Fast-ignition transport studies: Realistic electron source, integrated particle-in-cell and hydrodynamic modeling, imposed magnetic fields

Abstract

Transport modeling of idealized, cone-guided fast ignition targets indicates the severe challenge posed by fast-electron source divergence. The hybrid particle-in-cell [PIC] code Zuma is run in tandem with the radiation-hydrodynamics code Hydra to model fast-electron propagation, fuel heating, and thermonuclear burn. The fast electron source is based on a 3D explicit-PIC laser-plasma simulation with the PSC code. This shows a quasi two-temperature energy spectrum, and a divergent angle spectrum (average velocityspace polar angle of 52 • ). Transport simulations with the PIC-based divergence do not ignite for > 1 MJ of fast-electron energy, for a modest (70 µm) standoff distance from fast-electron injection to the dense fuel. However, artificially collimating the source gives an ignition energy of 132 kJ. To mitigate the divergence, we consider imposed axial magnetic fields. Uniform fields ∼50 MG are sufficient to recover the artificially collimated ignition energy. Experiments at the Omega laser facility have generated fields of this magnitude by imploding a capsule in seed fields of 50-100 kG. Such imploded fields are however more compressed in the transport region than in the laser absorption region. When fast electrons encounter increasing field strength, magnetic mirroring can reflect a substantial fraction of them and reduce coupling to the fuel. A hollow magnetic pipe, which peaks at a finite radius, is presented as one field configuration which circumvents mirroring.

Progress and prospects for an IFE relevant FI point design

“…Efficient escape through the mirror requires a mirror loss cone angle as large as the source cone angle, and analytic estimates suggest this limits the B field increase to <30%. Numerical modeling results [7] confirm a strong increase in ignition energy for B field increases >50%. This avenue of electron collimation is therefore blocked by mirror reflection.…”

“…One is compression of an axial B field around a cylinder of dense material that resists compression [7]. The other is auto-generation of an azimuthal B field by the electron beam using a radial change of resistivity in a current density j where dB/dt ∼ ∇ x j [8].…”

“…4 An effective way to collimate electrons is to use an axial magnetic field in which the electron Larmor radius is smaller than the ignition hot spot radius so that electrons spiral along the field lines from the laser focal spot to the ignition hot spot [6]. The required B field strength is >50 MG, and ignition energies at 450 g/cc are reduced to ∼ 260 kJ of 0.53 micron laser energy [7]. Preformed 50-kG fields can be compressed in the FI implosion to >50 MG, but unfortunately B field diffusion is too slow for effective penetration inside the FI target cone tip.…”

Cone-guided fast ignition withnoimposed magnetic fields

“…For mono-energetic 1.5 MeV fast electrons, without E and B fields, ignition can be achieved with fast electron energy E ig f = 30 kJ. This is 3.5× the minimal deposited ignition energy of 8.7 kJ for our fuel density of 450 g/cm 3 . Including E and B fields with the resistive Ohm's law E = J b gives E ig f = 20 kJ, while using the full Ohm's law gives E ig f > 40 kJ.…”

“…By "transport" we mean the propagation and deposition of fast electrons, with reasonably self-consistent coupling to the background radiation-hydrodynamics. To achieve this we coupled the hybrid-PIC code Zuma [2,3] to the rad-hydro code Hydra [4]. A detailed publication on this work [3] reports laserplasma PIC modelling that shows a large fast-electron divergence, along with mitigation ideas based on imposed magnetic fields.…”