Designing a periodic FODO Synchrotron from scratch Dr

Designing a periodic FODO Synchrotron – from scratch Dr. Carol Johnstone EBD meeting 06/17/2020 07/01/2010 Dr. Carol Johnstone 1

General L (half cell) f • 180 of phase advance is stability limit for a thin-lens FODO cell • Length of half cell = focal length, 90 is stability limit for half cell; • Normal Conducting (NC) magnets – A 1 T poletip is a good starting criterion – 90 has the smallest radial beam size, 45 for a half cell focal length; • Dipole contributions to focusing will be ignored – Dipole focusing in a synchrotron is much smaller than the strong-focusing field-gradient quads – Not true for a small ring

Applying Basic Technical Specifications

Example: Fermilab Booster 0. 5 m 3. 0 m 2. 89 m 1. 2 m 2. 89 m 3. 0 m

Calculate length of FODO cell

Example: Convert Booster to Separated Function 0. 5 m 3. 0 m 2. 89 m L=6. 28 m 1. 6 m 2. 89 m 3. 0 m

Figuring out realistic integrated quad strength

Figure out quad strength for SF Booster Individual beam particle =0, x’=0 L=6. 28 m f

Conversion: Booster to Separated Function 3. 0 m 0. 5 m 2. 89 m 0. 5 m 1. 2 m 2. 89 m L=4. 77 m 0. 25 m 2. 89 m 0. 5 m 3. 0 m 2. 89 m 0. 5 m 0. 25 m 2 x 0. 25 m • Now insert drifts at symmetry points to preserve injection optics – 2 x 3 m and 2 x 0. 6 m straight sections • Optics Conversion complete • But! Haven’t specified ring size ; 0. 5 m 3. 0 m L=4. 77 m 0. 5 m 1. 2 m 3. 0 m 0. 25 m

Figuring out number of cells

Conversion: Booster to Separated Function 0. 5 m 3. 0 m 2. 89 m 0. 5 m 3. 0 m 1. 2 m 2. 89 m L=4. 77 m 2. 89 m 3. 0 m 2. 89 m 0. 5 m 1. 2 m 3. 0 m 0. 25 m

Optics Comparison 0. 5 m L=4. 77 m 0. 5 m 2 x 0. 25 m Booster Sep Function Booster 0. 25 m No long drifts