## Low Mach-number collisionless electrostatic shocks and associated ion acceleration

The existence and properties of low Mach-number (M >~ 1) electrostatic collisionless shocks are investigated with a semi-analytical solution for the shock structure. We show that the properties of the shock obtained in the semi-analytical model can be well reproduced in fully kinetic Eulerian Vlasov-Poisson simulations, where the shock is generated by the decay of an initial density discontinuity. By using this semi-analytical model, we also study the effect of electron-to-ion temperature ratio and presence of impurities on both the maximum shock potential and Mach number. We find that even a small amount of impurities can influence the shock propertiesmore »