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Analysis of Lattice Configurations: FODO, Doublet, and Triplet Designs for Particle Accelerators

This document examines the performance of various cell structures in particle accelerator designs, specifically FODO, Doublet, and Triplet configurations. Key input values related to ring dimensions and magnetic field strength are outlined, followed by detailed calculations leading to outputs such as circumference, cell length, and dipole characteristics. The results provide comparisons showing that while the circumference remains relatively constant across different cell types, the Doublet and Triplet configurations yield larger free drift spaces at the cost of bending power, with the FODO structure exhibiting optimal bending strength.

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Analysis of Lattice Configurations: FODO, Doublet, and Triplet Designs for Particle Accelerators

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  1. PS2 Lattice Considerations PS2 Meeting, 14-March 07 Wolfgang Bartmann

  2. Outline • Input values • Output • Calculation • Results and comparison of the cell structures • Results for the ring • Conclusion

  3. Input Values (1) Regarding one half of the ring… Cells: # arc cells # empty cells (no dipoles in the long straight section) # dipoles per arc cell (nb) Straight Sections: ss1 = 1.2 m …before quadrupoles (FODO: 1.3m) ss2 = 0.5 m …between dipoles ss3 = 1.0 m …between quadrupoles (Doublet, Triplet)

  4. Input Values (2) Magnets: • Ekin = 50 GeV and B = 1.8 T define the bending values: 200 dipoles (nd,std) with 3 m length (ld,std) these values are used for scaling the: • # dipoles: nd = (# arc cells - 1) · 2 · nb …4 halfcells for dispersion • dipole length: ld = ld,std· nd,std / nd • the standard values for the quadrupoles are:lqu,std = 1.75 m and kstd = 0.094 m-2, which are used to scale: • k • lqu = lqu,std· k/ kstd

  5. Outputs • Circumference (C) • Cell length (Lcell) • Dipole number and length (nd and ld) • Total straight section (SStotal) • Free drift between two quadrupoles • Ekin for fixed circumference

  6. Calculation • # arc cells and nb determine the dipoles’ length and number • a fixed k sets the quadrupole length from these values, the cell length, the circumference, the total straight section and the free drift are obtained Ekin is calculated for a fixed circumference (1256.6m): Cfix and Lcell define the total arc length total arc length times the “cell fill factor” gives ρ with B = 1.8 T Ekin

  7. ss2 ss2 ss1 ss1 Results: FODO • provides smallest cell length and circumference • free drift space: 8 - 11.5 m • largest bending power per cell higher energies feasible • converse behaviour of βx and βy offers good possibilities to apply correctors FODO: nb = 6, ld = 2.94 m, lqu = 1.49 m

  8. ss2 ss2 ss1 ss1 ss3 Results: Doublet • 10% larger circumference than FODO • large free drift spaces: 16 – 22.5 m • 10% larger total straight section than FODO • about 12% lower kinetic energy for identical circumference • steem, asymmetric slopes of β Doublet: nb = 6, ld = 2.94 m, lqu = 2.42 m

  9. ss1 ss1 ss3 Results: Triplet • 22% longer than FODO in circumference • large free drift: 22.5 m • 22% longer total straight section than FODO • weak bending power per cell about 26% lower kinetic energy feasible • small β in the dipoles reduces magnet apertures ss2 ss2 Triplet: nb = 6, ld = 2.94 m, lqu = 1.86 m

  10. Results for the ring

  11. Conclusion • within a certain celltype (FODO, Doublet, Triplet), the circumference remains almost the same even if the magnet parameters (ld, nd)are changed • a variation of ld and nd will affect the cell length, the total straight section and the free drift • the Doublet and Triplet cells provide a remarkably larger free drift between two quadrupoles than the FODO cell • the bending power per cell, illustrated as Ekin for a fixed circumference, is determined by the cell type and depends hardly on the magnet parameters • the FODO structure has the largest bending power per cell

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