Question

At the 3-km-long Stanford Linear Accelerator, electrons are accelerated to final kinetic energies of 47 GeV.

a. Electrons increase their kinetic energies approximately uniformly every meter as observed in the laboratory frame. What is the energy gain in MeV/m?

b. Suppose the classical KE expression was correct – how far along the accelerator tube would the electrons need to travel before they reached light speed?

c. OK, but that isn’t really what happens – even at 47 GeV of kinetic energy, the electrons travel slower than light speed. Find the difference (1 – ß) between the speed of light and the final speed of the electrons as measured in the lab frame. Hint: when ß is very close to 1, we can approximate 1 - ß² = (1 + ß)(1 - ß) ? 2(1 - ß)

d. Suppose we set up a race between a light pulse and a 47 GeV electron – straight through Earth in a vacuum tube. They travel 12,740 km. Of course, light wins. But by what distance did it win?

e. How long does the 3-km-long SLAC tube appear to a 47 GeV electron?

Answer 1