  We present a simple, robust, narrow-linewidth, frequency-doubled
semiconductor laser source suitable for laser cooling and repumping of
$^9$Be$^+$ ions. A distributed Bragg reflector (DBR) laser diode operating at
626 nm is self-injection-locked to a frequency doubling cavity via
phase-stabilised optical feedback when the laser is resonant with the cavity
mode. The short-term laser instability is reduced from the MHz-level to
approximately 20 kHz by the injection process, thus eliminating the need for a
high-bandwidth feedback loop to suppress the otherwise troublesome
high-frequency laser noise. Long-term stability of the laser frequency is
achieved by feeding back to the length of the enhancement cavity utilising an
electro-optic frequency comb generator to produce a beatnote with a laser that
is detuned by 98 GHz. Long-term injection locking and frequency stabilisation
via a wavemeter are ensured using automatic relocking algorithms.
