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Resonance crossing and emittance growth

Resonance crossing and emittance growth. Shinji Machida KEK October 13-17, 2003 at BNL. Lattice. 10 FODO cell without bends. However, periodic boundary condition is imposed. Phase advance is about 90 deg. per cell. One inpulse gradient (or sextupole) error to excite harmonics.

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Resonance crossing and emittance growth

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  1. Resonance crossing and emittance growth Shinji Machida KEK October 13-17, 2003 at BNL

  2. Lattice • 10 FODO cell without bends. • However, periodic boundary condition is imposed. • Phase advance is about 90 deg. per cell. • One inpulse gradient (or sextupole) error to excite harmonics. • Knob to control half (or third) integer resonance strength. • No acceleration is included.

  3. Method • Tracking with independent variable of time (SIMPSONS). • Linear change of all K1 simultaneously. • Slope can be variable. • By single particle tracking • Phase space structure. • Time evolution of amplitude. • By multi particle tracking • Define 68th particle amplitude out of 100 macro particles as 68% emittance. • Same for 90% emittance.

  4. Half integer resonance • Four different resonance width • sbw (stop band width)=0.004, 0.008, 0.016, 0.038 • Tune excursion • nux=2.37 to 2.55 linearly. • 2nux=5 is excited. • Crossing rate (dnu/turn) • 0.0001/turn (slow) ~ 0.1/turn (fast) • Horizontal only

  5. Single particle behavior • Phase space (Poincare map) • Evolution of ‘invariant’. • > see Mathematica notebook

  6. Emittance growth

  7. Crossing speed is normalized

  8. 3rd integer resonance • Four different sextupole strength • rw (relative width)=0.1, 0.3, 0.5, 1.0 • Tune excursion • nux=2.40 to 2.25 linearly. • 3nux=7 is excited. • Crossing rate (dnu/turn) • 0.00002/turn (slow) ~ 0.1/turn (fast) • Horizontal only (with particle loss, emittance can be decreased.)

  9. Emittance growth

  10. Crossing speed is normalized

  11. conclusion • In half-integer crossing, almost no growth is observed when dnu/turn > resonance width. • When dnu/turn < resonance width, growth becomes larger with wider resonance width. • Similar in 3rd-integer crossing, but no clear dependence on the resonance strength.

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