and Sazhin, 1980; Sato and Kokubun 1980, 1981; Sato and Fukunishi, 1981; Tixier and Cornilleau-Wehrlin, 1986; Sazhin and Hayakawa, 1994)
The maximum amplitude frequency of the QP emission remains almost invariable while the frequency band pulses, the modulated emission refers to non-dispersive type (Sato and Kokubun, 1980; Sato and Fukunishi, 1981)
# as factors appears in Eq 1; in the frame of the model these factors conserve their values along the magnetic field line and can characterize plasma over all the interaction region
Summary
Frequency modulation in VLF range is closely associated with the observed intensity variations; it is most common for so-called quasi-periodic (QP) emissions observed outside the plasmapause (Sato et al, 1974; Likhter and Sazhin, 1980; Sato and Kokubun 1980, 1981; Sato and Fukunishi, 1981; Tixier and Cornilleau-Wehrlin, 1986; Sazhin and Hayakawa, 1994). As was estimated by Tixier and Cornilleau-Wehrlin (1986), the experimental value of the upper cut-off frequency shift appears to be too large to be consistent with the theoretical value given by the modulation mechanism proposed by Coroniti and Kennel (1970) when the weak pitch-angle diffusion regime of electrons is assumed. In the concept of Coroniti and Kennel, the electron cyclotron instability is disturbed by the compressional component of the geomagnetic pulsation This idea was used by Sato and Fukunishi (1981) when proposing the possible way of diffuse rising tone formation: they supposed a magnetosonic wave propagating radially toward the Earth which excites more and more lower L-shells. The whistler-mode dispersion relation used throughout the paper is (Cuperman and Landau, 1974):
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