We study the generation of helical magnetic fields in a model of inflationary magnetogenesis which is free from the strong coupling and back-reaction problems. To generate helical magnetic fields, we add an f^2 F̃^μν F_μν term to the lagrangian of Ratra model. The strong coupling and back-reaction problems are avoided if we take a particular behaviour of coupling function f, in which f increases during inflation and decreases post inflation to reheating. The generated magnetic field is fully

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... ical and has a blue spectrum, dρ_B/d k ∝ k^4. This spectrum is obtained when coupling function f∝ a^2 during inflation. The scale of reheating in our model has to be lower than 4000 GeV to avoid back-reaction post inflation. The generated magnetic field spectrum satisfies the γ-ray bound for all the possible scales of reheating. The comoving magnetic field strength and its correlation length are ∼ 4 × 10^-11 G and 70 kpc respectively, if reheating takes place at 100 GeV. For reheating at the QCD scales of 150 MeV, the field strength increases to ∼ nano gauss, with coherence scale of 0.6 Mpc.