# Study on Effects of Energy Deposition and Thermal Shock Wave by Electron Beam Irradiation
###### Abstract  
The electron beam is an important way to effectively simulate the thermodynamic effects of an intense pulsed X-ray and the materials for electron beam irradiation are of great significance to study the effects of energy deposition and thermal shock waves. Based on the input conditions like the actual current, voltage, and energy spectrum of an electron beam device (REB), the analytic method and the Monte Carlo method were used to calculate the energy deposition of a multi-energy-spectrum electron beam in materials of hard aluminum and carbon phenolic, the differences of the two methods were analyzed, the energy deposition profiles of different incident angles and energies were obtained, and the energy deposition of electron beam irradiation of a multilayer target was calculated as well. Through the numerical simulation and experimental study of thermal shock waves of electron beam irradiation materials, the calculation error was less than 10% by comparing the stress changes of thermal shock waves with different energies. This is helpful for studying the protective structure of spacecraft. electron beam; energy deposition; thermal shock wave; relativistic electron beam (REB); Monte Carlo; carbon phenolic +
Footnote †: journal: Applied Sciences
indirect external load applied on the remaining solid to study the thermal shock. The pulse width of the X-ray and the vaporization phase transition of the material usually occur at the order of 0.1 \(\upmu\)s, while the recoil impulse compression loading of the vaporized material and the generation and propagation of corresponding thermal shock waves often last microseconds. The time of energy deposition phase transition is negligible relative to the time of dynamic loading and response, so it is very reasonable to use the above methods to decouple complex problems. After decades of research, related authorities have summed up a set of theoretical calculation formulas for X-ray thermo-mechanical effects and developed corresponding numerical simulation programs. [PERSON] et al. [12] theoretically solved the thermo-mechanical effects of X-ray and used the Whitener formula to calculate the energy deposition and impulse formed in the materials under X-ray irradiation. ZEBRA, RIP, PETROS [13], and other numerical calculation programs [14] were successively developed to simulate and calculate energy deposition, material response, and structural response formed in materials under beam irradiation, respectively. [PERSON] et al. [15] used the Monte Carlo method to conduct the imaging simulation study on the measurement of the X-ray energy spectrum generated by the bombardment of a high-energy high-current electron beam on a high Z target. [PERSON] et al. [16] numerically simulated the plane strain thermo-mechanical effect of the X-ray irradiation cylinder, strictly calculated the energy deposition in the quadrilateral grid through the integral method, and obtained relatively accurate energy deposition results. [PERSON] [17] pointed out that when a high-current pulsed electron beam was used to indirectly simulate thermo-mechanical effects generated in materials under X-ray irradiation of nuclear detonation, the relevant energy deposition profiles in materials were usually taken as a key indicator to judge their equivalence. The second method was to calculate the pressure, momentum, and expansion velocity directly by using the PUFF state equation for the phase transition and recoil impulse produced by irradiation, and to use the conservation equation to calculate the shock wave propagation in solids and the surface vaporization. [PERSON] et al. [18] simulated the X-ray thermal shock problem in Ly-12 by the one-dimensional difference method. [PERSON] [19], [PERSON] [20], and [PERSON] [21] respectively adopted the finite difference method to simulate the thermal shock under the two-dimensional plane strain of the oval, spherical, and conical head and cylindrical shell.