Spectrometer: Time Separation

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The spectrometer is a series of rings each with an applied voltage that generates an electric field approximately parallel to the ion beam. The electric field accelerates fragments of different charge-to-mass ratio at different rates toward the detector. Suppose the ions have an initial velocity when they reach the interaction region and the electric field is uniform and confined to the region within the spectrometer. The acceleration of a fragment with charge and mass will be:

Setting the interaction region as the origin and the ion beam as the z-axis we obtain an expression for the position of the fragment as a function of time after interacting with the laser:

If the distance from the interaction region to the end of the spectrometer is the time it takes the fragment to reach the end of the spectrometer is:

If the distance to the end of the spectrometer to the particle detector is then the time for the fragment to travel from the end of the spectrometer to the detector is:

Therefore the total time of flight (TOF) is equal to

which can be expressed as a function of the charge-to-mass ratio

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