Temporal Characteristics of CSR Emitted in Storage Rings – Observations and a Simple Theoretical Model P. Kuske, BESSY „Topics in Coherent Synchrotron Radiation (CSR) Workshop : Consequences of Radiation Impedance“ Nov. 1st and 2nd 2010, Canadian Light Source
„Topics in Coherent Synchrotron Radiation (CSR) Workshop : Consequences of Radiation Impedance“ Nov. 1st and 2nd 2010, Canadian Light Source. Temporal Characteristics of CSR Emitted in Storage Rings – Observations and a Simple Theoretical Model. P. Kuske, BESSY. Outline of the Talk. - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Temporal Characteristics of CSR Emitted in Storage Rings – Observations and a Simple Theoretical Model
P. Kuske, BESSY
„Topics in Coherent Synchrotron Radiation (CSR) Workshop : Consequences of Radiation Impedance“Nov. 1st and 2nd 2010, Canadian Light Source
Outline of the Talk
I. Motivation
II. Observations – at BESSY II
III. Theoretical Model – μ-wave Instability„numerical solution of the VFP-equation with BBR-wake“
III. 1 BBR-ImpedanceIII. 2 Vlasov-Fokker-Planck-Equation – „wave function“ approachIII. 3 Numerical Solution of this VFP-equation
IV. ResultsIV. 1 Comparison to other SolutionsIV. 2 New Features and Predictions IV. 3 Comparison of Experimental and Theoretical Results
V. Conclusion and Outlook
2
I. Motivation
3
open questions and issues
related to CSR directly:
• spectral characteristic?
• steady-state radiation vs. emission in bursts – temporal characteristics?
• how can we improve performance?
more generally:
• some kind of impedance seems to play a role
• potential instability mechanism
• very often we operate with single bunch charges beyond the stability limit
• How does instability relate to CSR?
II. Observations at BESSY II
4
time dependent CSR-bursts observed in frequency domain:
0=14 ps, nom. optics, with 7T-WLS
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005, Frascati
Spectrum of the CSR-signal:
CSR-bursting threshold
Stable, time independent CSR
II. Observations at BESSY II
5
time dependent CSR-bursts observed in frequency domain:
0=14 ps, nom. optics, with 7T-WLS
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005, Frascati
Spectrum of the CSR-signal:
CSR-bursting threshold
Stable, time independent CSR
II. Observations at BESSY II
6
time dependent CSR-bursts observed in frequency domain:
0=14 ps, nom. optics, with 7T-WLS
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005, Frascati
Spectrum of the CSR-signal:
CSR-bursting threshold
Stable, time independent CSR
II. Observations at BESSY II
7
time dependent CSR-bursts observed in frequency domain:
0=14 ps, nom. optics, with 7T-WLS
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005, Frascati
Spectrum of the CSR-signal:
CSR-bursting threshold
Stable, time independent CSR
8
II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
9
II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
10
II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
11
II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
12
II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
13
II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
14
II. Observations at BESSY IIwith 4 sc IDs in operation
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
15
II. Observations at BESSY IIwithout sc IDs
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
16
II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
17
III. 1 Theoretical Model – BBR-Impedance
18
III. 1 Theoretical Model – CSR-Impedance
‚featureless curve with local maximum and cutoff at long wavelenght‘
19
III. 1 Theoretical Model – CSR-Impedance
20
III. 2 Vlasov-Fokker-Planck-Equation (VFP)
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005, Frascati
numerical solution based on: R.L. Warnock, J.A. Ellison, SLAC-PUB-8404, March 2000M. Venturini, et al., Phys. Rev. ST-AB 8, 014202 (2005)
S. Novokhatski, EPAC 2000 and SLAC-PUB-11251, May 2005
p
fpf
ptp
ffqFq
q
fp
f
dsc
2),,(
ts zzq / EEp /
RF focusing Collective Force Damping Quantum Excitation
solution for f(q, p,) can become < 0
requires larger grids and smaller time steps
(M. Venturini)
21
III. 2 Vlasov-Fokker-Planck-Equation (VFP) „wave function“ approach
p
fpf
ptp
ffqFq
q
fp
f
dsc
2),,(
p
gpg
ptp
ggqFq
q
gp
g
dsc 2
2),,( 2
Ansatz – “wave function” approach: Distribution function, f(q, p,) , expressed as product of amplitude function, g(q, p,) :
ggf
original VFP-equation:
f (q, p,) >= 0 and solutions more stable
22
III. 3 Numerical Solution of the VFP-Equation and BESSY II Storage Ring Parameters
Fsyn = 7.7 kHz
~60 Tsyn per damping time
Energy 1.7 GeV
Natural energy spread / 710-4
Longitudinal damping time lon 8.0 ms
Momentum compaction factor 7.3 10-4
Bunch length o 10.53 ps
Accellerating voltage Vrf 1.4 MV
RF-frequency rf 5002 MHz
Gradient of RF-Voltage Vrf/t 4.63 kV/ps
Circumference C 240 m
Revolution time To 800 ns
Number of electrons 5106 per µA
solved as outlined by Venturini (2005): function, g(q, p,), is represented locally as a cubic polynomial and a time step requires 4 new calculations over the grid
distribution followed over 200 Tsyn and during the last 160 Tsyn the projected distribution (q) is stored for later analysis: determination of the moments and FFT for the emission spectrum
grid size 128x128 and up to 8 times larger, time steps adjusted and as large as possible
M. Venturini, et al., Phys. Rev. ST-AB 8, 014202 (2005)
23
Theoretical ResultsVI. 1 Comparison with other Theories and Simulations
K. Oide, K. Yokoya, „Longitudinal Single-Bunch Instability in Electron Storage Rings“, KEK Preprint 90-10, April 1990
K.L.F. Bane, et al., „Comparison of Simulation Codes for Microwave Instability in Bunched Beams“, IPAC’10, Kyoto, Japan and references there in
24
Theoretical ResultsVI. 1 Comparison with other Theories and Simulations
25
Theoretical ResultsVI. 2 New Features
broad band resonator with
Rs=10 kΩ
26
Theoretical ResultsVI. 2 New Features
broad band resonator with
Rs=10 kΩ
27
Theoretical ResultsVI. 2 New Features
broad band resonator with
Rs=10 kΩ
28
Theoretical ResultsVI. 2 New Features – Islands of Stability
29
Theoretical ResultsVI. 2 New Features – Islands of Stability
30
Theoretical ResultsVI. 2 New Features – Hysteresis Effects