^{1}, He Zhang

^{1}, P. M. Duxbury

^{1}, Martin Berz

^{1}and Chong-Yu Ruan

^{1,a)}

### Abstract

Understanding space charge effects is central for the development of high-brightness ultrafast electron diffraction and microscopy techniques for imaging material transformation with atomic scale detail at the fs to ps timescales. We present methods and results for direct ultrafast photoelectron beam characterization employing a shadow projection imaging technique to investigate the generation of ultrafast, non-uniform, intense photoelectron pulses in a dc photo-gun geometry. Combined with N-particle simulations and an analytical Gaussian model, we elucidate three essential space-charge-led features: the pulse lengthening following a power-law scaling, the broadening of the initial energy distribution, and the virtual cathode threshold. The impacts of these space charge effects on the performance of the next generation high-brightness ultrafast electron diffraction and imaging systems are evaluated.

We acknowledge fruitful discussions with K. Chang, K. Makino, M. Doleans, and A. M. Michalik. This work was supported by the DOE under grant DE-FG02-06ER46309 and by a seed grant for the development of a RF-enabled ultrafast electron microscope from the MSU Foundation.

I. INTRODUCTION

II. MEASUREMENT OF SPATIAL AND TEMPORAL EVOLUTION OF PHOTO- ELECTRON PULSES

III. THE SPACE CHARGE EFFECTS AND MODELING

A. Fractional power-law dependence in the space-charge-led pulse lengthening

B. Density-dependent broadening of initial electron velocity distribution

C. Three step model of photoemission

D. Space-charge limitation of pulsed photoemission quantum yield

E. The effect of multi-photon photoemission

IV. SPACE AND TIME RESOLUTIONS IN ULTRAFAST ELECTRON DIFFRACTION AND IMAGING SYSTEMS

### Key Topics

- Space charge effects
- 44.0
- Photoemission
- 31.0
- Cathodes
- 20.0
- Phase space methods
- 20.0
- Electron diffraction
- 10.0

## Figures

(Color online) Electron point-projection imaging technique and results. (a) Schematic of the experiment. For illustration purposes, the angular span of the shadow is significantly increased from typical values ≤1 mrad. For this reason, the projection is nearly linear. (b) The snap-shots of the normalized shadow images at selected times. The magnification of the projection imaging is ≈33.

(Color online) Electron point-projection imaging technique and results. (a) Schematic of the experiment. For illustration purposes, the angular span of the shadow is significantly increased from typical values ≤1 mrad. For this reason, the projection is nearly linear. (b) The snap-shots of the normalized shadow images at selected times. The magnification of the projection imaging is ≈33.

(Color online) The results of electron point-projection imaging. (a) The CoM frame expansion dynamics of electron pulses with longitudinal pulse length σ_{ z }. The solid lines through the experimental data (symbols) are from N-particle simulations. (b) Dependence of pulse length on the electron sheet density at time 100 ps for various F and *F* _{ a } settings, showing a universal power-law increase with exponent roughly γ = 0.5. Predictions based on mean-field (Ref. 3) and one-dimensional (1D) fluid (Ref. 29) models are also presented.

(Color online) The results of electron point-projection imaging. (a) The CoM frame expansion dynamics of electron pulses with longitudinal pulse length σ_{ z }. The solid lines through the experimental data (symbols) are from N-particle simulations. (b) Dependence of pulse length on the electron sheet density at time 100 ps for various F and *F* _{ a } settings, showing a universal power-law increase with exponent roughly γ = 0.5. Predictions based on mean-field (Ref. 3) and one-dimensional (1D) fluid (Ref. 29) models are also presented.

(Color online) (a) The symbols represent the values of γ found at different delay times. The solid line represents results from an analytical Gaussian model (AGM) simulation using broadened initial longitudinal velocity spread due to near cathode space charge effect extracted by fitting the early time σ_{z} trajectory, which is presented in Fig. 4(c) and the text. (b) The symbols are the linescans of the shadow images recorded on the phosphor/CCD screen produced by photoelectrons (Σ = 7.12 × 10^{13} e/m^{2}) at different times. The linescans are fitted with a Gaussian profile (solid lines). A top-hat profile (dashed line), convoluted with the projection geometry, is also drawn for comparison. The magnification of the projection imaging is ≈33.

(Color online) (a) The symbols represent the values of γ found at different delay times. The solid line represents results from an analytical Gaussian model (AGM) simulation using broadened initial longitudinal velocity spread due to near cathode space charge effect extracted by fitting the early time σ_{z} trajectory, which is presented in Fig. 4(c) and the text. (b) The symbols are the linescans of the shadow images recorded on the phosphor/CCD screen produced by photoelectrons (Σ = 7.12 × 10^{13} e/m^{2}) at different times. The linescans are fitted with a Gaussian profile (solid lines). A top-hat profile (dashed line), convoluted with the projection geometry, is also drawn for comparison. The magnification of the projection imaging is ≈33.

(Color online) (a) The normalized “initial” longitudinal phase space employed in the N- particle simulations, which is parameterized by a thermal parameter a and scaled by the initial length σ_{ zi } and momentum spread σ_{ pz }. (b) The percentage change in the pulse length σ_{ z } obtained at 100 ps as a function of a. (c) The initial longitudinal velocity spread, Δ*υ* _{ z }(t = 0), obtained by fitting N-particle trajectories to the imaging data depicted in Fig. 2(a). The extraction field *F* _{ a } applied is 0 at the five lowest Σs, 0.32 MV/m at 40 × 10^{12} e/m^{2} and at 70 × 10^{12} e/m^{2}.

(Color online) (a) The normalized “initial” longitudinal phase space employed in the N- particle simulations, which is parameterized by a thermal parameter a and scaled by the initial length σ_{ zi } and momentum spread σ_{ pz }. (b) The percentage change in the pulse length σ_{ z } obtained at 100 ps as a function of a. (c) The initial longitudinal velocity spread, Δ*υ* _{ z }(t = 0), obtained by fitting N-particle trajectories to the imaging data depicted in Fig. 2(a). The extraction field *F* _{ a } applied is 0 at the five lowest Σs, 0.32 MV/m at 40 × 10^{12} e/m^{2} and at 70 × 10^{12} e/m^{2}.

(Color online) The symbols represent the experimental longitudinal pulse length (σ_{ z }) of the photoelectron pulses with different densities tracked at different times. The solid line represents the analytical Gaussian model simulation using the different initial longitudinal velocity spread specified by Fig. 4(c) and the initial slope of phase space set to 0. The dotted line represents the analytical Gaussian model simulation using a constant initial longitudinal velocity spread Δ*υ* _{ z }(Δt = 0) = 0.084 μm/ps.

(Color online) The symbols represent the experimental longitudinal pulse length (σ_{ z }) of the photoelectron pulses with different densities tracked at different times. The solid line represents the analytical Gaussian model simulation using the different initial longitudinal velocity spread specified by Fig. 4(c) and the initial slope of phase space set to 0. The dotted line represents the analytical Gaussian model simulation using a constant initial longitudinal velocity spread Δ*υ* _{ z }(Δt = 0) = 0.084 μm/ps.

(Color online) Momentum cut model for selecting electrons for photoemission used in the three step model. (a) The electron energy distribution before and after photoexcitation. In this model, the electrons are assumed to escape the cathode surface before thermalization and thus have the same Fermi-Dirac (FD) energy spread (exaggerated for illustration purpose) defined at the temperature prior to photoemission. The shaded area (E ≥ E_{ F } + Φ_{ eff }) represents the electron population that is qualified for photoemission. (b) The selection of electrons in the three-dimensional momentum phase space that are qualified for photoemission. The electron must have an energy larger than E_{ F } + Φ_{ eff }, as described in (a); it must also have a minimum longitudinal momentum () to overcome the work function in order to escape the surface, as specified by the shaded area.

(Color online) Momentum cut model for selecting electrons for photoemission used in the three step model. (a) The electron energy distribution before and after photoexcitation. In this model, the electrons are assumed to escape the cathode surface before thermalization and thus have the same Fermi-Dirac (FD) energy spread (exaggerated for illustration purpose) defined at the temperature prior to photoemission. The shaded area (E ≥ E_{ F } + Φ_{ eff }) represents the electron population that is qualified for photoemission. (b) The selection of electrons in the three-dimensional momentum phase space that are qualified for photoemission. The electron must have an energy larger than E_{ F } + Φ_{ eff }, as described in (a); it must also have a minimum longitudinal momentum () to overcome the work function in order to escape the surface, as specified by the shaded area.

(Color online) (a) The photoelectron velocity spread in the longitudinal (Δ*υ* _{ L }) and transverse (Δ*υ* _{ T }) directions. The solid symbols represent results obtained using N-particle simulation, and the hollow symbols represents results obtained by integrating the analytical equation reported in Ref. 39. (b) The longitudinal velocity distribution of photoelectrons generated by N-particle simulation based on the three step model.

(Color online) (a) The photoelectron velocity spread in the longitudinal (Δ*υ* _{ L }) and transverse (Δ*υ* _{ T }) directions. The solid symbols represent results obtained using N-particle simulation, and the hollow symbols represents results obtained by integrating the analytical equation reported in Ref. 39. (b) The longitudinal velocity distribution of photoelectrons generated by N-particle simulation based on the three step model.

(Color online) (a) Schematic of an extended three step model for intense photoemission. The net work function Φ′ is the sum of the Schottky potential Φ_{ Sch }, the surface dipole potential Φ_{ dp }, and the intrinsic work function Φ_{ w }. (b) The quantum efficiency derived based on modified TSM (dashed line) for Φ_{ w } = 4.26 eV and the experimental data with a fit to a constant behavior at low field and a linear behavior at high field. (Inset) The electron escape ratio, *R* _{ esp }, is calculated, including the dipole field of the virtual cathode and its image for Φ_{ w } = 4.26 eV. (c) Electron pulse sheet density as a function of fluence for high applied field and for zero applied field (inset).

(Color online) (a) Schematic of an extended three step model for intense photoemission. The net work function Φ′ is the sum of the Schottky potential Φ_{ Sch }, the surface dipole potential Φ_{ dp }, and the intrinsic work function Φ_{ w }. (b) The quantum efficiency derived based on modified TSM (dashed line) for Φ_{ w } = 4.26 eV and the experimental data with a fit to a constant behavior at low field and a linear behavior at high field. (Inset) The electron escape ratio, *R* _{ esp }, is calculated, including the dipole field of the virtual cathode and its image for Φ_{ w } = 4.26 eV. (c) Electron pulse sheet density as a function of fluence for high applied field and for zero applied field (inset).

(Color online) Concept of an electron beam injector column for ultrafast electron microscope demonstrated using an N-particle simulation of electron pulse propagation in an electron beam column with an RF cavity. (a) Phase space adjustment before and after the RF cavity. (b) The corresponding real space pulse profile at each electron optical components. The simulation is performed using 10^{4} electrons per pulse at 30 keV using the initial condition *a* = 1, as specified in Fig. 4(a).

(Color online) Concept of an electron beam injector column for ultrafast electron microscope demonstrated using an N-particle simulation of electron pulse propagation in an electron beam column with an RF cavity. (a) Phase space adjustment before and after the RF cavity. (b) The corresponding real space pulse profile at each electron optical components. The simulation is performed using 10^{4} electrons per pulse at 30 keV using the initial condition *a* = 1, as specified in Fig. 4(a).

(Color online) (a) Space-charge-limited temporal resolutions in ultrafast electron diffraction (UED) and microscopy (UEM) systems. Solid squares and hollow diamonds show the Coulomb-explosion-led pulse lengthening calculated for 100 keV UEM system (squares) with cathode-to-sample distance of 70 cm and 30 keV UED system (diamonds) with cathode-to-sample distance of 5 cm. The rectangular shaded areas depict experimental resolutions reported in current UED and UEM systems. In comparison, the solid stars and circles show the improvements in temporal resolution by employing an RF recompression in the UEM beam column (see panel (b)) optimized for nano-area diffractive imaging (stars) and for single-shot UED (circles). (b) Photoelectron pulse trajectory along an RF-enabled UEM column. The shaded regions represent the locations of the electron optical elements. (c) A scale-up view of the pulse profiles near the sample plane for nano-area diffractive imaging containing 10^{5} electrons/pulse. An aperture with radius of 15 μm is employed to thin out the peripheral electrons to achieve a divergence angle α ≤ 1.7 mrad. The minimum transverse radius σ_{ T } is 0.64 μm, and the minimum longitudinal pulse length σ_{L} is 0.80 μm. (d) A scale-up view of the pulse profiles near the sample plane for an ultrafast single-shot UED containing 10^{8} electrons/pulse. The minimum transverse radius σ_{T} is 51 μm, and the minimum longitudinal pulse length σ_{L} is 0.88 μm.

(Color online) (a) Space-charge-limited temporal resolutions in ultrafast electron diffraction (UED) and microscopy (UEM) systems. Solid squares and hollow diamonds show the Coulomb-explosion-led pulse lengthening calculated for 100 keV UEM system (squares) with cathode-to-sample distance of 70 cm and 30 keV UED system (diamonds) with cathode-to-sample distance of 5 cm. The rectangular shaded areas depict experimental resolutions reported in current UED and UEM systems. In comparison, the solid stars and circles show the improvements in temporal resolution by employing an RF recompression in the UEM beam column (see panel (b)) optimized for nano-area diffractive imaging (stars) and for single-shot UED (circles). (b) Photoelectron pulse trajectory along an RF-enabled UEM column. The shaded regions represent the locations of the electron optical elements. (c) A scale-up view of the pulse profiles near the sample plane for nano-area diffractive imaging containing 10^{5} electrons/pulse. An aperture with radius of 15 μm is employed to thin out the peripheral electrons to achieve a divergence angle α ≤ 1.7 mrad. The minimum transverse radius σ_{ T } is 0.64 μm, and the minimum longitudinal pulse length σ_{L} is 0.80 μm. (d) A scale-up view of the pulse profiles near the sample plane for an ultrafast single-shot UED containing 10^{8} electrons/pulse. The minimum transverse radius σ_{T} is 51 μm, and the minimum longitudinal pulse length σ_{L} is 0.88 μm.

## Tables

Location of electron optical components in the UEM column.

Location of electron optical components in the UEM column.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content