Accelerator Physics - Magnetic Quadrupoles Matrix problem

[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...

Homework Statement

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

http://www.khmsolutions.net/p1.jpg

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

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?

Homework Equations

help...

The Attempt at a Solution

help please...

 

[mfb]

x_out = M x_in

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

 

[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

http://www.khmsolutions.net/p4.jpg

 

[mfb]

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

"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.

 

[mrkhm]

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

 

[mrkhm]

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

Thanks again...