Title: Study of the third harmonic lasing in x-ray free electron laser Mentor: Ivan Bazarov Optical lasers are part of the everyday life of many scientists who use them as invaluable research instruments. Shorter wavelengths of light allow probing correspondingly shorter distances in matter, with hard x-rays matching the angstrom-like inter-atomic distance of the solid state, naturally making x-rays a powerful probe for solving a myriad of problems in material science. However, up until now, lasers have not been available in x-ray range, and researchers have been limited to the use of incoherent x-rays. The primary difficulty preventing extension of conventional lasers to very short wavelengths is the absence of high-reflectivity x-ray mirrors needed to set up the laser resonator cavity. This problem is solved in so-called free electron lasers (FELs) where an extremely dense cloud of ultra-relativistic electrons propagates in x-ray producing device called undulator. The high gain of free electron lasers allows production of copious coherent x-rays in a single pass without the resonator cavity. The requirements placed on electron cloud to establish lasing is increasingly demanding as the wavelength of the desired radiation gets shorter. Naturally occurring odd harmonics from the planar undulator, on the other hand, open the possibility of extending lasing on free electrons to shorter wavelengths with somewhat relaxed parameters. The goal of this REU project is understanding the physics of free electron lasers, in particular to study the third harmonic lasing process using the time-dependent 3-D free electron laser code GENESIS.