We comprehensively study the effects of bubble wall thickness and speed on the gravitational wave emission spectrum of collisions of two vacuum bubbles. We numerically simulate a large dynamical range, making use of symmetry to reduce the dimensionality. The high-frequency slope of the gravitational wave spectrum is shown to depend on the thickness of the bubble wall, becoming steeper for thick-wall bubbles, in agreement with recent fully 3+1 dimensional lattice simulations of many-bubble collisions. This dependence is present, even for highly relativistic bubble wall collisions. We use the reduced dimensionality as an opportunity to investigate dynamical phenomena which may underlie the observed differences in the gravitational wave spectra. These phenomena include `trapping, which occurs most for thin-wall bubbles, and oscillations behind the bubble wall, which occur for thick-wall bubbles.
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