n low emittance rings

Transcription

1 ectron clou ud instabilit n low emittance rings H. Jin (Postech), K. Ohmi (KEK) ECLOUD 1 10@Cornell Oct. 8-12, 2010

2 Introduction Fast head-tail instability in CesrTA and SuperKEKB. Multibunch instabil lity

3 Coherent strong head-tail instability Coherent motion between inner bunch and electron cloud. Electrons oscillate electric force inner bunch along z, ω = The instability is characterized by e ωeσz/c, number of electron oscillation along the bunch. λ r c p e 2 σ ( σ + σ ) y x y e-

4 hreshold of the strong head-tail instability (Balance of growth and Landau damping) bility condition for e z /c>1 3 λp r0 β Z ( ω ) 3 λ e p r0 β KQ λe L = γ ω σ c Z ν γ ω σ c 4 π λ σ ( σ + σ ) = s e z 0 s ce e = e /2 x y, 2γν s ωeσ z c ρe, th = 3KQr0 β L min(q nl, e z /c) Q nl =5-10?, depending on the nonlinear interaction. haracterizes cloud size effect and pinching. z/c~12-20 for damping rings. ω e = λ r c p e 2 σ ( σ + σ ) y x y e z p y x y Origin of Landau damping is momen compaction ν s σ z = ασ δ L s z δ

5 Parameters SuperKEKB SuperKEKB

6 (PEHTS) Electron clouds are located several or many s position in a ring. Potential solver based on 2D FFT. Beam is sliced into (> e z /c). o pieces

7 Simulation for CestTA I=1.3mA, N=2x10 10 Simulation ρth=1x10 12 m -3. Analytic ρth=1.7x10 12 m -3.

8 CesrTA 2 and 5 GeV 2GeV ρth=0.8x10 12 cm -3 5GeV High(2GeV) and low(5gev) ωeσz ρth=4x10 12 cm -3

9 Coherent motion in the simulation 2 GeV 5 GeV High(2GeV) and low(5gev) ωeσz/c.

10 Simulated Unstable spectra Lower sideband is dominant for high ωeσz (low emittance). 2 GeV Upper sideband is dominant for 5GeV 5 GeV

11 Simulated beam spectra 2 GeV Lower sideband is seen for high ωeσz/c, 2GeV. Upper sideband is seen for low ωeσz/c, 5 5 GeV GeV.

12 back Model, feedback with one turn delay M: revolution matrix α: feedback damping rate n: n-th turn ±: after or before feedback kick

13 B suppresses the instability little(2gev) High ωeσz/c, 2GeV. Dipole motion is suppressed a little, threshold increase a little.

14 (5GeV) Low ωeσz/c, 5GeV. Dipole motion is suppressed but head tail motion remains.

15 SuperKEKB Y. Susaki, K. Ohmi, IPAC1 This simulation is for old parameter νs=0.12. Presen νs=0.26. The threshold sho be twice higher. Simulation ρth=2.1x10 11 m -3. Analytic ρth=1.1x10 11 m -3. Target ρe< <1x10 11 m -3 Update parameters SuperKEKB). (both for CesrTA and Take care of high β section. Effects are

16 Incoherent effect in CesrTA Emittance growth due to nonlinear interaction with electron cloud

17 Slow growth lower than the ev threshold 1.2x10 12 ev Slower than radiation damping time 5x10 12

18 Study of multibunch instability Self consistent solution of the cloud build up and bunch motio on. Wake field calculation Self consistent simulation Multi-bunch instability induces a fast beam loss, though fast he ead-tail instability does not.

19 Self consistent build-up code,

20 Beam dancing with electron cloud Drift space Electrons move one way Bunch by bunch correlation is short, very low Q.

21 Beam dancing with electron cloud In solenoid magnets Electrons move along the chamber surface. Long life time electron, high Q wake.

22 Multi-bunch instability Beam dancing with electron cloud Electron cloud in bending magnet Does beam dance with electron cloud pillar? Wak Unstable

23 Correlation time of the pillar (stripe) Pillar position shifts Receive wake for from the shifted pi Bunch length ~1cm, bunch spacing

24 Characteristicc time of pillar formation DAFNE parameter, ~200ns Formed pillar and the en shift beam position Pillar position shifts to beam position in ~200ns.

25 Wake force for the pillar formation Bunch by bunch co orrelation of slowest mode, m=-1, will be induced.

26 Characteristics of the fast head tail instability is determined by ωeσz/c. Appearance of upper or lower sideband, and feedback response de epend on ωeσz/c. e The threshold (2GeV) is ρth=1x10 12 cm -3 for simulation and 1.7x10 12 cm -3 for analytic. The threshold (5GeV) is ρth=5x10 12 cm -3 for simulation and 7x10 12 cm -3 for analytic. Incoherent emittance positron machines. growth is week in Movies for coupled bunch instability. Slowest