  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.
