# Electron Diagnostics for Extreme High Brightness Nano-Blade Field Emission Cathodes

^{1}

^{2}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{2}, h is Planck’s constant, m is the mass of the electron, $\varphi $ is the work function, $\mu $ the Fermi energy of the illuminated material, e is the elementary electron charge, and E is the peak electric field parallel to the surface vector of the material.

^{12}and 10

^{13}W/cm

^{2}, we have peaks fields between 1–3 GV/m. Now to account for the blade rather than planar geometry we consider a calculation of electric field enhancements that one would obtain from the boundary conditions of the blade geometry. Using finite difference time domain (FDTD) simulations, we compute a factor of five increase of peak fields for an 800 nm pulse. We thus expect peak fields in the range 5–15 GV/m.

#### 2.1. Detectors

^{7}gain [14]. They are also able to be spatially resolved on the phosphor screen to be imaged with a CCD camera and also rough measurements of charge.

#### 2.2. Einzel Lens

#### Filtering Apparatus

#### 2.3. Hemispherical Deflection Analyzer

#### 2.4. Simulation

## 3. Results

^{12}W/cm

^{2}.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Scanning electron microscope (SEM) images of double-blade gold-coated silicon samples. (

**a**) Photo at 100 micron scale and 45 degrees relative to the longitudinal direction. (

**b**) Photo of transverse cross section at 100 nm scale. Note the lighter contrast corresponds to ≈15 nm thick gold coating.

**Figure 2.**${E}_{x}$ component of field enhancement for 800 nm pulse on gold coated blade using finite difference time domain (FDTD) simulations.

**Figure 3.**Plot of numbers of electrons emitted as a function of laser intensity in simplified model using Equation (1).

**Figure 4.**General optics table geometry involved in nano-blade illumination experiments before adding electron diagnostics.

**Figure 5.**Focusing in a generic three-cylinder einzel lens. Blue solid objects are cross sections of the three cylindrical electrodes; red tracks are full trajectories of every 100th electron in the simulation; green contours represent equipotentials which are solved numerically.

**Figure 7.**Electron emission from tungsten coated blades from multiple trials as measured by retarding field spectrometer for both tungsten and gold coated blades.

**Figure 8.**Electron emission as a function of polarization of incident light relative to the surface normal vector of the blade surface. Measurements performed at 6 × 10

^{12}W/cm

^{2}.

**Figure 9.**Schematic drawing of the electron spectrometer, including its three main components: einzel lens, HDA, and multichannel plate (MCP) detector.

**Figure 12.**Focusing in three different kinds of einzel lenses. It is clear that the two asymmetrical designs result in a tighter focus.

**Figure 13.**Energy preservation in three different kinds of einzel lenses. It is clear on the graph that the two asymmetrical designs result in less energy loss compared with the standard design.

**Table 1.**Simulated electron spectrometer figures of merit for machined geometry with real specifications compared with simplified geometry and no fringing fields which represents the upper bound on performance. Hemispherical deflection analyzer (HDA).

HDA Property | Ideal | Simulated |
---|---|---|

Calibration factor | ≈1.59 | ≈1.25 |

Magnification | 1 | ≈0.80 |

Acceptance angle | 0 | 13.75 |

Transmission efficiency | 100% | 80.9% ± 3.7% |

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## Share and Cite

**MDPI and ACS Style**

Lawler, G.; Sanwalka, K.; Zhuang, Y.; Yu, V.; Paschen, T.; Robles, R.; Williams, O.; Sakai, Y.; Naranjo, B.; Rosenzweig, J. Electron Diagnostics for Extreme High Brightness Nano-Blade Field Emission Cathodes. *Instruments* **2019**, *3*, 57.
https://doi.org/10.3390/instruments3040057

**AMA Style**

Lawler G, Sanwalka K, Zhuang Y, Yu V, Paschen T, Robles R, Williams O, Sakai Y, Naranjo B, Rosenzweig J. Electron Diagnostics for Extreme High Brightness Nano-Blade Field Emission Cathodes. *Instruments*. 2019; 3(4):57.
https://doi.org/10.3390/instruments3040057

**Chicago/Turabian Style**

Lawler, Gerard, Kunal Sanwalka, Yumeng Zhuang, Victor Yu, Timo Paschen, River Robles, Oliver Williams, Yusuke Sakai, Brian Naranjo, and James Rosenzweig. 2019. "Electron Diagnostics for Extreme High Brightness Nano-Blade Field Emission Cathodes" *Instruments* 3, no. 4: 57.
https://doi.org/10.3390/instruments3040057