Historical research guide · 0997 · 1985

Thermonuclear inverse magnetic pumping power cycle for stellarator reactors

Darwin D.-M. Ho · Russell M. Kulsrud

In one minute

A fusion reactor normally turns its energy into electricity the old way: heat water, spin a turbine. Darwin Ho and Russell Kulsrud at the Princeton Plasma Physics Laboratory proposed something better for a stellarator — squeeze the plasma and let it push back. Their cycle runs the plasma column like the piston of a car engine. Strengthen the ring-shaped magnetic field and the plasma is compressed; the helium nuclei thrown off by the fusion burn then reheat it at fixed volume; weaken the field and it expands. Because there is a ceiling on how much pressure a plasma will hold before it goes turbulent, the expansion happens at a higher pressure than the compression did, so over a full cycle the plasma does net work on the magnet coils — and that work appears as a voltage, electricity drawn straight out of the burn with no steam anywhere. For their sample ten-metre reactor the cycle delivers 2.2 gigawatts, about half of what the same machine’s neutrons would give.

Connection

Chapter 12 wants fusion that hands you electricity rather than heat, and this is a national-laboratory report showing one way to get it using nothing but the magnets the machine already has — which matters most for the neutron-lean fuels where there are almost no neutrons to boil anything with. Chapter 9 is about what a confined plasma does when you push on it, and here the plasma’s own pressure limit, normally a nuisance, is turned into the working stroke of an engine.

From the source

The cycle has three strokes and takes its work out as a voltage. Starting from an ignited, thermally balanced plasma, the external toroidal field is raised and the plasma column is compressed adiabatically in minor radius; then the field is raised further to hold the volume fixed while the alpha particles from the burn heat the plasma back up; then the field is lowered and the plasma expands to its original radius. Because the plasma pressure during the expansion exceeds the pressure at the corresponding radius during the compression, negative work is done on the plasma over a complete cycle. That work shows up as a mean back-voltage in the toroidal field coils, and electrical energy is taken directly from that voltage — no thermal cycle, no working fluid, no turbine.Section 1, Introduction; Section 2, Physics of the Cycle; Figures 1 and 3
Compression makes the plasma hotter, and that is the whole reason the cycle works. After an adiabatic compression the alpha-particle heating power per unit volume rises faster than the losses do. The report gives all three scalings for a compression ratio of one over 0.6: the alpha heating rises by a factor of 32.1, the neoclassical energy loss by the compression ratio to the fourth power, which is 7.72, and the bremsstrahlung radiation loss by the compression ratio to the fourteen-thirds power, which is 10.85. The plasma temperature therefore climbs on its own from 10 keV to 19.8 keV after the squeeze. The authors call this temperature rise of fundamental importance to the success of the power cycle, because the plasma must be at a higher pressure going out than it was coming in.Section 2, equations 5, 6 and 7 and the paragraph following them
The pressure ceiling that normally limits a fusion machine is what makes this engine run. During the expansion the plasma’s beta — the ratio of its kinetic pressure to the internal magnetic field pressure — is already at the maximum the machine will hold, so ballooning instabilities pin it there through turbulent convection, and the pressure then varies exactly as though the plasma had an adiabatic index of 2 rather than the five-thirds of the compression stroke. That asymmetry between the two strokes is the entire source of the work. The authors also note the trap: if the compression were carried out faster than the ninety-degree deflection time for ions it would be two-dimensional, the compression would follow the same index-2 law, and the cycle would deliver nothing at all.Section 2, equation 8 and the two paragraphs following it
Both the work and the efficiency depend on the compression ratio alone. For the constant-volume variant the net work normalised by the machine parameters is the compression ratio squared, minus three halves of the compression ratio to the four-thirds power, plus one half — zero at no compression, rising steadily thereafter — and the thermal efficiency approaches two-thirds as the compression ratio grows. The constant-pressure variant reaches a higher ceiling, four-fifths, but delivers less work, and the authors judge that for reactor economics it is the net work rather than the efficiency that matters. If the machine has no beta limit at all, the cycle becomes exactly the Otto cycle of an internal combustion engine, with efficiency one minus one over the compression ratio to the four-thirds power.Section 3.1, equations 13, 16 and 18; Section 3.2, equation 21; Figures 2, 3, 4 and 5
The sample reactor delivers 2.2 gigawatts, about half of what its neutrons would. Table I specifies a stellarator with a plasma density of 6 times 10 to the 14 per cubic centimetre, a temperature of 10 keV, a 50 kilogauss toroidal field, a beta of 19.3 percent, a major radius of 10 metres and a minor radius of 2 metres. At a compression ratio of one over 0.6 the plasma needs about 0.16 seconds to reach thermal balance again, and with the compression and expansion strokes each taking 0.01 seconds the cycle period is about 0.18 seconds, giving an averaged direct-conversion power of 2.2 gigawatts. The same reactor’s thermonuclear neutrons would give about 12.2 gigawatts of neutron power, or 4.1 gigawatts of electricity at a one-third conversion efficiency, so the cycle roughly doubles the harvest. Resistive dissipation in liquid-nitrogen-cooled copper coils comes to only a few percent of the net work.Section 4.2; Table I; Appendix C for the relaxation time
What to watch: the storage problem, and the fuels this is really for. The energy that must be recirculated to run the next compression is large compared with the net work the cycle delivers, so even a few percent loss in a capacitive, inductive or flywheel store would swallow the output. The authors’ answer is mechanical rather than electrical — run two or more stellarators in tandem, so that the expanding plasma in one directly compresses the plasma in the other, exactly as the cylinders of an engine take turns. They also name where the idea earns its keep: for advanced neutron-lean fuels, where there are few neutrons to convert by any other route, this cycle may become an important method of energy conversion. They leave tokamaks out of the paper because anomalous transport in a tokamak is too uncertain to analyse this way.Section 4.1; Section 5, Conclusions; Figure 6

The way in

https://doi.org/10.2172/5138614

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

PROMOTED FROM ABSTRACT-ONLY. PPPL-2249 is a Princeton Plasma Physics Laboratory report prepared for the United States Department of Energy under Contract No. DE-AC02-76-CHO-3073 and distributed through the Office of Scientific and Technical Information. It is a work of the United States Government and carries no copyright, so the full text is reproduced below. TEXT. Sections 1 to 5, the acknowledgments, Table I, the figure captions and the fourteen references are reproduced in full. Appendix A, which re-derives the cycle work from the voltage-current relation and confirms the pressure-volume result; Appendix B, on thermonuclear thermal stability; and Appendix C, on the temporal evolution of the plasma temperature after compression, are omitted for length, and the eight figures are not reproduced. The complete report is at the source. SCAN QUALITY. The OSTI copy is a 47-page scan run through ABBYY FineReader in 2009 and the extraction carries the usual damage: broken words, letters swapped for digits, and Greek letters lost. Obvious scanning errors have been corrected against the surrounding sentences; the Greek letters are written out as words — beta for the ratio of plasma kinetic pressure to internal magnetic field pressure, alpha for the helium nucleus released by fusion, gamma for the adiabatic index, eta for efficiency, tau for a characteristic time. EQUATIONS. Every displayed equation was destroyed by the scan. Where the equation can be stated unambiguously from the sentences that surround it, it is given here in words with the report’s own equation number; where it cannot, the sentences are kept and the equation is marked as not reproduced. No number, ratio or result is reproduced that is not printed in words in the surviving text. TABLE I. The seventh row of Table I survived with its value, 0.1, but not its label; the six labelled rows are given as printed. AUTHORS. The report signs the authors as D. D.-M. Ho and R. M. Kulsrud of the Plasma Physics Laboratory, Princeton University, with a footnote that Ho was by then at Lawrence Livermore National Laboratory. Their given names are supplied here from the published record.

How to cite it

Darwin D.-M. Ho, Russell M. Kulsrud (1985) Thermonuclear inverse magnetic pumping power cycle for stellarator reactors doi:10.2172/5138614

Where it sits in the curriculum

Fusion machines: pinches, focus devices and inertial drivers