pulsed power engineering engineering...

Pulsed Power EngineeringEngineering Simulations

June 13-17, 2011

Craig Burkhart & Mark KempPower Conversion Department

SLAC National Accelerator Laboratory

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Engineering Simulations in Pulsed Power Systems• Uses of engineering simulation• Tools• Typical methodology• Analytical estimates of electric field

USPAS Pulsed Power Engineering Burkhart & Kemp

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Pulsed Power Engineering Simulations

• Differential equations govern many processes of interest to pulsed power engineers.

– Ex. Heat flow, stress/strain, electric and magnetic field intensities• Simulations provide a straightforward method to solve these equations for

complex geometries and non-linear conditions.• Some Types of Simulations Used

– Finite Element Method (FEM)• Very common method; used for transient and non-linear problems

– Boundary Value Method (BVM)• Good for odd aspect-ratio problems with open spaces; quick simulation times

– Particle in Cell (PIC)• For particle trajectory problems and plasma simulation


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Types of Simulations

• Electrostatic/Magnetostatic– Electro, Maxwell 2D (free)/3D, Quickfield

• Multi-physics– ANSYS, ATILA (free)

• Capacitance/Inductance Solvers– FastHenry (free), FastCap (free)

• Electromagentic Solver– HFSS, Singula

• Particle-in-Cell– XOOPIC (free), LSP


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Electric Field Stress

CAD Drawing ofWater Capacitor

(azimuthally symmetric)

Electric FieldMagnitude Plots

Open Space

Along a Measurement Line

• What is the electric field stress for a certain geometry and voltage?• Shown is a rotationally symmetric capacitor.


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Electric Field Grading• Where should field shapers be placed to evenly grade the electric field along an

insulator?• Field response to geometry changes can be modeled.

Floating Conductors in aGas Discharge Switch

Equipotentials Electric Field Vectors


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Capacitance Matrices• Many electrostatic codes can generate a matrix of capacitance values from element

values to each other.• These values can be exported to circuit codes for transient simulations.

Effective CapacitanceBetween Isolated conductors

Simulation-Generated Capacitance Matrix


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Inductance Matrices

CAD Drawing

SimplifiedRepresentation

InductanceMatrix

• Simplified representations are in many time necessary and appropriate for simulating complex geometries.

• Self- and mutual- inductance matrices can be generated.


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PIC Cathode Design

• Some PIC codes can self-consistently model E&M systems.

• Above is a cathode design showing the effect of external fields and self-fields from electrons.

-200 kV -200 kV+300VGround


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Multi-Physics Design• In some cases, several systems interact. E.g.

mechanical, electrical, and thermal.

• For example, left is a simulation of a piezoelectric transformer. Coupled mechanical and electrical systems are simulated.

• ANSYS and ATILA (free) are two codes available.

Groundedelectrode +1kV

~35 kV


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Typical Work Flow

• Create Geometry– Through external CAD program– Through included CAD program– By manually entering text coordinates

• Define Boundaries and Sources– Ex. Force on a surface, voltage on a conductor, or charge in a volume.

• Define Solution Type• Create Mesh• Simulate• Post-Process


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Typical Workflow

• A complex geometry is created in a CAD program

• Can be 2D or 3D depending on the software and the nature of the problem


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Typical Workflow• The specific area of interest

is imported to the simulation software.

• Excitations and boundary conditions are set.

• Simulation settings are entered.


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Typical Workflow

• Once a problem has a converged solution, results can be viewed.

• Many programs have the option to view results in a post-processor program or export for processing elsewhere.


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Estimating Electric Fields

R

r

Concentric Spheres

EM =VR

r(R − r)

f =Rr

Rr

= 2

EM =2Vr

=4VR

EM = VR

r lnRr

f =

Rr

−1

ln Rr

Rr

= e

EM =Vr

=VeR

Concentric Cylinders(symbols as for concentric spheres)

Maximum Stress ( EM)

f =maximum stress

mean stress

Optimum ratio Rr

and correspondingmaximum stress

Maximum Stress ( EM)

f =maximum stress

mean stress

EM = VX

f ≅ V2r

for Xr

>>1

f =

Xr

+1+Xr

+1

2

+ 8

4≅ X

2r for X

r>>1

r

r

XD

Equal Spheres

Equal parallel Cylinders(symbols as for equal spheres

EM =V D2 − 4r 2( )

2r D − 2r( )ln D2r

+ D2r

2

−1

EM ≅V

2r lnDr

if D >> 2r

f =

Xr

2

+ 4 Xr

2ln X2r

+1 + 12

Xr

2

+ 4 Xr

f ≅X

2r lnXr

if Xr

>> 4


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Dependence of the ratio on electrode geometry for concentric cylinders and spheres (calculated from stress table) and for cylinder surrounded by a torus.

f =maximum stress

mean stress


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Dependence of the ratio on electrode geometry for separate spheres and separate cylinders (calculated from stress table) and sphere-plane and cylinder-plane assemblies

f =maximum stress

mean stress


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Control of High Stress Points

(triple point)


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