Study of self-consistent target heating and resistive field evolution driven by intense proton beams in dense plasmas

Intense proton beams have numerous potential scientific applications, including radiography and deflectometry, cancer therapy, warm dense matter generation, and inertial confinement fusion. With recent advancements in beam focusing mechanisms and energy conversion efficiency, the current densities of laser-driven proton beams approach 10¹⁰ A/cm², intense enough to induce strong resistive magnetic fields that may affect beam propagation within metals. Here, we give a theoretical model that can estimate the evolution of the resistive magnetic fields induced by intense proton beams (∼10⁹-10¹⁰ A/cm²) in aluminum. The analysis utilizes resistivity and heat capacity models applicable from cold solid to hot plasma regimes, so that the field evolution is valid through and above the warm dense matter regime. The magnetic field profile is theoretically calculated for both monoenergetic and Maxwellian beam distributions, and the roles of various beam parameters are investigated. The model shows that Maxwellian proton beams with temperature 5 MeV and total energy 10 J may generate up to 150 T fields in aluminum. Comparison of theoretical results with 2-D hybrid-PIC simulations shows good agreement and sheds light on the model’s theoretical limitations.