Calculating the Voltage Needed by the Accelerator Between Accelerating Tubes

The energy given to the proton in each gap between tubes is ${\text{PE}}_{\text{elec}}=\text{qV}$ where $q$ is the proton’s charge and $V$ is the potential difference (voltage) across the gap. Since $q=q_e=1.6\times {\text{10}}^{-19}\text{C}$ and $\text{1 eV}=\left(\text{1 V}\right)\left(1.6\times {\text{10}}^{-\text{19}}\text{C}\right)$, the proton gains 1 eV in energy for each volt across the gap that it passes through. The AC voltage applied to the tubes is timed so that it adds to the energy in each gap. The effective voltage is the sum of the gap voltages and equals 800 MV to give each proton an energy of 800 MeV.

There are 2000 gaps and the sum of the voltages across them is 800 MV; thus,

A voltage of this magnitude is not difficult to achieve in a vacuum. Much larger gap voltages would be required for higher energy, such as those at the 50-GeV SLAC facility. Synchrotrons are aided by the circular path of the accelerated particles, which can orbit many times, effectively multiplying the number of accelerations by the number of orbits. This makes it possible to reach energies greater than 1 TeV.