Linear and nonlinear amplification in the magnetosphere during a 6.6‐kHz transmission

Abstract

Reception at Dunedin of the magnetospheric signal at 6.6 kHz transmitted from Anchorage, Alaska, showed both linear and nonlinear amplification during an event lasting some 20 min near local midnight. Linear amplification of the transmitter signal was ∼20 dB. Natural whistlers were also amplified but often at frequencies sharply limited to those from the transmitter frequency upward. Nonlinear amplification (NLA) produced a signal positively offset from the transmitter frequency by 20–150 Hz at amplitudes over 40 dB above the unamplified transmitter signal. This signal appeared as a largely self‐sustaining embryo emission (EE) under the control of the transmitter signal. The phase of this EE signal in each NLA event was tracked with respect to a recorded phase reference. These phase studies showed that the accumulating phase of the offset EE signal is frequently interrupted by negative phase steps (‘N events’) which tend to reduce the offset frequency. Five of the NLA events during key‐down transmission were quenched by whistlers which themselves triggered free emissions at ½ƒBO. The theory of nonlinear wave‐wave interaction between the transmitter or input wave (IW) and the embryo emission is developed to explain these features. It is shown that coupling depends on the offset frequency δƒ and the ‘control frequency’ Fc: for δƒ > Fc the emission is effectively free; for δƒ < Fc, EE is controlled by IW. Curiously, Fc is determined by the EE amplitude (Bw) as Fc ∞ BW1/2, and is almost independent of IW amplitude. This control applies whether the emission was originally generated by IW or captured by it. Fc is determined from Bw measurement to be 60–120 Hz, which fits the observed behavior quite well. For δƒ < Fc a fraction of the phase‐bunched electrons are trapped by IW as they are detrapped by EE in the growth region. This superimposes a strong component oscillating in phase which can produce N events, effectively phase locking the low‐amplitude end of EE to IW. Amplitude fluctuations, δƒ, and Fc are interrelated in a complicated way which gives rise to short‐term instabilities and somewhat longer‐term stabilizing influences.