Analysis of the voltage hold off between WSC/ESC and inner field cage

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Analysis of the voltage hold off between WSC/ESC and inner field cage

Majka did original work calculating fields. This is follow-up work to look for more easy to build solutions. Eric has been working on this problem as well with Ansys but what will be shown here is work with SolidWorks Simulator.

the issue:Higher field region between support cylinders and the field cage resistor chain

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Old Shroud Design with IDS for FGT only installation

fiber glass insulator plus maybe Mylar

conductive surfacebiased to – 5.5 kV

conductive composite at ground potential

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•Calculations of electric fields with analogous thermal FEA•Verification of code with concentric cylinder geometry•Electric field calculations for some shroud geometries and joints•Electric field for biased shroud termination with field grading rings•Electric field calculations for some testing setups (these are for some physical tests of shroud designs and materials)

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Calculations of electric fields with analogous thermal FEA

Our version of SolidWorks Simulation (FEA code) does not do Electric fields, but it does do thermal conduction through solid materials.

The math is the same for either case and we can equate fixed temperature boundary conditions to fixed electric potential boundary conditions. The electric field is equated to temperature gradient. For electrostatic calculations with different dielectrics this can be handled using materials with appropriate ratios of thermal conductivity.

In principle sources of heat flux in the thermal code could be used to represent electric charge, but we have not done this in the following work.

There is a significant advantage in using the SolidWorks Simulation because of the ease of handling geometries and boundary conditions. The package is tightly integrated which facilitates rapid adjustment and changes. Cases with different geometry parameters can often be run with out changes to the FEA portion.

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r (cm) E formula (V/cm) E FEA (V/cm)

0.11 31343 315903112030950

2 1724 172417241724

.287 12013 12000

.671 5138 5137

1.19 2897 2903

1.53 2253 2257

1.85 1864 1861

r=2 cm

10000 V

r = .11 cm0 V

abr

VrEln

Test of SolidWorks Simulator Field Calculation using thermal analog for concentric cylinders

outer cylinder radius: binner cylinder radius: a

(default mesh)

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Example output for numbers aboveexchange deg C for Volts

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mesh control set to .01 cm inner surface. default was .027 cm

r (cm) E formula (V/cm) E FEA (V/cm)

0.11 31343 3134031270313403133031360

2 1724 172417241724

.14 24626 24650

.228 15122 15120

.464 7430 7425

.863 3995 3995

1.26 2736 2732

1.63 2115 2114

Test of SolidWorks Field CalculationWith concentric cylinders

.04 cm

(using mesh control)

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Conclusion:Field accuracy achieved with SolidWorks Simulator is better than 3 significant figures

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The following explores grounded shroud options using a variety of methods for joining the shroud with the WSC/ESC. Different shroud geometries are also explored.

Using a grounded shroud as opposed to a biased shroud eliminates the need for a large area insulating layer and it avoids problems of edge termination.

Most of the cases give a maximum field on the resistor chain of 5.7 kV/cm. This over a limited area and should be acceptable since we are currently running with 5.6 kV/cm between the gas vessel and the outer field cage.

Fields are calculated with SolidWorks Simulator using a thermal analog.

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joint type file page Max field on shroud (kV/cm)

1 raised hoop a few cm > Z WSC edge

Air_sh_out_hoop1.SLDPRT 11 6.2

2 knuckle butt joint few cm> Z WSC edge

Air_sh_out_rolled_joint1.SLDPRT 15 4.5

3 knuckle butt joint with 0.5 mm mis-alignment

Air_sh_out_rolled_joint2.SLDPR 19 5.1

4 modified shroud 2 cm radius knee no joint

WSC_sol.SLDPRT 21 6.2


WSC_sol2.SLDPRT 23 4.9

6 case 5 with double joint at WSC edge 3 mm fillet


7 case 6 with 6mm truncated fillet – Joe Silber design


8 case 6 with 0.5 mm mis-alignment


cases run

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Air_sh_out_hoop1.SLDPRT

hoop joint joining shroud pieces at 30.8 cm from the center, i.e. 17800 bias on the resistor chain cover shown on this side.

resistor side, note slight increase in the field where the resistor chain cover passes over the hoop bump

max field on the resistor cover: 5.3 kV/cm

Case 1

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Case 1

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cross section of hoop that covers seam between shroud sections


Case 1

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Case 1

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Air_sh_out_rolled_joint1.SLDPRT

3mm radius jointjoint 76.7 cm from center, i.e. 17800 bias

knuckle butt joint Air_sh_out_rolled_joint1.SLDPRT

Case 2

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maximum field on joint 4.5 kV/cm


Case 2

04/22/2023 17Air_sh_out_rolled_joint1.SLDPRT

Case 2

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Case 2

04/22/2023 19Air_sh_out_rolled_joint2.SLDPRT

offset one side of the joint radially by 0.5 mm and in z by 0.5 mm

This increased max field from 4.5 kV/cm to 5.1 kV/cm

max field point on the resistor chain side

max field on the high edge: 5.1 kV/cmmax field on the low edge: 4.7 kV/cm Case 3

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offset joint geometry


Case 3

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2 cm radius where the shroud breaks over the edge

20.7 kV on resistor chain surface

Shroud coupled to support cylinder without a joint perturbation. Can’t actually build a joint free geometry like this.

Case 4

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WSC_sol.SLDPRT

Case 4

04/22/2023 23WSC_sol2.SLDPRT

simplified shroud shape: cone cut plus filletsmain radius 90 mm

More rounded shroud geometry Case 5

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WSC_sol2.SLDPRT

Case 5

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3 mm radius filets at jointsshroud and WSC

WSC_sol3.SLDPRT

Rounded shroud geometry with joint Case 6

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3 mm radius filets at joints

WSC_sol3.SLDPRT

airCase 6


Case 6


Case 6

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WSC_sol4.SLDPRT

6 mm radius joints at WSC – Flange- ShroudCase 7

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WSC_sol4.SLDPRT

Case 7

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WSC_sol4.SLDPRT

Case 7

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WSC_sol4.SLDPRT

Case 7

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WSC_sol4.SLDPRT

Case 7


6 mm radius joints with 0.5 mm offset exposureCase 8


Case 8


Case 8


Case 8


Case 8


Surface field at the joint on the flat

Case 8


Case 8


Case 8

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joint type file page Max field on shroud (kV/cm)

1 raised hoop a few cm > Z WSC edge

Air_sh_out_hoop1.SLDPRT 11 6.2

2 knuckle butt joint few cm> Z WSC edge

Air_sh_out_rolled_joint1.SLDPRT 15 4.5

3 knuckle butt joint with 0.5 mm mis-alignment

Air_sh_out_rolled_joint2.SLDPR 19 5.1


WSC_sol.SLDPRT 21 6.2



6 case 5 with double joint at WSC edge 3 mm fillet


7 case 6 with 6mm truncated fillet – Joe Silber design


8 case 6 with 0.5 mm mis-alignment


cases run

best case

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Graded strip E field calculation using SolidWorks Simulator with Thermal Analog – air and dielectric insulator

•Using thermal conductivity to mock dielectric constants and surface temperatures to define conductive surfaces.

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Electric field for a graded structure using thermal analogue

top 2 kV

bottom 0 kV1 kV

0.8 kV0.6 kV

0.4 kV0.2 kV

1 cm

0.3 cm 0.3 cm

dielectric/grade test.SLDASM

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0.0250 cm 0.0254 cm ( 10 mil ) R 0.0050 cm

To simulate conductor, dielectric and air used different values for thermal conductivity. This may or may not be correct, but choose the following values

conductorair

dielectric

air 0.53 W/(mK) to be dielectric constant of 1dielectric 1.749 W/(mK) this is 3.3 times value used for air or dielectric constant of 3.3

i.e. dielectric to be Mylar with dielectric constant of 3.3

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Analysis done both as 3D and 2D. 3D takes ~2 minutes and 2D takes ~ 2 seconds.

1 kV : 1 deg C

dielectric2/grade test2.SLDASM

2D

read Celsius as kV

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1 kV/cm : 1 deg C/cmelectric field strength

2D

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2D

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2D

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2D

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3D

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brand Xnano amp floating

meter

-10 kV supply

brand Xnano amp floating

meter

-10 kV supply

aluminumground plate

24 in square aluminum high voltage plate

shroud insulator material

termination ring

shroud conductor material

rounded anti coronaconnection buttons

shroud testing setup

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15.75 in

quick check of fields in a test structure – design will be improved

A Ross Engineering Toroidwater jetted plate

ground planeshaped button cable connection electrode

20 kV bias

~5.6 cm

The cheaper design for testing using a commercial toroid

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read C/cm as kV/cm

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Tipped toroid connection

top of 3/8 in plate ¾ in below toroid center

plate to floor 5.3 cm

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tipped toroid connection

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can raise toroid to equalize field on disk with plate corner

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6 in radius sphere section

3/8 inch high

1/8 inch hole fillet radius .02 inch

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04/22/2023 62Hot spot is on disk edge for this case with top 7/8 inch below toroid center

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Ross Engineering T201 toroid

21 inch outside diameter3 inch diameter ring

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The T201 is rated for 200 kV

This is a check of this design to see what field they are running with a 200 kV rating.

Calculate the field with toroid far from ground boundaries with a 200 kV bias

The potential is shown here.

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The field strength is shown here.

The maximum field on the surface of the toroid is 20 kV/cm with a 200 kV bias. This is 2/3 of the breakdown field in air.

Ross Engineering T201 toroid biased to 200 kV

Date post:	24-Feb-2016
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Analysis of the voltage hold off between WSC/ESC and inner field cage

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