Accelerator Physics - Magnetic Quadrupoles Matrix problem

1. Dec 18, 2012

mrkhm

Dear reader ( and potential helper)

I appreciate the time you have taken to even just glance at this topic and for those able to shed some light in any helpful direction, your assistance is greatly appreciated...

1. The problem statement, all variables and given/known data

A thin magnetic quadrupole lens may be described by transfer matrices in trace space:

http://www.khmsolutions.net/p1.jpg [Broken]

and analogous for y and y′. Positive (negative) focal length f corresponds to focusing (defocusing) in the x-z-plane and defocusing (focusing) in the y-z-plane. Field-free drift over a length L is represented by

http://www.khmsolutions.net/p2.jpg [Broken]

Consider the combination of an x-focusing (y-defocusing) quadrupole (f1 > 0), a drift space (L1), an x-defocusing (y-focusing) quadrupole (f2 < 0), and another drift space (L2).

(i) What are the respective transfer matrices for this combination in the x-x′- and y-y′-trace spaces?

(ii)Under what conditions does this combination focus an initially parallel beam to a single point?

2. Relevant equations
help...
3. The attempt at a solution

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• p2.jpg
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Last edited by a moderator: May 6, 2017
2. Dec 18, 2012

Staff: Mentor

xout = M xin

This xout is the xin for the next element in your chain. You can multiply all those matrices to get the total transfer matrix.

3. Dec 19, 2012

mrkhm

Dear mfb (and anyone else)

Thanks for taking the time to glance at this and your advisement, please consider the attempt below, been advised something's wrong though....

http://www.khmsolutions.net/p3.jpg [Broken]

http://www.khmsolutions.net/p4.jpg [Broken]

Last edited by a moderator: May 6, 2017
4. Dec 19, 2012

Staff: Mentor

"something" is a bit unspecific.
If it just an error in matrix multiplication: Well, computers can do that.

As f1>0 and f2<0 are given, I think you should use "+" in both matrices for x. This just changes all signs where f2 appears in the equations.

5. Dec 19, 2012

mrkhm

once again, thank you, will give the "+"'s a go...

6. Dec 20, 2012

mrkhm

"+"'s were added to Y's as supposed to the X's and it worked.

Thanks again...