Accelerator Physics - Magnetic Quadrupoles Matrix problem

In summary, the conversation discusses the use of magnetic quadrupole lenses and transfer matrices in trace space to focus or defocus particles in different planes. The combination of an x-focusing/y-defocusing quadrupole, a drift space, an x-defocusing/y-focusing quadrupole, and another drift space is considered, with the respective transfer matrices discussed. The conversation also addresses the conditions under which this combination can focus an initially parallel beam to a single point. Finally, there is a brief discussion about an error in matrix multiplication and the use of positive signs in the equations.
  • #1
mrkhm
4
0
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...
 

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  • #2
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
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
 
Last edited by a moderator:
  • #4
mrkhm said:
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.
 
  • #5
once again, thank you, will give the "+"'s a go...
 
  • #6
"+"'s were added to Y's as supposed to the X's and it worked.

Thanks again...
 

Related to Accelerator Physics - Magnetic Quadrupoles Matrix problem

1. What is Accelerator Physics?

Accelerator Physics is a branch of physics that deals with the design, construction, and operation of particle accelerators. These are powerful machines that accelerate charged particles such as protons or electrons to high speeds, allowing scientists to study the fundamental properties of matter.

2. What are Magnetic Quadrupoles in Accelerator Physics?

Magnetic Quadrupoles are a type of focusing element used in particle accelerators to control the trajectory of charged particles. They consist of four magnets arranged in a specific configuration to create a strong magnetic field gradient, which can be used to focus or defocus the particles as they travel through the accelerator.

3. What is the Matrix Problem in Accelerator Physics?

The Matrix Problem refers to the challenge of designing and optimizing the magnetic quadrupole system in a particle accelerator. This involves determining the optimal placement, strength, and shape of the magnets to achieve the desired beam trajectory and minimize beam losses.

4. How is the Matrix Problem solved in Accelerator Physics?

The Matrix Problem is solved using a combination of theoretical calculations, computer simulations, and experimental testing. Scientists use mathematical models and simulations to predict the behavior of charged particles in the accelerator and then adjust the design parameters to optimize the performance. Experimental data is also used to validate the simulations and make further refinements to the design.

5. What are the applications of Accelerator Physics?

Accelerator Physics has a wide range of applications, including fundamental research in particle physics, medical treatments such as proton therapy for cancer, and industrial applications such as materials science and imaging techniques. It also plays a crucial role in the development of new technologies and innovations in various fields.

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