The Spheromak

An Alternative MFE Concept
Plasma Science Experiment

E. Bickford Hooper
Lawrence Livermore National Laboratory


Cris W. Barnes
Los Alamos National Laboratory

Response to Questions of the
FEAC/SciCom Alternates Panel

April 23-24, 1996


The spheromak is a toroidal magnetic/plasma configuration in which the magnetic field is generated primarily by plasma currents. The vertical field for equilibrium is generated by external poloidal field magnets or by a conducting flux conserver for times less than a magnetic soak-thru time of the conductor. As no toroidal magnetic field coils link the torus, there are exciting reactor opportunities if the physics will allow fusion parameters with sufficiently good energy confinement.

The Compact Torus Experiment (CTX) at LANL reached a core electron temperature of 400 eV in a series of experiments in 1989-90, some four years after OFE funding was terminated at the end of FY86. The decision to terminate funding was made at a time that the US alternatives program was winding-down, and was made on the basis of the difficult decisions needed as available funding declined. That the decision was not driven primarily by the physics is indicated in the continuation of the program until the fall of 1990 on Defense Programs funding for hypervelocity creation and on some internal monies.

During the course of examining the published results in 1994, Fowler hypothesized that the core energy confinement time in the CTX experiments was considerably better than recognized on the basis of the global confinement. He developed a model for the confinement which was compared with experiments in considerable detail by Hooper, et al. (enclosed). They concluded that the data is consistent with the hypothesis for decaying spheromaks (when the plasma is disconnected from the helicity source) but inconclusive for plasmas sustained by helicity injection from a coaxial source (Marshall gun). The result was a proposal for a program which would initially examine energy confinement in a sustained spheromak on timescales short compared to that of the flux conserver. Assuming success, the program would move into an Advanced Spheromak phase in which the issues of long pulse operation and the achievement of fusion temperatures (> 1 keV) would be explored.

The physics of the spheromak differs from that of the tokamak in several important ways, and is closer to that of the reversed-field pinch than other devices. Important, fundamental issues include: helicity conservation, injection, and decay; the magnetic dynamo; magnetic field reconnection; magnetic turbulence; and energy losses in the presence of magnetic turbulence. These issues are to a large extent poorly understood even today, and are important in the sun and other astrophysical plasmas. Thus, careful physics experiments using spheromaks will contribute to parts of science outside the tokamak regime.* Results will, in addition, be synergistic with those from the RFP in addressing similar issues in a different magnetic configuration and with different helicity drive techniques; for example, the helicity is driven inductively primarily near the magnetic axis in the RFP and electrostatically primarily at the edge in the spheromak. The possibility of volume helicity drive and minimal magnetic turbulence may provide important opportunities for both devices.

There are also significant issues to be addressed for long pulse operation, including equilibrium, control of low-n instabilities, and the role of (resistive) pressure driven modes if the amplitude of current-driven modes scales favorably with the magnetic Reynolds number. Innovations and improvements in cw helicity drive may also be required.

The following answers to the panel questions discuss these and related issues in more depth. In addition, attached to this material is a copy of a description of the status of the spheromak presented to FEAC as part of a statement on alternatives. Also attached is a recent publication which describes the status of understanding of confinement in the spheromak: E. B. Hooper, J. H. Hammer, C. W. Barnes, J. C. Fernández, and F. J. Wysocki, "A Reexamination of Spheromak Experiments and Opportunities," Fusion Tech. 29, 191 (1996). For a broader discussion of the status of spheromak research and for extensive references, we recommend: T. R. Jarboe, "Review of spheromak research," Plasma Phys. Control. Fusion 36, 945 (1994).


A) What is the current world-wide status of research and achievements:

A1) What are the present experimental achievements?

The spheromak was studied in several laboratories starting in the late 1970s and lasting for a period of about 10 years. The work ** included:

In addition to the achievements described above, these and other experiments made measurements of the magnetic field which showed that the configuration was very close to the Taylor minimum energy state (discussed below). The role of electric fields on open fieldlines provided an understanding of the global resistive decay. Power balance measurements included evaluation of impurity radiation and charge-exchange. The role of turbulence in heating the ions was demonstrated; in the final CTX experiments the turbulent amplitude became low enough that Ti ~ Te ; in earlier work Ti >> Te due to the heating. The conditions for the coaxial gun to couple helicity and energy efficiently into the confined spheromak were elucidated.

A number of experiments (at Caltech, UC Davis, and by the Canadian Fusion Fuels Technology Project) led to the use of compact tori for fueling tokamaks. These experiments built on the understanding developed by the earlier spheromak program and on the initial CT acceleration experiments on RACE at LLNL.

A2) What is the present theoretical understanding?

There are several significant aspects of the spheromak which are explained by theory:

A3) Do theory, modeling, simulations, and empirical scalings fit the experimental observations?

Comparison between theory and experiment in equilibrium and stability is described briefly in the answer to question A2. In addition, there has been recent progress in modeling core energy confinement. *** Fowler[7] has developed a model combining inward helicity transport due to magnetic turbulence and outward energy transport via Rechester-Rosenbluth transport along the resulting magnetic structure, which agrees reasonably well with the final CTX results for decaying spheromaks. However, there is limited data for the comparison and there is no adequate data for a hot spheromak sustained by helicity injection.[8] If the resulting energy confinement scaling holds, losses will be quite low in the thermonuclear regime. Achieving this will require careful attention to controlling the rate of helicity injection so as not to overdrive the turbulence. As in tokamaks, it will also be very important to control wall conditioning, gas, field errors, and other experimentally important issues.

B) What is the appropriate level of research for this concept:

B1) What are the major experimental and theoretical issues that should be addressed?


There is a hierarchy of experimental and theoretical issues to address. Experimentally, it is possible to separate the issues which can be studied in short-pulsed (< 10 ms) experiments, in which the equilibrium is supported by a conducting flux conserver, from those requiring that the equilibrium be supported by external fields.

The short-pulsed experiment can appropriately be classed as medium sized, with plasma radius no larger than about 3/4 m. As the goal is to study energy confinement at temperatures of several-hundred eV, the experiment must be done with attention to walls and other details, otherwise the result is likely to be unsuccessful for practical reasons. A complete diagnostic set is also needed to characterize the plasma as quantitatively as possible.

Important issues to be studied in the experiment include:

For a long pulsed experiment, critical issues include:


Most of the experimental issues have equivalent theoretical problems. Among the more important are:

B2) Do the above issues require

(a) launching new experimental facilities and/or theoretical activities?

(b) expanding the current experimental and theoretical activities?

(c) can they can be addressed at present level of research?

(d) or can they be addressed at a lower level of research?

A new facility is definitely needed. The only ongoing spheromak experiments are relatively small and focused on specific physics issues. Although these projects are making important physics contributions and should be better supported, they cannot explore issues at high temperature and fusion parameters. A cost effective approach will be to undertake experimental development in two phases as described in the answer to question B1: A medium-sized experiment to address short pulsed issues and, assuming success a larger experiment to address the physics of long-pulsed spheromaks. The medium sized experiment will cost $2M-$3M/year, although progress would obviously be faster if more resources were available. The experiment could draw on significant existing facilities, e.g. at LLNL, LANL and elsewhere, to keep the construction cost and time to a minimum. The cost is driven by the need for good diagnostics more than the facility construction.

In addition, support will be needed for theory, reactor studies, etc. At the present time there is little direct support from OFE for spheromak theory, although there is some spin-off, e.g. from MHD modeling. There is also a low level of effort at LLNL using internal funds. Thus, an expansion of support for theory will be highly desirable. The effort should be strongly coordinated with related research on the RFP.

The US is presently not supporting the spheromak as an alternative reactor concept. Thus, the proposed program will require the commitment of funds to increase the level of research. We suggest that we should aim for ~$5M for a program including a medium-sized experiment, supporting small experiments, theory and modeling, and reactor studies.

B3) What is an appropriate mix of research activity for this concept among

large facilities and mix of small supporting experiments,

theory and modeling, and concept design and evaluation studies?

It is highly desirable to have a mix of small supporting experiments to interact with the confinement experiment described above. Such experiments can focus on fundamental physics issues; support of innovative experiments and theory at the small scale will improve the science done at medium and large scale. Further, the independence of the experimenters provides a useful and important cross-check to the larger experiment. New diagnostics can be cost-effectively initiated in them.

There are presently several small efforts ongoing in the US which are addressing physics or technology related to spheromaks, including:

B4) What is the world-wide research plan (outside U.S.) to address the above issues?

B5) What is the proper level of US research in the context of the international program? In particular:

(a) Is it necessary to have more than ONE NEW international experimental facility?

(b) Given the world-wide plan, which areas US program should focus on?

Although there is interesting science being done within the international program, there is presently no activity addressing the issue of energy confinement at high temperature or of the equilibrium, sustainment, and control issues pertinent to long pulse spheromaks. As a consequence, the ongoing experiments are not focused on some of the issues which need to be addressed for fusion.

Even a medium-sized confinement experiment will be unique in the world; the US program can take the lead in this arena.

Thus, we recommend that the core of a US spheromak program be such a medium-sized experiment. The initial focus should be on energy confinement in a sustained spheromak, with close attention to the pertinent physics of helicity injection, magnetic turbulence, etc. We also recommend that there be several small experiments, typically at universities, addressing the physics of reconnection, magnetic turbulence and other issues of interest. These experiments will help new ideas to blossom, and will provide a "reality check" on the mainline, fusion device.

C) What is the potential impact of research on this concept on

C1) increasing our knowledge of general plasma physics?

Spheromak-related physics is important for increasing knowledge of general plasma physics. Science issues include the magnetic dynamo; helicity conservation, generation, and transport; and energy transport in the presence of magnetic turbulence. One application outsicde fusion, already being studied, is the role of reconnection in plasma astrophysics.

The physics of minimum-energy (Taylor) states, magnetic reconnection and turbulence are exciting and largely unexplored. These and related issues can best be studied in the open, easy-to-make geometry of a spheromak. They will be addressed both in small experiments and in the proposed medium, fusion-directed experiment. In the small devices, temperatures are typically low and diagnostics will be relatively straightforward. The physics will be extended as new techniques are developed and applied to the higher temperature regime in the medium-sized experiment, thus developing the understanding of recombination and turbulence at high magnetic Reynolds numbers. The combination of experiments, together with the related work in the RFP, will be an effective means to develop the physics.

Much of the micro-scale physics will almost certainly be different from the tokamak because of the macro-scale differences. It is difficult at this stage to predict what will turn out to be most important, but new experimental techniques to measure the plasma effects will be required and new theoretical concepts will undoubtedly evolve with the experiment.

C2) increasing our knowledge of fusion plasma physics (of this concept as well physics of other confinement concepts)?

There are major opportunities in advancing the knowledge of fusion plasma physics for this concept as well as others. There is a particularly strong synergism with the RFP; the OH transformer generates helicity primarily on the magnetic axis, whereas the coaxial gun used in a spheromak generates it near the seperatrix. We can undoubtedly learn more about the physics by comparing results.

The medium-sized experiment described earlier provides a possibly significant step to studying the critical physics issues at the high temperatures characteristic of the fusion regime.

C3) helping develop fusion as an energy source (help develop the data base for fusion development steps such as burning plasmas, volumetric neutron source, etc.)?

The goal of the program described here is to advance the spheromak as a fusion energy source. It is premature to predict whether this is a good route to a volumetric neutron source or other development on the path to a fusion reactor.

The compact torus injector for fueling, an outgrowth of the spheromak program, is an example of an application to the broader fusion reactor development.

C4) developing this concept as a candidate for a fusion power plant?

Because there are no toroidal field coils linking the plasma, a fusion reactor has the possibilities of simplicity and low cost of electricity (COE) if the physics allows. Hagenson and Krakowski[9] analyzed many of the issues, and concluded that the COE was potentially the lowest of the devices they considered. Fowler et al.[10] noted that in the spheromak the high current density, together with the projection of the hypothesized scaling, would allow ohmic ignition, thus bypassing the need for auxiliary heating.

A spheromak reactor may be able to use a significantly different blanket and/or first wall than in the tokamak. Preliminary studies suggest that it may be possible to use a "boiling pot" blanket (boiling NaK in a hot, liquid Li pot) or even internal liquid lithium walls to eliminate the first wall problem. The advantage of a concept such as the spheromak is that it triggers the possibility of such ideas.

The key caveat, of course, is "if the physics allows." The program proposed herein would tap the ingenuity of the plasma fusion community to proactively answer this. In undertaking this effort, we need to include the opportunity to advance new ideas; even in the tokamak we have recently seen the power of new concepts based on understanding the physics. We should do no less for the alternatives.