Destabilizing effect of transverse damper and airbag beam

Destabilizing effect of transverse damper and air-bag beam S. ANTIPOV, E. METRAL, AND D. AMORIM

Air-bag beam An air-bag beam model is a simple analytical model, useful to study the transverse modes Does the model contain all the relevant physics? 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 2

Destabilizing effect of resistive transverse damper E. Metral et al. , Destabilizing effect of the resistive transverse damper, APB-HSC meeting, 20. 02. 17 E. Metral, La Sapienza University, Rome, Italy, May 23 -26, 2017 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 3

Model predictions agree with Vlasov solvers S. Antipov et al. , ABP-HSC Meeting, 27. 03. 17 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 4

SPS, 0. 8 ns beam Energy: Impedace: E 0 = 26 Ge. V Rev. frequency: f 0 = 43. 29 k. Hz Tunes: Qx = 26. 13, Qy = 26. 18, Qs = 7. 3 x 10 -3 Bunch length: τb = 0. 8 ns Chromaticity: Q’ = 0 26. 06. 17 ◦ Broadband resonator model ◦ Q = 1, fr = 1 GHz, Rs = 10 MΩ/m AIRBAG BEAM AND RESISTIVE DAMPER 5

Linearized Vlasov Equation Polar coordinates unperturbed small S. Y. Lee, Perturbation Formalism in Physics of Collective Beam Instabilities in High Energy Accelerators 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 6

Airbag approximation 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 7

Single-bunch system A. Burov, Nested Head. Tail Vlasov Solver 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 8

ξ = 0 greatly simplifies the problem Only J 0 contributes Head tail phase Damper matrix: 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 9

ξ = 0 greatly simplifies the problem Head tail phase Impedance matrix: 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 10

ξ = 0 greatly simplifies the problem Head tail phase Impedance matrix: odd even odd 26. 06. 17 even AIRBAG BEAM AND RESISTIVE DAMPER odd 11

In the absence of damper the total matrix is real Given by Im Z Given by Re Z 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 12

Resistive damper Gain: Norm. intensity: 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 13

Resistive damper 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 14

Reactive damper 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 15

Non-zero chromaticity (Check ongoing) Head tail phase: Impedance: Damper: 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 16

χ > 0. Resistive damper 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 17

χ > 0. Reactive damper 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 18

Largest growth rate at small positive χ Damper: resistive, 100 -turn 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 19

Conclusion Air-bag model is a simple model that significantly reduces the computation Captures all the relevant physics of the problem The results agree qualitatively with the previous studies 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 20

Extras 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 21

NHT Running on lxplus !Thanks Olaf! Multiple threads 26. 06. 17 AIRBAG BEAM AND RESISTIVE DAMPER 22

1 am Be 26. 06. 17 2 Thanks J. Barranco for the help optimizing the crossing angle AIRBAG BEAM AND RESISTIVE DAMPER 23