Damping of instability with octupoles

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
• N292 turns, I10A (I_max20A)
• Octupole 150 T/m3 for I10 A or 300 T/m3
  for I_max20A
• Corresponding tune spread (rough estimate)
  0.006 (I10A)
• 
  0.013 (I20A)

3
Re(Z) for full 14-kicker system (May 2002)
Impedance model (EK) used in simulations January-
June02
4
Effect of octupoles full beam
5
Tune spreads
Red negative (10 A) Y octupoles
(b_y10m) Black- positive (20 A) Y
octupoles Green negative (10 A) X octupoles
(b_x11m)
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