Spaceships

Cyclotron Basics for a Proton

The kinetic energy K of a proton in a cyclotron is given by:

K=(q^2 * B^2 * R^2)/(2m)

where:

• q = charge of the proton (1.602×10−19 coulombs), electron is negative that
• B = magnetic field strength (teslas, 10 is a lot, 20 is a lot lot)
• r = radius of the cyclotron (meters)
• m = rest mass of the proton (1.673×10−27 kilograms), electron is 9.109×10−31

Lorentz

• K = (gamma - 1)(mc^2)
• gamma = 1 + K/(m * c^2)
• v=c*sqrt(1-((1/gamma)^2))

• gamma = 1 / (sqrt(1-((v/c)^2)))
• sqrt(1-((v/c)^2)) = 1/gamma
• 1-((v/c)^2) = (1/gamma)^2
• (v/c)^2 = 1-((1/gamma)^2)
• v/c = sqrt(1-((1/gamma)^2))
• v = c * sqrt(1-((1/gamma)^2))