By tailoring the target density to a radial gradient distribution, we propose a proton focusing mechanism. This mechanism is based on the focusing radial electric field self-induced by the radial density gradient. This field, different from the defocusing field of a uniform density target, focuses near the longitudinal axis of the target and is capable of producing a proton source with a nanometer-scale focal spot size, and an emittance on the order of ${10}^{-3}\mathrm{mm}\mathrm{mrad}$. This type of proton source offers further improvements in both focal spot size and collimation over other proton focusing enhancement mechanisms.

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• Beam control
• Beam processes
• Collimation
• High intensity beam dynamics
• High-energy-density plasmas
• Laser driven ion acceleration
• Laser-plasma interactions
• Nonlinear beam dynamics
• Particle acceleration in plasmas
• Particle interactions
• Plasma acceleration & new acceleration techniques
• Relativistic multiple-particle dynamics