Fast Ignition for Inertial Confinement Fusion

In Inertial Confinement Fusion a capsule of hydrogen isotopes (DT) implodes under ablation pressure and the isotopes fuse, releasing energy. Fast Ignition has been proposed to decouple the compression from the ignition process. It relies on the electrons at the surface of the compressed target to absorb the energy of an ultra-intense laser pulse, travel through the dense plasma, and deposit that energy to the pellet’s core. We performed 2D Particle-In-Cell simulations with the OSIRIS for the first pico-second of the interaction in a scaled-down fast ignition target isolated from the boundaries, in order to identify the key absorption physics and disentangle the mechanisms at work [1] - [2].

MOVIE 1 - Hole boring in a scaled-down fast ignition simulation. Filamentation of the electron density is seen near the laser-plasma interface. (See Ref. [1] - [2].)

A movie of the electron density near the laser-plasma interaction region is presented above. The laser drills a hole in the plasma and the plasma density increases considerably near the laser-plasma interface. Filaments in the electron density can also be observed in this high density shock-like structure. These correspond one-to-one to filaments in the transverse profile of the laser intensity as shown in Figure 2. The laser filaments thus act as a seed for the Weibel instability. This is corroborated by a simulation (Movie 2) in which the plasma boundary is sharp, and where the plasma density still filaments even though the laser does not. In this simulation the effect observed is exclusively due to the Weibel instability.

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FIGURE 2 - There is a one-to-one correspondence between laser intensity filaments and plasma density filaments. (See Ref. [2])
MOVIE 2 - Filamentation of the electron density is observed in a simulation where the plasma-vacuum boundary is very sharp and the laser intensity does not filament at all. This is a manifestation of the current filamentation (Weibel) instability.

Another unexpected effect observed in the fast ignition simulation was that not only did the electrons filament but the ions did as well. To explain this we developed an analytical theory for electromagnetic instabilities that includes the coupling to electrostatic modes (see below).

We are currently using the hybrid code OSIRIS-H to perform large fast ignition simulations. This code enables integrated simulations of realistic targets and time-scales.


Electromagnetic Instabilities

To explain the apparent fluid-like behavior of the current filamentation instability in fast ignition scenarios we developed analytical theory for the coupling of electromagnetic instabilities to electrostatic modes [3] - [4]. This theory shows that as cold electrons tend to filament at a faster rate than hot ones they pull with them the ions. Because hot electrons are usually in the mionority, the filaments of the bulk of the electron population overlap with those of the ions, which is exactly what one would have expected from a fluid instability (such as Rayleigh-Taylor.) Nevertheless, this is a purely kinetic electromagnetic phenomenon. The predicted growth rate was confirmed using Particle-In-Cell simulations and the physics is illustrated in Figure 3.

FIGURE 3 - Filamentation of counter-streaming electron beams (red/blue density isosurfaces) leads to filamentation of the background ions (green isosurfaces). The colder (blue) electron filaments attract the ions. (See Ref. [3].)

Finally, all of these effects in fast ignition were observed for electron distribution functions that did not exhibit any beam-like features, but analytical theory was only available for beam-like distributions, such as drifting Gaussian and Waterbag distribution. To resolve this we calculated the stability properties (growth/damping rate) of electromagnetic modes for arbitrary electron distribution functions [5].



[1] C. Ren, M. Tzoufras, F. S. Tsung, W. B. Mori, S. Amorini, R. A. Fonseca, L. O. Silva, J. C. Adam and A. Heron, Phys. Rev. Lett. 93, 185004 (2004) “Global Simulation for Laser-Driven MeV Electrons in Fast Ignition.”

[2] C. Ren, M. Tzoufras, J. Tonge, W. B. Mori, F. S. Tsung, M. Fiore, R. A. Fonseca, L. O. Silva, J.-C. Adam and A. Heron, Phys. Plasmas 13, 056308 (2006) “A global simulation for laser driven MeV electrons in 50µm-diameter fast ignition targets.”

[3] M. Tzoufras, C. Ren, F. S. Tsung, J. W. Tonge, W. B. Mori, M. Fiore, R. A. Fonseca and L. O. Silva, Phys. Rev. Lett. 96, 105002 (2006) “Space-Charge Effects in the Current-Filamentation or Weibel Instability.”

[4] M. Fiore, L. O. Silva, M. Tzoufras, C. Ren and W. B. Mori, Monthly Notices of the Royal Astronomical Society Volume 372, Issue 4, Page 1851-1855 (2006) “Baryon loading and the Weibel instability in gamma-ray bursts.”

[5] M. Tzoufras, C. Ren, F. S. Tsung, J. W. Tonge, W. B. Mori, M. Fiore, R. A. Fonseca and L. O. Silva, Phys. Plasmas 14, 062108 (2007) “Stability of arbitrary electron velocity distribution functions to electromagnetic modes.”