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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