We present an improved time‐domain model of the lightning electromagnetic pulse (EMP) interaction with the lower ionosphere. This improved model inherently accounts for the Earth's curvature, includes an arbitrary number of ion species, and uses a convolutional Perfectly Matched Layer (PML) boundary. We apply an improved model of electron heating due to the lightning EMP and electrostatic fields, and we include ionization, attachment, and detachment. In addition to modeling lightning, this model can be used for long‐distance VLF wave propagation in the Earth‐ionosphere waveguide, heating of the lower ionosphere by VLF transmitters, and heating in the F‐region ionosphere by lightning. In this paper we present three initial results of this model. First, we compare results of ionospheric heating and electron density disturbances with and without electron detachment taken into account. We find that detachment is important only for the QE effects on time scales longer than 1 ms. Second, we find a simple explanation for the recently‐reported “elve doublets”, which we find are an effect of the rise and fall times of the lightning waveform. In particular, we find that all elves are doublets, and the rise and fall times of the current pulse control the brightness and separation in time of the two successive halves of the elve. Third, we find a similar simple explanation for “ring” sprites, whole columns appear in a circle symmetric around the discharge axis. We find that ring sprites can be initiated for particular current waveforms, where the QE and EMP fields in the mesosphere produce a maximum reduced field away from the discharge axis.