Magnet Lattice Design for the Transmission of Power

Magnet Lattice Design for the Transmission of Power Using Particle Beams Daniel Marley & Jim Welch SULI SLAC Presentations 11 August 2011

Outline • Overview of the Grid • Particle Beams for Power Transmission • Particle Storage Rings • Magnet Lattice Design • Future Work

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= 1 Nuclear Reactor Source: U. S. Nuclear Regulatory Commission & NREL's Clean Energy Analyses Project: 2009 U. S. State Clean Energy Data Book

load Source: U. S. Nuclear Regulatory Commission & NREL's Clean Energy Analyses Project: 2009 U. S. State Clean Energy Data Book

Particle Beams for Power Transmission • Routinely used and operate at high voltages – 9 Ge. V at PEP-II, 500 Ge. V at Fermilab, & 7 Te. V at the Large Hadron Collider – Storage Rings, not linacs: Carrying Power • Few sources of energy loss – Residual gas scattering – Synchrotron Radiation

Issues with Using Particle Beams • Economic Feasibility – Tunneling, Vacuum, Material for the magnets • Power out of the beam – Superconducting RF Cavity at Generators & Loads • Magnet lattice design – The arrangement of quadrupoles and dipoles that comprise an accelerator.

Particle Storage Rings • Important criteria for lattice design: Beam width and response to energy changes. • Width is directly related to the β-functions

Transfer Matrix Method

Beam Parameters Parameter Values Circumference ∼ 10, 000 km Dispersion (max) 0. 1 m Beam Energy 9 -11 Ge. V Bend Radius (min) 100 m Beam Current 1 A Dipole Field 0. 1 T Emittance 5× 10 -10 m Quadrupole Gradient 10 T/m βx, y (max) ∼ 2000 m Beam Size (max) ∼ 1 mm

Software Implemented • Mathematica 8 to apply the Transfer Matrix Method for designing the lattice and testing stability • Methodical Accelerator Design (MAD) v. 8. 52 software developed by CERN to finalize the design of the beam, optimize variables and add constraints to variables

Lattice Design Components • FODO lattice combined with double bend achromats (DBAs) FODO lattice: DBA:

Future Work • Incorporate the terrain into the lattice design • Add RF cavities to MAD code • Compute precise emittance of the beam • Add nonlinear terms to MAD code – Resonances in the beam dynamics • Design magnets with Radia Package in Mathematica.

Conclusion • Magnet lattice can be designed for 10, 000 km circumference ring. • Increased the credibility of this project. • Encouragement to move forward with research and investigation into this method.

Acknowledgements • Department of Energy SULI Program at SLAC. • Advisor Jim Welch – Juhao Wu, Glen White, Mark Woodley, Min-Huey Wang, & Jim Turner for their help • Director Steve Rock, Maria Mastrokyriakos & Anita Piercey

• Questions? • E-mail me: demarley@ncsu. edu

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Transfer Matrix Method • Define focusing functions: • Write in terms of vector 19

eigenvalues reciprocals, added give trace. 20

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