1. Non-linear Magnetic Field Inserts for the IOTA Ring
Finn O’Shea
October 27, 2015

2. FHO - IOTA magnets - IMMW19 - October 27, 2015
Contents
A short description of RadiaBeam.
A short description of the IOTA principle.
What the magnets look like.
Field tolerances and what we are doing about them.
Field quality.
Relative alignment.
Phase I design and lessons learned.
Phase II design and progress.
The presentation is just as much about RadiaBeam talking about itself and one of its projects as it is about getting feed back from the measurement community.
FHO - IOTA magnets - IMMW19 - October 27, 2015

3. RadiaBeam Technologies
Founded in 2003 in Los Angeles as a spin off from UCLA PBPL.
~50 employees (about half are machinists and techs).
7 PhD scientists, 12 engineers.
A large fraction of our work comes from the SBIR program with the goal of taking accelerator technology to market.
Most of our customers are labs worldwide.
PBPL = Particle Beam Physics Laboratory
SBIR = Small Business Innovation and Research
FHO - IOTA magnets - IMMW19 - October 27, 2015

4. RadiaBeam Technologies II
About 1/3 of our sales jobs come from electro-magnet production:
Solenoids
Steering magnets
Dipoles
Quadrupoles
We also build permanent magnet optics for advanced accelerators.
We focus on small batches at the moment because we are still growing.
Another 1/3 comes from RF sales:
S-band acceleration structures
X or S-band deflecting structures.
We also make turn-key x-ray systems based on RF guns.
We are developing a betatron line.
Final 1/3 comes from diagnostics.
50 steering magnets at a time, quadrupoles triplets
FHO - IOTA magnets - IMMW19 - October 27, 2015

5. Non-linear Integrable Optics
Linear lattices are nice because they are easy to understand.
They are also unstable perturbations and suffer from chromaticity.
Both of these can be corrected by non-linear elements (sextupoles and octupoles).
But these elements limit dynamic aperture because the systems are far from integrable.
These problems can be ameliorated if the system is both non-linear and integrable from the very beginning.
This requires a magnetic element in which the magnetic field depends on x, y and s.
V. Danilov and S. Nagaitsev, PR ST-AB 13, (2010).
FHO - IOTA magnets - IMMW19 - October 27, 2015

6. Integrable Optics Test Accelerator
IOTA is a project at FermiLab to perform a proof-of-principle experiment on the integrable optics concept.
Scale: 32 m circumference, 150 MeV electron ring, β = cm
FHO - IOTA magnets - IMMW19 - October 27, 2015

7. High level view 2 meters long 18 segments with independent motion
Highly custom internal vacuum chamber

8. FHO - IOTA magnets - IMMW19 - October 27, 2015
The inserts
The magnetic potential:
There is a pair of infinities at x = ±(c√β), y = 0
This limits the region over which the expansion can possibly work
Maybe we could try to place a current there
who wants to mess around with an infinity?
Didn’t seem to work well in simulation anyhow!
FHO - IOTA magnets - IMMW19 - October 27, 2015

9. One solution to rule them all
Universal Solution
Normalize the tranverse coordinates by c√β.
Typical multipole design
Find an equipotential surface
Put iron on one side of that surface
Correct for edges
Energize the iron with some kind of B-field source
By finding a solution in normalized space, we can solve the equipotential problem only once

10. Return to real space To make the universal solution useful
Segments 1,5 and 10
To make the universal solution useful
Extend the top up to increase the good field region in y to y ≲ 0.8 β1/2 c (found with 2D sims)
Cut off the corner near x = β1/2 c
Put in a return yoke so that a coil can be added.
Add reluctance gap

11. Error Tolerances Preliminary tolerances:
Co-axial to d = 100 μm
Less than 1% deviation from ideal field
As large an aperture as possible
Manufacturing tolerances set via 3D simulation
This made a tolerance table we think we can hit
Want to maintain the good field region from the 2D simulations:
y ≲ 0.8 β1/2 c
x ≲ 0.6 β1/2 c

12. FHO - IOTA magnets - IMMW19 - October 27, 2015
Phase I prototype
FHO - IOTA magnets - IMMW19 - October 27, 2015

13. Microscope Image of Probe
Hall Probe Details
Probe Assembly
Microscope Image of Probe
Hall probes from Arepoc, S. R. O. Bratislava, Slovakia.
F. H. O'Shea - AAC San Jose

14. FHO - IOTA magnets - IMMW19 - October 27, 2015
Phase I measurements
Skew Harmonics
Sent the Phase I prototype to Argonne for measurement on a rotating coil.
We were not thrilled with the results.
The motion of the reluctance gaps was not repeatable, so it was very hard to tune the whole device at once.
It is kind of hard to see how good or bad the harmonic content is with typical harmonic content chart.
Upright
Harmonic
Content
FHO - IOTA magnets - IMMW19 - October 27, 2015

15. What we learned in Phase I
Repeatability was a significant problem. The yokes just wouldn’t move back in to the same position.
Trying to pass the flux through a vacuum chamber is therefore a bad idea.
Put everything in vacuum or don’t, but don’t try to split the difference.
Alignment was ok, but we can do better
Build a vibrating wire system to define the magnetic axis of each segment, this will further allow FermiLab to move things themselves if they want.
Harmonic content wasn’t very good
Improve this by more sophisticated manufacturing, like is used for synchrotron multipoles.

16. FHO - IOTA magnets - IMMW19 - October 27, 2015
Specifying the EDM Cut
Wire EDM is expensive, but really good at precise finishing cuts.
Had to develop a set of tolerances for the final cuts while controlling cost.
Wrote a Python script to push points on the highlighted red line around in Poisson.
Identified critical features and combined them all to simulate poles.
Statistics say if we make 3 of each, we have a 92% of keeping the field errors below 2% in 2 of them. If we make only 2 poles, we’ll have a 68% chance.
The program compares the calculated field to the theory field on an ellipse with axes x = 6 mm and y = 7 mm. 40 points are taken in azimuth for an ellipse that goes from the +x axis to the +y axis, i.e. a quarter ellipse.
FHO - IOTA magnets - IMMW19 - October 27, 2015

17. FHO - IOTA magnets - IMMW19 - October 27, 2015
Measurements
Vibrating wire for locating the centers
This is a no-brainer, we want to develop our capabilities.
Others have proven the technique to the ~um level, which is well more than we need.
However, we have to do it all by hand.
Our CMM is short (70 cm), so we can only do magnets ~7 cm long.
Conversion of a pulsed wire system that was used to tune a 0.5 meter undulator.
Initial testing is showing ~10 um repeatability and ~10 um statistical uncertainty on a dummy PMQ.
If the measured region is less than 1 mm from the axis, I don’t think we have to worry about the higher order terms.
But even so, higher order terms don’t seem to affect the zero crossing calculation.
FHO - IOTA magnets - IMMW19 - October 27, 2015

18. Field measurement and testing
Lakeshore 460 Gaussmeter.
3-axis motion using off-the- shelf stages (0.8mx0.3mx0.2m).
6-axis stand for the magnet.
High-pot and short testing.
We don’t yet have a working rotating coil, so we will have to go somewhere else for that measurement.
We are currently commissioning an AC hall probe system for the betatron measurements.
FHO - IOTA magnets - IMMW19 - October 27, 2015

19. New Vacuum Chamber Conforms to the changing dimensions of the segments
Many Al parts will be e-beam welded together
Made from 2219 aluminum, by request of welder.
How difficult will torr be? We’ll find out.
8 mm
10.3 mm

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Summary
RadiaBeam Technologies has been making electromagnets for about 10 years.
We focus on smaller batch magnets (catch ups, refills, etc)
We develop our capabilities as project work allows it.
The IOTA project is giving us the opportunity to:
Design and commission a vibrating wire system for “quadrupole” axis finding.
Design a new type of magnet.
Develop tolerances outside the context of multipole magnets.
Build a vacuum chamber for a FermiLab accelerator.
Thank you.
FHO - IOTA magnets - IMMW19 - October 27, 2015

21. Test Weld Results