Charged Particle Beam Transport and Analysis

If we examine the magnetic held from such a quadrupolar device, we will hnd that the held along the central axis is exactly zero and increases linearly to a maximum value at each pole face. (The pole tips should be hyperbolic surfaces to conform to the shape of the magnetic held, although cylindrical pole tips are often used for ease of manufacture.) Quadrupole magnets are thus characterized by the gradient of the magnetic held, dB/dr, where r is a radial coordinate and 

Example Problem A dipole magnet deflects charged particle beams through an angle of 22.5° with a radius of 2.0 m. For ease of construction the magnet has rectangular pole pieces 0.5 x 1.5 m long. The beam enters normally at the 

Solution We need to evaluate the angles a, and a2 in order to solve this problem. From the problem definition we know that = 0. A little geometry will show that in this case the exit angle is equal to the bend angle  

Such different focal lengths, a weaker focus in vertical compared to horizontal, as in this situation are a common occurrence in beam transport systems. 

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