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CST EUC 2013, 23-25 April 2013, Stuttgart
Paul Scherrer Institute
Study of wake fields for short electron bunches using CST Particle Studio
Dr Sladana Dordevic
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Introduction Analytical results CST Particle Studio results and comparison Summary
Outline
The 8th CST European User Conference (EUC) 23-25 April 2013, Stuttgart, Germany
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The SwissFEL accelerator requires a high quality, ultra short electron bunch. The bunch travels parallel to the axis of the axially symmetric structure. The electromagnetic field of the charge bunch interacts with the surrounding accelerating structure generating the wake fields that act back on the bunch itself. Knowledge of the short range wakefields in accelerator structure in needed to predict the bunch energy spread and emittance.
Introduction
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Analytical approach is not suitable for complex geometries, leaving numerical simulation with CST Particle Studio as the alternative. Unfortunately, for particle bunches shorter than ~200fs, the simulations are time consuming or even impossible due to the large number of mesh points required. In this study, the following conditions are taken: resistive wake fields, a simple round pipe and on-axis ultra-relativistic bunches with longitudinal Gaussian distribution. Analytic results are compared to wake fields from CST Particle Studio. Different meshing parameters in Wakefield Solver are compared in order to find the results in the best agreement with analytical results for progressively shorter bunch lengths. This allows at least an estimation of wake fields for bunches <33fs for complex structures.
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Analytic equations are used for longitudinal impedance calculation of simple geometries *. With the calculated impedance, the wake function is found with inverse Fourier Transform, then convolved with bunch shape to give wake potential.
Analytic results
* A. W. Chao, “Physics of Collective Beam Instabilities in High Energy Accelerators”, John Wiley & Sons, Inc.1993.
Impedance Wake function Wake potential
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In analytical study two different regimes of conductivity are considered:
DC Conductivity model – field is constant between electron collisions
AC Conductivity model – field changes between electron collisions (frequency dependant)
0
1AC iσ
σωτ
=−
electron relaxation time (mean time between electron collisions)
DC wake function is valid for cτ /s0<<1
AC Conductivity Model needed
σDC = σ0
s0=(2r2/Z0σ0)1/3
Two materials are considered: Cu, σCu=6.45x107 S/m, =2.7x10-14 s Al, σAl=4.22x107 S/m, =8.1x10-15 s τ
τ
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20 um Gaussian bunch
For bunches ≥20um:
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Longitudinal resistive wall wake potential W(s) versus the relative longitudinal displacement from the bunch head s for different bunch length (Cu and AC model)
-10000
-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
-20 0 20 40 60 80 100s [um]
W(s
) [V/
pC/m
]
10um Gaussian bunch 10um 5um 2.5um 1um - wake function
10 um Gaussian bunch
For bunches ≤10um:
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CST Particle Studio results and comparison
The lossy metal is modelled through a boundary condition
Integration Methods available for Wakefield Solver
Beam path
Integration path
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Indirect Testbeams is used for simulation
Factor of 1000 discrepancy Factor of 100 discrepancy
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Meshing parameters
Local mesh properties in longitudinal direction to improve
the dispersion characteristics
Local mesh properties in all directions
Global mesh properties
Since wakefield computations can be very time and resource consuming it is advisable to inspect the mesh.
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Different meshing parameters in Wakefield Solver are compared in order to find the results in the best agreement with analytical results for progressively shorter bunch lengths: 500um, 200um, 100um, 75um and 50um. .
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For ultra short bunches <10um (<33fs), a different method is proposed but not yet tried. Analytic results show that curves of wake potential have the same shape as wake function with opposite sign. The idea is to use CST Wakefield Solver with a longer bunch to find the impedance of a complex structure. With this impedance, the wake function for shorter bunches could be estimated with the inverse Fourier Transform.
Summary
Local meshing gives the minimal number of mesh cells for short bunches and resistive wake fields for bunches above 50um and gives results in very good agreement with analytical ones.
