  In non-hadronic axion models, which have a tree-level axion-electron
interaction, the Sun produces a strong axion flux by bremsstrahlung, Compton
scattering, and axio-recombination, the "BCA processes." Based on a new
calculation of this flux, including for the first time axio-recombination, we
derive limits on the axion-electron Yukawa coupling g_ae and axion-photon
interaction strength g_ag using the CAST phase-I data (vacuum phase). For m_a <
10 meV/c2 we find g_ag x g_ae< 8.1 x 10^-23 GeV^-1 at 95% CL. We stress that a
next-generation axion helioscope such as the proposed IAXO could push this
sensitivity into a range beyond stellar energy-loss limits and test the
hypothesis that white-dwarf cooling is dominated by axion emission.
