Higher energies and shorter distances

[ghery]

Hi:

In experimental HEP, Why are higher energies associated with shorter distances , and by the way, in order to reach higher energies or shorter distances, an increase in the size of the detectors is needed, Could you please tell me why?. For instance Why do we meed a particle accelerator as big as the LHC to obtain 14 TeV, couldn`t they just build a smaller accelerator that reached the same energy?

Thans a lot for your help

 

[ZapperZ]

Hi:

In experimental HEP, Why are higher energies associated with shorter distances , and by the way, in order to reach higher energies or shorter distances, an increase in the size of the detectors is needed, Could you please tell me why?. For instance Why do we meed a particle accelerator as big as the LHC to obtain 14 TeV, couldn`t they just build a smaller accelerator that reached the same energy?

Thans a lot for your help

I was hoping that someone in high energy physics would answer at least the first part. Oh well.

The energy scale relates to the length scale that can be probed. If you have keV electrons, for example, and you shoot it at an atom, you can then probe up to the atomic length scale since that is all those electron can interact. Anything else at the nuclear level is shielded. It means you need higher energy probe, and that includes using other particles such as protons, etc. So the higher the energy of the "probe particle", the deeper and closer you can gain some information.

Hitoshi Murayama had http://aac08.lbl.gov/plenarytalks/PL01_Murayama.pdf" he did at the last Advanced Accelerator Workshop this past Aug. that you might want to check (note: the download takes about a minute or so). On Page 26 of his presentation, he has some rough estimate on an energy scale relating to a length scale.

As for the second part on why the particle accelerators have to be so big (technically, why it has to be so LONG), it is more of a technical/physics issue. Currently, the accelerating structure that is commonly used is made out of ordinary metal, usually copper. These copper structures appear to have a physical limitation in the amount of RF gradient that it can withstand before undergoing a catastrophic electrical breakdown (currrently ~50 MV/m). Thus, to give charge particles a higher energy, we have to stack many of these one after another, so that the acceleration is done in stages. That's why to get to TeV scale, such accelerator facility tends to be very long. It is all due to these accelerating structures.

So the obvious question following that is, in circular accelerator such as the one at the Tevatron and LHC, where the particles can be accelerated each time it comes back around and passes through these accelerating structures again and again, why do they have to be so big in diameter? The naive answer: losses due to synchrotron radiation. As you make the speed and energy of the particles larger and larger, the curvature of the path will cause even more radiation being emitted. This will not only affect the energy of the particles rather quickly. Furthermore, we also need to remember that we're accelerating not just one or two particles, but rather bunches of them. These energy losses can easily create a wider energy and momentum spread in each bunch, something you don't want since a larger variation in each bunch may get amplified each time it passes through an accelerating structure.

Zz.

 

[malawi_glenn]

why we need so big?

- momentum (and energy) depends on radius and magnetic field of the accelerator:
$$p = 0.3*B*r$$
where B is in Teslas and r is the radius in metres -> gives you p in units GeV/c

then:
$$E^2 = (pc)^2 + (mc^2)^2$$

Why need high energy to see small things?
- In order to resolve objects, one needs wavelengths of the same order or smaller to see diffraction patterns, you can't see atoms in solids using ordinary light, you must use things that has shorter wavelenghts - use electron beams.
- Associated with a particle is a wave property, see deBroigle wavelength.
- Also one wants high energy in accelerators to create new, heavy, particles