^{1}, K. Haupt

^{1}, N. Erasmus

^{1}, E. G. Rohwer

^{1}and H. Schwoerer

^{1,a)}

### Abstract

We have designed a femtosecond electron gun suitable for ultrafast electron diffraction experiments, operating in the 30–100 kV regime. The concept is based on recompression of chirped expanding electron pulses emitted from a direct current photogun using a novel dispersion-corrected reflectron concept. We show, using detailed numerical simulations, that our design is capable of producing electron pulses containing 200 000 electrons with a full width at half maximum pulse duration of 130 fs, a root mean squared (rms) pulse radius of , and transverse coherence length of 1.5 nm at 100 kV. Our analysis includes the bunch properties at the sample, as well as interactions of the main pulse of high charge density with diffracted electrons. Since our design employs only static electron optics, we believe that it will be easier to implement than concepts based on radio frequency compression.

We thank Klaus Floetmann (DESY) for his help with the ASTRA code and Anton du Plessis (CSIR) for fruitful discussions on time of flight spectroscopy. This work is based on research supported by the South African Research Chairs Initiative of the Department of Science and Technology and the National Research Foundation.

I. INTRODUCTION

II. ELECTRON BEAM PARAMETERS

III. REFLECTRON BUNCH COMPRESSION SETUP FOR UED

A. Setup overview

B. Reflectron compression

C. Bending magnets

D. Simulation detail

1. Electric and magnetic fields

2. Particle simulation

IV. RESULTS AND DISCUSSION

A. Bunch parameters

B. Postsample signal distortions

C. Practical considerations and stability

V. CONCLUSION

### Key Topics

- Coherence
- 21.0
- Magnets
- 20.0
- Space charge effects
- 13.0
- Electron diffraction
- 11.0
- Femtosecond dynamics
- 9.0

## Figures

Schematic of the proposed femtosecond electron gun employing a dispersion-compensated reflectron bunch compressor. The bunch is predispersed by a pair of bending magnets and with bending angle and a separation distance . A reflectron of length and inclination angle to the horizontal reflects and compresses the pulse onto the sample with incident angle . Typical electron pulse shapes at various points in the setup are also shown. At the sample, the pulse front is tilted relative to the propagation direction by a few degrees as seen by the blowup in the figure. The shortest pulse width occurs in a direction normal to the tilt plane.

Schematic of the proposed femtosecond electron gun employing a dispersion-compensated reflectron bunch compressor. The bunch is predispersed by a pair of bending magnets and with bending angle and a separation distance . A reflectron of length and inclination angle to the horizontal reflects and compresses the pulse onto the sample with incident angle . Typical electron pulse shapes at various points in the setup are also shown. At the sample, the pulse front is tilted relative to the propagation direction by a few degrees as seen by the blowup in the figure. The shortest pulse width occurs in a direction normal to the tilt plane.

(a) Illustration of the chirp-inverting effect of a reflectron with potential , length , and electric field . The incident pulse with fast (blue) electrons of momentum at point b in front and slower (red) electrons of momentum at point at the back is reversed in both direction and chirp. The initial and final pulse durations are denoted by and , respectively. (b) Dispersion of the pulse entering the reflectron at an angle. Faster electrons travel further parallel and perpendicular to the -direction. (c) Dispersion due to a pair of bending magnets. Slower electrons undergo a larger deflection.

(a) Illustration of the chirp-inverting effect of a reflectron with potential , length , and electric field . The incident pulse with fast (blue) electrons of momentum at point b in front and slower (red) electrons of momentum at point at the back is reversed in both direction and chirp. The initial and final pulse durations are denoted by and , respectively. (b) Dispersion of the pulse entering the reflectron at an angle. Faster electrons travel further parallel and perpendicular to the -direction. (c) Dispersion due to a pair of bending magnets. Slower electrons undergo a larger deflection.

Geometry and potential lines of the 54 mm reflectron. The electron bunch enters and exits the reflectron at the entry opening on the ground pole side (see also Fig. 1) and turns around at the negative pole. The geometry differs slightly from the reflectron depicted in Fig. 1 in that only one entry opening has been simulated.

Geometry and potential lines of the 54 mm reflectron. The electron bunch enters and exits the reflectron at the entry opening on the ground pole side (see also Fig. 1) and turns around at the negative pole. The geometry differs slightly from the reflectron depicted in Fig. 1 in that only one entry opening has been simulated.

rms pulse radius and rms temporal duration vs propagation distance for the 30 kV (solid lines) and 100 kV (dotted lines) designs. Pulse duration values are calculated assuming a constant bunch center velocity corresponding to 30 and 100 kV for the respective pulses. The position of the solenoid lenses, the reflectron, and the temporal foci are shown.

rms pulse radius and rms temporal duration vs propagation distance for the 30 kV (solid lines) and 100 kV (dotted lines) designs. Pulse duration values are calculated assuming a constant bunch center velocity corresponding to 30 and 100 kV for the respective pulses. The position of the solenoid lenses, the reflectron, and the temporal foci are shown.

Current density vs time profiles of (a) the 30 keV pulse containing 50 000 electrons and (b) the 100 keV pulse containing 200 000 electrons at the temporal focus. The FWHM pulse duration as well as the percentage of electrons contained therein are also shown. The current density profiles have been calculated relative to an optimal fitting plane that is slightly tilted with respect to the plane. The front and side profiles of the 30 keV pulse is seen in (c) and (d), respectively.

Current density vs time profiles of (a) the 30 keV pulse containing 50 000 electrons and (b) the 100 keV pulse containing 200 000 electrons at the temporal focus. The FWHM pulse duration as well as the percentage of electrons contained therein are also shown. The current density profiles have been calculated relative to an optimal fitting plane that is slightly tilted with respect to the plane. The front and side profiles of the 30 keV pulse is seen in (c) and (d), respectively.

Simulated diffraction spot shapes with and without interaction of the diffracted signal with the unscattered pulse for (a) 50 000, 30 kV electrons at a camera length of 20 cm and diffraction angle of 30 mrad, and (b) 200 000, 100 kV electrons with a camera length of 40 cm and diffraction angle of 15 mrad. The pulses with interaction included have been shifted to the right for visual purposes since they overlap with the pulses where interaction is neglected. The vertical shift is an actual displacement due to signal-pulse interaction.

Simulated diffraction spot shapes with and without interaction of the diffracted signal with the unscattered pulse for (a) 50 000, 30 kV electrons at a camera length of 20 cm and diffraction angle of 30 mrad, and (b) 200 000, 100 kV electrons with a camera length of 40 cm and diffraction angle of 15 mrad. The pulses with interaction included have been shifted to the right for visual purposes since they overlap with the pulses where interaction is neglected. The vertical shift is an actual displacement due to signal-pulse interaction.

## Tables

Design parameters for the reflectron gun. , , and are the distance of the acceleration gap, the distance between the centers of the bending magnets, and the reflectron length, respectively. *and * denote the bending magnet deflection angle and the reflectron incidence angle, respectively, while , , and are the electron flight distances from the cathode at solenoids and and the sample, respectively. All distances are given in mm.

Design parameters for the reflectron gun. , , and are the distance of the acceleration gap, the distance between the centers of the bending magnets, and the reflectron length, respectively. *and * denote the bending magnet deflection angle and the reflectron incidence angle, respectively, while , , and are the electron flight distances from the cathode at solenoids and and the sample, respectively. All distances are given in mm.

Optimal values of important bunch parameters at the sample. In the transverse direction, both the values in the - and -directions are reported due to the slight astigmatism of the beam focus. The rms temporal duration is calculated with respect to the tilted plane that best fits the bunch at the temporal focus (see Fig. 1).

Optimal values of important bunch parameters at the sample. In the transverse direction, both the values in the - and -directions are reported due to the slight astigmatism of the beam focus. The rms temporal duration is calculated with respect to the tilted plane that best fits the bunch at the temporal focus (see Fig. 1).

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