Spaceships: Difference between revisions

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* r = radius of the cyclotron (meters)
* r = radius of the cyclotron (meters)
* m = rest mass of the proton (1.673×10−27 kilograms), electron is 9.109×10−31
* m = rest mass of the proton (1.673×10−27 kilograms), electron is 9.109×10−31
= Lorentz =
[[File:Lorentz Velocity.png|thumb]]
* 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))

Latest revision as of 01:42, 6 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

Lorentz Velocity.png
  • 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))