The Dynomak

Nick Rolston
February 19, 2015

Submitted as coursework for PH241, Stanford University, Winter 2015

Fusion Power: More than a Pipedream?

Fig. 1: Image of the toroidal cross-section of a tokomak magnetic confinement fusion device. (Source: Wikimedia Commons).

The possibility of using nuclear fusion as a sustainable energy source is an alluring concept. Free from the volatile radioactive byproducts that fission produces, fusion power offers an essentially unlimited source of fuel that is available at any time. Fusion power operates on the concept that the isotopes of hydrogen are abundant on the planet. [1] The primary difficulty in creating a fusion reaction is the similar charges of light nuclei that generate Coulombic repulsive forces and limit the possibility of a nuclear reaction without massive amounts of energy. The sun is an example where extreme temperatures (~1,000,000°K) and pressure leads to a sufficiently large cross section for fusion. [2] The nuclei produce a plasma at these levels of thermal energy. In order to generate a net positive energy yield, the fusion reaction must satisfy the Lawson criterion, which outlines the relation between temperature, relative velocity, fusion cross-section, and kinetic energy of the reaction products. [3] The two primary methods for creating a suitable environment satisfying the Lawson criterion are magnetic confinement (MCF) and inertial confinement (ICF). The former involves low-density plasma at long confinement times while the latter uses extremely high density plasma for a very short duration. [2]

Magnetic Confinement Fusion

MCF operates on the principle that plasma confinement occurs from applying a magnetic field of particular strength and direction. The charged particles in the plasma follow a helical trajectory, and most devices take advantage of this curved path by designing a ring or toroidal shaped configuration to maximize particle confinement and minimize drift. [2] The tokamak is one such example of a fusion device that is the most common MCF to date, and the toroidal cross-section of the Tokamak a Configuration Variable (TCV) of the École Polytechnique Fédérale de Lausanne is shown in Fig. 1. The tokamak design sought to satisfy the milestones of research administrations involving scientific, technical, and commercial feasibility. [4] Research showed the high-field, compact tokomak offered potentially the most viable option for fusion power, largely from the high densities and confinements occurring by Coppi and colleagues in the Alcator tests at MIT. [4] Although known for its stability, the tokamak has disadvantages in terms of reactor engineering, especially in terms of the need for toroidal field coils. [5] It is possible to eliminate this design criterion through enabling the plasma itself to create the toroidal field. In the low-aspect ratio limit, the configuration is known as a spheromak. [5] Thus, the pricey superconducting magnetic coils are rendered unnecessary and instead the magnetic fields are generated from within the spheromak. [6]

Along Comes the Dynomak

In 2012, a discovery at the University of Washington revealed a physical mechanism entitled imposed- dyamo current drive. [6] The concept involves direct current injection into the plasma to create a stable helical magnetic field confining the plasma and allowing steady-state fusion in a somewhat portable configuration. [6] Describing their configuration as a dynomak, this spheromak reactor uses a number of inductive helicity injectors on the exterior region of the reactor to equilibrate the plasma with a circular (poloidal) cross-sectional geometry. [7] The respective equations governing the magnetic field at the wall of the reactor and the beta (ratio of plasma pressure to the magnetic pressure) values are given in the following equations:

Bwall = μ0Ip
2π a
βwall = 0p

where μ0 is the magnetic permeability of free space, Ip is the toroidal plasma current, and a is the minor radius. In order to generate a plasma with the above parameters, the toroidal and poloidal plasma currents need sustainment to prevent decay due to finite plasma resistivity. [7] A diagram showing a spheromak design similar to the proposed dynomak setup is shown in Fig. 2. In terms of economical viability, pricing individual components of the dynomak is almost impossible since large-scale production methods are not currently in place for the highly specialized components of the reactor.

Fig. 2: Schematic of a cross-section of a high-temperature spheromak device. (Source: Wikimedia Commons).

The World is Ready ...

There is little controversy regarding the desirability of the world to switch to use nuclear power once it becomes cost-effective and feasible to produce in the proper quantities. Lockheed Martin announced in the past year that it is working on a portable fusion reactor that would fit on the bed of a truck. [6] A number of other companies such as Helion Energy, Lawrenceville Plasma Physics, and General Fusion are working on similar initiatives in addition. Many of the hype-generating claims such as the announcement from Lockheed Martin and other "secret designs" are questionable in their validity. Currently, the tokamak is one of the few designs that has been rigorously verified through examining the underlying plasma theory and has withstood the test of time. As such, the dynomak offers potential promise with its fundamental operational principles rooted in that of a tokamak. Nonetheless, the dynomak is certainly not a panacea- significant concerns exist over the potential to readily control the plasma profile, position, and sufficiently high confinement. [6] The current dynomak prototype is about one-tenth of the needed size to create a working commercial reactor and has three of the six helicity injectors to control the delivery of the magnetic fields to the plasma. [7] It remains to be seen if the many question marks enshrouding the potential of such fusion technology will be resolved in the near future. One thing is clear- the world is ready for fusion and is awaiting the release of fusion technology.

© Nick Rolston. 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] K. Miyamoto, Plasma Physics for Nuclear Fusion (MIT Press, 1979).

[2] L. C. Woods, Theory of Tokamak Transport, (Wiley-VCH, 2006).

[3] J. D. Lawson, "Some Criteria for a Power Producing Thermonuclear Reactor," Proc. Phys. Soc. London B 70, 6 (1957).

[4] C. M. Braams and P. E. Scott, "Nuclear Fusion: Half a Century of Magnetic Confinement Research (CRC Press, 2002).

[5] M. N Rosenbluth and M. N. Bussac, "MHD Stability of Spheromak," Nucl. Fusion 19, 489 (1979).

[6] E. Ackerman, "Enter the Dynomak," IEEE Spectrum 51, No. 12, 11 (2014).

[7] D.A. Sutherland et al., "The Dynomak: An Advanced Spheromak Reactor Concept with Imposed-Dynamo Current Drive and Next-Generation Nuclear Power Technologies," Fusion Eng. Des. 89, 412 (2014).