tomclarke wrote:It is true that technically the temperature of a coherent mono-energetic high energy beam can be low (and, more technically, relativity shows that mono-energetic beams are at some level equivalent to stationary particles).
Not “technically low” but totally low temperature. Motion in beams has two components: coherent and thermal. When coherent component is much higher (55 keV vs. 1-2 eV in that example) we have a right to speak about coherent system.
tomclarke wrote:Add a monoergetic coherent beam (for simplicity of the same particles) of energy E1/particle. The beam consists of M particles (so we can be quantitative).
Assume that after some time the system equilibrates to a Boltzmann KE distribution.
Conservation of energy within the box tells you, trivially, that the temperature of the box is now (E0N+E1M)/(N+M).
From which we derive an effective temperature for the monoenergetic beam (in this context) of T1 = E1/k as everyone here except ypou would expect.
There is no necessity in such assumptions (“system equilibrates to a Boltzmann KE distribution”) and in invention of new non-standard term of effective temperature. As all is thought out many many years ago by people who were more qualified than you and me.
Simply if we would input the energy into certain media (e.g. background plasma) injecting there beam, temperature of that media increases, coherent component of beam decreases while thermal component increases. And we can speak about thermalization of beam when its thermal component will become comparable with coherent.
We would be right to use this term thermalization for any such process: low thermal + high coherent => thermal comparable with coherent.
Regardless to that did such system reach thermal equillibrium or not.
Now again about temperature.
Not on your non-standard term of "effective temperature" but on its classical understanding.
When thermal component increases, so increases the temperature of system. And what is it? This is heating, my friend.
Thanks.