Seed lasers are employed to improve the temporal coherence of free-electron laser (FEL) light. However, when these seed pulses are short relative to the particle bunch, the noisy, temporally incoherent radiation from the unseeded electrons can overwhelm the coherent, seeded radiation. In this paper, a technique to seed a particle bunch with an external laser is presented in which a new mechanism to improve the contrast between coherent and incoherent free electron laser radiation is employed together with a novel, simplified echo-seeding method. The concept relies on a combination of longitudinal space charge wakes and an echo-seeding technique to make a short, coherent pulse of FEL light together with noise background suppression. Several different simulation codes are used to illustrate the concept with conditions at the soft x-ray free-electron laser in Hamburg, FLASH. Short-wavelength, high-brightness light sources, like free-electron lasers (FELs) driven by particle accelerators, are in demand for experiments studying ultrafast processes in matter. The FEL community has pursued methods to improve the temporal coherence properties of the light [1][2][3][4][5][6][7] and to generate shorter, tunable FEL pulses [5][6][7][8][9][10][11][12]. When the temporal coherence of FEL light is determined by the shot noise of an electron beam, as in self-amplified spontaneous emission (SASE), it is poor [13][14][15], but if it is determined by an external seed laser, the FEL light takes on the excellent temporal coherence properties of the external laser in the region that has been seeded. However, if the seed pulse is short while the electron bunch is long, the noisy SASE background signal can overwhelm the seeded radiation, wiping out the benefits of the seed.To reduce this noisy background, the FEL radiator is typically made short enough that the unseeded portion of the bunch does not reach saturation while the seeded portion does, but this can be limited in the case of short seeds with low seed power [1,[5][6][7]. Alternatively, the electron bunch could be made short relative to the seed, but this puts challenging constraints on the synchronization between the femtosecond-scale seed and the electron bunch. Ideally, the electron bunch would be much longer than the femtosecond duration seed, so that with the best observed 25 fs (rms) synchronization between electron beam and external laser in an FEL facility [16], the seed laser would hit the electron bunch on every shot, but then a method is needed to suppress the SASE background in conjunction with the seeding of the short pulses.As a relativistic seeded and bunched beam propagates along a drift, the microbunches experience a longitudinal space charge (LSC) impedance that modulates the energy of the beam in proportion to the peak current of the microbunches according towhere Z 0 ¼ 377 Ω is the impedance of free-space, I A ¼ 17 kA is the Alfen current, ρ k is a small current perturbation at some wave number k, and γ is the Lorentz factor. Depending on the strength of th...