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In this article we address the problem of tunability of seeded free-electron lasers (FELs), working typically in the domain of the vacuum ultraviolet. The seeding of FELs with an external laser permits us to obtain FEL pulses with both good longitudinal coherence and good stability properties (contrary to an amplification starting from noise). However, with a fixed external laser wavelength, only amplification at harmonics of this wavelength is possible. If full tunability is wanted, it is necessary to have a tunable external source; but this type of source has much less power, hence it is much harder to reach high harmonics numbers. Here we propose the so-called frequency mixing scheme (from its analogy with the similar process in nonlinear optics), based on two laser/electron interactions. Numerical and analytic studies show that it permits to increase significantly the tunability at short wavelengths using a low-energy tunable source. Numerical simulations are made with the parameters of FERMI-FEL 1, the first seeded FEL for user operation

Frequency mixing in accelerator based sources and application to tunable seeded free-electron lasers