Using symmetries with CST Particle Studio Andrea Passarelli 02/09/2013 1
Transcript
Using symmetries with CST Particle Studio Andrea Passarelli
02/09/2013
1
Presenter
Presentation Notes
Good afternoon to everyone, I’m Andrea Passarelli the new technical students from the university of Napoli Federico II.
• Introduction
• Use of the symmetry plane in a simple structure
• Magnetic symmetry
• Electric symmetry
• Summary
I’m working on: Evaluate the impedance of the LHC goniometer using CST – Particle studio (Wakefield solver)
I’m simplifying the structure also by exploiting the symmetries to decrease the number of meshes to have faster simulation times
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Presenter
Presentation Notes
Presently I’m working on a project of UA9 that is the evaluation of the impedance of the LHC goniometer using CST – Particle Studio with the help of Alessandro Danisi and with the supervision of Carlo Zannini. I start this study simplifying the structure to reduce the number of meshes and the simulation time
Advantages in using simplified structure:
• Better understanding of the results • Estimation of the impedance contribution of
details of the structure • Use of Symmetry Planes
– decrease of the simulation time – decrease of memory occupation
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Presenter
Presentation Notes
Now I want to show you why I use the simplified structure. The first benefit is to have a better understanding of the results, indeed we can complicate the structure step by step and study the relation between the variation of the impedance and the changing of the structure. With the simple structure we can easily use the symmetry planes, and doing this we decrease the number of meshes so the simulation time and the memory occupation and we have a reliability improvement of the simulation results that is a plane on which we know that the result is right.
• Introduction
• Use of the symmetry plane in a simple structure
• Magnetic symmetry
• Electric symmetry
• Summary
Study of the symmetry in a simple structure using CST Particle Studio
2b
2a
δ
OPEN Conductive
wall
Cond. 1e6 S/m
6
Source and test superimposed
baq 35.0 =⇒=
Presenter
Presentation Notes
My talk will focus on the study of the symmetry planes. As example I studied a simple case of a rectangular chamber and I did it because CST – Particle studio uses the hexahedral mesh, and this is to have a best fitting of the structure. This structure has a top-bottom and left-right geometrical symmetry and I used conductive wall with conductivity 10^6 Siemens/m, and open boundaries along the z axis. In this case the beam and the test are displaced of a length δ from the centre of the structure that is significantly smaller than the pipe aperture. And we consider an aspect ratio of the guide of 0.5.
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We evaluate vertical generalized term of the
Wake Potential
yWyWW quady
dipyy += 0
Study of the symmetry in a simple structure using CST Particle Studio
Presenter
Presentation Notes
Now let’s go to see the study and we want to evaluate the vertical generalized term of the Wake potential. Why we use the offset of the beam significantly smaller than the pipe aperture? Because we can neglect the non linear terms, and doing this we remind that the generalized term in a symmetric structure is composed by a dipolar and a quadrupolar wake component. In this formula y0 is the offset of the source and the y is the offset of the test from the centre of the structure.
• Introduction
• Use of the symmetry plane in a simple structure
• Magnetic symmetry
• Electric symmetry
• Summary
We use the magnetic (Ht=0) symmetry in the YZ plane.
Magnetic symmetry
Y Y_verticalsymmetry
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Magnetic symmetry 1/9
x
y
z
Presenter
Presentation Notes
We can start now studying the symmetries and as we usually do in this case we exploit the left-right symmetry using the YZ magnetic symmetry plane. And we make a comparison between structure without the symmetry and the structure using the YZ magnetic plane. All the simulation that I’ll show are with the same parameters of number of meshes, integration method, wakelenght
Magnetic symmetry
Exactly superimposed
Y Y_verticalsymmetry
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Magnetic symmetry 2/9
x
y
z
Presenter
Presentation Notes
As we expected, the results of the wake potential are exactly superimposed, so we confirm that we can use the magnetic symmetry plane in the case of geometry and beam symmetry. And we can do this because the beam direction is along the z axes, so the tangential component of the magnetic field in the center of the structure is zero.
We do NOT have the top-bottom symmetry, because of the beam
position. Magnetic symmetry
Y Y_horizontalsymmetry
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Magnetic symmetry 3/9
x
y
z
Presenter
Presentation Notes
We would like to profit by all of the symmetry of the geometrical structure, so we would like to use ¼ symmetry, so we start to study the XZ magnetic symmetry plane. And we compare the structure without symmetry planes with the structure with the XZ magnetic symmetry plane.
Magnetic symmetry
Y Y_horizontalsymmetry
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Magnetic symmetry 4/9
x
y
z
Presenter
Presentation Notes
As we expected there is a difference between the two results. And now we want to understand the meaning of the green curve, that is the case with the magnetic symmetry plane.
Magnetic symmetry
Y_horizontalsymmetry
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Magnetic symmetry 5/9
yWyWW quady
dipyy += 0
XZ magnetic symmetry plane
NO dipolar wake Only quadrupolar wake
x
y
z
Presenter
Presentation Notes
As we said the generalized term is composed by a dipolar and a quadrupolar wake component. But in this case the magnetic symmetry force to zero the dipolar wake so there is only the quadrupolar wake component.
Magnetic symmetry
Y_horizontalsymmetry
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Y_quadrupolar
Test
Source
Magnetic symmetry 6/9
x
y
z
Presenter
Presentation Notes
If we make a comparison between the structure with the XZ magnetic symmetry plane and the standard simulation of the quadrupolar term of the wake we can find a factor of two due to the presence of the second beam for the Image Theory.
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Magnetic symmetry 7/9
Scaled by two
Presenter
Presentation Notes
Indeed if we scale the curve of a factor two they are exactly superimposed as we expected.
Magnetic symmetry
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Magnetic symmetry 8/9
yWyWW quady
dipyy += 0
Independent from the offset of the source (y0)
x
y
z
Presenter
Presentation Notes
So doing a comparison between these two simulation we understand that the magnetic symmetry doesn’t allow to dipolar term of the wake. So doing some simulation with different value of the offset of the source the value of the wake shouldn’t change in the approximation of the first order.
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Magnetic symmetry 9/9
20ykyWW quad
yy +=
y0
0261.0=k
s = 0.77mm
Presenter
Presentation Notes
But we can see that the variation of the wake at different value of the offset of the beam is due to the second order terms. Indeed if we fit the curve of the maximum value of the wake varying the offset of the source we have a quadratic trend.
• Introduction
• Use of the symmetry plane in a simple structure
• Magnetic symmetry
• Electric symmetry
• Summary
We study the electric (Et=0) symmetry in the XZ plane.
Electric symmetry
Y_horizontalsymmetry (E) Y
19
Electric symmetry 1/5
Magnetic symmetry
x
y
z
Presenter
Presentation Notes
We have shown that the yz magnetic symmetry plane works. So now we do the same study, but now we using the XZ electric symmetry plane.
Y
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Electric symmetry
Y_horizontalsymmetry (E)
Magnetic symmetry Electric symmetry 2/5
x
y
z
Presenter
Presentation Notes
We compare the structure without symmetries and the structure with the electric symmetry. And we can see the difference between the two curves.
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Electric symmetry
Y_horizontalsymmetry (E)
Magnetic symmetry Electric symmetry 3/5
yWyWW quady
dipyy += 0
XZ electric symmetry plane
NO quadrupolar wake Only dipolar wake
x
y
z
Presenter
Presentation Notes
As we said the generalized term is composed by a dipolar and a quadrupolar wake component. Dually to the magnetic case the electric symmetry force to zero the quadrupolar wake so there is only the quadrupolar wake component.
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Y_dipolar
Electric symmetry
Y_horizontalsymmetry (E)
Magnetic symmetry
Source
Test
Electric symmetry 4/5
x
y
z
Presenter
Presentation Notes
As the magnetic symmetry I have showed before we make a comparison between the structure with the XZ electric symmetry plane and the standard simulation of the dipolar term of the wake, and we can find a factor of two due to the presence of the second beam for the Image Theory.
23
Scaled by two
Electric symmetry 5/5
Presenter
Presentation Notes
if we scale the curve of a factor two they are in a very good agreement superimposed.
• Introduction
• Use of the symmetry plane in a simple structure
• Magnetic symmetry
• Electric symmetry
• Summary
Summary 1/2 •
25
Magnetic symmetry
• Electric symmetry Magnetic symmetry
Wsimulation = 2*dipolar wake
Wsimulation = 2*quadrupolar wake
x
y
z
Presenter
Presentation Notes
Obviously this is the case of the vertical component, but the same study can be applied to the horizontal component. So we understand that if we apply the magnetic symmetry in the plane where the beam doesn’t pass we can achieve the quadrupolar wake component, otherwise with the electric symmetry we obtain the dipolar wake component.
Summary 2/2
• Quadrupolar and dipolar wake/impedance could be calculated using the same degree of geometrical symmetry of the device under test.
Presenter
Presentation Notes
So we can calculate the quadrupolar and the dipolar wake component using the same degree of the geometrical symmetry of the DUT.
Thank you for your attention
27
Presenter
Presentation Notes
Thank you
29
Given an electrical current at a distance x from the PMC plane, the plane can be replaced by a current equal and with the same sign, at
a distance x below the original PMC surface.
+
+
Magnetic symmetry Image theory Magnetic symmetry
Magnetic symmetry
30
Magnetic symmetry
Y_horizontalsymmetry Y_doublebeam
+
+
Exactly superimposed
Electric symmetry
Y_horizontalsymmetry (E)
Electric boundary
Y_halfguide_boundaries (E)
Exactly superimposed
31
Electric symmetry
32
+
-
Electric symmetry Image theory
PEC
Given an electrical current at a distance x from the PEC plane, the plane can be replaced by a current equal and with the opposite sign,
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