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Simulations of interactions of high-energy proton beam with high dense matter based on two-dimensional quantum hydrodynamic model

  • Ya Zhang (a1), Yuan-Hong Song (a1) and You-Nian Wang (a1)

This paper presents numerical simulations to study the heating of a solid target under a proton beam pulse interaction. The target is heated by the proton beam pulse with particle energy Eb, intensity N and focal radius rb of transverse Gaussian distribution, with a fixed pulse time 10 ps. The dynamics of target and beam ions are described by a classical hydrodynamic model and the target electrons are described by the quantum hydrodynamic model. Numerical simulations are carried out by employing the two dimensional flux-corrected transport methods. The target is heated to 0.5−5 eV, therefore, warm dense matter is created in the heated target region on a picosecond time scale.

Corresponding author
Address correspondence and reprint requests to: You-Nian Wang, School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian, China116024. E-mail:
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Barnard, J.J., Armijo, J., More, R.M., Friedman, A., Kaganovich, I., Logan, B.G., Marinak, M.M., Penn, G.E., Sefkow, A.B., Santhanam, P., Stoltz, P., Veitzer, S., Wurtele, J.S. (2007). Theory and simulation of warm dense matter targets. Nucl. Instrum. Methods Phys. Res A 577, 275283.
Boris, J.P., Landsberg, A.M., Oran, E.S. & Gardner, J.H. (1993). LCPFCT–Flux-Corrected Transport Algorithm for Solving Generalized Continuity Equations. NRL Memorandom Report 6410, Washington, DC: Naval Research Laboratory, 20375–5320.
Brambrink, E., Roth, M., Blazevic, A. & Schlegel, T. (2006). Modeling of the electrostatic sheath shape on the rear target surface in short-pulse laser-driven proton acceleration. Laser Part. Beams 24, 163168.
Chen, Z., Cockburn, B., Gardner, C.L. & Jerome, J.W. (1995). Quantum hydrodynamic simulation of hysteresis in the resonant tunneling diode. J. Comput. Phys. 117, 274280.
Deutsch, C. (1986). Inertial confinement fusion driven by intense ion beams. Ann. Phys. (Paris) 11, 1111.
Deutsch, C., Maynard, G., Bimbot, R., Gardes, D., Dellanegra, S., Dumail, M., Kubica, B., Richard, A., River, M.F., Sernagean, A., Fleurier, C., Sanba, A., Hoffmann, D.H.H., Weyrich, K. & Wahl, H. (1989). Ion beam-plasma interaction: A standard model approach. Nucl. Instrum. Methods Phys. Res A 278, 3843.
Deutsch, C. (1992). Ion cluster interaction with cold targets for ICF: Fragmentation and stopping. Laser Part. Beams 10, 217226.
Haas, F., Manfredi, G. & Feix, M. (2000). Multistream model for quantum plasmas. Phys. Rev. E 62, 2763.
Hoffmann, D.H.H. (2008). Intense laser and particle beams interaction physics toward inertial fusion. Laser Part. Beams 26, 295296.
Hoffmann, D.H.H., Fortov, V.E., Kuster, M., Mintsev, V., Sharkov, B.Y., Tahir, N.A., Udrea, S., Varentsov, D. & Weyrich, K. (2009). High energy density physics generated by intense heavy ion beams. Astrophys Space Sci. 322, 167177.
Hoffmann, D.H.H., Tahir, N.A., Udreal, S., Rosmej, O., Meister, C.V., Varentsov, D., Roth, M., Schaumann, G., Frank, A., Blažević, A., Ling, J., Hug, A., Menzel, J., Hessling, TH., Harres, K., Günther, M., El-Moussatil, S., Schumacher, D. & Imran, M. (2010). High energy density physics with heavy ion beams and related interaction phenomena. Plasma Phys. 50, 715.
Hora, H. (2007). New aspects for fusion energy using inertial confinement. Laser Part. Beams 25, 3745.
Manfredi, G. & Haas, F. (2001). Self-consistent fluid model for a quantum electron gas. Phys. Rev. B 64, 075316.
More, R.M., Warren, K.H., Young, D.A. & Zimmerman, G.B. (1988). A new quotidian equation of state (QEOS) for hot dense matter. Phys. Fluids 31, 30593078.
Nellis, W.J. (2006). Dynamic compression of materials: metallization of fluid hydrogen at high pressures. Rep. Prog. Phys. 69, 14791580.
Nettelmann, N., Holst, B., Kietzmann, A., French, M., Redmer, R. & Blaschke, D. (2008). Ab initio equation of state data for hydrogen, helium, and water and the internal structure of jupiter. Astrophys. J. 683, 12171228.
Patel, P.K., Mackinnon, A.J., Key, M.H., Cowan, T.E., Foord, M.E., Allen, M., Price, D.F. & Ruhl, H. (2003). Isochoric Heating of Solid-Density Matter with an Ultrafast Proton Beam. Phys. Rev. Lett. 91, 125004.
Stöckl, C., Frankenheim, O.B., Roth, M., Suß, W., Wetzler, H., Seelig, W., Kulish, M., Dornik, M., Laux, W., Spiller, P., Stetter, M., Stöwe, S., Jacoby, J. & Hoffmann, D.H.H. (1996). Interaction of heavy ion beams with dense plasmas. Laser Part. Beams 14, 561574.
Tahir, N.A., Deutsch, C., Fortov, V.E., Gryaznov, V., Hoffmann, D.H.H., Kulish, M., Lomonosov, I.V., Mintsev, V., Ni, P., Nikolaev, D., Piriz, A.R., Shilkin, N., Spiller, P., Shutov, A., Temporal, M., Ternovoi, V., Udrea, S. & Varentsov, D. (2005). Proposal for the study of thermophysical properties of high-energy-density matter using current and future heavy-ion accelerator facilities at GSI Darmstadt. Phys. Rev. Lett. 95, 035001.
Tahir, N.A., Kim, V., Matvechev, A., Ostrik, A., Lomonosov, I.V., Piriz, A.R., Cela, J.J.L. & Hoffmann, D.H.H. (2007). Numerical modeling of heavy ion induced stress waves in solid targets. Laser Part. Beams 25, 523540.
Tahir, N.A., Schmidt, R., Shutov, A., Lomonosov, I.V., Piriz, A.R., Hoffmann, D.H.H., Deutsch, C. & Fortov, V.E. (2009). Large Hadron collider at CERN: Beams generating high-energy-density matter. Phys. Rev. E 79, 046410.
Tahir, N.A., Shutov, A., Piriz, A.R., Lomonosov, I.V., Deutsch, C., Spiller, P. & Stöhlker, TH. (2011). Application of intense heavy ion beams to study high energy density physics. Plasma Phys. Control. Fusion 53, 124004.
Zhang, Y., Song, Y.-H. & Wang, Y.-N. (2011). Stopping power for a charged particle moving through three-dimensional nonideal finite-temperature electron gases. Phys. Plasmas 18, 072701.
Zhang, Y., Song, Y.-H. & Wang, Y.-N. (2011). Nonlinear wake potential and stopping power for charged particles interacting with a one-dimensional electron gas. Phys. Plasmas 18, 112705.
Zhao, Y., X, G., Xu, H., Zhao, H., Xia, J., Jin, G., Ma, X., Liu, Y., Yang, Z., Zhang, P., Wang, Y., Li, D., Zhao, H., Zhan, W., Xu, Z., Zhao, D., Li, F. & Chen, X. (2009). An outlook of heavy ion driven plasma research at IMP-Lanzhou. Nucl. Instrum. Methods Phys. Res B 267, 163166.
Zhao, X. & Shin, Y.C. (2012). A two-dimensional comprehensive hydrodynamic model for femtosecond laser pulse interaction with metals. J. Phys. D: Appl. Phys. 45, 105201.
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Laser and Particle Beams
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