# The Fundamental Parameter Space of Controlled Thermonuclear Fusion

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Few people are aware of the many conditions under which fusion can occur. Luckily, Irv Lindemuth et al have written a review of fusion to help the rest of us identify the density-temperature space where fusion gain can be achieved. The analysis offers a general understanding why there is such an extreme difference between the conventional approaches to controlled fusion, MCF (which uses a giant “magnetic cage” and ICF (which uses hundreds of laser beams pointed at a small target). It also helps us see how much of the parameter space of fusion has yet to be explored.

This clarifying overview of fusion came to our attention at the Fusion Power Associates Meeting, where Dr. Lindemuth presented a talk, now available (PDF file): Fusion Parameter Space from First Principles

See also: Article by I. R. Lindemuth, R. E. Siemon, Am. J. Phys., Vol. 77, No. 5, May 2009.

## The abstract

We apply a few simple first-principles equations to identify the parameter space in which controlled fusion might be possible. Fundamental physical parameters such as minimum size, energy, and power as well as cost are estimated. We explain why the fusion fuel density in inertial confinement fusion is more than 10

^{11}times larger than the fuel density in magnetic confinement fusion. We introduce magnetized target fusion as one possible way of accessing a density regime that is intermediate between the two extremes of inertial confinement fusion and magnetic confinement fusion and is potentially lower cost than either of these two.

Lindemuth and Siemon shine a light on magnetized target fusion, but their framework can be leveraged for plotting and comparing other approaches as well. It’s a handy document and covers a lot of the basics of fusion.

We also provide a unifying framework to make it possible for those familiar with one approach to be conversant in any other approach.

## MCF and ICF

From the introduction:

The two commonly recognized paths to controlled thermonuclear fusion energy have proven to be long and costly. Physicists not working in the fusion field are generally aware of two approahes to achieving controlled fusion reactions, magnetic confinement fusion (MCF) and intertial confinement fusion (ICF), and that these approaches are embodied in two multi-billion dollar facilities known as ITER (formerly an acronym for International Thermonuclear Experimental Reactor) for magnetic confinement fusion and NIF (National Ignition Facility) for inertial confinement fusion.

Most physicists are also aware that fusion reactions occur only at high temperatures, hence the name thermonuclear fusion.

There is more limited awareness that the density of the fusion fuel (a deuterium-tritium mixture) in the two approaches differs by a factor of more than 10

^{11}. The fuel density in ITER will be about 10^{14}ions/cm^{3}(mass density p=4.2 x10^{-10}g/cm^{3}), and the hot spot of a NIF target will be greater than 10^{25}ions/cm^{3}(p=42g/cm^{3}).This very large density difference leads to different physics challenges, for example, contrast the challenge of steady state magnetic confinement of MCF with the hydrodynamic implosion stability of ICF.

The problem-solving approach is also different; MCF relies heavily on empirically determined scaling laws, and ICF relies heavily on large-scale computer simulations.

## A Bridge from this article

This article was written with the goal of bridging the gap from plasma specialists to a broader audience of physicists.

It’s still written for physicists.

We’d like to take steps to get this framework even more comprehensible, such that a general audience can relate to it.

The article is available at the American Association of Physics Teachers website for $28. I got my copy from Dr. Lindemuth while at the FPA meeting. I’ll see what we can do about discounted distribution to members or incorporating it in educational materials here.

Enjoy!