^{1}, I. W. Choi

^{1}, H. T. Kim

^{1}, I J. Kim

^{1}, K. H. Nam

^{1}, T. M. Jeong

^{1}and J. Lee

^{1,a)}

### Abstract

The pointing instability of energetic electron beams generated from a laser-driven accelerator can cause a serious error in measuring the electron spectrum with a magnetic spectrometer. In order to determine a correct electron spectrum, the pointing angle of an electron beam incident on the spectrometer should be exactly defined. Here, we present a method for absolutely calibrating the electron spectrum by monitoring the pointing angle using a scintillating screen installed in front of a permanent dipole magnet. The ambiguous electron energy due to the pointing instability is corrected by the numerical and analytical calculations based on the relativistic equation of electron motion. It is also possible to estimate the energy spread of the electron beam and determine the energy resolution of the spectrometer using the beam divergence angle that is simultaneously measured on the screen. The calibration method with direct measurement of the spatial profile of an incident electron beam has a simple experimental layout and presents the full range of spatial and spectral information of the electron beams with energies of multi-hundred MeV level, despite the limited energy resolution of the simple electron spectrometer.

The authors would like to acknowledge the fruitful discussions with T. J. Yu, S. K. Lee, J. H. Sung, J. W. Yoon, C. M. Kim, K. H. Pae, and P. V. Nickles and the technical support by S. W. Kang, C. W. Lee, J. M. Lee, J. H. Jeong, J. M. Yang, and H. Yun. This work was supported by the Ministry of Knowledge and Economy of Korea through the Ultrashort Quantum Beam Facility Program.

I. INTRODUCTION

II. EXPERIMENTAL SETUP AND CONDITIONS

III. RESULTS AND DISCUSSION

A. Absolute energy calibration for an electron beam with pointing instability

B. Energy spread of an electron beam and energy resolution of an electron spectrometer

C. Scattering of an electron beam passing through a scintillating screen

IV. CONCLUSION

### Key Topics

- Electron beams
- 72.0
- Particle beam bending magnets
- 30.0
- Electron spectrometers
- 28.0
- Magnetic fields
- 13.0
- Calibration
- 12.0

## Figures

Schematic of the experimental setup (M: mirror, L: lens).

Schematic of the experimental setup (M: mirror, L: lens).

Top-view image of a self-guided plasma channel formed above a supersonic He gas jet nozzle having a length of 4 mm.

Top-view image of a self-guided plasma channel formed above a supersonic He gas jet nozzle having a length of 4 mm.

Schematic showing the absolute energy calibration for an electron beam with pointing instability. The pointing angle *θ* is determined by measuring the distances *a* and *b*. The final distances *x* _{ 0 } and *x* are determined by the absolute electron energy *E*, the magnetic field strength *B* and the length *d* of the dipole magnet, and the distance *f*.

Schematic showing the absolute energy calibration for an electron beam with pointing instability. The pointing angle *θ* is determined by measuring the distances *a* and *b*. The final distances *x* _{ 0 } and *x* are determined by the absolute electron energy *E*, the magnetic field strength *B* and the length *d* of the dipole magnet, and the distance *f*.

Variation of the energy deviation between the absolute energy *E* and the misread energy *E* ^{′} in terms of 1/*E* ^{′} − 1/*E* as a function of the pointing angle.

Variation of the energy deviation between the absolute energy *E* and the misread energy *E* ^{′} in terms of 1/*E* ^{′} − 1/*E* as a function of the pointing angle.

Spatial and spectral characteristics of two quasi-monoenergetic electron bunches incident on a dipole magnet at normal incidence in the horizontal direction. (a) Electron beam divergence and pointing measured on Lanex 2, (b) energy spectra measured on Lanex 1. The upper black region in (b) shows an energy scaler that is adjusted to normal incidence of an electron beam.

Spatial and spectral characteristics of two quasi-monoenergetic electron bunches incident on a dipole magnet at normal incidence in the horizontal direction. (a) Electron beam divergence and pointing measured on Lanex 2, (b) energy spectra measured on Lanex 1. The upper black region in (b) shows an energy scaler that is adjusted to normal incidence of an electron beam.

Spatial and spectral characteristics of a quasi-monoenergetic electron bunch incident on a dipole magnet at an oblique angle in the horizontal direction. (a) Electron beam divergence and pointing measured on Lanex 2, (b) energy spectrum measured on Lanex 1. The upper black region in (b) shows an energy scaler that is adjusted to normal incidence of an electron beam.

Spatial and spectral characteristics of a quasi-monoenergetic electron bunch incident on a dipole magnet at an oblique angle in the horizontal direction. (a) Electron beam divergence and pointing measured on Lanex 2, (b) energy spectrum measured on Lanex 1. The upper black region in (b) shows an energy scaler that is adjusted to normal incidence of an electron beam.

Variations of (a) the misread electron energies and (b), (c) ratios of the energy deviation to the energy corresponding to normal incidence on Lanex 1 as a function of the pointing angle of an electron beam on Lanex 2. The thin lines represent the calculation results not considering the fringe field effect and the thick lines represent the calculation results considering the fringe field effect. The results are based on the algorithm in Fig. 3. In the horizontal axes, the positive and negative values represent the pointing angles of electron beams incident to the left and right sides, respectively, with respect to normal incidence in Fig. 3. In (a), the electron energy range in the vertical axis is limited from 100 MeV to 1 GeV due to the resolving power of the permanent dipole magnet.

Variations of (a) the misread electron energies and (b), (c) ratios of the energy deviation to the energy corresponding to normal incidence on Lanex 1 as a function of the pointing angle of an electron beam on Lanex 2. The thin lines represent the calculation results not considering the fringe field effect and the thick lines represent the calculation results considering the fringe field effect. The results are based on the algorithm in Fig. 3. In the horizontal axes, the positive and negative values represent the pointing angles of electron beams incident to the left and right sides, respectively, with respect to normal incidence in Fig. 3. In (a), the electron energy range in the vertical axis is limited from 100 MeV to 1 GeV due to the resolving power of the permanent dipole magnet.

(a) Energy spectra measured on Lanex 1 of an electron beam incident on Lanex 2 with normal incidence (Fig. 4) and (b) comparison of the energy spectrum measured on Lanex 1 with the calibrated one of an electron beam incident on Lanex 2 with oblique angle (Fig. 5).

(a) Energy spectra measured on Lanex 1 of an electron beam incident on Lanex 2 with normal incidence (Fig. 4) and (b) comparison of the energy spectrum measured on Lanex 1 with the calibrated one of an electron beam incident on Lanex 2 with oblique angle (Fig. 5).

Variations of the energy resolutions of electron spectrometers as a function of the divergence angle of an electron beam on Lanex 2. The spectrometer parameters were (a) *B* = 1.5 T, *a* = 120 cm, and *d* = *f* = 40 cm and (b) *B* = 0.965 T, *a* = 10 cm, and *d* = *f* = 20 cm, respectively. The calculations were performed at the conditions that the pointing angles of electron beams were zero.

Variations of the energy resolutions of electron spectrometers as a function of the divergence angle of an electron beam on Lanex 2. The spectrometer parameters were (a) *B* = 1.5 T, *a* = 120 cm, and *d* = *f* = 40 cm and (b) *B* = 0.965 T, *a* = 10 cm, and *d* = *f* = 20 cm, respectively. The calculations were performed at the conditions that the pointing angles of electron beams were zero.

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