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Update of Microwave Instability Study in SuperKEKB Damping Ring Using Vlasov Fokker-Planck Solver L. Wang, SLAC In collaboration with H. Ikeda, K. Ohmi, K. Oide, D. Zhou 6.15.2012 KEKB Physics Meeting 1
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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. 2
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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 3
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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 10 10 ) The microwave instability starts at bunch population 6 10 10 when both geometry wake and CSR wake are included Geometry wake only CSR wake only & both g-wake and CSR wake 4 Numerical parameters: qmax=8, nn=300, ndt=1024
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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 5
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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 6 Although our bunch is long, but micro-wave instability occurs at micro-bunch level
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With higher frequency CSR-1 With High frequency 1.5THz CSR impedance There is a similar threshold, but a much stronger instability above the threshold A clear Saw-tooth instability; Near threshold N=5.5E10 above threshold N=8.5E10 7 However, no saw-tooth instability found with the CSR impedance of f~477GHz
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Higher frequency CSR effect above threshold N=8.5E10 High frequency CSR impedance is important: Saw-tooth type of instability is found with high frequency CSR impedance only 8
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Higher frequency CSR effect above threshold N=8E10 High frequency CSR impedance is important: 9 f up to 500GHZ f up to 1500GHZ
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With higher frequency CSR-2 instability near threshold N=5.5e10 10 Phase plot
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With higher frequency CSR-3 MWI above threshold N=8.5e10 11 Clear Saw-tooth instability occurs Phase plot shows high order modes Phase plot Saw-tooth instability driven by CSR Saw-tooth Period:110 syn. period 517Hz
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Time step check above threshold N=8.5E10 Ndt (steps per synchrotron period) =1024 is good enough 12
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Summary 13 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
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discussion 14 How to include high frequency impedance: (1)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 It would be very helpful (for both machine and beam dynamics) to observe the CSR & MWI in DR as proposed by Prof. Fukuma (3) Instead of convolution with a Gaussian bunch, directly using impedance (Demin IPAC12, Bob) green function (direct FFT of impedance)? other approaches?
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Thank You! 15 Y. Cai and B. Warnock for fruitful discussions Thanks to Demin for his great help on the simulations
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