coaxial simulations using hfss and maxwell - cern · pdf fileintroduction simulations coaxial...

IntroductionSimulations

Coaxial Wire Method SimulationsImpedance by Power Loss

Conclusions and Future WorkBibliography

Coaxial Simulations using HFSS andMaxwell

Hugo Day

February 28, 2011

With thanks to E. Metral, A. Grudiev, F. Caspers, B. Salvant, C.Zannini, N. Mounet for useful discussions and suggestions

Hugo Day Coaxial Simulations using HFSS and Maxwell




Contents

1 Introduction

Wakefields and ImpedancesAnalytical Models (Tsutsui/Metral-Zotter)Coaxial Wire Method - Principles and Analysis

2 Simulation Results

Graphite Collimator - HFSS & Maxwell

3 Conclusions and Future Work





Introduction

AIM: To test the validity of a new analysis technique to measure thelongitudinal, dipolar (driving) and quadrupolar (detuning) impedances ofasymmetric structures.

Last time (14th Sep’ 2010) presented work on a symmetric(Tsutsui-type) Ferrite Kicker magnet - Could not replicatequadrupolar impedance accurately.

Main issue was with the replication of the dipolar impedance

Solution - Use a structure where the dipolar impedance has beenmeasured before... graphite collimator [1]

And thus our adventure begins





Overview of Impedance

The passage of a moving charged particle causes the emission of EMfields - Within a particle accelerator these fields can interact withthe surrounding structures to create time evolving fields whichinteract with trailing particles - Called wakefields

The impedance is the fourier transform of these fields into thefrequency domain - Important as a large number of acceleratorcomponents exhibit frequency dependent properties (materialproperties, resonant modes, etc.)

Zlong (ω,~r) =

∫ ∞−∞

Ez(z ,~r)e jkzdz (1)

Zx/y (ω,~r) =

∫ ∞−∞

[Ex/y (z ,~r)− vzBy/x(z ,~r)

]e jkzdz (2)





We may further break down the transverse impedance into thedipolar and quadrupolar impedances, defined as in figure 1. Theseare important for beam dynamics considerations

x

y

x

y

x

y

x

y

Inducing Particle

Witness Particle

Horizontal Vertical

Quadrupolar

Dipolar

Figure 1: The four transverse impedances how they relate the relativepositions of the source and test particles





Analytical Models

Two models were used for comparison to the simulated impedances,the Tsutsui model and the Metral/Zotter model adjusted with theYokoya factors for two parallel plates (see fig 2

Vacuum

Jaw Material

Tsutsui Metral-Zotter

Figure 2: Comparison of the two theoretical models used for comparison tothe simulation results





Coaxial Wire Method

Ultra-relativistic charged particles emit a EM in a transverse profile(assuming γ →∞), i.e. TEM profile. Like a short electrical pulsealong a coaxial wire (see [2][3] for more in depth study)

Using one wire (longitudinal) and two wires (dipolar) we maymeasure the impedance of a device without the need to use aparticle beam

For a structure with top/bottom, left/right symmetry: By acombination of both we may measure the quadrupolar impedancealso (eqn 3)

Zl,total(f ) = Zlong (f ) + x2Zx(f ) + y2Zy (f ) (3)

where Zx/y = kZ⊥,x/y = k[Zdip,x/y ± Zquad

]is the total horizontal or

vertical transverse impedance, x/y the horizontal/vertical displacement ofthe wire respectively and k the wavenumber that the measurement iscarried out at.





Coaxial Wire Method

For asymmetric structures the analysis is more involved - We canstill use the two wire method to measure the dipolar impedance

However, the longitudinal impedance has a more general form

Z (a, θ)tot = A1 + ae−jθA2 + ae jθA3 + a2e−2jθA4 + a2e2jθA5 + a2A6 (4)

where a is the displacement of the wire from the centre of structure, θthe radial displacement of the wire and A1−6 are complex coefficients tobe determined. By some mathematics and working it can be shown that(see [2] for more details)

Z quadrupolar =Z dipx − Z dip

y

2− A4 + A5

k(5)

I.E. - We need to obtain measurements that let us determine A4 and A5





Coaxial Wire Method

By seperating A4/5 into the real and imaginary parts and expandingthe complex exponentials and lots of considering of angles itbecomes possible to isolate A4 + A5

A4+A5 =Zlong (θ = 0) + Zlong (θ = π)− 2Zlong (θ = π

2 )− 2Zlong (θ = 3π2 )

4a2(6)

NOTE: This will mean Zquad will depend on your definition of θ = 0.Aligning it with the relevent Courant-Snyder coordinates would seemsensible

Also requires less measurements than vertical/horizontal scan, andallows verification through considering many displacements





Simulation Methodology

We use two methods of simulation to obtain impedances1 Measuring S21 for a coaxial system (HFSS)2 Measuring the power loss from a short current source (to avoid

phase changes) in the DUT (Maxwell)

The first allows us to measure the real and complex impedances, thesecond only the real impedance

Both can be used for single and two wire simulations and both overa large frequency range (subject to code applicability)





Coaxial Wire Method - Transmission Method

We measure S21 from waveguide ports at either end of the testgeometry. Subsequently using the distributed impedance formula wecan obtain the impedance

Z = −2ZchLn

(S21,DUT

S21,ref

)(7)

Where Zch is the characteristic impedance of the structure andS21,ref the transmission coefficient through a perfectly conductionreference tube (for these simulations analysed analytically, i.e. just aphase compensation)





Coaxial Wire Method with Maxwell

So, after a lot of intimate time spent with the computer...

10-6 10-5 10-4 10-3 10-2 10-1 100 101

Frequency (GHz)

10-5

10-4

10-3

10-2

10-1

100

101

102

Impedance

(Ω/m

)

Graphite Collimator - Comparison Longitudinal Impedance

My Sims Re(Z)My Sims Im(Z)Tsutsui Sims Re(Z)Tsutsui Sims Im(Z)Analytical - Re(Z)Analytical - Im(Z)

10-6 10-5 10-4 10-3 10-2 10-1 100 101

Frequency (GHz)

104

105

106

107

108

Impedance

(Ω/m

2)

Graphite Collimator - Comparison Horizontal Dipolar Impedance

Tsutsui - Re(Z)Tsutsui - Im(Z)My Simulation - Re(Z)My Simulation - Im(Z)Analytical - Re(Z)Analytical - Im(Z)

Figure 3: 3(a)) Longitudinal and 3(b) horizontal dipolar impedance ascalculated using HFSS





Coaxial Wire Method Simulations

10-6 10-5 10-4 10-3 10-2 10-1 100 101

Frequency (GHz)

104

105

106

107

108

Impedance

(Ω/m

2)

Graphite Collimator - Comparison Vertical Dipolar Impedance

Tsutsui - Re(Z)Tsutsui - Im(Z)My Simulation - Re(Z)My Simulation - Im(Z)Analytical - Re(Z)Analytical - Im(Z)

10-3 10-2 10-1 100 101

Frequency (GHz)

104

105

106

107

Impedance

(Ω/m

2)

Quadrupolar Impedance

Re(Z) - SimsIm(Z) - SimsAnalytical Real - TsutsuiAnalytical Imag - Tsutsui

Figure 4: 4(a) Vertical dipolar and 4(b) quadrupolar impedance as calculatedusing HFSS





We can replicate the longitudinal and dipolar impedances well, butnot the quadrupolarIf the parabolas created by the displaced wire sweeps areinvestigated it becomes apparent that the quality of parabola is notgood (e.g. fig 5)It becomes apparent that we need better resolution for between thedisplaced data than HFSS can provideExamine other ways...

Figure 5: An example of the parabola for the displaced wire scan done withHFSS (10MHz vertical scan)





Impedance by Power Loss

Other method first used by T. Kroyer (2007)[4]

We use a short cross section of the DUT, and pass a currentthrough it. If we consider the conductive losses in the surroundingstructure we can see that they are proportional to the real part ofthe impedance

P =I 2<e (Z )

2(8)

<e (Z ) =2P

I 2(9)

where P is the power loss in the structure, I the current in thecentral conductor, <e (Z ) the real impedance of the DUT

Has been used to obtain very good dipolar results in the past, andcan be used to simulate one and two wire measurements





10-1 100 101 102 103 104 105 106 107 108 109

Frequency

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

Impedance

(Ω/m

)

Maxwell SimsAnalytical Tsutsui

10-1 100 101 102 103 104 105 106 107 108 109 1010

Frequency

100

101

102

103

104

105

106

Impedance

(Ω/m

2)

Maxwell SimsAnalytical TsutsuiAnalytical BLSimulations T. Kroyer

Figure 6: 6(a) Longitudinal and 6(b) vertical dipolar impedance by the powerdissipation method using Maxwell





10-1 100 101 102 103 104 105 106 107 108 109 1010

Frequency

100

101

102

103

104

105

106

Impedance

(Ω/m

2)

Maxwell SimsAnalytical TsutsuiAnalytical BLSimulations T. Kroyer

10-1 100 101 102 103 104 105 106 107 108 109

Frequency (Hz)

100

101

102

103

104

105

106

Impedance

(Ω/m

2)

Horizontal QuadrupolarVertical QuadrupolarAsymmetric QuadrupolarQuadrupolar Tsutsui

Figure 7: 7(a) Horizontal dipolar and 7(b) quadrupolar impedance by thepower dissipation method using Maxwell





Impedance by Power Loss

We replicated the parabola method and...

We can replicate the quadrupolar impedance using the asymmetricformula! YAHOO!

However... it can be seen for all impedances that there is somedetuning of the results from what would be expected from theTsutsui theory

Is the Tsutsui theory the correct theory to be using for this structure(low conductivity material), or is the presence of the wire causing ashift in the boundary conditions?

Previous work has indicated that this is the case below cut off forgeometric impedances[5], could it be the same for resistive wall?





Conclusions and Future Work

ConclusionsWe can replicate the quadrupolar impedance for a graphitecollimator using the asymmetric impedance methodWe have established a discrepency between the analytical theory andthe measurements taken using the coaxial wire method

Future WorkTry and replicate these simulations using a ferrite kicker magnet(not possible in Maxwell due to not being able to define frequencydependent µ)See if we can extend this to HFSS (much greater freedom indefining materials). Possibly consider the fields surrounding thestructure to obtain the impedanceEventually consider an asymmetric structure (C-Core ferrite kicker)to see if we can replicate asymmetric impedancesMake a consideration between resistive wall coaxial cable impedanceand waveguide impedance





Bibliography

1 ”Resistive wall impedance of an LHC collimator”, H. Tsutsui,CERN-LHC-Project-Note-318

2 ”On single wire technique for transverse coupling impedancemeasurement”, H. Tsutsui, SL-Note-2002-034-AP

3 ”Validity of coupling impedance bench measurements”, H. Hahn,Phys.Rev.ST Accel.Beams 3 (2000) 122001

4 ”Simulation of the low-frequency collimator impedance”, T. Kroyer,CERN-AB-Note-2008-017

5 ”The Stretched Wire Method: A Comparative Analysis performed bymeans of the Mode Matching Technique”, M. R. Masullo, V.G..Vaccaro, M.Panniello, IPAC2010


coaxial simulations using hfss and maxwell - cern · pdf fileintroduction simulations coaxial...

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