Numerical Modeling of Radiative Kinetic Plasmas

Transcription

1 2014 US-Japan JIFT Workshop on Progress in kinetic plasma simulations Oct.31-Nov.1, 2014, Salon F, New Orleans Marriott, New Orleans, LA, U.S.A Numerical Modeling of Radiative Kinetic Plasmas T. Johzaki Hiroshima University, JAPAN Y. Sentoku, R. Mancini, R. Rolye, and I. Paraschiv University of Nevada, Reno, USA S. Sunahara Institute for Laser Technology, JAPAN Institute for Laser Technology

2 Contents Motivation Numerical modeling of radiative kinetic plasma simulation Applications 1. X-ray emissions from intense laser produced plasmas. 2. Characteristic emission, K-α and K-β, driven by hot electrons. 3. γ-ray emissions from relativistic laser - matter interaction. 4. XFEL-matter interaction, photoionization, and relaxation processes of photoelectrons in solid target.

3 Motivation

4 Motivation of code development Laser interactions with high-z target materials generate hot, dense, radiative plasmas where the radiation effects become interesting and important. e.g. K-α, γ-ray. The high intensity X-ray lasers (XFELs) are now available and are becoming alternative way of producing hot dense plasmas. e.g. solid material beyond a million degrees (~ 100 ev) The radiative plasmas has been studied mainly by radiation hydrocodes. However there is no simulation code available to study the radiation processes in kinetic plasmas. We are interested in the radiations in intense laser heated plasmas, such as hard x-rays from characteristic emissions and γ-rays via Bremsstrahlung or radiative damping. Moreover we would like to study the plasma formation driven by the intense x-rays, like XFEL light produced plasma.

5 intense laser-produced plasmas emit copious amounts of radiation spatial and temporal resolutions are limited } Everything happens in less than a picosecond (10-12 s) (Information is very limited in experiments...) We intend to study the radiation physics in dense plasmas and simulate the spatiotemporal evolution of X-ray emissions, which we can compare directly with experimental observations.

6 laser-produced plasma have large density and optical scales laser We cannot simplify the radiation processes by assuming an optically thin or optically thick plasma. We must directly solve the radiation transport equation.

7 Numerical modeling of radiative kinetic plasma simulation

8 Structure of relativistic electromagnetic PIC code PICLS for HEDP Partially ionized Fusion reaction Coulomb collision XFEL Neutron yields Radiative processes PICLS (1D, 2D, 3D) Platform Relativistic electromagnetic particle code Energy transfer between particles Update Z, ne, Te Collisional radiation Ionization Brems from fast ele. Bound-bound Boud-free Collisional Brems from thermal ele. Field Radiation energy transport Reference Y. Sentoku, and A. J. Kemp J. Comput. Phys. 227, 6846 (2008) R. Mishra, P. Leblanc, Y. Sentoku, M. S. Wei, and F. Beg, Phys. Plasmas 20, (2013)

9 The radiation transport module solves the 2D radiative transfer equation by direct integration Radiative transfer equation I(r,W, n, t) : intensity of radiation c : speed of light h(r,w, n, t) : emissivity c(r,w, n, t) : opacity (a) Multi-group method for frequency Radiation energy is divided into groups of finite energy width. The transport equation is integrated over the energy width for each group, then solved to obtain the radiation intensity for each group, I g. 10 kev 10 ev hn 1 hn 2 hn g hn g+1 Group-1 Group-g (b) S N method for direction For the angular variables (polar angle m and azimuthal angle h), we apply the discrete ordinate method. The transport equation is solved for each discrete direction (m,n) to obtain the radiation intensity in that direction, I m,n Lee, C.E., Los Alamos Scientific Laboratory Report LA-2595, 1962

10 advection solved by CIP method I(r,Ω,hν,t) : intensity of radiation η(r,hν,t) : emissivity χ(r,hν,t) : opacity The constrained interpolation profile (CIP) scheme is used, which solves the profile together with its gradient CIP method gives 3 rd -order spatial accuracy to advection term This explicit method is suitable for MPI parallelization advection T. Yabe, et al., CPC 66 (1991) 233., F. Xiao et al., CPC 93 (1996) 1, F. Xiao et al., CPC 94 (1996) 103.

11 Coupling PIC and Radiation transport p rad is divided into fine PIC cell PIC Rad dt PIC Fine PIC cell Reduced cell For radiation dt PIC < dt Rad dt rad Cell averaged values for radiation t PICLS (Sentoku,UNR) n i, T e, (Material) for bulk plasma in each cell dt (for radiation cal.), and bulk plasma info. (Z, <Z 2 >, n i, T e ) in each cell p rad for bulk electron in each cell positive heating rate by radiation negative energy loss rate Radiation Transport (Johzaki, Hiroshima Univ.) Opacity table FLYCHK & FLYSPECTRA* (Paraschiv, Mancini, UNR) h, c for each cell in Radiation transport *H.-K. Chung, M.H. Chen, W.L. Morgan, Y. Ralchenko, HEDP 1, 3 (2005).

12 Applications

13 PICLS+Radiation Transport can simulate By preparing emissivities or opacities for different propblem, we can apply the code for Radiation Transport energy loss/deposit of X- rays Cu X-ray emissions from intense laser produced plasmas Characteristic emission, K-α and K-β, driven by hot electrons. γ-ray emissions from relativistic laser - matter interaction. XFEL-matter interaction, photoionization, and relaxation processes of photoelectrons in solid target. Y [μm] X-ray emission X-ray reabsorptio n

14 (1) direct comparison of X-rays with experiment, including characteristic (K α ) emissions [erg/cm 3 ] 2 μm thin copper foil Electron energy density Kα energy density (8.04 kev) Time integrated distribution on back surface (at 1 ps) Bright spot ~50 μm Y [μm] I=2x10 19 W/cm 2, 350fs pulse, 8μm spot Figure: 2D monochromatic X-ray image of K α (8 kev) of a 2 μm thick copper foil heated by the 100 TW Leopard laser (Hiroshi Sawada, UNR)

15 Does K-α image really show the distribution of the hot electrons? Spot size of K-α is about 40um, which is 5x larger than the spot size and does not depend on the target size. Figure: 2D monochromatic x-ray image of K-α (8keV) of a 2μm thickness thin copper foil heated by the 100 TW Leopard laser light. (2x10 19 W/cm 2, duration 350fs, spot 8μm) Courtesy of Dr. Hiroshi Sawada, UNR

16 Electron loses the K-shell binding energy for K-α emission X-ray (~8keV) is emitted when the L-shell electron transits into the K-shell. Model of Characteristic Emission [1] C. Hombourger, J. Phys. B 31, 3693 (1998). [2] J. Davis, R. Betti et al., Phys. Plasmas 20, (2013). Hombourger s expresion for any element [1] fk is fluorescence yield, for copper. K-hole Fast electron B: K-shell binding energy [ev]

17 Simulation of K-α from a thin copper target heated by intense laser light PICLS2d + Radiation Transport Ionization model: impact and field ionizations Collision model: relativistic binary collision Leopard laser (P-pol, λ=1μm) I=2.5x10 19 W/cm 2 Pulse duration: 300fs Spot size: 8um preplasma 5um Copper solid (reduced mass) thickness 2um width 250um Mass : 64Mp Z : 29 (Initial Z=3) Ion dens. : 100nc ρ : 8.9g/cm 3 nc= /cm 3 Radiation Transport Photon energy 1eV - 10keV (150 groups) Sn direction : 146/2π for upper hemisphere FLYCHK (NLTE) plus K-α emissivity

18 Simulation of K-α from a thin copper target heated by intense laser light Electron energy density [erg/cm 3 ] K-α energy density (8.04keV) K-α Time integrated spectrum at 940fs in the central area.

19 K-α spot is wider than the area of distribution of hot electrons (>10keV) laser spot Comparing the K-α distribution and the hot electrons (>10keV) number distribution in the back surface layer (0.2um). Both distribution is time integrated up 860fs and spatially integrated in a 0.2 um layer of back surface.

20 K-a signals might overestimate the actual hot e- distribution Al foil 120μm 20μm Copper R. Stephens et al., PRE 69, (2004) Al CH W/cm 2 100um Al or CH target Aluminum shows a small single spot while CH does not! K-alpha image from the copper layer 50um PICLS2d result of Al taget P. Leblanc* and Y. Sentoku, Phys. Rev. E 89, (2014)

21 (2) γ-ray production in extremely intense LPI 10 μm copper target γ-ray emissions are implemented in the radiation transport. Models of relativistic Bremsstrahlung and radiative damping will be introduced. Using the spatiotemporal information of γ-rays we can study the critical details of positron creation, nuclear reaction (γn), etc. I = W/cm 2, 30 fs pulse, 5 μm spot

22 γ-rays and pair production Experiment Theory Positron spectra from 1 mm thick Au target with diameter of 20 mm (red) and from EGS code (blue). The inset shows the peak energy of positrons as a function of the inverse of target surface area. Hui Chen, et al., PRL 105, (2010) Pair production by a laser of intensity 4x10 23 W/cm -2 striking an aluminum target. The laser (red contours) bores a hole into the solid target (blue density map). γ-rays (blue density map) and positrons (red dots) are generated in the interaction. C. P. Ridgers, et al., PRL 108, (2012)

23 Bremsstrahlung from Relativistic Electrons Photon energy J. Jakson, Classical Electrodynamics Angular distribution Bremsstrahlung from non-relativistic electrons is calculated from the emissivity in the precomputed database. (uniformly emitted)

24 Simulation of ultrafast heated copper thin target PICLS2d + Radiation Transport Ionization model: impact and field ionizations Collision model: relativistic binary collision Laser (P-pol, λ=1μm) I=10 21 W/cm 2 Pulse duration: 66fs Spot size: 5um preplasma 2um Mass : 64Mp Z : 29 (Initial Z=3) Ion dens. : 100nc ρ : 8.9g/cm 3 nc= /cm 3 Copper solid 30um Radiation Transport Photon energy 1 MeV MeV (50 groups) Sn direction : 144/2π Bremsstrahlung

25 Simulation of ultrafast heated copper thin target Electron energy density (time-averaged) Bz (instantaneous) Hard x-ray energy density (instantaneous)

26 pair production calculated in the γ-ray transport X-ray spectrum and positron energy distribution Positron density time- integrated at the production point In the current simulation, positrons and electrons produced in the pair production are not fed back into the PIC simulation.

27 Summary We have developed 2D Particle-in-Cell, PICLS, with Radiation Transport code, that can self-consistently model the laser-plasma formation and development, and the subsequent X-ray radiation emission and transport. The non-equilibrium, collisional-radiative atomic kinetics 0-D code FLYCHK was used to generate a database of emissivities and opacities as functions of photon frequency for a given array of densities and temperatures. The characteristic emission by hot electrons on the X-ray spectrum is installed, by taking into effect the inner K-shell ionizations, and subsequent emission of the K a line emission. The direct comparisons of experiments and simulations indicate the overestimation of electron spot size from the K-a emission profile Bremsstrahlung from the relativistic electrons is implemented in the radiation transport code, which makes us available to see γ-ray propagation during the laser - matter interaction. We demonstrated the pair production using obtained γ-ray profiles. The next challenge is coupling of radiation kinetic plasma simulation and atomic processes.