The Fusion Two-Step

Simulations elucidate the physics of fast ignition

To a dance aficionado, the term two-step may refer to the ballroom dance that evolved into the foxtrot, or to country/western dances like the Texas two-step and the Cajun two-step. But in the realm of alternative energy sources, one of the hottest new trends is the two-step fast ignition concept for inertial confinement fusion (ICF).

ICF is the process of initiating a nuclear fusion reaction by heating and compressing a fuel target, usually a pellet of deuterium-tritium (DT) ice. If a 10 milligram DT fuel pellet was completely consumed by fusion, it would release energy equivalent to more than half a barrel of oil.

Until recently, the most common approach to ICF has been hot-spot ignition, in which the fuel pellet is compressed and heated in one step by a multi-beam laser. This is the concept around which the National Ignition Facility (NIF), scheduled to be completed in 2009 at Lawrence Livermore National Laboratory, was designed.

In the newer fast ignition concept, compression and ignition are separated into two steps: first, a compression laser compresses a spherical shell of DT ice to high density at low temperature, without a central hot spot; then a second very high-intensity laser delivers an extremely short pulse of energy that ignites the compressed fuel.

The two ignition concepts are sometimes compared to a diesel engine (pure compression) and a gasoline engine (where the fast ignitor is equivalent to a spark plug). Compared to hot-spot ignition, fast ignition promises much higher gain (the ratio of energy output to energy input) for the same driver energy, possible reduction of the driver energy necessary to achieve ignition, and less stringent compression symmetry requirements.

The ignition step is the least understood aspect of fast ignition and is the subject of the INCITE project “Three-Dimensional Particle-in-Cell Simulations for Fast Ignition,” led by Chuang Ren, Assistant Professor of Mechanical Engineering and Physics at the University of Rochester, and Warren Mori, Professor of Physics and Electrical Engineering at UCLA.

The hole-boring scheme

Since the ignition laser cannot directly reach the dense core region, the laser energy needs to be converted into an energetic (super-hot) electron beam that can penetrate to the core and deposit its energy there. The electron beam needs to be generated as close to the core as possible to reduce energy loss along its path to the core. One way to do that is the hole-boring scheme, in which the ignition laser pulse is preceded by a channeling laser pulse to create a channel through the underdense corona and into a critical density surface, beyond which it cannot penetrate (Figure 1). The ignition pulse is then sent in tandem to reach the critical surface and may continue to push forward into the overdense plasma, in the meantime heating the plasma to generate the energetic electron beam. This beam will penetrate through the dense plasma and deposit the energy in the core, heating a small area to a high-enough temperature to ignite the fusion reaction.

Figure 1. A sketch of the hole-boring scheme for fast ignition. (Click image for larger view)

“Compressing the fuel to high density is relatively easy to achieve, but high temperature is more challenging,” Ren said. “You need to convert the laser energy into electron energy, and these electrons need to be collimated [focused], because if they spread to a large area, you need much more energy to heat a large area. You need to focus the laser down to a very small spot, say a 20 micron radius, and make the electrons go forward, not just spread.”

Ren continued: “The ignition laser has to heat the pellet in a very short time, 10 to 20 picoseconds, so its intensity is a lot higher than the compression laser, which works on the time scale of 1 nanosecond and has intensity of 10¹⁴ watts per square centimeter. But the ignition laser will need intensity of 10¹⁹ to 10²⁰ watts per square centimeter. So we understand less about the interactions between the more intense ignition beam and a plasma. Our computation is about this process.”

Particle-in-cell (PIC) methods provide the best available simulation tool to understand the highly nonlinear and kinetic physics in the ignition phase. Ren’s project covers almost all the physics in the ignition phase with the goal of answering the following questions:

• Can a clean channel be created by a channeling pulse so that the ignition pulse can arrive at the critical surface without significant energy loss?
• What are the amount and spectrum of the laser-generated energetic electrons?
• What is the energetic electron transport process beyond the laser-plasma interface in a plasma with densities up to 10²³ cm^–3?

Millimeter-scale simulations

Most of the previous channeling experiments and simulations were done in 100 micrometer-scale plasmas, but the underdense region of an actual fast ignition target is 10 times longer. “If you extend the experiment 10 times longer in both size and time, you see new phenomena,” Ren said.

Using the OSIRIS code, which can run on over 1000 processors with more than 80% efficiency, Ren’s team ran the first 2D simulations of channeling at the millimeter scale.[1] These simulations, which ran on Seaborg and Bassi, employed up to 8 × 10⁷ grids, 10⁹ particles, and 10⁶ time steps. NERSC’s User Services Group increased the researchers’ disk quota and queue priority to accommodate the scale of these calculations. The Analytics Team also assisted by reducing network latency for remote performance of Xlib-based applications.

Figure 2. Simulation of laser channeling through an underdense plasma. (a) Ion density at t = 0.8 ps showing micro channels formed; (b) laser E-field showing laser hosing and (c) ion density showing channel bifurcation at t = 3.4 ps; (d) ion density at t = 7.2 ps showing channel self-correction. (Click image for larger view)

The results of the simulations showed important new details of the channeling process, including plasma buildup in front of the laser, laser hosing (an undulating motion like water coming out of a garden hose), and channel bifurcation and self-correction (Figure 2). The simulations demonstrated electron heating to relativistic temperatures, a channeling speed much less than the linear group velocity of the laser, and increased transmission of an ignition pulse in a preformed channel.

The simulation results also shed light on the question of how to save energy during the channeling process. “You want to spend as little energy as possible on creating the channel and save it for ignition,” Ren said, “so what kind of laser intensity do you use for the channeling? High intensity will create a channel more quickly, but you may spend more energy. You can also use a low intensity laser but it takes longer, so it was not clear before how to minimize that. We showed that a lower intensity laser takes more time to produce the channel but does it effectively using less energy than a high intensity laser. This result will provide some guidance for designing experiments.”

The group’s 2D simulations of hot electron generation and transport were the largest ever in target size and the first with isolated targets. These simulations employed 5 × 10⁸ grids, 10⁹ particles, and 10⁵ time steps. The results showed that the temperature of electrons emitted at high laser intensities is only half of that predicted by an empirical formula used in many fast ignition feasibility studies. The simulations also found that the laser absorption rate increases with the laser intensity. “Higher-intensity lasers are desirable since they bore a deeper hole and deliver their energy to a smaller area, creating a hot spot of higher temperature,” Ren explained. The combination of these effects means that ultra-high-intensity lasers can produce an electron flux with a majority of electrons in the usable energy range.

“But there are important effects that cannot be simulated in two dimensions,” Ren pointed out. “Simply scaling up our 2D simulations to 3D would require more than a 4000-fold computation increase. That is not feasible even on the largest computers available. So we will combine 3D simulations at reduced scales with full-scale 2D results and theory to figure out what happens.”

Ren is a researcher at the University of Rochester’s Laboratory for Laser Energetics, home of the recently completed OMEGA EP laser system, the world’s leading system for fast ignition experiments. He also collaborates with other investigators in the DOE’s Fusion Science Center for Extreme States of Matter and Fast Ignition Physics, which coordinates research in all aspects of fast ignition. Fast ignition is also going to be tested at the FIREX facility in Japan and the Z machine at Sandia National Laboratories. The National Ignition Facility could be adapted for full-scale fast ignition experiments, and the proposed HiPER facility in Europe is being designed for just that purpose. All of these experiments will benefit from the insights gained in Ren’s simulations, which gives his work a sense of urgency.

“This research will help toward the realization of fusion as a controllable energy source, and can help solve the energy crisis facing the world today,” he concluded.

This article written by: John Hules, Berkeley Lab.