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= Lorentz = | = Lorentz = | ||
[[File:Lorentz Velocity.png|thumb]] | [[File:Lorentz Velocity.png|thumb]] | ||
* gamma = 1 + K/(m * c^2) | |||
v=c*sqrt(1-((1/gamma)^2)) | * v=c*sqrt(1-((1/gamma)^2)) | ||
Revision as of 22:05, 5 June 2024
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
- gamma = 1 + K/(m * c^2)
- v=c*sqrt(1-((1/gamma)^2))