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Damping of instability with octupoles

Damping of instability with octupoles. How much tune spread we can introduce with octupole correctors? How is it effective with space charge? 3. How much tune spread do we need with space charge? 4. Does it introduce significant beam loss due to octupole resonances?. Octupole correctors.

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Damping of instability with octupoles

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  1. Damping of instability with octupoles • How much tune spread we can introduce with octupole correctors? • How is it effective with space charge? 3. How much tune spread do we need with space charge? 4. Does it introduce significant beam loss due to octupole resonances?

  2. Octupole correctors 4H and 4V N=292 turns, I=10A (I_max=20A) Octupole: 150 [T/m^3] for I=10 A or 300 [T/m^3] for I_max=20A Corresponding tune spread (rough estimate) : 0.006 (I=10A) 0.013 (I=20A)

  3. Re(Z) for full 14-kicker system (May 2002) Impedance model (EK) used in simulations January- June’02

  4. Effect of octupoles – full beam

  5. Tune spreads Red – negative (10 A) Y octupoles (b_y=10m) Black- positive (20 A) Y octupoles Green – negative (10 A) X octupoles (b_x=11m)

  6. Tune spread (10 and 20 Amp positive y-octup.)

  7. Tune spread (10 Amp octupoles)

  8. Effect of octupoles – full beam

  9. 10 Amp positive Y-oct. – 1060-turn painting 1MHz 12MHz

  10. 17 Amp positive Y-oct., 1060-turn painting 1MHz 12MHz

  11. Halo after 1060-turn injection Blue – no impedance Black – impedance, no octupole correctors (halo due to instability) Red – 10A positive y-octupoles Pink – 17A positive y-octupoles Green- 40A positive y-octupoles

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