Deflector: Spatial Separation

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The deflector is essentially a parallel plate capacitor. The electric field between the plates accelerates fragments of different charge-to-mass ratios at different rates in a direction perpendicular to the ion beam axis. Suppose that the electric field  is uniform and confined to the region between the plates. Let the y-axis point in the direction of the electric field of the deflector. The acceleration  of a fragment with charge and mass  in the y direction will be:

Suppose that the deflector is length  in the ion beam direction. If the fragment enters the deflector with a velocity  in the ion beam direction then the time  that it spends inside the deflector is:

When the fragment exits the deflector it will have a velocity  in the y-direction given by:

Therefore the fragment will be deflected by an angle  measured from the axis of the ion beam (z-axis) given by:

Letting , we can express  as:

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