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Simulation of Trajectories of Charged Particles in Magnetic Fields

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1 Author(s)
Vineyard, George H. ; Department of Physics, University of Missouri, Columbia, Missouri

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A ball rolling on a rotating surface is shown to simulate the motion of a charged particle in a magnetic field. The theory is given for the case of a warped surface undergoing arbitrary rotation about a fixed axis and translation perpendicular thereto, while the system from which the ball is observed partakes of similar but independent motion. With approximations based on not too large departure of the surface from flatness, the following cases can be simulated: (a) The magnetic field is homogeneous and constant. The electric field is perpendicular to the magnetic field, and irrotational, but otherwise arbitrarily spatially dependent, and arbitrarily time dependent within certain limits. (b) The magnetic field is homogeneous but arbitrarily time dependent. The electric field is perpendicular to the magnetic field and may have a variety of space and time dependences, including a part which encircles the axis and has just the right magnitude to produce acceleration in a circular orbit as in the betatron. Results of rudimentary experiments are presented which indicate that the method is capable of good accuracy.

Published in:

Journal of Applied Physics  (Volume:23 ,  Issue: 1 )

Date of Publication:

Jan 1952

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