On the frequency modulation of VLF emissions

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 _m/_m 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 are small; here is the total-to-warm electron content ratio and is the electron parallel beta. It is also shown that relative shift of the maximum intensity frequency _m/_m 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.