How does the dipole magnet accelerate protons in the LHC?

Answer 1

Initially, the protons are accelerated to very high velocities via a linear accelerator that feeds into the LHC. This is done simply by sectioning off the accelerator into different voltage "compartments" causing the protons to speed up as they reach each one of these "compartments" that have different voltages applied across them.

Once they enter the LHC, they encounter a multitude of superconducting dipole magnets, each one being tuned to have a bit stronger magnetic field than the last. The protons hit these magnetic fields and bend around a circular ring according to the Lorentz force, F = q(v X B), where v is the velocity vector of the protons, q is their charge, and Bis the applied magnetic field vector. The X in the middle of the v and B variables signifies the vector cross product, and is equal to the magnitudes of the proton's velocity and the applied magnetic field multiplied by the sine of the angle between them, or vBsin(θ), where θ is the angle between the v and B vectors. To make life easy, this angle is usually designed to be 90o, meaning that sin(θ) equals 1.

Additionally, the cross product tells you that the force is going to be in a direction found by using the "right-hand rule." That means that if you point your right hand in the direction of the proton's velocity and then curl your fingers in the direction of the applied magnetic field, your extended thumb points in the direction of the force. And, you guessed it, to keep the protons moving around a horizontal ring, the magnetic field must be pointing upwards (go ahead and test that out using the right-hand rule).

As the magnetic fields increase, the force on the protons increase, thereby increasing velocity. To keep the protons within the ring, as opposed to having them just collide with the wall, the magnetic field needs to be increased to compensate for the increased velocity. This, however, effectually increases the force once again, and therefore the proton's velocity once again, meaning that an even stronger magnetic field needs to be applied once again to compensate. This procedure of compensating for increased velocity with increased magnetic fields, which occurs thousands of times, is called "tuning the beam," and let me tell you, it's an art.

Eventually, the incremental increases of the proton's velocity, due to the relativistic law that a particle with mass can't travel faster than the speed of light, become so minor that the magnets can all hold a more or less steady field (adjusting for synchrotron radiation of course) while the protons continue to zip around the ring.