Matlab code for plotting magnetic scalar potential of a sextupole

[TooFastTim]

First let me introduce myself. I'm and electronics engineer with 10 years of experience in the instrumentation of particle beams. I left the field for 10 years and have been fortunate to be granted a second lease of life on particle accelerators. Slowly over time the job has come to involve more and more control of beams so I'm trying to clue myself up on the "mechanics" of the magnets commonly used (e.g. dipole, quads and sextupoles). I've managed to get my head around dipoles (easy) and quads (not so easy and very subtle) but I've run into a dead-end (for me) regarding the magnetic scalar potential for a sextupole. I'm trying to plot it in either MATLAB or scilab but it ain't so simple. The maths I think I've got a resonable handle on considering it's fifteen years since i studied this.

So the equation describing the magnetic scalar potentials in cartesian co-ords is:

3*y*x^2+y^3=V/C

where V is the scalar potential and c is a constant. All of this is well & fine but the blasted thing goes complex on me. (actually it's a complete beast because you need to calculate the roots of a cubic equation to plot. Not difficult but very tedious) I have the same result if I use the cylindrical co-ords:

((V/C*sin(3*theta))*(0.333))*sin(theta).

In the previous institute at which I worked I had lots of support for this stuff but not at the present. So can anybody help me get my heard around this? Has anybody plotted the magnetic scalar potentials for a sextupole? Or can anybody explain what it means when it goes complex, bearing in mind I'm a humble electronics engineer who hasn't had to deal with thsi stuff since uni?

 

[mmwave]

Hello, it's great to meet another scientist who is interested in particle accelerators and their instrumentation. I can understand your frustration with trying to plot the magnetic scalar potential for a sextupole. It can definitely be a complex and tedious task, especially if you haven't worked with this type of math in a while.

I have some experience with plotting magnetic scalar potentials for sextupoles, and I might be able to offer some help. First, let's talk about what it means for the potential to go complex. In simple terms, this means that the solution to the equation has imaginary numbers, which can be represented by the square root of a negative number. This is not unusual for sextupoles, as they have a more complex shape compared to dipoles and quads.

To plot the potential, you will need to use a special type of plot called a contour plot. This will allow you to see the changes in the potential as you move along the x and y axes. You can also use software such as MATLAB or scilab to help with the calculations and plotting.

If you still have trouble, I would recommend reaching out to other scientists or engineers who have experience with sextupoles. They may be able to offer more specific guidance or share their own methods for plotting the potential. Additionally, there are also online forums and communities where scientists and engineers discuss and share information about particle accelerators, so you may find some helpful resources there.

I hope this helps and good luck with your research!

 

[oswaler]

I can understand your frustration in trying to plot the magnetic scalar potential for a sextupole. This is a complex mathematical problem and it requires a good understanding of both mathematics and electromagnetism. I would suggest seeking help from a physicist or mathematician who has experience in this area. They may be able to guide you through the process and provide you with the necessary tools and techniques to plot the potential.

In terms of the complex results, it is important to note that the magnetic scalar potential is a complex quantity. This means that it has both a real and imaginary component, which can be represented as a complex number. In this case, the complex nature of the potential may be due to the nonlinear behavior of the sextupole magnet. Without a deeper understanding of the problem, it is difficult to say for sure. Again, seeking help from an expert in this field would be beneficial.

I would also recommend looking into resources and literature on the topic of magnetic scalar potential for sextupoles. There may be existing code or methods that can help you in your plot. Additionally, reaching out to colleagues or attending conferences and workshops on particle accelerators may also provide valuable insights and assistance.

In conclusion, I understand that this may be a challenging task, but with the right guidance and resources, I am confident that you will be able to successfully plot the magnetic scalar potential for a sextupole. Best of luck in your efforts.