## Mixed Pressure-Release - Rigid Reflector

Predictions using the KZK equation for an HM3-type lithotripter with a reflector that is made of material that is half pressure-release and half rigid. For this simulation the centre section is made of pressure-release material and a outer ring that is rigid. The first figure shows the propagation curves; that is the pressure amplitude along the axis; the upper curve is the peak-positive pressure (P+) and the lower curve the peak-negative pressure (P-). The geometrical focus of the lithotripter is at 12.8 cm. Note that both the peak-positive (P+) and peak-negative (P-) pressures dip dramatically at the focus. This is because of near cancelling, of the inverted wave from the pressure-release material and the non-inverted wave fromthe rigid material, in the vicinity of the focus. On either side there are peaks because the two pulses from the two materials arrive at different times and do not cancel - this is classic behaviour in the focussing of a short transient.

The predicted waveforms at three locations are show below - the pressure is given in MPa. Prefocally (11.3 cm) the negative pulse from the pressure-release section of the reflector arrives first. Post-focally (15.8 cm) the positive pulse from the rigid reflector arives first.

## Mixed Rigid - Pressure-Release Reflector

For this simulation the centre section is made of rigid material and a outer ring is pressure-release. The first figure shows the propagation curves; that is the pressure amplitude along the axis; the upper curve is the peak-positive pressure (P+) and the lower curve the peak-negative pressure (P-). The geometrical focus of the lithotripter is at 12.8 cm. In this case the structure of the field is more complicated. The is a small dip in P+ and P- around 13 cm; however the nature of the pulses involved measn that they don't cancel as cleanly as in the case of the pressure-release - rigid scenario.

The predicted waveforms at eight locations along the axis are show below - the pressure is given in MPa. Prefocally (8.8 cm) the pulse from the rigid reflector arrives first; the pulse from the pressure-release is just starting to interact with the tail of the rigid pulse. Around the geometrical focus the negative peaks of the two troughs coincide giving a large negative peak. Just beyond the focus (13.4) the waveforms almost overlap and provide some sort of cancelling. Post-focally (18.8 cm) the positive peak from the rigid reflector pulse coincides with positive pulse from the pressure release reflector superimpose to give a large positive peak.