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In this Letter, we report the possibility of generating intense, highly energetic proton beams using terawatt, sub-nanosecond class laser system by irradiating modified cavity pressure acceleration-type targets. In this approach, the main source of few-mega electron volt protons is thermonuclear deuterium–deuterium reaction; therefore, the energy spectrum of accelerated particles and their number is not as strongly related to the laser intensity (laser pulse energy and pulse duration in particular) as in the case of the most common ion acceleration mechanism, namely, target normal sheath acceleration. Performed Monte Carlo simulations suggest that using mentioned mechanism to generate proton beam might be beneficial and efficient driver for laser induced proton–boron fusion when moderate-to-low laser pulse intensities ( ⩽ 10 16 W / cm 2 ) and thin, lower than 100 μ m boron foils are used as catchers. [ABSTRACT FROM AUTHOR]