# A Method to Optimize the Electron Spectrum for Simulating Thermo-Mechanical Response to X-ray Radiation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Optimized Method

#### 2.1. The Differences between X-ray and Electron Interaction with Materials

#### 2.2. The Optimized Method for Electrons

_{max}, and the minimum is zero (Figure 3). The energy span of the whole electron spectrum is divided into m energy bins, and in the jth energy bin, the midpoint value of the energy per electron is e

_{j}(j = 1, 2, …, m), the total number of electrons is a

_{j}(j = 1, 2, …, m). This means the continuous spectrum has been changed to a discrete spectrum (see Figure 4). The optimization purpose is to get the number of electrons a

_{j}in each energy bin;

_{j}), the deposited energy in the ith part is e

_{ij}which can be calculated with the MCNP software.

**A**, which satisfied the Equation (6), can tell us how to distribute the electron numbers in each energy bin, and together with m energy bins was exactly the optimized electron spectrum that we want.

## 3. Specific Results

_{j}, the energy depositing in the ith part results can be calculated in advance for a specific material, that is, the value e

_{ij}has been known before optimization. The spectrum to be simulated is 1 keV and 3 keV X-ray spectrum with the energy fluence w = 200 J/cm

^{2}and 300 J/cm

^{2}.

#### 3.1. The effect of X-ray spectrum

^{2}was accomplished, and the optimized results are shown in the Figure 5 and Figure 6.

^{2}, the optimized results are shown in Figure 7 and Figure 8. From the comparison of Figure 5 and Figure 6 with Figure 7 and Figure 8, we can see that the electron spectrum after optimization does not change but the number varies which means the fluence is merely related with the number of electrons. In other words, the optimization method presented here can be applied to X-ray with any fluence by only changing the number of electrons.

#### 3.2. The Effect of Material

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Doron, K.; Eli, W. Hard X-ray Emission from Accretion Shocks around Galaxy Clusters. J. Cosmol. Astropart. Phys.
**2010**, 25, 1–14. [Google Scholar] - George, R.S.; David, H.M.; Hani, K. Radioisotope electric propulsion (REP): A near-term approach to nuclear propulsion. Acta Astronaut.
**2010**, 7, 501–507. [Google Scholar] - Andreas, B.; Bernd, S.; Martin, B.K. Introduction to the Topical Volume: Recent Advances in Nuclear Explosion Monitoring. Pure Appl. Geophys.
**2010**, 7, 373–379. [Google Scholar] - Lomov, I.; Herbold, E.B.; Antoun, T.H. Influence of mechanical properties relevant to standoff deflection of hazardous asteroids. Procedia Eng.
**2013**, 58, 251–259. [Google Scholar] [CrossRef] [Green Version] - Hammerling, P.; Remo, J.L. NEO interaction with nuclear radiation. Acta Astronaut.
**1995**, 36, 337–346. [Google Scholar] [CrossRef] - Holsapple, K.A. About deflecting asteroids and comets. Mitig. Hazard. Comets Asteroids
**2004**, 113–140. [Google Scholar] - Qiu, A.C.; Zhang, J.S.; Peng, J.C. Research progress about high power pulse ion beam of imitating X-ray thermal-mechanical response. Nucl. Technol.
**2002**, 36, 714–719. [Google Scholar] - Yang, H.L.; Qiu, A.C.; Zhang, J.S. Simulation calculation for the energy deposition profile and the transmission fraction of intense pulsed electron beam at various incident angles. High Power Laser Part. Beams
**2002**, 14, 778–782. [Google Scholar] - Jane, L.; Fox, M.I.; Galand, R.E. Energy deposition in planetary atmospheres by charged particles and solar photons. Space Sci. Rev.
**2008**, 39, 213–220. [Google Scholar] - Mihailo, D.R.; Dragan, D.M. Laser beam spatial profile determination by pulsed photoacoustics: Exact solution. Meas. Sci. Technol.
**2010**, 21, 065603. [Google Scholar] - Lai, D.G.; Zhang, Y.M.; Li, J.X. Design of bremsstrahlung composite thin converter for high current electron beams. High Power Laser Part. Beams
**2013**, 25, 1396–1400. [Google Scholar] - Wang, J.G.; Niu, S.L. Handbook for the Parameters of High-Altitude Nuclear Explosion Effects, 1st ed.; Atomic Energy Press: Beijing, China, 2010; pp. 45–55. [Google Scholar]
- Hu, L.; Lei, Y.; Zhu, J. Simulation on distributed target material impacted by high intensity current multi-pulse electron beam. High Power Laser Part. Beams
**2013**, 25, 2125–2129. [Google Scholar] - Esam, M.A.H. Monte Carlo Particle Transport with the MCNP Code. Ph.D. Thesis, University of New Brunswick, Fredericton, NB, Canada, 2011; pp. 1–57. [Google Scholar]

**Figure 1.**The energy-deposited profiles of electron beam and X-ray of the same energy fluence in aluminum.

**Figure 5.**The optimized results for 1 keV X-ray with fluence 300 J/cm

^{2}. (

**a**) The electron spectrum after optimization; (

**b**) Comparison of the energy-deposited profiles between X-ray and electron.

**Figure 6.**The optimized results for 3 keV X-ray with fluence 300 J/cm

^{2}. (

**a**) The electron spectrum after optimization; (

**b**) Comparison of the energy-deposited profiles between X-ray and electron.

**Figure 7.**The optimized results for 1 keV X-ray with fluence 200 J/cm

^{2}. (

**a**) The electron spectrum after optimization; (

**b**) Comparison of the energy-deposited profiles between X-ray and electron.

**Figure 8.**The optimized results for 3 keV X-ray with fluence 200 J/cm

^{2}. (

**a**) The electron spectrum after optimization; (

**b**) Comparison of the energy-deposited profiles between X-ray and electron.

**Figure 9.**Comparison of the electron spectrums used to simulate 1 keV X-ray in three materials: aluminum, copper, and tantalum.

**Figure 10.**Comparison of the electron spectrums used to simulate 3 keV X-ray in three materials aluminum, copper and tantalum.

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**MDPI and ACS Style**

Ran, X.; Wang, B.; Zhang, K.; Tang, W.
A Method to Optimize the Electron Spectrum for Simulating Thermo-Mechanical Response to X-ray Radiation. *Symmetry* **2020**, *12*, 59.
https://doi.org/10.3390/sym12010059

**AMA Style**

Ran X, Wang B, Zhang K, Tang W.
A Method to Optimize the Electron Spectrum for Simulating Thermo-Mechanical Response to X-ray Radiation. *Symmetry*. 2020; 12(1):59.
https://doi.org/10.3390/sym12010059

**Chicago/Turabian Style**

Ran, Xianwen, Bo Wang, Kun Zhang, and Wenhui Tang.
2020. "A Method to Optimize the Electron Spectrum for Simulating Thermo-Mechanical Response to X-ray Radiation" *Symmetry* 12, no. 1: 59.
https://doi.org/10.3390/sym12010059