Magnetized Liner Inertial Fusion

Andy Castillo
February 15, 2022

Submitted as coursework for PH241, Stanford University, Winter 2022

Using Z-Pinch for Fusion

Fig. 1: The Z machine during an experiment. (Courtesy of the DOE. Source: Wikimedia Commons.)

Magnetized Liner Inertial Fusion (MagLIF) uses a pulsed-powered accelerator to send an electrical pulse through a liner, which is a cylindrical shell that holds fusion fuel. [1] As the current runs along the liner, it induces an azimuthal magnetic field, and the combined presence of the current and field create an inwardly directed Lorentz force (known as the Z-pinch). With a large enough Z-pinch the liner implodes, compressing the fuel inside to a large enough temperature and pressure that fusion reactions can occur. However, in order to produce enough fusion reactions to surpass the energy put into the liner, the fuel must be heated and confined for a considerable amount of time after the electrical pulse. [1] With present-day capabilities of pulsed-power accelerators to implode the liner with velocities around 70 km/s, the Z-pinch alone is insufficient for generating considerable fusion reactions. [2]

The concept of directing energy to implode a fuel capsule is also found in inertial confinement fusion (ICF), where lasers are used to heat and implode spherical capsules. With implosion velocities greater than 300 km/s, this method has shown greater success in generating fusion energy. [2] Thus, in order to be considered a potential energy source method, MagLIF incorporates two additional components. First, external coils are used to apply an axial magnetic field to the liner. This functions to confine plasma generated from the implosion, which mitigates heat losses and consequentially reduces the thermodynamic requirements for sustained fusion reactions. [2] Additionally, MagLIF incorporates its own laser that pre-heats the fuel as soon as the implosion process commences. [2] With these and further improvements, MagLIF aims to become a noteworthy effort in fusion energy production.

Experiments at the Z Machine

The Z machine, shown in Fig. 1, is a pulsed-power facility located at Sandia National Laboratories. Known as the largest X-ray generator in the world, it is primarily used for creating and studying environments relevant for the Stockpile Stewardship Program. [3] However, this facility has also been used for investigating MagLIF through a series of experiments in the 2010's. [3] The first major experiment in 2013 consisted of an electrical pulse with a peak current of 18 MA, Helmholtz-like coils that apply an axial magnetic field with strength of 10 T, and a TW-class, frequency doubled Nd:glass laser that deposits 0.5 kJ of preheat energy to the liner. [3] This experiment was able to reach a large enough temperature and confinement to produce 2 × 1012 neutrons, where a single neutron is produced from each primary fusion reaction. [2] Considering ICF experiments at the National Ignition Facility generating up to 1.9 × 1016 neutrons, the result at the Z machine may not seem advantageous. [4] However, the 2013 experiment successfully showed the largest temperature values and neutron production from a magneto-inertial fusion concept. It also confirmed the need for the preheating laser and applied axial magnetic field to optimize results. [2] Subsequent experiments illustrated the scalability, opportunities, and limitations of MagLIF.

Experiments at the Z machine were focused on increasing the gain, which is the ratio of fusion energy produced to the energy delivered to the liner. While experiments with larger current electrical pulses, applied magnetic field, and preheat laser energy yield improved results, certain limiting factors needed to be addressed. Firstly, increasing power of the implosion process exacerbates the Magneto Rayleigh-Taylor instability, a phenomenon with a non-magnetic analog occurring in ICF. [3] This instability forms regions of lower pressure in the liner that results in lower confinement times, and, despite continued investigation and mitigation attempts, it continues to deter the performance of the experiment. [3] Additionally, the preheating laser causes material of and on the liner to mix with and contaminate the fuel, increasing radiation losses. [3] However, a co-injection method which separates the laser's contribution into two pulses has shown to decrease this contamination. Another important limitation is the strength and uniformity of the applied magnetic field using external Helmholtz-like coils, where the inductance of the current-carrying transmission lines can affect the coils. [3] To increase capabilities, an auto-magnetizing liner is being considered which incorporates a conductor that is wrapped around the liner in a helical form within an insulating layer. With this layer, an initial electrical pulse can be used to induce the axial magnetic field with larger strengths. [3]

Outlook

Like most fusion energy efforts, MagLIF experiments have been making improvements and increased scaling to attempt to surpass the scientific breakthrough, which is a gain larger than 1. However, if this concept is to be considered as an economical energy source, it must also reach engineering breakthrough. This breakthrough would mean that the yielded fusion energy is large enough to cover the electrical needs of the power plant, the energy required for the experiment, and the losses in converting the yield to usable electricity. [3] Initial estimates for a hypothetical MagLIF plant would require a gain of at least 50. [3] While this goal seems unattainable, 1D and 2D simulations based on the Z machine experiments show promising results using the design of prospective pulsed-power facilities, Z300 and Z800. [5] Considering that the Z800 would be designed for a peak current of 65 MA, simulations that incorporate an additional layer of deuterium-tritium ice in the liner shows results with gains as large as 70. [5] Despite the many hurdles that would follow achieving engineering breakthrough, such as increasing the frequency of electrical pulse to more than one per day, capturing the fusion energy yield, and converting it to electrical energy, the possibility of MagLIF achieving such a high gain presents a noteworthy opportunity for fusion energy research. [3]

© Andy Castillo. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] S. A. Slutz et al., "Pulsed-Power-Driven Cylindrical Liner Implosions of Laser Preheated Fuel Magnetized with an Axial Field," Phys. Plasmas 17, 056303 (2010).

[2] M. R. Gomez et al., "Experimental Demonstration of Fusion-Relevant Conditions in Magnetized Liner Inertial Fusion," Phys. Rev. Lett. 113, 155003 (2014).

[3] D. Yager-Elorriaga et al., "An Overview of Magneto-Inertial Fusion on the Z Machine at Sandia National Laboratories," Nucl. Fusion 62, 042015 (2021).

[4] S. Le Pape et al., "Fusion Energy Output Greater than the Kinetic Energy of an Imploding Shell at the National Ignition Facility," Phys. Rev. Lett. 120, 245003 (2018).

[5] S. A. Slutz et al., "Scaling Magnetized Liner Inertial Fusion on Z and Future Pulsed-Power Accelerators," Phys. Plasmas 23, 022702 (2016).