(II) The 1.0-km radius Fermilab Tevatron took about 20...

Name: Problem 9, Chapter 32: Physics: Principles with Applications
Uploaded: 2020-06-28T03:27:10-08:00
Duration: 3 min 3 s
Channel: Ren Jie Tuieng
Description: (II) The 1.0-km radius Fermilab Tevatron took about 20 seconds to bring the energies of the stored protons from 150 GeV to 1.0 TeV. The acceleration was done once per turn. Estimate the energy given to the protons on each turn. (You can assume that the speed of the protons is essentially c the whole time.)

(II) The 1.0-km radius Fermilab Tevatron took about 20 seconds to bring the energies of the stored protons from 150 GeV to 1.0 TeV. The acceleration was done once per turn. Estimate the energy given to the protons on each turn. (You can assume that the speed of the protons is essentially c the whole time.)

Key Concepts

Synchrotron Accelerator Principles

In circular accelerators, also called synchrotrons, charged particles (such as protons) are accelerated in a circular path by a series of accelerating pulses or energy kicks at each turn. The accelerator ramps up the kinetic energy of the particles by applying an electric field once or more times per revolution, which enables a controlled and incremental approach to achieve very high energies over many turns.

Relativistic Particle Motion

When particles are accelerated to speeds close to the speed of light, relativistic effects mean that their velocities do not change significantly even as their energies do. This allows one to assume that the speed is nearly constant (and approximately the speed of light), simplifying calculations such as the number of revolutions per unit time and the time intervals involved in each turn.

Circumference and Revolution Time Calculation

The circumference of the circular accelerator, determined by the radius, is a crucial geometric factor since it dictates the distance a particle travels in one complete revolution. By calculating the circumference (using the formula 2?r) and dividing by the speed of the particles (which is roughly constant and equal to the speed of light in relativistic cases), one can determine the time it takes for one full turn and thereby the number of revolutions during the acceleration period.

Energy Increment per Turn Estimation

To estimate the energy given to the particles on each turn, one needs to determine the total energy increase over the entire acceleration period and divide it by the total number of turns. This calculation highlights the incremental nature of the acceleration process in synchrotrons and shows how small energy increments per turn, when accumulated over nearly a million cycles, can lead to a significant total energy gain.

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