Temporal Characteristics of CSR Emitted in Storage Rings – Observations and a Simple Theoretical Model P. Kuske, BESSY „Topics in Coherent Synchrotron

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

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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

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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


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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


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II. Observations at BESSY IIwithout sc IDs


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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)


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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Rs=10 kΩ

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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

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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

Documents

Temporal Characteristics of CSR Emitted in Storage Rings – Observations and a Simple Theoretical Model P. Kuske, BESSY „Topics in Coherent Synchrotron