How many particles can a particle accelerator accelerate at once?

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.

• 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) . – Keith McClary Dec 15 '15 at 3:57
• 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. – mng Dec 17 '15 at 4:07
• 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? – Gyro Gearloose Jan 4 '16 at 22:18

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.