Two-dimensional particle-in-cell simulations are used to explore laser-driven collisionless shock acceleration of ions in a multi-species plasma. Simple plasma slab simulations consisting of electrons, protons, and fully ionized carbon are used, varying the carbon ionization state, the relative fraction of ions, and the ratio of downstream to upstream plasma density. We find that two shocks can simultaneously propagate with different velocities defined by the dominant ion species reflected by each shock. The appearance of two shocks allows for ions to be accelerated twice, but can also cause trapping and heating of ions. We modify the current collisionless electrostatic shock theory where ions are treated as a single fluid to include a second ion fluid. This fluid model is unable to calculate the Mach number at which both ions will reflect, therefore we propose a kinetic model that may better model multi-species shocks. Scans are also performed in simulations with a laser pulse and realistic density profile that show reduced proton peak energies with the inclusion of carbon ions. Double shocks are only seen in simulations with steep density profiles, demonstrating the experimental importance of tailored density profiles.
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