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Does a particle accelerator lose its accelerating effectiveness as the number of particles being accelerated increases? According to Wikipedia, the mean acceleration of a proton in the Large Hadron Collider is 190,000,000 g's. Could the LHC accelerate one gram worth of protons at the rate while using the same amount of power? I suspect not, but I don't know why.

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  • $\begingroup$ For the LHC about 300 trillion in each beam. But if you were to slow them down and allow them to form a gas at normal temperature and normal pressure, the gas would occupy a space about one hundredth the size of a grain of salt. Everything you wanted to know about the Large Hadron Collider: BY THE GAZETTE (MONTREAL) . $\endgroup$ – Keith McClary Dec 15 '15 at 3:57
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    $\begingroup$ Keep in mind that particle accelerators are not just about quantity -- quality is also a concern. The ultimate objective is to collide beams together, and thus there are a whole host of more subtle issues that come along with that. $\endgroup$ – mng Dec 17 '15 at 4:07
  • $\begingroup$ Excuse me to ask some spin-off from that question here: is it possible to accelerate neutrons (as prototype of simple and neutral particles), and if so, how? $\endgroup$ – Gyro Gearloose Jan 4 '16 at 22:18
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In general the total voltage $V$ seen by a particle (for a 1 TeV proton must be 1 trillion volts), multiplied by the beam current $I$, gives you the beam power: $ P = VI $. So in principle you may have some trade off between the two of them, but often there are other limitations both to $V$ and to $I$. The designs of most of the existing machines have stretched these limits as much as possible (either because of cost or physical/technological problems) so it will not be immediately possible trade $V$ for $I$ or vice versa.

For instance at the LHC the energy is limited by the maximum bending field that the magnets are capable to produce, so even accelerating a single proton, you wont be able to push it beyond the nominal energy (currently 6.5 TeV). On the other hand you cannot arbitrary increase the current as collective behaviours of the beams may lead to instabilities and beam losses. Moreover, due to field quality issues, the LHC cannot even accept particles at an energy lower than 450 GeV.

So basically the number of particle that an accelerator can accept is the design one. Most of the time, at an operating machine, it cannot be easily increased even giving up something else (a counter example is the fully-loaded linac of CTF3). During the design phase you can optimize it, but this may lead to completely different design! Have a look at the (experimental) fusion reactors: those are basically very-low energy and quality accelerators (they just need to overcome the Coulomb barrier and particles scatter everywhere) which however store a huge amount of particles. Their designs do not share much with the high energy accelerators.

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  • $\begingroup$ Cannot accept lower than 450 GeV is a strong statement. Plans for a test injecting at 225 GeV are ongoing, as it would be an important part for FCC: indico.cern.ch/event/662862/contributions/2712504 $\endgroup$ – bjorn Nov 14 '18 at 15:04
  • $\begingroup$ @bjorn Yes, I was at that meeting, there are actually a couple of talks from myself :) However as things were (and still are today I believe), injecting below 450 GeV is not possible. Quite a lot of setup and MD time will be necessary to demonstrate a lower energy acceptance. $\endgroup$ – DarioP Nov 15 '18 at 12:26
  • $\begingroup$ ah, so it won't happen before LS2 then I guess...? $\endgroup$ – bjorn Nov 15 '18 at 13:53

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