PHYSICAL REVIEW E 103, 063215 (2021) Molecular dynamics investigation of the stopping power of warm dense hydrogen for electrons Yun Liu , 1 Xing Liu , 2 Shen Zhang, 3 Hao Liu , 1 , * Chongjie Mo , 4 , † Zhenguo Fu , 5, ‡ and Jiayu Dai 3 1 Department of Applied Physics, School of Physics and Electronics, Hunan University, Changsha 410082, China 2 Center for Applied Physics and Technology, School of Physics, Peking University, Beijing 100086, China 3 Department of Physics, National University of Defense Technology, Changsha 410073, China 4 Beijing Computational Science Research Center, Beijing 100193, China 5 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China (Received 2 December 2020; revised 16 April 2021; accepted 1 June 2021; published 28 June 2021) A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400–10000 eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas. DOI: 10.1103/PhysRevE.103.063215 I. INTRODUCTION The stopping power for charged particles in matter is a fun- damental problem in numerous pivotal fields, such as medical radiation therapy [1–3], space exploration [4], astrophysics [5,6], DNA damage [7–9], and inertial confinement fusion (ICF) [10–13]. The energy deposition behavior of the hot electrons in the dense target is the key physical process in the fast ignition scheme of ICF. Considering that the warm dense matter (WDM) state is a typical state of materials in ICF [14–20], it is of great significance to study the energy deposition process of hot electrons in warm dense hydrogen [21–24]. A series of theoretical works have been carried out to ex- plore the influence of various physical effects on the stopping power for charged particles under different conditions. The development of theoretical models of stopping power can be divided into two categories: one is the model developed based on collision concept, such as Landau-Spitzer (LS) model [25,26] and Li-Petrasso model (LP) [23], which is suitable for the thermal and fully ionized plasmas where collisions between particles are weak and dominated by the small an- gle scattering process. The other is based on the dielectric * haoliu@hnu.edu.cn † cjmo@csrc.ac.cn ‡ fu_zhenguo@iapcm.ac.cn response function of the plasma to the charged particles like random phase approximation (RPA) model [27–29]. Recently, there are also models that combine the two-body collision and dielectric response, such as Brown, Preston, and Single- ton (BPS) [30] model, in which the Lenard-Balescu kinetic equation and Boltzmann equation of pure Coulomb scattering are used to describe the long-distance collective excitation and short-distance hard collision of the plasma, respectively. However, different theoretical models have different ranges of applications. Considering the complexity of the warm dense state, the applicability of various theoretical models under the warm dense state needs to be verified by experiments or numerical simulation methods. The previous experimental works on the stopping power for charged particles mainly focus on the incidence of ion beams in solids [31–33] and plasmas [34–38]. The time-of- flight (TOF) method with a semiconductor detector [39] is widely used for the measurement of the stopping power for the charged projectiles. However, only a few preliminary experi- ments have been reported until recently that study the energy loss of electrons in a gaseous target [40,41]. For instance, the mass stopping power for low-energy electrons traveling in gaseous H 2 , which is unavailable straightforward in experi- ments, is obtained via intermediate measurements of electron energy loss spectra, which has to be artificially corrected for instrumental transmission effects [40]. So far, there is still a lack of accurate experimental data on the stopping power of warm dense plasmas for electron. 2470-0045/2021/103(6)/063215(12) 063215-1 ©2021 American Physical Society