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

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Particle Beams for Power Transmission Routinely used and operate at high voltages – 9 GeV at PEP-II, 500 GeV at Fermilab, & 7 TeV 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

9 Transfer Matrix Method

Beam Parameters ParameterValueParameterValues Circumference ∼ 10,000 km Dispersion (max)0.1 m Beam Energy9-11 GeVBend Radius (min)100 m Beam Current1 ADipole Field0.1 T Emittance5× mQuadrupole Gradient10 T/m β x,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 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? me:

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

20 eigenvalues reciprocals, added give trace.

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