Accelerating Charge Radiates, so why can't we make a laser emitter out of it? I've been taking class where we learnt about different types of laser, it reminded me of an old question I had before.
There's been issues with making very short wavelength laser pulse with traditional technologies, such as molecules, crystals, diodes, e.t.c. But as it's been known that accelerating charge radiates, so why can't we make a laser emitter out of it in rotational motion, where we seem to have full capability of control over the power of emission? It seemed much better than thermal or traditional electro excitation.
Something like rotational motion and Larmor radiation (https://www.cv.nrao.edu/course/astr534/PDFnewfiles/LarmorRad.pdf), one might agree that we only had the expression for power output, but not the one for the wavelength. So here's another question, what's the expression for radiated/emitted photons(Suppose a unit charge in a circular motion of speed $v$ and radius $r$)?
 A: As @John Custer stated, the free electron laser is based on the acceleration of free electrons. Such tools can lase at very short wavelength. Electrons are accelerated and then sent through a strong alternating magnetic field, a so called wiggler. During their zigzag motion they emit coherent radiation. Very powerful lasers of very short wavelengths can be engineered in this way. 
A: First, you are asking whether you can make a laser out of an accelerated charge, because it radiates.
This charge needs to be in your case a macro object, like a electromagnet, because your cited link says:


For example, Larmor'sequation incorrectly predicts that the electron in a hydrogen atom will quickly radiate away all ofits kinetic energy and fall into the nucleus.


So Larmor's law can only be used in the case of macro objects, macro size charges. In your case you need a macro size object, a charge, that will be in constant circular motion, thus it accelerates.
If you can keep the macro sized charge (like an electromagnet) constantly in circular motion (thus it accelerates), then yes it will radiate photons.
Now you are asking whether you can use that as a laser. To do that, you would need to emit photons with certain conditions (polarized, with certain relative phase).
Now the biggest problem would be, that the photons would be emitted in the circular directions, where the charge is rotating. There is no way (or at least it would be very hard) you could re-direct all randomly emitted photons from a circularly moving charge into the same direction. 
