Heating in short-pulse laser-driven cone- and nail-capped wire targets R. J. Mason*, M. Wei1, J. King1, F. Beg1 and R. B. Stephens2 *Research Applications Corp. 1UCSD, 2General Atomics, 49th Annual Meeting of the APS Division of Plasma Physics Rosen Center Orlando, Florida November 12-16, 2007 *Work performed in part under SBIR Grant No. DE-FG02-07ER84723

ABSTRACT · We study the interaction of short pulse lasers with the ends of copper wire targets capped with cones and nail heads. · Beams at 4.0 x 1020 and 2.0 x 1019 W/cm2 intensity are propagated to critical, where they generate Mev particle-electrons that transport down the wires, drawing resistive cold-fluid return-currents. · We model this phenomenology with the new implicit/hybrid code e-PLAS.

We have looked at “coned” systems with the laser striking the inside of the cone, and “nail-headed” systems. Both systems provide challenging targets for experiment and simulation. Here we explore wires varying from 100 to 10 mm in diamter. Cone head Laser Scale measure: varying from 200 to 1000 mm in our simulations

One goal it to approach the modeling of cone-wire target shot at RAL PW July 2006 (Aluminum cone glued to Cu 10,20 or 40 micron diameter Cu wire*) Glue *Jim King, UCSD 13µm 5µm ~0.945 to 0.959mm ~0.966 to 1.015mm 0.010mm 0.703 to 0.708mm 30° Shot 1: 39µm Shot 2: 32µm Shot 3: 32µm Shot 4: 34µm Shot 5: 30µm 0.05mm

We use the RAC e-PLAS code Features: 2-D, Implicit Moment E & B-fields, PIC hot electrons, fluid background electrons and ions, relativistic corrections, electron scatter and drag off ions, background (cold) electron resistivity, laser light propagation to hot emission at critical surface, ponderomotive effects, cartesian (x,y) or cylindrical (r,z) geometry. Special Capabilities: •High target densities (>1025 e-/cm3), vacuum regions, •No Dt restraint from wpDt <1, global problems •Particle instabilities

Classical collisional treatment includes: • Scatter done at the Spitzer rate, but modified for metals by a floor (at typically 100 eV) on the background temps. • Hot electron scatter and drag rates relativistically corrected to match Jackson’s and Mosher’s analysis. • Heated cold e- (from the hot drag and cold scatter) coupled to the ions at a Spitzer rate. When nc-i ~ nh-c cold heating is directly mirrored in the ions.

A traditional ICF light deposition package is used for efficient laser-interaction studies • Grid-following - no need for an extra-fine mesh to propagate light waves. Density limited PMF. • Dump-all, inverse-bremsstrahlung, and anomalous absorption. • PIC hot electrons emitted in a relativistic Maxwellian or shell momentum distribution, isotropic or in a beam.

surface plot of nh (hot e-) To start, we have explored 100 mm diameter wires with cones. Early in our runs we see: I = 4x1020 W/cm2 t = 488 fs cone walls cold e- density surface plot of nh (hot e-) ponderomotive steepening ions Laser intensity cold e- hot e-

The electron & ion densities evolve as: t = 488 fs 1.5 ps 3.01 ps 6.02 ps laser hot e-

While the B-field near the wire changes as: t = 488 fs 1.5ps 3.01 ps 6.02 ps nh flux

Cold electron and ion temperatures in the wire remain modest (~1 Cold electron and ion temperatures in the wire remain modest (~1.0 keV) over 6 ps and 1000 mm t = 488 fs 3.01 ps 6.02 ps Tc Ti hot e- surface plots in cone in wire

Similarly, we have looked at nail-headed at 2 x 1019 W/cm2 - obtaining for a 50 mm copper wire (Z = 15) 30 mm spot (but FWHM = 10 mm), t=940 fs hot e- density trapped near spot filamentary break-up 10-fold decay over 100 mm 2 keV peak In head

The self-consistent B- and E-fields trap and retard the hot e- transport resistive E-field nodal B-field In spot wire surface B-field

Flux and phase plots document the trapping t=940 fs circulating hot e- returning colds hot e- phase space 13.3 -13.3 vg/c 300 X(mm) reduced hot e- flux with penetration trapping near critical

We have studied changes as the wire diameter is paramet-rically reduced to 40 mm, then 20 mm, and finally to 10 mm. D = 40 mm 20 mm 10 mm Zni nh t = 2 ps

Correspondingly, we see the central cold temperature profile evolve as: D=40 mm 20 mm 10 mm Tc head0.8 1.1 keV 0.7 keV Ti wire t = 2 ps

Observations Both the “cone-” and “nail-headed” targets trap significant hot electrons in the target heads … while wire temperatures remain modest. The ion temperatures approach the ~1.0 keV cold electron temperatures at the longer 6 ps time scales explored with the cone headed targets, but stay below 350 eV in the shorter time and space scaled nail headed target studies. With the nail heads significant hot electron penetration limited at 220, 200, and 170 mm, respectively, as the wire is narrowed. The maximum cold temperature just near the nail heads go from 0.7, to 0.8, to 1.1 keV with the narrowing. But 20 mm inside it drops from 0.7, to 0.6 to 0.5 keV. The wire surface tends to be hottest, corresponding to favored hot penetration there (surface colds are really hots). Thermoelectric B-fields in the cap reach ~200 MG with the cones, but up to 500 MG in the smaller nail-headed studies.

Conclusions Implicit plasma simulation can provide useful insight for short-pulse hot electron driven heating experiments. A significant fraction of the energy appears to remain in the heads of cone- and nail-headed targets. The simulations show acceptable coupling to the ions over the longer time scales uses with the cones.