# Development of High-Voltage Electrodes for Neutron Scattering Sample Environment Devices

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## Abstract

**:**

## 1. Introduction

## 2. Electric Field Modeling

## 3. Electrode Profile

_{0}(Figure 1). The second part is sinusoidal with a radial extension distance of A (distance from the endpoint of the plane area to the center of the circular part), terminated in a circular part with a radius of R

_{e}. Each section needs to tangentially merge into the next. The smoothness and specifications of each section, however, need to be further confirmed and improved through simulations. It has to be mentioned that field uniformity also significantly relies on the ratio between the overall diameter (D) and gap distance of electrodes (d) [22].

_{e}and X

_{0}must be defined as follows [33]:

_{0}) was selected as 40 mm for the subsequent simulations. Previous studies on the surface field distribution of electrodes confirmed that a uniform field intensity distribution could be obtained when the electrode thickness was maintained equal to or more than twice the nominal gap spacing [33]. Therefore, the gap spacing (d) in the simulations is always half of the electrode thickness (T) for saving space. From Equations (11) and (12), one can see that R and T are both highly related to A and α. The smaller the characteristic angle in the sinusoidal region, the smaller the T and R, leading to a smaller interval. Otherwise, a much bigger gap distance between the electrodes will be required when the characteristics angle of the sinusoidal section is increased. The space for integrating other modules or coupling with other conditions will be significantly limited in that case. Five potential electrodes with various geometries were examined with respect to the uniformity and strength of the electric field (Table 1).

## 4. Electric Field Simulation

^{6}Siemens/m due to a much higher breakdown voltage. Polyether ether ketone (PEEK) with an ${\epsilon}_{r}$ of 3.1 and a bulk conductivity of 10 × 10

^{7}Siemens/m was applied as the electrode support because of its high temperature resistance and good insulation performance. All parameters of the applied materials in the simulation are listed in Table 2.

## 5. Results and Discussion

#### 5.1. Electric Field Distribution

#### 5.2. Effect of Electrode Geometries on Field Intensity and Uniformity

^{5}V/m (Model A), and as the electrode gap distance increases, the field strength gradually decreases to 2.89 × 10

^{5}V/m (Model E). A homogenous field along the line can be achieved within a specified region in each model, but the region size and the achievable strength vary with the geometry.

#### 5.3. Effect of Chamber Size on Field Strength

## 6. Electrode Applications for High-Voltage Sample Environmental Devices

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sectional schematic diagram of the Bruce electrode [32].

**Figure 2.**SolidWorks 3D modeling (

**Left**), ANSYS Maxwell 2D model (

**Middle**), and the calculation domain (

**Right**) for the simulation of electrodes.

**Figure 4.**Field strength distribution of (

**a**) Model A, (

**b**) Model B, (

**c**) Model C, (

**d**) Model D, and (

**e**) Model E, and (

**f**) the variation in field strength along the black line in Model E for all five models.

**Figure 5.**(

**a**) Selected positions of Model E (39 mm gap spacing) for field strength comparisons; (

**b**) field strength along the surface of the top electrode and the center of the gap between the electrodes, respectively; (

**c**) field strength along the gap axis (from top to bottom) in various sections; and (

**d**) the zoomed version of (

**c**).

**Figure 6.**Field strength distribution between the electrodes of Model E when a chamber with a diameter (minimum distance between upper electrode edge and chamber shell) of (

**a**) 450 (70), (

**b**) 500 (95), (

**c**) 550 (120), (

**d**) 600 (145), and (

**e**) 650 (170) mm is applied, and (

**f**) the strength curves of the electrodes obtained along the black line in Figure 4e.

**Figure 7.**(

**a**) Field intensity distribution along the line on the upper electrode surface shown in Figure 5a and (

**b**) plot of maximum field strength as a function of the minimum distance between upper electrode edge and chamber shell.

**Table 1.**Specifications of Bruce electrode geometries. Notes: R

_{0}: Radius of the plane area; α: Characteristic angle of the sinusoidal section; A: Distance from the plane section to the center of the circle section; D: Overall diameter of electrodes; T: Electrode thickness; R

_{e}: Circle radius; d: Electrode nominal gap spacing.

Model | R_{0}/mm | α/° | A/mm | D/mm | T/mm | R_{e}/mm | d/mm |
---|---|---|---|---|---|---|---|

A | 40 | 40 | 15 | 130 | 23 | 10 | 11.5 |

B | 40 | 45 | 15 | 137 | 28 | 13.5 | 14 |

C | 40 | 50 | 19 | 162 | 45 | 22 | 22.5 |

D | 40 | 55 | 20 | 184 | 60 | 32 | 30 |

E | 40 | 60 | 20 | 208 | 78 | 44 | 39 |

Parameters | Anode (Aluminum) | Cathode (Aluminum) | Vacuum | Electrode Support (PEEK) | Vacuum Chamber (Stainless Steel) |
---|---|---|---|---|---|

Relative permittivity (${\epsilon}_{r}$) | 1 | 1 | 1 | 3.1 | 1 |

Conductivity (Siemens/m) | 38 × 10^{6} | 38 × 10^{6} | 0 | 10 × 10^{7} | 11 × 10^{5} |

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**MDPI and ACS Style**

Sun, G.; Guo, T.; Yuan, B.; Yang, X.; Wang, G.
Development of High-Voltage Electrodes for Neutron Scattering Sample Environment Devices. *Instruments* **2024**, *8*, 26.
https://doi.org/10.3390/instruments8020026

**AMA Style**

Sun G, Guo T, Yuan B, Yang X, Wang G.
Development of High-Voltage Electrodes for Neutron Scattering Sample Environment Devices. *Instruments*. 2024; 8(2):26.
https://doi.org/10.3390/instruments8020026

**Chicago/Turabian Style**

Sun, Guoliang, Tingting Guo, Bao Yuan, Xiaojing Yang, and Guang Wang.
2024. "Development of High-Voltage Electrodes for Neutron Scattering Sample Environment Devices" *Instruments* 8, no. 2: 26.
https://doi.org/10.3390/instruments8020026