  An approach using topology reveals a new understanding and knowledge of laser
particle acceleration. Laser pulse irradiation on a thin-foil target is
examined using two-dimensional particle-in-cell simulations. Through topology,
laser ion acceleration schemes are classified depending on whether the deformed
target shape after laser irradiation is homeomorphic with respect to the
initial target. High energy ions are generated with high-efficiency when the
deformed target shape is non-homeomorphic. In this case, the target thickness
greatly affects the obtained ion energy. However, when the deformed target
shape is homeomorphic, the obtained ion energy is low, and the effect of the
target thickness is small.
