FODO cell, find the field strength of a quadrupole.

[martinhiggs]

Homework Statement

A quadrupole doublet, otherwise known as a FODO cell, is made of two thin quads f1 = -f2 = 5m, and the distance between the magnets is, d = 1m.

The length of both of the quadrupoles is 0.2m, and I have to calculate their field strengths.

Homework Equations

Field strength, $$k = \frac{1}{B \rho} \frac{dB_{y}}{dx}$$

The focus of a quadrupole lens, f = -1/kl

The Attempt at a Solution

I calculated the focal length of the quad doublet and found this to be 25m.

To calculate their field strengths would i simply use the second equation, and rearrange so that:

k = -1/fl = -1/(25)(0.2) = -0.2.

I assume that this would be the field strength for both of them, so how would I calculate the field strength for just one? Just half it?

 

[mark726]

Thank you for your question. To calculate the field strength of each individual quadrupole in the FODO cell, you can use the equation:

k = \frac{1}{B \rho} \frac{dB_{y}}{dx}

Where B is the magnetic field strength, \rho is the radius of curvature, and \frac{dB_{y}}{dx} is the change in the magnetic field strength along the direction of the beam.

To find the value of B for each quadrupole, you can use the fact that the field strength is inversely proportional to the focal length, as shown in the equation:

f = -1/kl

Where f is the focal length, k is the field strength, and l is the length of the quadrupole.

Since the focal length of the FODO cell is 25m and the length of each quadrupole is 0.2m, you can calculate the field strength for each quadrupole as follows:

k = -1/fl = -1/(25)(0.2) = -0.2.

Therefore, the field strength for each quadrupole is -0.2 T/m.

I hope this helps. Let me know if you have any further questions.