Main Criticisms

Posted by Lerner on Jul 05, 2006 at 10:16 PM
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There are two main criticisms of focus fusion:

  1. Hydrogen-boron fuel allows too much x-ray cooling
  2. Plasmoids can’t exist

Hydrogen-boron fuel allows too much x-ray cooling

  • The hot plasma of this fuel will emit x-rays too quickly,
  • the energy lost through the x-rays will always be more than the energy gained by fusion reactions.
  • the fusion reactions would not heat the plasma suffieicntly,
  • thus the very high temperatures required for burning hydrogen-boron completely would not be reached.

Why x-ray cooling is a bigger problem with hydrogen-boron fuel

  • The rate of radiation depends on the square of the electrical charge on the nucleus involved,
  • Thus boron, with 5 charges, causes 25 times more radiation than, for example, deuterium, with one charge.
  • this x-ray emission process is termed bremsstrahlung

The electrons emit the x-rays when they collide with the ions and the hotter the electrons are, the faster they radiate. For fusion reactions, on the other hand, it is critical that the ions be hot so that they have enough energy to fuse when they collide. So to reduce the bremsstrahlung cooling of the plasma, the ions must be much hotter than the electrons.

For more on this criticism see:  Fundamental Limitations on Advanced Fuel Fusion.

Response to x-ray cooling criticism:

Fortunately, there is a way to reduce the bremsstrahlung cooling with the dense plasma focus by using the magnetic field effect. This effect, which critics of hydrogen-boron fusion do not take into account, slows down the transfer of energy from the ions to the electrons to by as much as a factor of twenty in the presence of extremely high magnetic fields, without affecting the transfer of energy from the electrons to the ions. This means that the ions could be 20 times hotter than the electrons. In turn, this would reduce x-ray emission by a factor of about 5.

The magnetic field effect was discovered theoretically by R, McNally in 1975 and it has been studied extensively in theoretical and observational studies of neutron stars, which have enormous magnetic fields. For example, in 1987 G. S. Miller, E.E. Salpeter, and I. Wasserman, published in the prestigious Astrophysical Journal an analysis showing that energy transfer to electrons could indeed drop by as much as 20-fold in strong magnetic fields.

FFS Executive Director Eric Lerner was the first to apply this well-known effect to the plasma focus, showing in 2003 that with magnetic fields of around 15 giga-gauss(GG) ion temperatures would be 10-20 times higher than electron temperatures.  In this case, fusion power will well exceed x-ray cooling and nearly all the fuel in the tiny plasmoids would be burned up. This would allow net power production.

In the plasma focus fields of about 0.4 GG have been observed. But Lerner calculated that a six-fold increase could be obtained by using smaller electrodes and higher currents, since the final magnetic field is proportional to the starting magnetic field in the device. In addition, the magnification of the magnetic field as the energy compresses itself into the plasmoid increases with the mass and change of the nuclei in the fuel. This will provide another factor of 6-7, bring the field up to 15 GG. These theoretical extrapolations will be tested in the experiment now under way in Chile.

Plasmoids can’t exist

A second objection is that dense, self-confined plasmoids can’t exist, and therefore the very high magnetic fields needed for the magnetic field effect also can’t exist. This argument shows up on some Wikipedia pages and goes like this:  “On theoretical grounds self-confined plasmoids can’t exist. Therefore, the only way to confine plasma is with magnetic fields contained by solid objects. But no solid objects can withstand the intense forces generated by giga-gauss magnetic fields. Therefore such giga-gauss fields can’t exist.”

The argument that plasmoids can’t exist rests on an application of the “virial theorem”, a general result in physics theory that relates to the energy contained in a collection of particles. The argument is that this theorem proves that NO collection of particles and electromagnetic fields can stably exist and confine itself. If this argument were valid, not only would plasmoids not exist, but neither would solid objects, which are also held together by electromagnetic forces!

Answer to criticism:

This argument that plasmoids can’t exist has been refuted by repeated observations.  Plasmoids have been observed in the plasma focus, in other fusion devices and in nature, for decades by many groups of researchers.  Winston Bostick and Victorio Nardi reported in the 1970’s observations of plasmoids with magnetic field of up to 200 Mega-gauss, lasting for tens of nanoseconds. Many scientists have observed plasmoids in the magnetosphere of the earth. In recent years, J. Yee and P.M Bellan at California Institute of Technology studied in detail how plasmoids form in the laboratory and their stability. Plasmoids are contained by their own magnetic fields and currents through the pinch effect, in which currents moving in the same direction attract each other.

The theoretical argument is not valid, either. As far back as 1958, S. Chandrasekhar, one of the leading astrophysicists of the 20th century, and L. Woltjer showed that magnetically self-confined stable configurations, later dubbed plasmoids by Bostick and others, can exist in space. They concluded that, since such plasmas would have currents moving around their surfaces, the forces generated by the interaction of these currents and the magnetic field would confine them. They showed mathematically that there was no contradiction with the virial theorem. (Proc. Nat Acad Sci., 44, 285)

To get an idea of how a plasmoid field and currents can confine it, imagine a plasmoid as a smoke ring which both rotates around its axis and rolls as it moves through the air. The key point is that currents that move in the same direction attract each other, while currents moving in opposite directions repel. As the toroid “rolls”, the currents on opposite sides of the donut are moving in the same direction, confining it from expanding into an every greater circle. At the same time, the strong currents moving inside the donut, in the circular direction, compress it and prevent it from blowing up like a balloon.

Over than past 50 years, other groups of researcher have shown mathematically that plasmoids can be stable, at least for times very long compared with the time it takes particles to cross them. For this reason, there is no theoretical problem with the existence of plasmoids with fields of billions of gauss. Whether such field can in fact be produced practically is what ongoing experiments will test.

References for further reading on these scientific questions:


Magnetic field effect:

McNally, J.Rand, 1975, Simple physical model for the effect of a magnetic field on the coulomb logarithm for test ions slowing down on electrons in a plasma. Nucl. Fusion, 15, 344

G. S. Miller, E.E. Salpeter, and I. Wasserman, 1987, Deceleration of infalling plasma, Astrophysical J, 314, 215


Observations of plasmoids:

Bostick, W.H. et al, Production and Confinement of High Density Plasmas Ann. NY Acad. Sci., 251, 2 (1975).

Colloques internationaux CNRS no. 242, p.129-138.

J. Plasma Physics 8, 7(1972)


Theory of self-confined plasmas:

S. Chandrasekhar and L. Woltjer, On Force - Free Magnetic Fields, Proc. Nat Acad Sci., 44, 285

D. Wells and L.C. Hawkins, Containment Forces in low energy states of plasmoids, J. Plasma Physics, 38, 263

L. Fadeev and A.J. Niemi Phys. Rev Lett 85,3416 and


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There are (4) comments.

Warwick's avatar

virial theorem, shurely, not viral theorem.

Warwick's avatar

Nope, my bad, there is such a thing as the viral theorem.

Rezwan's avatar

Yes, but I think this is the virial theorem.  A typo.

Brian H's avatar

There’s another critique I keep coming across, that the electrodes degrade and erode so fast that it’s not practical to have or claim sustained use. Does using Be eliminate/mitigate this problem?

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