1. Cb Magnet and Lattice Status
January 20, 2016
Stephen Brooks, Cbeta Meeting

2. From last time: Iron quads
Currently a fall-back rather than main option
Holger produced quad designs with pole tip radii 16mm, 23mm
Very good apart from mechanical conflict with vacuum chamber, mostly in strong QF quadrupole
Georg also wanted 12mm not 6mm beam centroid-to-pipe clearance
Iron poles
16mm
6mm
Extremal beams in QF
Pipe shape(s)
January 20, 2016
Stephen Brooks, Cbeta Meeting

3. Current magnets: Halbach-derivedQF BD
37.2mm
30.7mm
12mm
Outer radii = 62.4mm (QF), 59.4mm (BD)
January 20, 2016
Stephen Brooks, Cbeta Meeting

4. Differences Halbach vs. Iron
Iron Poles
Halbach
Field quality + tuning
Determined by iron pole shape. Adjustment would be via conventional pole shimming.
Determined by block magnetisation vectors. Adjustment via floating shims/iron wires just inside aperture.
Field strength + tuning
Iron shunts to partially short-circuit flux applied to outside.
Determined by block magnetisation vectors. Tune with EM normal quad and dipole online correctors.
Temperature sensitivity + compensation
0.1%/K for NdFeB but can (at ~25% strength penalty) incorporate NiFe material to passively compensate.
0.1%/K for NdFeB, cancelled by using EM normal quad and dipole online correctors.
Cross-talk in doublet + compensation
Few percent cross-talk, can be corrected with shunts.
Negligible cross talk, mu~1 linear field superposition.
Correctors (online/EM)
Can be coils would around each pole.
(Putting coils within the bore turned out too crowded).
Window-frame outside Halbach magnet using field superposition, because Halbach is magnetically transparent.
January 20, 2016
Stephen Brooks, Cbeta Meeting

5. Magnet Prototyping Status
Pieces ordered from AllStar Magnetics
NB: ±5° magnetisation angle tolerance (bad?)
Ordered 3 cells (3xBD, 3xQF) for $10`863.99
Delivery 70 days (end of March)
Shin-Etsu quoted for similar pieces, 3 cells
±1° magnetisation angle tolerance (much better)
$52k including $23.7k one-off tooling
Also ordered Holger’s iron quad (lowers risk)
January 20, 2016
Stephen Brooks, Cbeta Meeting

6. Rotating Coil at BNL Magnet Dept.
Prototype Halbach quadrupole bought in 2014 for an eRHIC magnet lab-directed R&D (LDRD)
January 20, 2016
Stephen Brooks, Cbeta Meeting

7. Halbach Quad + Iron Wire Shims
January 20, 2016
Stephen Brooks, Cbeta Meeting

8. “eRHIC” Quad Prototype vs. Cb
Parameter
eRHIC prototype quad “5A”
Cb requirement QF BD
Gradient
27.5 T/m (measured)
-23.6 T/m
19.1 T/m
Central dipole
0 (by realignment) T
Material
SmCo R26HS
(Shin-Etsu)
NdFeB N35SH (AllStar Magnetics)
Min R of physical magnet pieces
22.5mm (design)
23.5mm (measured)
37.2mm
30.7mm
Max R of beam centroid
10mm (rotating coil)
15mm (extrapolated)
20.2mm
13.7mm
Rmax,beam/Rmin,magnet
43% (coil)
64% (extrapolated)
54%
45%
January 20, 2016
Stephen Brooks, Cbeta Meeting

9. Stephen Brooks, Cbeta Meeting
Shimming Results
Unshimmed
Shimmed sextupole only
Shimmed all poles
Error fields across horizontal aperture, extrapolated from measured harmonics
Max relative error:
4.7e-3 (unshimmed)
1.2e-3 (shimmed) BD
45% QF
54%
January 20, 2016
Stephen Brooks, Cbeta Meeting

10. Computer-generated Model of BD Magnet  3D Printer Software
January 20, 2016
Stephen Brooks, Cbeta Meeting

11. Dummy Blocks as Spacers during Construction
January 20, 2016
Stephen Brooks, Cbeta Meeting

12. Co-Optimisation of Lattice with Magnets
Developed an automated tool to output the outer radius (and cross-sectional area) of combined-function Halbach magnets given their dipole, quad and bore requirements
Optimised the lattice to minimise largest outer radius of either magnet
NB: Halbach quad radii tend quickly to infinity if the bore*gradient goes too high
Then we have to wrap an EM quad corrector outside it
January 20, 2016
Stephen Brooks, Cbeta Meeting

13. Stephen Brooks, Cbeta Meeting
Cb Brooks_ Cell
QF magnet
By(local x) = B0 + Gx
B0 = T
G = T/m
Length = m
BD magnet
By (local x) = B0 + Gx
B0 = T
G = T/m
Length = m
ORIGIN
Cell x
Beams local x range: (fieldmap)
to m
Cell z
Local x
Cell entry point
(z,x) = (0,0)
q = 0
Local x=0 line
Beams local x range: (fieldmap)
to m
QF start
(z,x) = ( , ) m
q = rad
Local x
QF end
(z,x) = ( , ) m
q = rad
Local x=0 line
BD start
(z,x) = ( , ) m
q = rad
BD end
(z,x) = ( , ) m
q = rad
NB: this spec shows the original “lattice” combined-function magnets; the physical BD was later realigned to span the orbits symmetrically and QF to be a B0=0 pure quad.
Next cell entry point (origin)
(z,x) = ( , ) m
q = rad
January 20, 2016
Stephen Brooks, Cbeta Meeting

14. Stephen Brooks, Cbeta Meeting
Orbits to Scale
January 20, 2016
Stephen Brooks, Cbeta Meeting

15. Tracking Racetrack with Fieldmaps
Fieldmaps imported directly from Nick Tsoupas’ OPERA-3D models, no strength scaling
January 20, 2016
Stephen Brooks, Cbeta Meeting

16. Stephen Brooks, Cbeta Meeting
Dynamic Aperture
Chris Mayes has more detailed views of the apertures but…
In the resonance simulations I launched uniform beams of r=1cm size (huge!)
~10% gets through, so area p/10 cm2
This is for lowest (67MeV) energy, which has worst DA due to the high tune
Beams of 500 mm.mrad normalised emittance get through with minimal distortion
January 20, 2016
Stephen Brooks, Cbeta Meeting

17. Old Lattice Resonance-Space Plot
20 T/m F gradient 30 T/m
Each coloured square represents the transmission of a simulation of a large beam with varied magnet strengths.
Trenches of losses are resonance features.
This forms part of the canonical “necktie” example below.
15 T/m
Qx = 0.321
Qy = 0.252
D gradient
Lattice shown with ★
25 T/m
January 20, 2016
Stephen Brooks, Cbeta Meeting

18. New Lattice Resonance-Space Plot
90% F strength 110%
90%
Qx = 0.380
Qy = 0.283
±5% beam momentum errors OK with reasonable apertures
D strength
Tracked using fieldmaps, transmissions are lower because I forgot the pipe apertures in the last one
110%
January 20, 2016
Stephen Brooks, Cbeta Meeting

19. Vacuum Pipe Shape Issues
A variable-sized pipe is required for this lattice
Consequences of using a fixed radius is shown by Chris Mayes’ lattice
Magnet outer radii below
Magnet
Variable radius pipe
Fixed-size pipe (Chris) QF
62.4mm
55.8mm BD
59.4mm
87.4mm
BD becomes quad-like, requires far larger magnet
Potentially serious problem for quad EM correctors
January 20, 2016
Stephen Brooks, Cbeta Meeting

20. Provisional List of Magnet Types
Area
Subarea
Name
Type
Notes
FFAG
Arc QF
PM+EM corrector
Halbach quad BD
Combined-function Halbach
Transition
BDT
Combined-function Halbach with extended good field range to B=0
Straight
QFS
Small Halbach quad
BDS
Splitter
Common
Common dipole EM
Wide-aperture splitting dipole
Fan-out
Septum dipole 1
Bends 3,4 but avoids 2
Septum dipole 2
Bends 4 but avoids 3
Lines
Splitter dipole PM
Halbach dipole ~0.9T
Splitter dipole adjust
Electromagnetic dipole
Splitter quad
All quads are the same
January 20, 2016
Stephen Brooks, Cbeta Meeting

21. Stephen Brooks, Cbeta Meeting
Conclusion
Should make lattice choice ASAP so work on design and CDR can continue
Choice hinges on practicality of vaccum pipe
vs. practicality of EM correctors if they get large
Exploit commonality to reduce magnet types
Get fieldmaps for all types allowing end-to-end simulation with fieldmaps
This also means we will have 3D physics designs for all of them in hand
January 20, 2016
Stephen Brooks, Cbeta Meeting