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

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