Introduction to accelerator and their applications: Exercize 1 Gabriele Chiodini - INFN Lecce - May 2015 ! ! ! ! ! !

Introduction to accelerator and their applications: Exercize 1 Gabriele Chiodini - INFN Lecce - May 2015

PhD lessons in Physics for Università del Salento 2015 (20 hours, 4 CFD)

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Using the notation of special relativity theory verify the following equations:

A. γ=E/m⁰c² where E is the relativistic energy of the particle, m0 is the rest mass of the particle and c is the speed of light (γ=E/E0

where E0=m0c² is the rest energy of the particle).

B. β=pc/E where p is the moment of the particle.

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The kinetic energy of a proton T is 1 GeV and its rest mass is 0.9383 GeV/c². Determine its total energy E in GeV and its momentum p in GeV/c.

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A betatron has a donut for the beam of radius 0.1 m and it powered with a generator having a repetition frequency of 200 Hz. Its magnetic field guide has a peak value of 1 T and the average magnetic field satisfies the relationship 2 : 1. Which is the peak energy of the accelerated electrons?

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Calculate the frequency rotation of the particles in a cyclotron with a magnetic field of 1.2 Tesla having a radius of 1 m. What about if the field is doubled? And if the radius it is halved?

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A synchrotron of 25 m radius accelerates protons (atomic mass A = 1, atomic number Z = 1) from 50 to 1000 MeV. At 1000 MeV energy the magnetic field dipoles saturated. What is the maximum acceleration energy for deuterons (atomic mass A = 2, atomic number Z = 1). Calculate also the rotation frequency of protons and deuterons accelerated to their maximum energy.

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What is the size of an electron storage ring at the North Pole for 10 keV electron beam using the Earth's magnetic field as bending field?

In which direction the electrons rotates?

(The Earth's magnetic field is similar to a dipole centered with the earth and tilted of 11.30 degrees with respect to the rotation axis of the Earth. At the orth pole B=0.5 Gauss.)

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