FSC 1 Benchmark Modeling of Electron Beam Transport in Nail and Wire Experiments Using Three Independent PIC Codes Mingsheng Wei Annual Fusion Science Center Meeting August 4-5, 2007 San Diego Center For Energy Research University of California, San Diego This work was supported by the US Dept of Energy through various grants from the Office of Fusion Energy Sciences. FSC Voss Scientific RAC

FSC 2 Lawrence Livermore National Laboratory R.R. Freeman, L. Van Woerkom, D. Offerman, K. Highbarger, R. Weber D. Hey M.H. Key, A.J. MacKinnon, A. MacPhee, S. Le Pape, P. Patel, S. Wilks R.B. Stephens J. Pasley, T. Ma, J. King, E. Shipton, F.N. Beg A. Solodov Y. Sentoku R. Mason RAC D.R. Welch Collaborators

FSC 3 Outline Motivation Benchmark experiments using novel nail and wire targets Codes used Simulation results Summary and future work

FSC 4 Details of transport of fast electrons with huge currents remains uncertain Numerical simulations help to understand instabilities, electron beam spreading, energy loss and heating mechanisms etc. in the transport process 10n c 1000n c High intensity laser Fast electrons 40µm 100’s µm Density gradient in conventional FI via hole boring Density gradient in cone guided FI MeV electrons have to propagate through 10’s to 100’s µm to heat the compressed fuel 500n c 5000n c High intensity laser ~ 50 µm Guiding cone Electron transport is a key issue for fast ignition

FSC 5 millimeter scale target ps short pulse with ns pedestal Full scale modeling is impossible Simulations are descriptive Modeling Experiments Benchmark simulations against a simple experiment to validate the algorithms and transport models used in the codes — using simple target geometry — known laser parameters — well-characterized preformed plasmas — hydro code to model the preformed plasma — hybrid PIC codes to study the electron transport We need a simple experiment to validate transport codes Experiments Simulations

FSC 6 Benchmark experiments using low mass wire targets have been performed on the Titan laser at LLNL Wire targets are accessible to various diagnostics Targets are small enough to be included in the simulations K  imagers diagnose the production and transport of the fast electrons XUV imagers provide information of target heating Titan Laser parameters: Energy ~ 130 J Pulse length ~ 500 fs Spot size ~ 10 µm Peak intensity ~ W/cm 2 Simple Ti wire: 50 µm in diameter Cu nail target Head:100 µm diameter Wire: 20 µm diameter with 2 µm Ti coating on the surface to examine surface vs. bulk transport

FSC 7 Typical experimental observations 4.5 keV 8.0 keV 100 µm Ti K  emission from the surface Cu K  emission from the bulk Long range surface heating 68 eV XUV 1 mm ~800um Energy concentrated in the nail head Limited propagation lengths along the wire Long range plasma thermal emissions from the wire surface

FSC 8 We aim to accurately model the wire experiments That means modeling the experiment as fielded, in addition to properly simulating the physics: -Target geometry -Preformed plasma produced by the nanosecond prepulse -Physically generate current -Direct comparison with the experimental data

FSC 9 Preformed plasma is modeled by the 2D hydro code h2d Laser prepulse creates substantial preformed plasma, i.e., critical surface has moved away from original target surface by ~ 30 µm Such preformed plasmas are included in the hybrid simulations the measured prepulse profile of the Titan short pulse laser Initial target surface Critical surface (on axis) N e ~10 20 cm -3 (on axis) h2d simulation results

FSC 10 PICLSe-PLASLSP 2D (Cartesian) EXPLICIT PIC code All kinetic equations Full relativistic Coulomb collision between e-e, e-ion, ion- ion T c threshold 10 eV 2-D (Cartesian) IMPLICIT hybrid PIC code (use of momentum equ.) Fluid background electrons, & ions, kinetic for selected species (hot electrons) Relativistic corrected Spitzer collision model T c initial 100 eV Fully 3D (cylindrical or Cartesian) IMPLICIT hybrid PIC code (direct approach) Fluid background electrons, & ions, kinetic for selected species (hot electrons and ions) Classic Spitzer collision model T C initial 100 eV Self consistent model of hot electron production Conventional laser deposition package, critical surface can be tracked Hot electrons produced by heuristic scaling and excited at the critical surface Electrons can either be self- consistently produced from LPI or excited from the background electrons Three PIC codes used to model the transport experiments

FSC 11 Fast electrons are trapped near the interaction region R = 1 µm R = 7.6 µm R = 25 µm Initial interface of kinetic electrons and fluid electrons Z (µm) R (µm) laser e-PLAS LSP v  /c X(  m) trapping near critical by intense B-fields hot e - phase space

FSC 12 Fast electrons have a overall limited propagation length of ~ 100 µm µm LSP e-PLAS PICLS Number density (cm -3 ) In both LSP and e-PLAS, n e hot drops to cm -3 in a distance of ~ 100 µm In PICLS, electron energy density decreases by more than one order of magnitude in about 200 µm (this difference could be due to a lower e - number density used in the simulations) Z (µm) on-axis e - energy density

FSC 13 Long range surface currents and the resultant surface heating have been observed in simulations PICLS Temperature (eV) Z (µm) Temperature (eV) near axis at surface LSP e-PLAS higher T c on surface At a greater distance, the wire surface is heated more than the inside due to the ohmic heating by the surface current Pronounced surface heating in PICLS simulations

FSC 14 Strong electric and magnetic fields are observed Z (µm) B  (MG) R (µm) -40 B  (MG) 40 B Z contours B Z (MG) laser LSP e-PLAS - 1.5e7 E r (kV/cm) 1.5e7 Z (µm) Surface radial E field : MV/µm Surface azimuthal B field: 10’s MG in LSP MG in e-PLAS E&B fields are consistent with surface transport Intense azimuthal B field is also produced at the deformed interaction region

FSC 15 SUMMARY Benchmark simulations using implicit/hybrid PIC codes, LSP and e-PLAS as well as the fully PIC code, PICLS, have been performed to study the fast electron beam transport in the nail/wire experiments Simulations have shown good qualitative agreement among the codes, which are also in consistent with the experiments:  Localized energy deposition due to trapping of the fast electrons by B-fields.  Overall propagation length of about 100 µm in the bulk of the target predominantly due to resistive inhibition and B-field trapping at the interaction region  Long range surface current and surface heating  Intense surface E & B fields which guide the surface current Quantitative differences are also observed: – Higher degree target heating in PICLS --- a lower density being used – Pronounced surface current (?) in PICLS --- a lower density being used – e-PLAS predicts extremely high surface B-fields (200 MG) – Low temperature in LSP due to the low laser energy in the input.

FSC 16 On-going and future work using the LSP code  Calculate K  production and transport using the ITS code coupled to LSP  Analyze the simulation results in terms of diagnostics  Use more accurate EOS models to obtain background temperatures (currently, ideal gas model for all three codes, temperatures over estimated)  Continue the integrated LSP simulations to study short-pulse hot electron driven heating experiments using low-mass targets  Model electron beam transport and target heating in Omega EP FI experiments

FSC 17 Supplemental slides attached next

FSC 18 Fast electrons produced in the latest integrated LSP simulations have a two-temperature energy distribution >40% of the laser energy is transferred to the fast electrons Average energy in the hot tail is comparable to the ponderomotive energy The not-so-hot component fits to an average energy of MeV

FSC 19 0ns3.5ns 7ns #3 18 th Sept #5 18 th Sept #5 14 th Sept E-M wave from boundary PIC (kinetic) electrons and ions Fluid electrons and ions E-M wave is launched from the boundary Energetic electrons are self-consistently produced from laser plasma interaction (LPI) Solid wire targets are treated as fluid background. 450 µm 50 µm I peak ~ 7  W/cm 2  = 0.5 PS (FWHM)  =15 µm 15 µm thick preformed plasma (  cm -3 ) Ti wire: z=15, n e =8.45  cm -3, initial temperature 100 eV Simulation box Integrated LSP simulation setup

FSC 20 PICLS 2D simulation setup Laser (Titan): a=8, I= W/cm 2, pulse length=500 fs (gaussian) spot=20um (gaussian), Energy input=130 J Target: nail target, Z=15, Cu ion density= /cm 3, e- density= /cm 3 wire diameter=20um preplasma (5µm scale length, /cm 3 ) at top of nail System size: 400um x 100um Ion energy density (n/n 0 )  : 1eV-100keV t=1.5ps

FSC 21 e-PLAS simulation setup  Laser: I=1.7 x W/cm 2, 1 ps pulse (top hat), 10 µm spot  Target: copper wire (z=15) preceded with a 20 µm density ramp; initial temperature 100 eV  Electron beam generation: hot electrons are promoted from the critical surface with an isotropic Maxwellian spectrum at ponderomotive energies (  = 10.5)  System size: 100 µm by 300 µm

FSC 22 2D LSP simulations using the excitation model for fast electron generation without the preformed plasma Fast Electron Density – Plasma Temperature at 1.5 ps r=0 r=7 µm r=10 µm Cu 15+ nail target Laser: 81 J, I = 5  W/cm 2, gaussian pulse 0.5 ps (fwhm), focal spot size 16.4 µm (fwhm) Energy concentrated in the nail head Surface current and resultant surface heating Surface E and B fields