Hello Georgi,

I'm not sure I understand the question, but what you write about emittance as a measure of the electron beam phase space distribution is correct. If you speak of an electron beam in a storage ring, then it will naturally assume a Gaussian shape. The emittance sets the size of this Gaussian distribution. In a single pass system, say out of a linac, the beam is not necessarily a Gaussian. Typically the word emittance means two things- one can speak of the single particle emittance, which is a conserved quantity of the dynamics (more formally it is the "action" from Hamiltonian mechanics") or one can speak of the average value of this conserved quantity over the beam distribution when there are many electrons. The wikipedia article is not so good, but has some further information:

http://en.wikipedia.org/wiki/Beam_emittance

I hope this is helpful.

Regards,

Boaz

Dear Boaz! Thank you for your ansver and recomendation. I now onli wish add in discussion that we can also speak for not-gaussian beams, using as example "r.m.s. emittance" . For me is interesting to discuss that question, newertheless that we work in different fields. I am working on application of electron beams, as example for welding. We use quantity "emittance", taking it from accelerator field, but in connected quantities and parametaers not all definitions are clear.

In my field the quality of beam means it possibility to be focused in a small spot and to be transported to enought long distances with enough high power density. From practical point of wiev users buy electron beam welding equipment knowing only beam current and electron energy and not know any-thing about angular and radial distribution and kinetics of beam charakteristics along interaction zone beam/material

Emittance is a measure of the beam transverse phase space area. This area, and in some conditions, is preserved during propagation, as a consequence of the Liouville theorem. This holds only under a series of assumptions and therefore the statement that emittance is a good indicator of the beam quality is not completely general, in the sense that emittance "alone" is not a good indicator. The projected emittance, which means the beam phase space area obtained by projecting all the particles on a specific transverse direction, for a mono-energetic beam affected only by linear (internal or external) forces, is preserved along a transport beam line. In linear or circular accelerators where the particles energy is not constant, the emittance is not invariant. In this case the normalised emittance is defined and this is conserved during acceleration. Even so, if the beam has e.g. a large relative energy spread, the transverse emittances are not preserved. As an example consider the simple propagation in a FODO beam line. The focusing properties of magnetic elements depend on energy and chromatic effects may increase the beam emittance, as it may happen in the propagation of the tiny beams generated by laser-plasma acceleration. So I would say emittance is an important indicator of the beam quality but it has to be considered together with other parameters as charge, current, energy, energy spread, beam size (Twiss parameters) … It can be a good indicator if used to compare beams in similar conditions, as when the beam is produced by similar devices.

Dear Vesselin, I am talking really on electron beam welding. There after focusing system the electron beam, containing practically monoenergetic electrons of 20-60 keV (some-times up to 150 keV) is propagated in draft space of technology vacuum chamber with residual gase pressure 10-2 to 10-5 Torr. There are really case of welding with beam on atmosphere, but this is special case. Also in zone of interaction of beam with workpiece is crieted key-hole (i.e. a crater) filled with metal vapors (and plasma) and there are also higher pressure, self-focusing of the beam , scattering, etc.