Ex-Situ NMR: Design Approach to High Field Quality G. Sabbi, LDRD Progress Report 2/25/03

1. Ex-Situ NMR: Design Approach to High Field Quality G. Sabbi, LDRD Progress Report 2/25/03

2. Field Quality Requirements Ex-situ NMR technique aims at reducing FQ requirements with respect to standard NMR But - for the moment ~10-5 homogeneity is still needed (!) Minimal requirement for high resolution spectroscopy: <10-4 in 3 mm cube We are setting a design goal of 10-4 in 10 mm radius (then correct to 10-5 using trim coils or magnetic shims) Field measurement (to set correctors) will be an issue, use of NMR techniques may be best strategy Best magnet design to date: ~3*10-4 in 5 mm radius

3. Design strategy Presently following “accelerator magnet” approach: • coil has a “long” straight section, field is optimized in 2D • 3D design to eliminate end effects with minimal coil length Motivations: • our main expertise is in accelerator coils • appears to be the most promising strategy for high field quality • potential for stretching the good field volume along the axis Alternative design approaches: Nested solenoids (a design based on normal conducting coils is being pursued in parallel to SC magnet effort). “2.5d” field optimization. Conductor in groove for more freedom in conductor placement (may also be good for correctors) Others….

4. Design “algorithm” • Optimize coil cross section (efficiency, 2D field quality) • 2D iron design (shielding, saturation, stray field) • Iterate on cross-section to adjust systematics • Find minimal coil length for no significant 3D effects • Try to further reduce coil length (3D coil, iron geometry) • Estimate random errors (tolerances, sweet spot distance) • Design corrector package (trim coils or magnetic shims) Main challenge: 2D cross-section optimization for - High efficiency (sweet spot field vs. coil peak field) - Low systematic harmonics (esp. a4, b5)

5. y y - I + I a x p (r, J) F d x t - I + I 2D Field Quality Optimization

6. Cross-section design We looked at designs with 4, 6, 8 blocks/layer. Field quality depends on geometric center of block. However: • Narrow blocks allow more design space • Narrow blocks allow better efficiency Trying to work with aligned, identical blocks for design simplicity (however, relative y-shifts & spacers are needed for best results) Assuming RD configuration for best field quality (find one solution first, then will have another look at HD)

7. Coil cross-sections (Phase I) • Based on SM coil design • Optimize upper layer, then correct for lower layer • 2D issues: • blocks are too wide – limits on 2D harmonics • narrow island decreases efficiency • narrow island can result in vertical forces • 3D issues: • insufficient ratio of coil length to sweet spot distance • decreasing sweet spot distance makes design less attractive & makes 2D optimization more difficult (high order systematics, random errors)

8. Phase I – 2D cross-sections Six blocks/layer (2D): B1 = 3320 Gauss (11 kA) B1/Bpk = 0.037 For Rref = 1.5 mm a2 <0.1, b3 <0.1, a4=-0.4 Four blocks/layer (2D): B1 = 2600 Gauss (11 kA) B1/Bpk = 0.025 For Rref = 1.5 mm a2=0.1, b3=19.4, a4=1.1

9. Coil cross-sections (Phase II) Still based on RD coils, but: • RD3c type design with central spacer • drop restrictions on length & top/bottom distance • NbTi assumed, with same cable geometry as SM Advantages: • doubled degrees of freedom for same # coils & splices • better efficiency (main field to peak field ratio) • better control on conductor positioning • standard approach to 3D effects

10. RDopt3 RDopt4 RDopt5 Phase II – 2D cross-sections (1 layer)

11. Phase II Performance Parameters (2D)

12. Case study: RDOPT4 Starting from the single layer RDOPT4 cross-section, the following calculations were performed: Requirements on layer-to-layer separation (18 cm) Field enhancement due to iron shield (10%) Iron saturation effect (none) Cross section iteration to correct harmonics (ok) Coil length (upper bound) for no end effect (80 cm)

13. Optimized Design Parameters (NbTi)

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