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Is it possible to accelerate a very large number of protons in a particle accelerator as opposed to only a few as is regularly done? What's to keep someone from accidentally dumping too many particles into an accelerator and destroy the facility with its kinetic energy and enormous thrust?

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    $\begingroup$ It's not possible. The space charge would blow such a large cloud of protons apart. It is, indeed, fairly hard to accelerate beams with more than a few amperes of beam current efficiently because the space charges make focusing difficult. $\endgroup$ – CuriousOne Dec 23 '15 at 1:51
  • $\begingroup$ Lhc uses a lot of fuses :) the protons come from a devices chain , each one with its own limits , that can't deliver too much material. To get the targeted collisions ratio, all is fine tuned $\endgroup$ – user46925 Dec 23 '15 at 1:59
  • $\begingroup$ interesting to compute the kynetic energy needed to accelerate 1kg until 99.99% of c . Note that the time at this speed is very short at the collision node $\endgroup$ – user46925 Dec 23 '15 at 2:05
  • $\begingroup$ a summary of the process : How the Large Hadron Collider Works $\endgroup$ – user46925 Dec 23 '15 at 4:32
  • $\begingroup$ You could rule it out just by considering the energy required to accelerate 1kg to 0.9c $\endgroup$ – Robert Stiffler Dec 23 '15 at 10:48
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The LHC cannot accelerate 1 kg of particles at once, and neither the experiments would be able to cope with such a big number of collisions. I have already partially answered here: How many particles can a particle accelerator accelerate at once?, without further details (just to allow you to google them up), the limiting effects at the LHC are (in order of importance): electron cloud, beam-beam, impedances-wakefields, space charge. but I would like to focus on your last question:

What's to keep someone from accidentally dumping too many particles into an accelerator and destroy the facility with its kinetic energy and enormous thrust?

This requires to understand how particles are "dumped" (or better: injected) into an accelerator. You always need to start with a source or gun. In case of protons it is a bottle of (high-purity) hydrogen gas, which is extracted and ionized for instance by an electric discharge. As the electrons leave you are left with protons which can start to gain energy for instance by a DC voltage (a capacitor). While the protons are at low energy, they are very susceptible to external perturbations, including the ones coming from the nearby protons. Therefore if for some reason the proton production is strongly increased at the source, you will start to see odd behaviours right after the source, where the low energy makes the beam much less destructive.

Before being injected into the LHC the protons have to reach 450 GeV, going through an accelerator chain (see Particle colliders: why do they need an accelerator chain) which means that the beam is prepared and transferred between many intermediate accelerators where there is plenty of time to monitor it and eventually abort the injection if the required parameters are not met.

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