# Equation for Determining the Velocity of a Proton in a Cyclotron?

Hello,

I'm always seeing the energy of a particle being accelerated in a cyclotron expressed in MeV or GeV. How do I determine the velocity of a proton in m/s ?

Thanks!!

jtbell
Mentor
Look up (or Google for) the relativistic kinetic energy formula and solve it for v. First convert electron volts to joules: 1 eV = 1.60e-19 J.

Hello,

I'm always seeing the energy of a particle being accelerated in a cyclotron expressed in MeV or GeV. How do I determine the velocity of a proton in m/s ?

Thanks!!

Id base the calculation on mass, charge (e) Voltage and Magnetic field strength (T). the cyclotron is imparting momentum to a massed particle with charge q. accel is based on q while energy and velocity are related to both mass and acceleration due to the electrostatic forces.

to calculate electrostatic forces

F = k (q1q2/r^2) -- same as grav eq, different constants

Charge of cas column

bulk charge = n * q ( n Avogadro etc)

n = q * k * v (approx).

Determining the total maximum ionized charge of the gas in the cyclotron is now related to the frequency and mass of the involved proton cloud

E = 1/2* Moment of inertia * radians per sec (w) ^ 2 (rotational kinetic energy of synchrotron)

now one can solve for tangential average velocity of the proton cloud using the radians per second times arc length relation to solve for an approximate

w = f * 2 PI

V = w * r

I'm hoping at least a few hundred meters per second...that will start to get into a few tens of mega joules.

The magnetic field lines in this case will point through the center of the device with the protons orbiting that. To achieve a good design ( im working on this mentally). The device is essentially a scaled up atom where a proton cloud replaces the electron. The Dees create the alternating high voltage electrostatic field, while a central coil provides a magnetic "pivot" for the charged particles to rotate around.

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