Fig. 1. Laser acceleration of a micro-foil in the laboratory and the rest frame of references.

Fig. 2. Micro-foil velocity as a function of the laser pulse duration in units of , where is the initial density, is the foil thickness and is the laser intensity.

Fig. 3. Laser energy per unit area as a function of micro-foil velocity (in units of c).

Fig. 4. Acceleration efficiency () of the micro-foil acceleration as a function of micro-foil velocity (in units of c).

Fig. 5. (a) Nanosecond laser pulses compressing a ring target. (b) A multi-petawatt picosecond laser pulse accelerating a micro-foil into the pre-compressed target. (c) The impact shock waves upon the collision of the micro-foil with the pre-compressed target.

Fig. 6. Heat wave temperature space profile at three times, .

Fig. 7. The micro-foil velocity threshold for heat wave fast ignition of deuterium–tritium (DT) fuel as a function of the heat efficiency for three cases of : , and .