conditions for no periodic solutions

[irgallard]

Hello,

I am trying to create a DRL environment with Ocelot, with this default configuration of elements in the lattice: https://nbviewer.org/github/ocelot-collab/ocelot/blob/master/demos/ipython_tutorials/1_introduction.ipynb

To achieve this, I have been analyzing how the Twiss parameters change with small increments in the strength of the quadrupoles. However, during my experiments, I encountered a particular issue with some configurations and changes that resulted in the following situation:

Are there any guidelines to follow in order to update the strengths? Managing multiple magnets at once maybe?
If so, it would be nice to know how to avoid such solutions. Otherwise I am considering their use as a "game over" condition for the learning algorithm.

Thank you all for your time and support!

Best regards,
Galo

[sergey-tomin]

Hi,

do you need a periodic solution for your lattice every time ? If yes, you can look in a accelerator handbook the condition for existence of the periodic solution. Or you can look in ocelot: lines 152-157 https://github.com/ocelot-collab/ocelot/blob/master/ocelot/cpbd/optics.py
maybe you can check this condition earlier

[st-walker]

As Sergey says, some lattices are fundamentally unstable and have no stable solutions. Often this applies to when quadrupoles become too strong and over-focussing (as opposed to too weak).

How to adjust quadrupoles?

If you have a MagneticLattice instance:

mlat = MagneticLattice(my_sequence)
quads_i_want = ["quad1", "quad2", "quad4"]
quads = {element.id: element for element in mlat.sequence if element.id in quads_i_want}
quads["quad1"].k1 = 3.0
quads["quad2"].k1= 1
# etc...

Actually I wish we had a native container type that allowed for addressing elements within a sequence easily by name. That would make this all much easier. Currently we just use lists.

[st-walker]

Based on your reply and the documentation (above), then I can just run the simulations for a particle array without trying to find a stable solution (periodic), for any magnetic lattice.

Well not a ParticleArray necessarily but some initial tws0 Twiss instance. Then it will just propagate the twiss parameters to the end of the lattice.

Would you say that not all linear accelerators need to have stable solutions, depending on the accelerator's objective? (i.e delivering a beam with certain shape and energy to a target).

Yes. A linac having no stable solution means nothing. It doesn't need to be stable because it's single pass.

[irgallard]

Thanks! My last two questions now:

• Following up what you just said, how do we know the initial Twiss parameters we have to input in each case/configuration?
• When you inject particles for the particle arrray you can track the beam through the lattice, and even check the final distribution of particles for this specific set up (like here, 20k: Notebook). In what amount of time does this process happen? What is the injection rate?

[st-walker]

Following up what you just said, how do we know the initial Twiss parameters we have to input in each case/configuration?

Well that's for you to know. It depends on your machine. Ultimately it depends on how you generated your charged particle beam and how you manipulated it (in real life) with electromagnetic fields. We have a photocathode here, then a solenoid and accelerating cavities. LHC uses a bottle of hydrogen and then I don't know what. I don't know what you use.

When you inject particles for the particle arrray you can track the beam through the lattice, and even check the final distribution of particles for this specific set up (like here, 20k: Notebook). In what amount of time does this process happen?

The main computation goes into the collective effects calculations, not the magnetic tracking. So space charge, coherent synchrotron radiation effects, these take time. But maybe for your beam if it is at a high energy then you maybe don't care about space charge, and if the bunch is long you don't care about coherent synchrotron radiation effects, and so on. If you do not care about collective effects then tracking 20k particles is very fast, but how long is a piece of string? How fast depends on how long your machine is. But for EuXFEL injector to track 50m without any collective effects it is on the order of several seconds. If you want to know how long that jupyter lab example takes to run, then you should run it and time it.

What is the injection rate?

I don't know what this means.

[irgallard]

I see!

With injection rate I meant how fast these 20k particles are introduced into the lattice. All at once?

[st-walker]

Yes the particles are tracked all at once. In general this is more computationally efficient. If you read about CPU caches and vectorisation then you will understand why this is.

[sergey-tomin]

you can address by element itself. See example:

q1 = Quadrupole(l=0.5, k1=1)
q2 = Quadrupole(l=0.5, k1=-1)
d = Drift(l=1)
cell = [q1, d, q2]
lat = MagneticLattice(cell)

# you can change quads strength in any moment 
q1.k1  = 2
q2.k1 = -2

etc.