Joseph Chikva wrote:
(1/T)= (dS/dU) Holding N and V constant. More irrelevant information coming right up.
MSimon is correct tho. Let me show you the math,
1eV=1.6022 x 10^(-19) J
k(b)=1.380650 x 10^(-23) J/K
So 1eV/k(b)= 1.160 x 10^(4) K
The Boltzmann constant, k, is a bridge between macroscopic and microscopic physics, since temperature (T) makes sense only in the macroscopic world, while the quantity kT gives a quantity of energy which is on the order of the average energy of a given atom in a substance with a temperature T.
Now if temperature (T) makes sense only in the macroscopic world let's define what is 1 eV
By definition, it is the amount of energy gained by the charge of a single electron moved across an electric potential difference of one volt.
So, if single electron moves across an electric potential difference of one volt that gains the 1 eV
Does for that electron "temperature" make sense? The same is correct for all accelerators. But MSimon speaks about "heating" of beams instead of "acceleration.
Others as above have explained at top level. But you obviously want more detail. So here goes. It is common sense + physics.
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).
However if you consider the practical interactions of such a beam with another system you can easily work out the effective temperature.
So: take an equilibrium plasma or gas enclosed in perfect reflective walls with temperature T0. Assume for simplicity we have only a single species of N particles, average energy E0. We know that:
E0 = kT0.
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.
In reality this effective temperature comes from increase in entropy in the mono-energetic beam energy as this passes to the (high entropy) system.
It is technically an abuse of notation to talk of a high-energy particle beam as having a temperature related to its particle energy but you can see that it makes good sense, and explains how such a beam can heat a gas or plasma providing its particle energy is higher than the gas particle energy. All of which is accepted by people who talk about such things.
Now, I am all for looking one level deeper and noting that a coherent beam in fact technically has a low temperature. But only if you also note that its effect when coupled thermodynamically to an equilibrium particle distribution is that of a high temperature source because of its low entropy and embodied energy.
What we want to do, when reasoning about these systems, is to have a good intuitive understanding of what is going on. That can be at any level of approximation. But viewing a high energy coherent beam as having low temperature, without a lot of extra work, satisfies none of these levels of approximation and is plainly stupid.
MSimon (and others here who are engineers) will I am sure bear this out: maths is the most important tool when analysing complex systems. You can't do anything without it. But understanding systems requires not just the blind application of math equations, but realising what they mean in specific contexts so you use appropriate approximations. That is a lot more difficult than just learning math. But also more fun.
Now - back to topic. Why not admit that the ONR commisioned panels who have reviewed Polywell science have the expertise and data to give it the thumbs down if it were obviously
daft? So if you think this you need to reexamine your own assumptions.
EDIT - gas thermodynamics is not what I usually work with. So others will correct any errors in the above I am sure.