  A novel intense beam-driven scheme for high yield of the tri-alpha reaction
11B(p,{\alpha})2{\alpha} was investigated. We used a foam target made of
cellulose triacetate (TAC, C_9H_{16}O_8) 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
{\alpha} particles 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.
