An international journal published by K. N. Toosi University of Technology

Document Type : Research Article


School of Physics, Damghan University, P. O. Box 36716-41167, Damghan, Iran


Indirect drive inertial confinement fusion (ICF) holds promise for achieving practical energy generation through controlled fusion reactions. However, the efficiency of ICF is constrained by the Be ablator material used to contain the fuel. To overcome this limitation, researchers have proposed doping Be with various elements. In this study, we investigate the effects of Na and Br dopants, incorporated at concentrations of 4.86% and 2.1%, respectively, using a one-dimensional MULTI-IFE hydrodynamic code. This code serves as a numerical tool dedicated to analyzing Inertial Fusion Energy microcapsules, facilitating the examination of the Be ablator's performance in indirect drive ICF. Our results indicate that the addition of a beryllium layer doped with Na and Br significantly enhances the target gain, elevating it from the break-even value (G ≈ 1) to approximately G ≈ 12. Furthermore, we delve into the impact of these dopants on the plasma fuel conditions during the implosion, shedding light on the underlying physics of the system. These findings demonstrate that Na and Br doping in the Be ablator represents a viable approach for improving the efficiency of indirect drive ICF, potentially paving the way for the development of practical fusion energy systems.


  • ICF is a promising approach to generating practical energy through controlled fusion reactions.
  • The efficiency of ICF is currently limited by the use of Be ablator material to contain the fuel.
  • Researchers have proposed doping Be with various elements to enhance its performance as an ablator material.
  • This study investigates the use of Na and Br dopants to improve the performance of Be ablator in indirect drive ICF.
  • The results demonstrate that Na and Br dopants can improve the performance of Be ablator in indirect drive ICF


Atzeni, S. and Meyer-ter Vehn, J. (2004). The physics of inertial fusion: beam plasma interaction, hydrodynamics, hot dense matter, volume 125. OUP Oxford.
Craxton, R., Anderson, K., Boehly, T., et al. (2015). Direct-drive inertial confinement fusion: A review. Physics of Plasmas, 22(11):110501.
Dittrich, T., Hurricane, O., Callahan, D., et al. (2014). Design of a high-foot high adiabat ICF capsule for the National Ignition Facility. Physical Review Letters, 112(5):055002.
Haan, S., Amendt, P., Dittrich, T., et al. (2004). Design and simulations of indirect drive ignition targets for NIF. Nuclear Fusion, 44(12):S171.
He, X. and Zhang, W. (2007). Inertial fusion research in China. The European Physical Journal D, 44:227–231.
Hinkel, D., Hopkins, L. B., Ma, T., et al. (2016). Development of improved radiation drive environment for high foot implosions at the National Ignition Facility. Physical Review letters, 117(22):225002.
Huang, H., Xu, H., Youngblood, K., et al. (2012). Dopant Distribution in NIF Beryllium Ablator Capsules. In APS Division of Plasma Physics Meeting Abstracts, volume 54, pages GO4–012.
Kawata, S. (2021). Direct-drive heavy ion beam inertial confinement fusion: a review, toward our future energy source. Advances in Physics: X, 6(1):1873860.
Kline, J., Batha, S., Benedetti, L., et al. (2019). Progress of indirect drive inertial confinement fusion in the United States. Nuclear Fusion, 59(11):112018.
Kritcher, A., Clark, D., Haan, S., et al. (2018). Comparison of plastic, high density carbon, and beryllium as indirect drive NIF ablators. Physics of Plasmas, 25(5):056309.
Landen, O., Bradley, D., Braun, D., et al. (2008). Experimental studies of ICF indirect drive Be and high density C candidate ablators. In Journal of Physics: Conference Series, volume 112, page 022004. IOP Publishing.
Lindl, J. (1995). Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain. Physics of Plasmas, 2(11):3933–4024.
Lindl, J. D., Amendt, P., Berger, R. L., et al. (2004). The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Physics of Plasmas, 11(2):339–491.
Lindl, J. D., McCrory, R. L., and Campbell, E. M. (1992). Progress toward ignition and burn propagation in inertial confinement fusion. Phys. Today, 45(9):32.
Logan, B. G., Perkins, L., and Barnard, J. (2008). Direct drive heavy-ion-beam inertial fusion at high coupling efficiency. Physics of Plasmas, 15(7):072701.
Loomis, E. N., Yi, S. A., Kyrala, G. A., et al. (2018). Implosion shape control of high-velocity, large case-to-capsule ratio beryllium ablators at the National Ignition Facility. Physics of Plasmas, 25(7):072708.
McClarren, R. G., Tregillis, I., Urbatsch, T. J., et al. (2021). High-energy density hohlraum design using forward and inverse deep neural networks. Physics Letters A, 396:127243.
McCrory, R., Meyerhofer, D., Betti, R., et al. (2008). Progress in direct-drive inertial confinement fusion. Physics of Plasmas, 15(5):055503.
McEachern, R. and Alford, C. (1999). Evaluation of boron-doped beryllium as an ablator for NIF target capsules. Fusion Technology, 35(2):115–118.
Murakami, M. and Meyer-ter Vehn, J. (1991). Indirectly driven targets for inertial confinement fusion. Nuclear Fusion, 31(7):1315.
Pfalzner, S. (2006). An introduction to inertial confinement fusion. CRC Press.
Ramis, R., Eidmann, K., Meyer-ter Vehn, J., et al. (2012). MULTI-fs–A computer code for laser–plasma interaction in the femtosecond regime. Computer Physics Communications, 183(3):637–655.
Ramis, R. and Meyer-ter Vehn, J. (2016). MULTI-IFEA one-dimensional computer code for Inertial Fusion Energy (IFE) target simulations. Computer Physics Communications, 203:226–237.
Ramis, R., Schmalz, R., and Meyer-ter Vehn, J. (1988). Multia computer code for one-dimensional multigroup radiation hydrodynamics. Computer Physics Communications, 49(3):475–505.
Rosen, M. D. (1999). The physics issues that determine inertial confinement fusion target gain and driver requirements: A tutorial. Physics of Plasmas, 6(5):1690–1699.
Slutz, S., Bailey, J., Chandler, G., et al. (2003). Dynamic hohlraum driven inertial fusion capsules. Physics of Plasmas, 10(5):1875–1882.
Tikhonchuk, V. (2020). Progress and opportunities for inertial fusion energy in Europe. Philosophical Transactions of the Royal Society A, 378(2184):20200013.
Yamanaka, C. (1999). Inertial confinement fusion: The quest for ignition and energy gain using indirect drive. Nuclear Fusion, 39(6):825–827.
Zylstra, A. B., Yi, S. A., MacLaren, S., et al. (2018). Beryllium capsule implosions at a case-to-capsule ratio of 3.7 on the National Ignition Facility. Physics of Plasmas, 25(10):102704.