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"Fundamental Limitations on Plasma Fusion Systems Not in Thermodynamic Equilibrium"

(Created 96-10-29. Last revised 97-01-04. By Art Carlson.)

Yet each man kills the thing he loves,
  By each let this be heard,
Some do it with a bitter look,
  Some with a flattering word,
The coward does it with a kiss,
  The brave man with a sword!

    Oscar Wilde, "The Ballad of Reading Gaol"
    Part I, Stanza 7 (1898)
This is my personal summary and critique of the Ph.D. thesis of Todd Rider entitled "Fundamental Limitations on Plasma Fusion Systems Not in Thermodynamic Equilibrium" (MIT, June 1995). Of particular interest may be his criticism of "advanced aneutronic fuels" and of certain configurations (inertial-electrostatic confinement and migma). I am a professional plasma physicist, but the content expressed here is not in any way sanctioned by my employer.

Todd Rider's goal was to find general limitations on the feasibility of fusion systems, that is, fundamental physical constraints which can be used to rule out entire classes of containment configurations or fuels, not just specific embodiments. He was remarkably successful. Of course, watertight proofs of impossibility are impossible, but if you espouse one of the systems he deals with, you have to address his criticism. On the other hand, his work can be used to focus attention on the remaining potential loopholes.

The first table in the thesis lists the ratio of bremsstrahlung to fusion power for various fuels under the assumption that the only chain of energy transfer is fusion products to fuel ions to electrons to bremsstrahlung (sometimes referred to as the "hot ion mode") and under the assumption of nearly Maxwellian velocity distributions. The first assumption is wildly optimistic, the second is examined in detail in the rest of the thesis. What comes out is:

     fuel     P_brem/P_fus
     -------  ------------
     D-T        0.007
     D-He3      0.19
     D-D        0.35
     He3-He3    1.39
     p-B11      1.74
     p-Li6      4.81
In other words, D-T has no problem with bremsstrahlung. D-He3 and D-D can in principle overcome bremsstrahlung loss, but they can't afford to lose much on any other front. The nearly aneutronic fuels are not merely more difficult, but are impossible, unless you can find a very large loophole.

Well, maybe the assumption of Maxwellian distributions was too severe. Rider goes on to estimate the (recirculating) power required to maintain a non-Maxwellian distribution, e.g., a depletion of the low energy electrons which mediate the energy transfer. The recirculating power "fraction" required to halve the bremsstrahlung losses for the deuterium based fuels fuels was found to be:

     fuel     P_recirc/P_fus
     -------  --------------
     D-He3        4.7
     D-D          2.3
The minimum recirculating power "fraction" required to reduce the bremsstrahlung losses for the nearly aneutronic fuels to 50% of the fusion power is found to be:

     fuel     P_recirc/P_fus
     -------  --------------
     He3-He3      5.0
     p-B11       42
     p-Li6      210
A significant reduction in the power loss through the electrons by modifying their velocity distribution is thus unrealistic.

These tables represent much of the meat of the thesis. Rider also considered a mechanism that modifies the electron distribution "passively" but found it to be rather small. He considered the possibility of non-Maxwellian ion distributions, but again found the recirculating power requirements to outweigh the benefits. Anisotropic distributions were also shown not to help.

Rider's summary of the "outlook for advanced aneutronic fuels" (He3-He3, p-B11, and p-Li6) was: "Thus there is very little hope of ever being able to produce net power with any of these fuels."

Finally he considers how to minimize the neutron output of the D-He3 reaction. He finds a lower bound of 0.2% for the fraction of the total fusion power carried by neutrons, but considers 1% to be a more realistic figure, or 5% if the tritons are burned up in the plasma. "The bottom line is that realistic D-He3 reactors will be limited to at best a neutron power fraction of the same order as fission reactors, and the D-He3 reactors will also produce substantial amounts of tritium."

Among the specific systems which Rider has ruled out (in his own words, with minor editing) are:

This study has done much to firm up my feeling that fusion will probably have to work with toroidal magnetic confinement (tokamak or stellarator) and some amount of neutrons (D-T or possibly D-D or D-He3) or not at all. Rider's opinion is that this solution will not be acceptable, but something better will, despite the barriers he has discovered, eventually be found.