A series of six experiments with the EISCAT HF heater device assisted by the EISCAT (European-Incoherent-Scatter) radar were carried out with the purpose of producing artificial magnetic pulsations in the 0.1–3 Hz frequency range. In only 3 of the 30 h of experiment time under a variety of ionospheric conditions was an artificial magnetic signal detected by ground-based magnetometers. A numerical model was used to explain the sporadic nature of the artificial signal in terms of ionospheric parameters. For several experiments the EISCAT radar provided an in situ electric field and/or electron density values; otherwise standard neutral atmosphere and ionosphere models were used. The PGI model was only partially successful. It could produce the right order of magnitude for the artificial signal when it was observed and it could demonstrate the different efficiencies when using either the O- or the X-mode of the HF wave, but it could not explain why the artificial signal was observed at a particular time and not at others. This is only partially due to the uncertainty in one or more input parameters. When the artificial signal was observed its spectrum usually exhibited spectral resonance structures of the Ionospheric Alfvén Resonator (IAR), indicating that a “DC approach” is insufficient and that the generation of oscillating field-aligned currents, and thereby shear Alfvén waves, has to be taken into account. We believe, however, that even with the introduction of the IAR into the model it will not be possible to resolve the sporadic character of the heating-induced artificial magnetic signal entirely. A more realistic way of D-region modeling will without doubt also be an important factor in resolving the puzzle.