Design Methodology for High Voltage Insulators Including Effects of Surface Charging

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1 Design Methodology for High Voltage Insulators Including Effects of Surface Charging Robert Treseder Engineering Manager James Boye Senior Engineer Varian Medical Systems X-ray Products

2 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: Oak Ridge Associated Universities

3 History of X-ray Generation Early x-ray equipment posed risk of high voltage shock and unregulated x- ray dose.

4 History of X-ray Generation Starting in the mid-1930s, x-ray tubes began to employ a rotating anode to spread the heat created by the electron beam. Photo: Oak Ridge Associated Universities

5 History of X-ray Generation Shown here are typical metalcentered tubes for mammography and medical CT. In the 1980s Varian pioneered the metalcentered x-ray tube. Replacing the glass bulb with a metal frame results in a tube able to withstand the stresses of modern medical equipment.

6 History of X-ray Generation 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.

7 History of X-ray Generation 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.

8 X-ray Tube High Voltage Insulator Insulator roles: High voltage stand-off Vacuum wall Structural support Heat conduction

9 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.

10 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)

11 The OBC (Oblique Boundary Condition) Method 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)

12 The OBC (Oblique Boundary Condition) Method General potential solution with surface BCs and volume charges: r r 1 dv ϕ r ϕ = ρ + ϕ ds 4πε v r 3 r r r S (4) Divide the charge surface into a finite number of small areas: N ρ = αnρn n= 1 (5) Each small area (n=1 to N) will contribute to the potential solution: r r S v 1 dv ϕ n ϕn = ρn ds 4πε + r r (6) The n=0 load case is subject to BCs present with no charges absent: ϕ r ϕ0 0 = ϕ 0 ds (7) 3 r r S r r r

13 The OBC (Oblique Boundary Condition) Method The total solution is the sum of the N+1 load cases previously defined: N = 0 + n= 1 ϕ ϕ α ϕ n n (8) The charge weights (α n ) 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.

14 The OBC (Oblique Boundary Condition) Method 1 ( ) α = Fρ µ F ρ F0 µ F0 (13) 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: F = F + F α (14 a) 0 0 ρ F = F + F α (14 b) ρ

15 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, pp , 1989.

16 Enloe Diode Test Case Good agreement with Enloe with regards to the computed potential along the dielectric surface without charging

17 Enloe Diode Test Case and with surface charging.

18 Brainard and Jensen Neutron Tube Test Case Electric fields in a neutron tube with ceramic insulator subject to surface charging. 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, pp , 1974.

19 Brainard and Jensen Neutron Tube Test Case Comparison of results: charged uncharged

20 Brainard and Jensen Neutron Tube Test Case Comparison of results: charge density

21 High Voltage Ceramic Design Tool Vertical application developed jointly with Enductive Solutions to design and analyze high voltage insulating systems for x-ray tubes

22 High Voltage Ceramic Design Tool Create model within the SolidWorks environment

23 High Voltage Ceramic Design Tool Launch design tool Define analysis type

24 High Voltage Ceramic Design Tool Assign materials Assign BC types and values

25 High Voltage Ceramic Design Tool Create files for ANSYS: Materials file SolidWorks assembly file ANSYS input command file IGES solid model file Launch ANSYS

26 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

27 Flat High Voltage Ceramic Design Case 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.

28 Flat High Voltage Ceramic Design Case Electrostatic solution equipotentials, with and without charging

29 Flat High Voltage Ceramic Design Case Conduction solution equipotentials

30 Flat High Voltage Ceramic Design Case Charge distribution along the vacuum side of the alumina insulator

31 Flat High Voltage Ceramic Design Case Voltage and tangential field along the alumina surface for the three analysis types.

32 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 Enductive Solutions using the OBC method and the ANSYS solver is an easy-to-use, practical design tool.

33 Thank You