Characteristic Frequency Ratio Research Articles

Hydromagnetic discontinuities from the evolution of nonlinear Alvén waves

To study the large‐amplitude Alfvén waves that are frequently observed in the solar wind, the nonlinear equations of electron and ion fluids coupled to Maxwell equations have been solved to obtain the relationships between the fluid density and magnetic field for finite amplitude Alfvén waves in the cold plasma limit. Two regimes of the parameter ωc/Ω (ratio of characteristic frequency to the ion Larmor frequency) are examined. When ωc/Ω = 0, we obtain an exact simple wave solution for the linearly polarized Alfvén wave, and recover the earlier results of [Montgomery, 1959a]. For finite ωc/Ω geometric optics approximation which is valid for large wave numbers yields a new relationship which involves elliptically polarized Alfvén waves. Both of these waves can be shown to evolve into shocks.

Chaotization of the electron motion as the cause of an internal magnetotail instability and substorm onset

A new mechanism is proposed that is able to explain the sudden disruption of the magnetotail energy storage and the explosive onset of isolated magnetospheric substorms. During the growth phase the magnetotail accumulates additional magnetic flux and evolves in such a way that the special parameter κe = (Bn/Bo)(L/ρeo)1/2 describing the ratio of characteristic frequencies of the electron motion along and across the field reversal region quickly decreases. Here Bn and Bo are the components of magnetic field across and along the central plasma sheet, L is the thickness of the field reversal region, and ρeo is the Larmor radius of thermal electrons in the field Bo. When κe reaches a critical value κe|crit ≅ 1.6, a nonlinear interaction between the degrees of freedom of electron motion becomes strong enough to cause a chaotization of the electron orbits. This effect results in a fast growth of a collisionless tearing mode instability even within the framework of the WKB approximation, i.e., in a wide interval of possible wavelengths 1 > kL > Bn/Bo. The proposed theory‐ gives the mechanism of the formation of new reconnection region in the near‐Earth magnetotail, based exclusively on intrinsic properties of the magnetotail evolution. This reveals the natural relation between the onsets of isolated substorms and an internal large‐scale magnetotail instability of the tearing type considered in this paper.

The frequency response and other properties of single fibres in the guinea‐pig cochlear nerve

1. Micro-electrode recordings were obtained from over 100 single fibres in the cochlear nerve of the pentobarbitone or urethane anaesthetized guinea-pig. The acoustic system was calibrated at the tympanic membrane and threshold sound level measurements so corrected.2. The minimum thresholds of the fibres approached with 10-20 dB of the behavioural thresholds reported in the literature. Exceptions to this were fibres from preparations where there was evidence of malfunction of the cochlea either from abnormally low perfusion or local damage, and a few high frequency fibres. With these high threshold fibres excepted, the range of thresholds at a given frequency in any one animal was less than 20 dB.3. The slopes of the low and high frequency cut-offs of the frequency-threshold curves (;tuning curves') within 25 dB of minimum threshold, ranged from 10 to 60 and from 20 to 125 dB/octave respectively for fibres with characteristic frequencies below 2 kHz, increasing to 90-180 and 200-600 dB/octave respectively for fibres with characteristic frequencies at about 8 kHz. These slopes represent the minimum values for the high-frequency cut-offs, which increase towards 1000 dB per octave in some cases at higher levels above threshold. At 30-50 dB above threshold, the low frequency cut-offs become suddenly less steep and approximate to 5 dB per octave.4. The relative sharpness of the frequency-threshold curves, measured as the ;Q(10 dB)', i.e. the ratio of characteristic frequency to the band width at 10 dB above minimum threshold, ranged from 1 to 4 for fibres with characteristic frequencies below 2 kHz, to 3-15 for fibres with characteristic frequencies near 10 kHz.5. The slopes and ;Q(10 dB)' measures of the frequency-threshold curves of most of the abnormally high threshold fibres approximated to, or were lower than those of analogous measurements of the guinea-pig basilar membrane vibration patterns.6. Four fifths of the cochlear nerve fibres had spontaneous discharge rates greater than 1/sec. No consistent relationship was observed between the rate of this activity and response properties, with the exception that nearly half of the high threshold fibres were silent. In these and other respects the response properties to tonal and click stimuli resembled those of cochlear nerve fibres in the cat. In no case was inhibition of the spontaneous discharge by single tones observed.7. It is concluded that, contrary to earlier reports, the cochlear nerve fibres of the guinea-pig are substantially more frequency selective than the existing measurements of the guinea-pig basilar membrane displacement. In terms of band width, this discrepancy approaches a factor of ten. The finding of a considerable range of band widths within optimal preparations, and frequency-threshold curves approximating to the mechanical functions in fibres from pathological cochleas, provides circumstantial evidence for a physiologically vulnerable sharpening mechanism occurring within the cochlea subsequent to the displacement pattern of the basilar membrane.