  We report the development and characterization of a pulsed 243 nm laser that
is optimal for the cooling of positronium (Ps). The laser, which is based on
the recent chirped pulse-train generator (CPTG) demonstrated by K. Yamada et
al. (Phys. Rev. Appl. 16, 014009 (2021)), was designed to output a train of
pulses with linewidths of 10 GHz, and with the center frequency of each pulse
shifting upward (up-chirped) in time by $4.9\times10^2\,\mathrm{GHz\,\mu
s^{-1}}$. These parameters were determined by the mechanism of chirp cooling,
which is the best scheme for cooling many Ps atoms to the recoil temperature of
laser cooling. To achieve the designed performance, we drove an optical phase
modulator in the CPTG with a deep modulation depth based on the operating
principle of the cooling laser. Time-resolved spectroscopic measurements
confirmed that the developed laser satisfied the chirp rate and linewidth
requirements for efficient chirp cooling. Combined with pulse energy of
hundreds of microjoules, we believe that the experimental demonstration of Ps
laser cooling has become possible using realistic methods for the generation
and velocity measurement of Ps.
