Assume there are 5.0 ×10^13 protons at 1.0 TeV stored in the...

Assume there are $5.0 \times 10^{13}$ protons at $1.0 \mathrm{TeV}$ stored in the 1.0 -km-radius ring of the Tevatron. (a) How much current (amperes) is carried by this beam? (b) How fast would a $1500-\mathrm{kg}$ car have to move to carry the same kinetic energy as this beam?

Key Concepts

Energy Equivalence in Macroscopic Systems

Comparing the stored energy in a particle beam to the kinetic energy of a macroscopic object, such as a car, involves equating the total energy of the beam to the classical kinetic energy formula, (1/2)mv². This approach demonstrates how extremely high energy densities in accelerator beams translate into significant kinetic energies, even when distributed over massive objects.

Particle Beam Kinetic Energy

Each high-energy proton in the accelerator has a kinetic energy given in teraelectronvolts (TeV), a unit appropriate for particle physics. To find the total energy stored in the beam, one must multiply the energy per proton by the total number of protons. This concept also involves converting energy units from electronvolts to joules when comparing with macroscopic systems or using classical equations.

Electric Current in Charged Particle Beams

Electric current is defined as the rate of flow of electric charge. In the context of a particle accelerator, the current carried by the beam is calculated by dividing the total charge of all the circulating particles by the time it takes for one complete revolution around the ring. This involves understanding that each proton carries a fixed elementary charge and that the repetitive circulation of the beam contributes cumulatively to the current.

Revolution Frequency

The revolution frequency describes how many times per second a particle traverses the circular path of the accelerator. It is determined by the circumference of the ring and the speed of the particles, which in high-energy accelerators is very close to the speed of light. This frequency directly influences the calculation of the beam's current, as it sets the time interval over which the total charge is delivered.

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