ESLS XX 1920 November 2012 Berlin CSRdriven Single

ESLS XX, 19/20 November 2012, Berlin CSR-driven Single Bunch Instability P. Kuske, Helmholtz Zentrum Berlin

Content of the Talk I. INSTABILITY FOR RESISTIVE AND INDUCTIVE IMPEDANCE II. CSR-DRIVEN INSTABILITY COMPARISON OF THEORETICAL AND EXPERIMENTAL THRESHOLDS: II. 1 MLS II. 1. 1 SIMILARITY BETWEEN RESISTIVE AND CSR-WAKE II. 1. 2 THRESHOLD DETERMINATION II. 2 BESSY II III. INSTABILITY THRESHOLDS WITH HIGH RF-GRADIENT IV. SUMMARY AND OUTLOOK DETAILS ON THE VFP-SIMULATIONS IN MY ICAP ‘ 12 CONTRIBUTION 2

I. 1 Results for some Fundamental Interactions – Resistive Impedance • Analytical solutions for the Haiissinski equation are known – most obvious features of wake/impedance: • Vind(t)=I 0 T 0·R·I(t) • Result of measurements of the synchronous phase shift at DIAMOND (G. Rehm, et al. DIPAC 2011) • Loss factor 50 – 70 V/p. C leads to energy loss per turn increases with intensity, triangular shape of I(t), weak instability above certain threshold (K. Oide, 1995) 3

I. 1 Results for some Fundamental Interactions – Resistive Impedance Instability thresholds: black solid line - weak instability theory by K. Oide, Part. Accel. 51, 43 (1995), numerical results for the Diamond Light Source (DLS) and BESSY II DLS: Vrf=2, 4, 8, and 16 MV BESSY II: Vrf=0. 7, . . 14000 MV. Oide's dimensionless parameter: weak instability – damping time matters Typical values: R ~ 4Ω · circumference [m] 4

I. 2 Results for some Fundamental Interactions – Inductive Impedance • Wake/impedance: • bunch lengthening proportional to I 1/3, amplitude dependent synchrotron tune, instability for neg. mom. compaction factor • Bunch length measurements at BESSY II and Diamond (R. Fielder, ESLS 2011): Vind(t)= I 0 T 0·L·d. I(t)/dt Typical values: L·T 0/2 ~ 1 mΩ · circumference [m] 5

II. CSR-Impedance Broad band resonator with low Q: Fres/c=( /24 h 3)1/2 BESSY II: Fres ~ 100 GHz MLS: Fres ~ 44 GHz R. L. Warnock, PAC'91, PAC 1991_1824, http: //www. JACo. W. org 6

II. Storage Ring Parameters for Simulations Parameter BESSY II MLS Energy, E 0/Me. V 1700 629 Bending radius, /m 4. 35 1. 528 7. 3 10 -4 1400 330 2 500 800 160 7. 0 10 -4 4. 36 10 -4 Zero current bunch length, 0/ps 10. 53 1. 549 Longitudinal damping time, l/ms 8. 0 11. 1 2 7. 7 2 5. 82 3. 5 4. 2 Momentum compaction, α Cavity voltage, Vrf/k. V Accelerating frequency, rf/MHz Revolution time, T 0/ns Natural energy spread, E Synchrotron frequency, s/k. Hz Height of the dipole chamber, 2 h/cm normal low-alpha mode 7

II. 1 CSR-Threshold Currents for the MLS Solution of Vlasov-Fokker-Planck equation Solid black line: K. L. Bane, et al. , Phys. Rev. ST-AB 13, 104402 (2010) 8

II. 1 CSR-Threshold Currents for the MLS Solid black line: K. L. Bane, et al. , Phys. Rev. ST-AB 13, 104402 (2010) 9

II. 1. 1 Comparison of CSR- and Resistive Wake 10

II. 1. 1 CSR-Threshold Currents for the MLS Solid black line: K. L. Bane, et al. , Phys. Rev. ST-AB 13, 104402 (2010) 11

II. 1. 1 CSR-Threshold Currents for the MLS Solid black line: K. L. Bane, et al. , Phys. Rev. ST-AB 13, 104402 (2010) 12

Threshold Determination MLS – Experimental Result M. Ries, et al. , IPAC’ 12, WEPPR 046 II. 1. 2 13

II. 1. 2 Threshold Determination MLS – Theoretical Result Simulated temporal CSR spectra - tracking with CSR-wake, 1 Mio. particles, αo=1. 3· 10 -4 and Vrf=330 k. V 14

II. 1. 2 CSR - Theoretical Threshold Determination 15

II. 2 CSR-Threshold Current Measurement BESSY II, Fsyno=1 k. Hz, o~1. 5 ps Many modes visible in the Fourier transformed CSR 16

II. 2 CSR-Threshold Currents for BESSY II Solid black line: K. L. Bane, et al. , Phys. Rev. ST-AB 13, 104402 (2010) 17

II. 2 First Unstable Modes BESSY II Slope agrees with resonance Fres~100 GHz 18

III. Thresholds with High RF-Gradients Theoretical MLS threshold currents vs. zero current bunch length: Target for BESSY-VSR is 100 times increased RF-gradient – MLS-data is a major step already and has triggered these simulations: In certain regions no increase of threshold currents, for short bunches smaller increase than expected. Scaling according to Bane, et al. only valid for long bunches, in region of strong instability. 19

III. High RF-Gradient 20

IV. Summary and Outlook • PREDICTIONS USING THE SHIELDED CSR-WAKE ARE IN SURPRISINGLY GOOD AGREEMENT WITH MEASUREMENTS AT BESSY II AND THE MLS. • THE OBSERVED RESONANCE-LIKE FEATURES SHOW THE IMPORTANCE OF THE VERTICAL GAP OF THE DIPOLE VACUUM CHAMBER. • SIMULATIONS DEMONSTRATE THE WEAK NATURE OF THE CSR DRIVEN INSTABILITY - ALSO IN THE REGION OF SHORT BUNCHES WHERE THE SHIELDING IS LESS IMPORTANT. • BELOW THE THRESHOLD MULTI-PARTICLE-TRACKING IN BETTER AGREEMENT WITH OBSERVATIONS THAN “NOISE FREE” VFP-SOLUTIONS. • EXPERIMENTAL DETERMINATION AND SCALING OF THRESHOLD CURRENTS NEEDS MORE ATTENTION. • PRELIMINARY RESULTS FOR VERY HIGH RF-GRADIENTS (HIGHER HARMONIC, DOUBLE RF-SYSTEM) HAVE SHOWN NOT QUITE THE EXPECTED INCREASE OF INSTABILITY THRESHOLDS. • THE VFP SOLVER AND MULTI PARTICLE TRACKING ARE CURRENTLY USED TO MODEL THE BEHAVIOR OF BUNCHES ABOVE THRESHOLD CURRENTS. 21