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Update of Microwave Instability Study in SuperKEKB Damping Ring Using Vlasov Fokker-Planck Solver

Update of Microwave Instability Study in SuperKEKB Damping Ring Using Vlasov Fokker-Planck Solver. 6.15.2012 KEKB Physics Meeting. L. Wang, SLAC In collaboration with H. Ikeda, K. Ohmi, K. Oide, D. Zhou. Motivation.

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Update of Microwave Instability Study in SuperKEKB Damping Ring Using Vlasov Fokker-Planck Solver

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  1. Update of Microwave Instability Study in SuperKEKB Damping Ring Using Vlasov Fokker-Planck Solver 6.15.2012 KEKB Physics Meeting L. Wang, SLAC In collaboration with H. Ikeda, K. Ohmi, K. Oide, D. Zhou

  2. Motivation Systematic study the microwave instability using Vlasov solver to validate the results: We checked the numerical parameters: mesh size, domain, time step and the CSR impedance Our goal is to empirically find the appropriate parameters/way for the simulation of MWI.

  3. Wakes • Geometry wake • CSR Impedance(rectangular geometry 34mmX24mm) @Demin’s code (Japanese Journal of Applied Physics 51 (2012) 016401) • The CSR Wake is given by the convolution of a 0.5 mm long Gaussian bunch with CSR impedance (frequency up to 477GHz) Geometry wake CSR wake

  4. Microwave instability with different wakes (Yunhai’s code) • With CSR wake only, the energy spread starts to increase near the nominal bunch current (N= 51010 ) • The microwave instability starts at bunch population 61010 when both geometry wake and CSR wake are included Geometry wake only CSR wake only & both g-wake and CSR wake Numerical parameters: qmax=8, nn=300, ndt=1024

  5. Effect of domain, mesh size and time step • The simulation is done in the normalized phase space, which is rectangular region with maximum domain qmax (and minimum –qmax). (16X16) • The whole domain contains (2*nn+1) mesh points: (1001X1001) • The time step is given by ndt, the number of steps per synchrotron period. Requirement: nn: 500 qmax: 8 Time steps: 1024/syn. period

  6. Effect of CSR impedance at high frequency Previous study using impedance with frequency up to 500GHz; CSR impedance with frequency up to 1.4 THz The wake is convoluted by a 0.2 mm Gaussian bunch More high frequency component Although our bunch is long, but micro-wave instability occurs at micro-bunch level

  7. With higher frequency CSR-1 There is a similar threshold, but a much stronger instability above the threshold A clear Saw-tooth instability; However, no saw-tooth instability found with the CSR impedance of f~477GHz Near threshold N=5.5E10 With High frequency 1.5THz CSR impedance above threshold N=8.5E10

  8. Higher frequency CSR effect High frequency CSR impedance is important: Saw-tooth type of instability is found with high frequency CSR impedance only above threshold N=8.5E10

  9. Higher frequency CSR effect High frequency CSR impedance is important: f up to 500GHZ f up to 1500GHZ above threshold N=8E10

  10. With higher frequency CSR-2instability near threshold N=5.5e10 Phase plot

  11. With higher frequency CSR-3MWI above threshold N=8.5e10 • Clear Saw-tooth instability occurs • Phase plot shows high order modes Saw-tooth instability driven by CSR Phase plot Saw-tooth Period:110 syn. period 517Hz

  12. Time step check Ndt (steps per synchrotron period) =1024 is good enough above threshold N=8.5E10

  13. Summary The microwave instability in SuperKEKB Damping Ring is simulated using the Vlasov-Fokker-Planck code. It suggests a threshold slightly above the designed bunch current. PIC (Particle-In-Cell) code also confirms similar threshold The simulation of microwave instability with CSR impedance is nontrivial. We carefully checked the numerical parameters used in the simulation: the good numerical parameters are qmax=8 (domain), nn=500(mesh), ndt=1024 (time step) The most important finding: The high frequency part CSR impedance (f~1.4THz) plays an important role in the saw-tooth instability. High order modes observed

  14. discussion • How to include high frequency impedance: • Calculate high frequency CSR impedance • It is straightforward and only a matter of CPU, using parallel computation. • (2) convolution with a short Gaussian bunch, <=0.1mm (3) Instead of convolution with a Gaussian bunch, directly using impedance (Demin IPAC12, Bob) green function (direct FFT of impedance)? other approaches? It would be very helpful (for both machine and beam dynamics) to observe the CSR & MWI in DR as proposed by Prof. Fukuma

  15. Thank You! Thanks to Demin for his great help on the simulations Y. Cai and B. Warnock for fruitful discussions

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