New class of self-similar solutions for vacuum plasma expansion admitting mono-energetic ion spectra

We report a new class of self-similar solutions for plasma expanding into vacuum that allows for quasi-monoenergetic ion spectra. A simple analytical model takes into account externally controlled time-dependent temperature of the hot electrons. When the laser temporal profile is tailored properly, the quasi-neutral self-similar expansion of the plasma results in ion concentration in the phase-space at a particular velocity thus producing a quasi-monoenergetic spectrum. We prove this analytical prediction using a 1D partice-in-cell (PIC) simulation where the time-dependent plasma temperature is controlled by two laser pulses shot at a foil at a suitable time delay.