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The energy loss rate of a magnetized electron gas emitting axions a due to the process e^- → e^- +a is derived for arbitrary magnetic field strength B. Requiring that for a strongly magnetized neutron star the axion luminosity is smaller than the neutrino luminosity we obtain the bound g_ae 10^-10 for the axion electron coupling constant. This limit is considerably weaker than the bound derived earlier by Borisov and Grishina using the same method. Applying a similar argument to magnetic whitedoi:10.1103/physrevd.56.1313 fatcat:sk2oofzf5bb5pkonkcqctdxwt4