Energy loss enhancement of very intense proton beams in dense matter due to the beam-density effect

Thoroughly understanding the transport and energy loss of intense ion beams in dense matter is essential for high-energy-density physics and inertial confinement fusion. Here, we report a stopping power experiment with a high-intensity laser-driven proton beam in cold, dense matter. The measured energy loss is one order of magnitude higher than the expectation of individual particle stopping models. We attribute this finding to the proximity of beam ions to each other, which is usually insignificant for relatively-low-current beams from classical accelerators. The ionization of the cold target by the intense ion beam is important for the stopping power calculation and has been considered using proper ionization cross section data. Final theoretical values agree well with the experimental results. Additionally, we extend the stopping power calculation for intense ion beams to plasma scenario based on Ohm's law. Both the proximity- and the Ohmic effect can enhance the energy loss of intense beams in dense matter, which are also summarized as the beam-density effect. This finding is useful for the stopping power estimation of intense beams and significant to fast ignition fusion driven by intense ion beams.