Proton rings from late-forming ballistic sheath fields

Many laser-driven ion experiments have seen ring-like patterns in the proton angular distribution across a wide array of laser and target parameters. These rings can impede measurement due to the small acceptance angle of detectors and often inhibit potential applications. A myriad of explanations for their formation have been proposed, yet most studies attribute them to some aspect of the laser–plasma interaction. Using 3D particle-in-cell simulations, we show that late-forming strong radial electric fields can arise due to charge separation while the beam is in flight, long after the laser–plasma interaction. These fields can accelerate ions to significant divergences (≈10°) as they propagate away from the target. We compare our results to a recent experiment where a high intensity, short pulse laser (I0≈1021 W/cm2, τ≈30 fs) was incident upon thin (≈1 μm) liquid crystal targets. Our simulations capture all the main features of the experimental results—namely, robust ring formation and larger rings for higher energy protons. In addition, we show that rings do not form for sufficiently short preplasma scale lengths. Finally, we develop a phenomenological model to describe the spatiotemporal structure of the radial electric field and use this to explain the proton rings' energy and preplasma dependencies.