# 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 $$r$$)?

• Like a free electron laser? – Jon Custer Mar 9 at 2:07

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.

• Thank you. I read about it and was definitely a good answer to the first question. However, as it was pointed out, the acceleration of electron was necessary and was in the range of relativistic mechanics. I'm more thinking about classical mechanical motions that could be safer and to bring in large intensities at the same time, such as pump to the vacuum, confine charges in sharp edge, and then rotates or oscillates. However, that's where question 2 comes in because I'm not sure how to determine the frequency in those cases. – user9976437 Mar 9 at 5:00
• I didn't think direction was quite an issue because one can use mirror and then go statistical. – user9976437 Mar 9 at 5:01

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.