A novel intense beam-driven scheme for high yield of the tri-alpha reaction 11B(p,α)2αwas investigated. We used a foam target made of cellulose triacetate (TAC, C9H16O8) doped with boron.It was then heated volumetrically by soft X-ray radiation from a laser heated hohlraum and turned into a homogenous, and long living plasma. We employed a picosecond laser pulse to generate a high-intensity energetic proton beam via the well-known Target Normal Sheath Acceleration (TNSA) mechanism. We observed up to 10^10/sr αparticles per laser shot. This constitutes presently the highest yield value normalized to the laser energy on target. The measured fusion yield per proton exceeds the classical expectation of beam-target reactions by up to four orders of magnitude under high proton intensities. This enhancement is attributed to the strong electric fields and nonequilibrium thermonuclear fusion reactions as a result of the new method. Our approach shows opportunities to pursue ignition of aneutronic fusion.