Double- Focusing Sector Spectrometers:

Magnetic /electrostatic sector instruments use magnetic and electric fields to disperse ions according to their momentum and translational energy. Like the magnetic sector, the electric sector applies a force perpendicular to the direction of ion motion, and therefore has the form of an arc.  

     

The dependence of mass-to-charge ratio on the electric and magnetic fields is easily derived as below. All ion formed in the ion source are accelerated to a kinetic energy, T of

T = eV = mn² / 2

Solving for the velocity v we get: 

From the Lorentz force law, the magnetic field applies a force evB that must be equal to the centripetal force mv**2/r as the ions move in an arc through the magnetic sector: 

e vB =  m υ ²  / r

Substituting for v, we arrive at the working equation for a magnetic sector mass spectrometer: 

m/e = B²r² / 2V

Therefore ions are accelerated out of the source and are collimated into a narrow beam by a set of slits. As the ions pass through the electrostatic sector, they are dispersed according to their translational energy. Only those ions that have the correct translation energy pass through the slits at the end of the electrostatic sector. Finally the magnetic sector disperses the ions according to their mass to charge ration.

A mass spectrum is obtained by scanning the accelerating voltage (electric field) while hold B constant and scan V  to bring ions with different m/z ratios sequentially to focus at the detector.