The Fusor

Brannon Klopfer
March 19, 2012

Submitted as coursework for PH241, Stanford University, Winter 2012

Fig. 1: The Hirsch-Meeks fusor, a variation on the Farnsworth-Hirsch electrostatic confinement fusor. [7] Source: Wikimedia Commons


In nuclear fusion, multiple nuclei "fuse" together to form the nuclei of a heavier element. (In the following, I will assume that only two nuclei are fusing.) Nuclear fusion is in a sense the "opposite" of nuclear fission, where one element splits into multiple lighter elements. The fusion (and fission) process is accompanied by a change in energy, the sign of which depends on the the specifics of the reaction. This can be seen by looking at the nuclear binding energy per nucleon as a function of number of nucleons, noting that there is a maxima at around 58 nucleons. [1] That is, fusion between lighter elements - such as hydrogen - will release energy, whereas fusion between heavier elements tends to consume energy. The corollary to this is that nuclear fission of heavy elements - such as fission of uranium in a power plant's nuclear reactor - releases energy.

Nuclear fusion as a man-made power source has, as of this writing, been elusive (though the sun is most certainly a fusion power source, albeit not man made!). But despite being elusive for power generation, man-made fusion has been around for almost 80 years, since Oliphant et al. demonstrated fusion of hydrogen isotopes with a gas-discharge apparatus in 1934. [2] However, a fusion reactor in the laboratory is emphatically not the same as a viable fusion power source, in that such fusions consume vastly more energy than they produce. It is in this category - namely, reactors which consume energy more than they produce - which the Farnsworth-Hirsch fusor lives.

The Fusor

Unlike fission reactions, the cross section for fusion reactions to occur is a dramatically increasing function of energy, or put another way, fusion reactions occur preferentially at incredibly high temperatures. These energies are of order tens of KeV, or many millions of Kelvins - so high that physical materials are inadequate for containment. [3] A very rough analogy to building a fusion reactor out of conventional materials would be that of trying to build a coal-burning steam engine out of papier-mâché. As such, a fusion reactor requires novel methods of containment. The Farnsworth-Hirsch fusor ("the fusor") and the related Hirsch-Meeks fusor are fusion reactor designs based on an inertial electrostatic method of confinement, that is, the use of an electrostatic potential well to confine the fuel (as opposed to a physical means of confinement in, say, a coal-burning steam engine). This fusion technology is in contrast to other methods of confinement, such as inertial, magnetic and gravitational (such as fusion in stars). [4,5]

The fusor creates a potential well for the fuel (e.g., hydrogen isotope ions). In a typical setup, a "hollow" cathode (that is, semi-transparent to the ion "fuel") is surrounded by an anode held at ground. Ions are injected into the chamber and fall towards the center, picking up kinetic energy from the difference in voltage; if ions do not undergo fusion, they are allowed to recirculate, assuming no interaction with the cathode, and thus have multiple chances to undergo fusion. In other incarnations of the fusor, the ions were not injected, but supplied by a dilute mixture of fuel in the chamber. (See Fig. 1 which depicts the Hirsch-Meeks fusor, a design which utilizes many of the same principles as the Farnsworth-Hirsch fusor.) Practically speaking then, the fusor is essentially a gas-discharge lamp, albeit with a geometry more conducive to fusion.


Although the fusor has not proven to be a viable power source, its design principles can be utilized for neutron sources. The German company NSD-Fusion has built neutron sources based on the inertial electrostatic confinement design which claim neutron production of over 107 neutrons/second operating with deuterium fuel (undergoing deuterium-deuterium fusion), and are developing a deuterium-tritium system with a target of 1011 neutrons/second. [6] These designs make use of space charges (rather than injection), and are cylindrical rather than spherical.

© Brannon Klopfer. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] J. R. Taylor, C. D. Zafiratos and M. A. Dubson, Modern Physics for Scientists and Engineers, 2nd Ed. (Prentice Hall, 2004).

[2] H. Hora, "Developments in Inertial Fusion Energy and Beam Fusion at Magnetic Confinement," Laser and Particle Beams 22, 439 (2004).

[3] P. T. Farnsworth, "Method and Apparatus for Producing Nuclear-Fusion Reactions," U.S. Patent 3386883, 4 Jun 68.

[4] M. W. Browne, "New Shot at Cold Fusion By Pumping Sound Waves Into Tiny Bubbles," New York Times, 20 Dec 94.

[5] M. W. Browne, "Cold Calculations Chill the Hot Pursuit of Cheap Fusion Power," New York Times, 10 Dec 96.

[6] A. B. Ludewigt, "Neutron Generators for Spent Fuel Assay," Lawrence Berkeley National Laboratory, LBNL-4426E, December 2010.

[7] R. L. Hirsch and G. A. Meeks, "Apparatus for Generating Fusion Reactions," US Patent 3530497, 22 Sep 70.