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
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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
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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
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II. Observations at BESSY II
Investigation of the temporal structure of CSR-Bursts at BESSY II, Peter Kuske, PAC’09, Vancouver
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III. 1 Theoretical Model – BBR-Impedance
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III. 1 Theoretical Model – CSR-Impedance
‚featureless curve with local maximum and cutoff at long wavelenght‘
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III. 1 Theoretical Model – CSR-Impedance
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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)
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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
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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)
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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
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Theoretical ResultsVI. 1 Comparison with other Theories and Simulations
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Theoretical ResultsVI. 2 New Features
broad band resonator with
Rs=10 kΩ
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Theoretical ResultsVI. 2 New Features
broad band resonator with
Rs=10 kΩ
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Theoretical ResultsVI. 2 New Features
broad band resonator with
Rs=10 kΩ
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Theoretical ResultsVI. 2 New Features – Islands of Stability
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Theoretical ResultsVI. 2 New Features – Islands of Stability
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Theoretical ResultsVI. 2 New Features – Hysteresis Effects
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Theoretical Results - burstVI. 3 BBR: Rs=10kΩ, Fres=200GHz, Q=4 and Isb=7.9mA
32
Theoretical Results – lowest unstable modeVI. 3 BBR: Rs=10kΩ, Fres=100GHz, Q=1 and Isb=2.275mA
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Theoretical ResultsVI. 3 BBR + R + L in Comparison with Observations
BBR: Rs=10 kΩ, Fres=40 GHz, Q=1; R= 850 Ω and L=0.2 Ω
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Theoretical ResultsVI. 3 BBR + R + L in Comparison with Observations
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V. Conclusion and Outlook
a simple BBR-model for the impedance combined with the low noise numerical
solutions of the VFP-equation can explain many of the observed time dependent
features of the emitted CSR:
• typically a single (azimuthal) mode is unstable first
• frequency increases stepwise with the bunch length
• at higher intensity sawtooth-type instability (quite regular, mode mixing)
• at even higher intensitiy the instability becomes turbulent, chaotic, with many modes involved
Oide‘s and Yokoya‘s results are only in fair agreement with these calculations
do not show such a rich variety of behavior – why?
are better approaches available?
simulation can serve as a benchmark for other theoretical solutions
need further studies with more complex assumption on the vacuum chamber impedance
the simple model does not explain the amount of CSR emitted at higher photon energy –
much higher resonator frequencies required
is this produced by a two step process, where a short wavelength perturbation is first created
by the traditional wakefield interaction and in a second step another wake with even higher
frequency comes into play? (like bursting triggered by slicing)
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Acknowledgement
K. Holldack – detector and THz-beamline
J. Kuszynski, D. Engel – LabView and data aquisition
U. Schade and G. Wüstefeld – for discussions
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