Photoelectric-effect laser The question is whether it is physically possible to build a laser using only the photoelectric effect in the vacuum, with no lasing material. 
I know that there is a whole history of laser development in which people found all sorts of materials that lase if you pump them hard enough, but my question is simpler and more fundamental. Is it really necessary to have a lasing material in order to have a laser? 
There already exists a patented optical amplifier using the photoelectric effect in the vacuum, and so I think it should be possible to build a laser, which is basically an optical amplifier between two mirrors. The advantage of such a photoelectric-effect laser is that the applied voltage would allow you to smoothly vary the color of the light produced, instead of relying on a pre-existing electronic-state transition in your gas molecules or a fixed energy band gap in your semiconductor material. 
 A: There exists the free electron laser 

A free-electron laser (FEL), is a kind of laser whose lasing medium consists of very-high-speed electrons moving freely through a magnetic structure, hence the term free electron. The free-electron laser is tunable and has the widest frequency range of any laser type, currently ranging in wavelength from microwaves, through terahertz radiation and infrared, to the visible spectrum, ultraviolet, and X-ray.

The magnetic structure generates the coherence in the photons produced.
Maybe with nanotechnology the design can be miniaturized by using a photoelectric source ( which I suppose will in any case be the source of the electrons in the FEL  beam) 
A: I think that your question is basically the generation of laser via electron impact. The basic principle behind laser radiation which makes it coherent is stimulated emission of photons in population reversed media. If you have free electrons (whether thermionic or via photo electric effect) and you accelerate it to certain voltage then make it fall on a material, it will certainly generate a radiation. This is a basic principle behind the x ray tubes. However the radiation will not be coherent because each atom will generate photons according it its own phase and the coherence (which is gained by stimulated emission) will be lost. The duration of this radiation is a convolution of the lifetime of the transition level and the duration of electron pulse.
It may also be noted here that the spectrum will not be narrow band (like laser) in this case and only the characteristic x rays generated in this process have narrow band spectrum and this is again incoherent radiation.
The broad spectrum is due to the fact that electron do not loose its energy in one impact but it rather looses its energy continuously in several impacts. The radiation generated in this process is both Bremsstrahlung and line radiations.
