Harmonic minimization waveforms for modulated heating experiments at HAARP

Abstract

Modulated High Frequency (few MHz) heating of the D-region ionosphere under the auroral electrojet is capable of generating extremely low frequency (ELF) radio waves in the few kilohertz range by affecting the conductivity of the D-region. The HF heating is nonlinear and results in the generation of harmonics at integer multiples of the ELF modulation frequency with 1% of the total power outside the fundamental when sinusoidal amplitude modulation is applied to the HF carrier. For the purpose of harmonic minimization, we present a modulation scheme designed to create a sinusoidal change in the Hall conductivity at a particular altitude in the ionosphere. The modulation waveform is generated by inverting a numerical HF heating model, starting from the desired conductivity time series, and obtaining the HF power envelope at the bottom of the ionosphere. The inverted envelopes (referred to as inv-sin waveforms) are highly sensitive to the assumed ionospheric density profile and simulations indicate that these waveforms have less harmonic distortion compared to sinusoidal modulation when the actual ionospheric density is similar to or less dense than the one assumed. Experimental results indicate that sinusoidal amplitude modulation may still be preferred since it is more robust to the highly variable ionospheric profile while square wave modulation is more efficient in generation of ELF waves when harmonic distortion is not important. The inv-sin waveforms are more efficient than sinusoidal modulation while still suffering from less harmonic distortion than square wave modulation suggesting a tradeoff between harmonic distortion and ELF generation efficiency.