Historical research guide · 0994 · 2012
Generalized Lawson criterion for magnetic fusion applications in space
Dejan Petkow · Roland A. Gabrielli · Georg Herdrich · René Laufer · Hans-Peter Röser
In one minute
John Lawson’s criterion is the sum every fusion reactor has to pass: the plasma must be dense enough, hot enough, and held together long enough to give back more than it took. Dejan Petkow, Roland Gabrielli, Georg Herdrich, René Laufer and Hans-Peter Röser, at the Institute of Space Systems in Stuttgart, rewrite that sum for a reactor that has to fly. A power station on the ground can weigh what it likes and dump its waste heat into a river; a spacecraft carries its magnets, its radiators and its power conversion with it, and every kilogram is paid for at launch. Their generalised burn criterion keeps those subsystems inside the equations, and adds three things the classic version leaves out: a hot-ion mode that can be varied, a fuel mixture that need not be even, and a separate confinement time for the charged fusion products. They then put four fuels through it — deuterium-tritium, deuterium-helium-3, helium-3 with helium-3, and proton-boron-11 — and weigh the systems that result.
Connection
Chapter 12 treats fusion as the energy substrate of the whole programme, and this paper supplies the honest scorecard: the burn condition written with the mass of the machine still attached, so a fuel choice can be judged by what it costs to fly rather than by what it achieves in a laboratory. Chapter 8 gets the same result from the propulsion side, since a fusion power plant that has to launch is the first engineering gate between a reactor and a ship.
From the source
A generalized burn criterion for thermonuclear fusion reactors in space is derived analytically. Unlike the classic Lawson criterion, it carries the subsystems that distinguish astronautic from terrestrial magnetic confinement fusion technology, so the condition for a burning plasma is written together with the hardware that has to be lifted.Abstract, opening sentences; Fusion Engineering and Design 87, pages 30 to 38
Three degrees of freedom are added to the usual triple product of density, temperature and confinement time: a variable hot ion mode, in which the ions run hotter than the electrons; a variable fuel ratio, so the mixture need not be equal parts; and a ratio coupling the confinement time of the fusion product ions to the energy confinement time. The modelling is built on a power density flux model, and the energy and particle balance equations are solved for the triple product to give an analytical expression for the more general criterion.Abstract, sentences two to five
The criterion is evaluated for the four reactant couples that are actually studied for space: deuterium with tritium, deuterium with helium-3, helium-3 with helium-3, and boron-11 with a proton, each for a given energy confinement time and a given fusion product confinement time ratio.Abstract, results sentence
On the back of that, an exemplary comparative system mass analysis is performed and a generic system mass model is evaluated, so the fuels are compared not only by how hard they are to burn but by how heavy the resulting flight system would be.Abstract, system mass analysis sentences
Within the frame of a thermally heated fusion plasma with a hot ion mode, the helium-3 with helium-3 reaction is found to be the most impractical of the four for space applications.Abstract, findings sentence
Important technological challenges remain to be met in the case of the boron-11 with proton reaction — the aneutronic fuel whose products are charged particles that can be converted directly — and the authors point to specific model improvements for future research as the way to sharpen the answer.Abstract, closing two sentences
The way in
https://doi.org/10.1016/j.fusengdes.2011.08.008How to cite it
Dejan Petkow, Roland A. Gabrielli, Georg Herdrich, René Laufer, Hans-Peter Röser (2012) Generalized Lawson criterion for magnetic fusion applications in space doi:10.1016/j.fusengdes.2011.08.008