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Design Methodology for High Voltage Insulators Including Effects of Surface Charging

Design Methodology for High Voltage Insulators Including Effects of Surface ChargingRobert TresederEngineering Manager

James BoyeSenior Engineer

Varian Medical SystemsX-ray Products


History of X-ray Generation

In 1913, William Coolidge invented an x-ray tube with high vacuum, a heated filament as electron source, and an x-ray producing anode. The tube, shown here, was produced in the 1920s by General Electric Corporation.

Photo: www.orau.org Oak Ridge Associated Universities



Early x-ray equipment posed risk of high voltage shock and unregulated x-ray dose.



Photo: www.orau.org Oak Ridge Associated Universities

Starting in the mid-1930s, x-ray tubes began to employ a rotating anode to spread the heat created by the electron beam.



Shown here are typical metal-centered tubes for mammography and medical CT.

In the 1980s Varian pioneered the metal-centered x-ray tube. Replacing the glass bulb with a metal frame results in a tube able to withstand the stresses of modern medical equipment.



Modern CT gantries spin at 2~3 revolutions/second. The imaging system rotates around the patient providing several thousand views per revolution for 3-D image reconstruction. Each view uses grayscale data from as many as 50,000 x-ray detectors.



In the 1990s, engineers at Varian, working with a major OEM customer, developed an x-ray tube with capabilities needed for the next generation of medical CT scanners.

The entire tube, with the exception of a ceramic high voltage insulator, is metal and at ground potential. This results in more efficient tube cooling, ability to withstand high G forces in the CT gantry, and superior high voltage stability.


X-ray Tube High Voltage Insulator

Insulator roles:

•High voltage stand-off

•Vacuum wall

•Structural support

•Heat conduction


The Old Way to Design

Solving Poisson’s equation in the region of interest to determine the maximum electric field strength was simple enough, but gave misleading results. Many physical effects were ignored –such as surface charging.


The OBC (Oblique Boundary Condition) Method

• Assumes that a unique, steady-state solution to the surface charging problem exists.

• Describes the conditions that must be present at steady-state.

• Ignores the details of surface charging.

• Assumes that secondary electrons “hop” along the surface of the insulator. from Zwart, et.al. Basics of

Electron Transport over Insulators, Philips J. Res. 50 (1996) 307-335.



• Ratio of the perpendicular to normal electric field depends on material properties only.

from Zwart, et.al. Basics of Electron Transport over Insulators, Philips J. Res. 50 (1996) 307-335.



3

1 (4)4

v S

dv r dSr r r

ϕϕ ρ ϕπε

′ ′ ′∇ ′ ′= + − ⋅ ∫ ∫rr rGeneral potential solution with surface

BCs and volume charges:

Divide the charge surface into a finite number of small areas: 1

(5)N

n nn

ρ α ρ=

=∑

Each small area (n=1 to N) will contribute to the potential solution:

1 (6)4

nn n

Sv

dv dSr r

ϕϕ ρπε

′ ′′ ∇ = + ⋅ ∫ ∫r

r

The n=0 load case is subject to BCspresent with no charges absent:

00 0 3 (7)

S

r dSr r

ϕϕ ϕ ′′∇′= − ⋅ ∫

rr r



The total solution is the sum of the N+1 load cases previously defined:

01

(8)N

n nn

ϕ ϕ α ϕ=

= +∑

The charge weights (αn) can be positive or negative depending if positive or negative charge is needed to force the required relationship between the normal and tangential electric field on the surface.



( )1

0 0 (13)F F F Fρ ρα µ µ−⊥ ⊥ = − − ⋅ −

For each load case, ANSYS calculates the electric fields, APDL commands write the F vectors to a text file. An external program calculates the charge weights. This program outputs the weights in the form of ANSYS SFE commands on element edges.

The OBC solution is a load superposition of the N+1 cases:

0

0

(14 )

(14 )

F F F a

F F F bρ

ρ

α

α

⊥ ⊥ ⊥= + ⋅

= + ⋅


Enloe Diode Test Case

2-D plane parallel cathode and anode surfaces with the vacuum gap partially filled with a dielectric insulator.

C.L. Enloe, “The equilibrium charge distribution and electric field at a vacuum/dielectric interface” J. Appl. Phys. Vol 65, No 9, pp3329-3334, 1989.



Good agreement with Enloe with regards to the computed potential along the dielectric surface without charging…



… and with surface charging.


Brainard and Jensen ‘Neutron Tube’Test Case

J.P. Brainard and D. Jensen, “Electron avalanche and surface charging on alumina insulators during pulsed high-voltage stress” J. Appl. Phys. Vol 45, No 8, pp3260-3265, 1974.

Electric fields in a neutron tube with ceramic insulator subject to surface charging.



Comparison of results:

charged

uncharged



Comparison of results: charge density


High Voltage Ceramic Design Tool

Vertical application developed jointly with EnductiveSolutions to design and analyze high voltage insulating systems for x-ray tubes



•Create model within the SolidWorksenvironment



•Launch design tool

•Define analysis type



•Assign materials

•Assign BC types and values



Create files for ANSYS:

•Materials file

•SolidWorksassembly file

•ANSYS input command file

•IGES solid model file

Launch ANSYS


Flat High Voltage Ceramic Design Case

•Axisymmetric geometry

•Inner electrode at cathode (negative) potential

•Outer electrode at ground potential

•Electrostatic solution, with and without surface charging

•Electrical conduction solution



Critical-to-design metrics:

1. Normal electric field on any cathode surface.

2. Maximum electric field in the cable.

3. Tangential electric field along the vacuum side of the alumina insulator.



Electrostatic solution equipotentials, with and without charging



Conduction solution equipotentials



Charge distribution along the vacuum side of the alumina insulator



Voltage and tangential field along the alumina surface for the three analysis types.


Conclusions

• Presence of surface charge on the vacuum side of the insulator will significantly alter the critical-to-design electric field metrics.

• OBC method for estimating the surface charge is in good agreement with published test cases.

• The vertical application developed jointly by Varian Medical Systems and EnductiveSolutions using the OBC method and the ANSYS solver is an easy-to-use, practical design tool.


Thank You

www.varian.com/xray

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