Prospects for Low Cost Fusion Development

Contact: Gordon Long — glong@mitre.org

November 2018
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14. ABSTRACT

In 2014 ARPA-E initiated the three-year $30M ALPHA program to explore magneto-inertial fusion (MIF) concepts in aspan of 105 in plasma density (1018 – 1023 ions/cm3), lying between the mainline tokamak (1014/cm3) and inertial (NIF at
1026/cm3) approaches. ALPHA’s goal was to identify ways to accelerate progress toward fusion power.
With the ALPHA program nearing completion, ARPA-E asked JASON to assess its accomplishments and the potential offurther investments in this field. JASON members listened to two days of briefings that included participants in ARPAE’s ALPHA program, MIF teams not supported by ALPHA-E, and teams working on pure magnetic confinement fusion.
JASON also surveyed nine teams for quantitative metrics of past, present, and projected progress along critical physicalparameters.
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Contents
EXECUTIVE SUMMARY

1

1 INTRODUCTION

3

2 CONTEXT
5
2.1 The Space Between ITER and NIF ............................................................................................... 6
2.2 A Brief History of ‘Alternative’ Approaches .............................................................................. 7
2.3 Fusion in the Energy Landscape ............................................................................................... 11
2.4 Why Now? ..................................................................................................................................... 16
3 PHYSICS BACKGROUND
19
3.1 Cross Sections ............................................................................................................................... 19
3.2 Reaction Rates.............................................................................................................................. 23
3.3 Thermodynamics........................................................................................................................... 23
3.4 Dissipation ..................................................................................................................................... 24
4 MIF PHYSICS
27
4.1 Size Scaling: Why ITER is Big and NIF Targets are Small................................................................ 27
4.2 Elements of a MIF System ............................................................................................................. 27
5 RECENT ADVANCES IN ALPHA PROJECTS AND ELSEWHERE
33
5.1 Progress Along Key Metrics ......................................................................................................... 33
5.2 Examples from Select Projects .................................................................................................... 34
5.3 Classification by Dimensionless Parameters ............................................................................... 35
6 FUNDAMENTAL TECHNOLOGY NEEDS TO ADVANCE MIF RESEARCH
39
6.1 Computational Modeling of Experiments in the MIF Regime ..................................................... 39
6.2 Instabilities and Loss Mechanisms .............................................................................................. 41
6.3 Diagnostics................................................................................................................................... 44
7 NON-ENERGY APPLICATIONS
45
7.1 Spacecraft Propulsion.................................................................................................................. 45
7.1.1 Comments on a conceptual design for a fusion-propelled spacecraft .............................. 46
7.1.2 General physical and economic considerations ................................................................ 47
7.2 Stockpile Stewardship ................................................................................................................. 50
7.2.1 Pulsed neutron production ................................................................................................ 50
7.2.2 Tritium production ............................................................................................................. 51iii

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8 MORE BANG FOR THE BUCK: Cost-drivers for MIF Development

53

9 COMMERCIALIZING FUSION
57
9.1 The Ecosystem for Private Fusion Companies............................................................................. 57
9.2 Commercialization Challenges .................................................................................................... 59
9.3 Lessons from Fission ................................................................................................................... 60
9.4 Lessons from Wind and Solar ..................................................................................................... 61
10 FINDINGS AND RECOMMENDATIONS65

APPENDIX A: Statement of Work (SOW)67

APPENDIX B: Briefings

69

APPENDIX C: Briefer Questionnaire

71

APPENDIX D: Evaporation of Liquid Pb Liners by High-flux Neutrons73iv

JSR-18-Task-011 - FUSION

18 December 2018EXECUTIVE SUMMARY
Controlled thermonuclear fusion has been pursued for more than 60 years. In recent decades,
US funding has focused on laser-driven inertial confinement (ICF) for national security purposes and on
magnetic confinement (MCF), primarily in tokamaks, for energy production. The major component of thelatter international program is the $25B ITER project, expected to begin DT operation in 2035.
In 2014 ARPA-E initiated the three-year $30M ALPHA program to explore magneto-inertial fusion(MIF) concepts in a span of 105 in plasma density (1018 – 1023 ions/cm3), lying between the mainline
tokamak (1014/cm3) and inertial (NIF at 1026/cm3) approaches. ALPHA’s goal was to identify ways toaccelerate progress toward fusion power.
With the ALPHA program nearing completion, ARPA-E asked JASON to assess its accomplishments
and the potential of further investments in this field. JASON members listened to two days of briefings
that included participants in ARPA-E’s ALPHA program, MIF teams not supported by ALPHA-E, and teams
working on pure magnetic confinement fusion. JASON also surveyed nine teams for quantitative metricsof past, present, and projected progress along critical physical parameters.
The findings of this study are summarized as follows:
1. Magneto-Inertial Fusion (MIF) is a physically plausible approach to studying controlled thermonuclear
fusion in a region of parameter space that is less explored than Inertial Confinement Fusion (ICF) or
Magnetic Confinement Fusion (MCF).
2. MIF research is immature. Despite having received ~1% the funding of MCF and ICF, MIF experiments
have made rapid progress in recent years toward break-even conditions, and some (e.g. MagLIF) arewithin a factor of 10 of ‘scientific break-even’.
3. There are many plausible and distinct approaches to MIF. Some early projects supported by the
ALPHA program are showing rapid progress in critical physical parameters and have not yet reachedinsurmountable obstacles. As in ICF and MCF, instabilities may make scientific break-even MIF morechallenging than simple scaling estimates suggest.
4. ALPHA program support for development of broadly applicable technologies has accelerated progressof multiple efforts. All MIF approaches would benefit from improved understanding of plasma
instabilities and liner-plasma interactions, better computational tools, and improved diagnostics.
5. While scaling from current experiments is uncertain, it is likely that reaching scientific break-even witha single MIF prototype will cost at least several $100M and possibly much more. Considerably larger
expenditures would be required to go from scientific breakeven to a demonstration power plant; andeven more from a demo to a production capability.
6. Given the immaturity of the technologies, the future ability of fusion-generated electricity to meetcommercial constraints cannot be usefully assessed. Rapidly developing infrastructures for natural
gas and renewable energy sources and storage will compete with any future commercial fusion
efforts. Nevertheless, there is a small but growing private-sector community investing in and pursuingcommercial fusion projects.
7. The pursuit of MIF could lead to valuable spinoff technologies, and to non-power fusion applications,with broad civilian and military import. Some approaches have low enough mass to be candidates forspace propulsion, but it is too early to impose the relevant design constraints (low weight, low thermal
dissipation) on ongoing research.

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8. MIF research could productively absorb a significantly higher level of funding than the $10M/yr of the
ALPHA program.
These findings lead to the following recommendations:
1. MIF activities should be supported by an investment in basic research to:x study plasma instabilities and transport under MIF conditions, andx study plasma-liner interactions.
2. The National Laboratories should contribute their unclassified state-of-the-art simulation codes tocollaborations with academic and commercial efforts, and support training of qualified users.
3. Targeted technology development programs should focus on development of components, including
plasma guns (high Z and low Z), pulsed power and electronics, diagnostics, and advanced magnets andmaterials.
4. The near-term goal should be scientific break-even (thermonuclear energy out > mechanical +electromagnetic energy into the fuel) in a system that plausibly scales to a commercial plant. Until
that goal is achieved, set aside questions of neutron economy (tritium breeding) or balance of plant.
Pursue system integration only insofar as it is needed to demonstrate scientific break-even.
5. Explore pulsed neutron sources and space propulsion as motivating applications with different
constraints than grid electricity. Efforts in these speculative directions should supplement, notreplace, basic MIF research.
6. Support all promising approaches for as long as possible. Do not concentrate all resources on early
front-runners.

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1 INTRODUCTION
This document reports on an ARPA-E-sponsored JASON assessment of the “Prospects for Low Cost
Fusion Development.” Specifically, the question is whether magneto-inertial fusion (MIF) is a promising
approach toward achieving controlled thermonuclear fusion at dramatically lower costs than otherapproaches. MIF operates at ion densities from 1018 – 1023 ions/cm3, part-way between the main-line
approaches of Magnetic Confinement Fusion (MCF, 1014 ions/cm3) and Inertial Confinement Fusion (ICF,
1026 ions/cm3). MIF techniques combine aspects of the two main-line approaches: magnetic fields areused to suppress cross-field particle and heat transport, as in MCF. Impulsive mechanical compression isused to reach high density and temperature, as in ICF. If MIF research is found to be promising, how can
the government best support progress?

Figure 1. Fusion landscape. Magneto-inertial fusion resides at an intermediate density between
Magnetic Confinement Fusion (MCF) and Inertial Confinement Fusion (ICF). Image adapted from P.
McGrath, ARPA-E.
In 2014 the Advanced Research Projects Agency-Energy (ARPA-E) initiated a program on
Accelerating Low-cost Plasma Heating and Assembly (ALPHA) to support MIF research. Between 2015 and2018 the program disbursed $30M in grants to 9 teams. As the ALPHA program ends, ARPA-E and thefederal government must decide how to build upon the initial efforts.
Some of the key questions are:
1. What areas of MIF research show promise of reaching scientific break-even?
2. What are the key technical and schedule risks?
3. What areas of investment or support would best accelerate further progress toward MIF scientificbreak-even?
The complete Statement of Work is given in Appendix A.
Our study was informed by an extensive collection of public documents, as well as two days ofbriefings from a broad range of stakeholders, including ARPA-E and NASA, the private sector, anduniversities (Appendix B). In addition, we surveyed teams working on MIF projects to gather quantitative
metrics on progress and plans, and to gather community input on the key remaining challenges(Appendix C).

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2 CONTEXT
For a fusion reaction to provide useful energy, the energy released by the reaction must exceed themechanical and electromagnetic energy supplied to assemble the reactants. This condition is called‘scientific break-even’, and the ratio of energy out to energy in is called ‘scientific gain’. Even with acharitable definition of “energy in”, that condition was only recently approached in an ICF experiment at
the National Ignition Facility (NIF) in Summer 2018 1, but that system does not lie on a route to a practicalfusion reactor.
Scientific break-even is necessary, but not sufficient, to produce a functioning fusion power plant.
There are additional energy losses associated with the energy conversions upstream of fuel assembly anddownstream of the fusion reaction (Figure 2). For power plant gain (electrical energy out/electrical energyin) to exceed one, the scientific gain must exceed ~10. In this report, we focus primarily on the challengeof finding a path to scientific gain > 1 in a high repetition-rate platform, as the proximate challenge along
the path toward fusion as a practical energy source.

Figure 2. Energy flow in a fusion reactor. This notional diagram of a fusion power plant shows anapparatus that draws electrical energy from the grid, and through a series of transformations compresses,heats, and confines a fusion fuel. Some energy is converted to waste heat during each step. The fusion
fuel reacts, releasing high-energy nuclear products. The energy from these products is converted toelectrical energy with thermodynamically limited efficiency. The salable electricity is the difference
between the electricity produced and the electricity that must be recycled to operate the plant.
The physical requirements for scientific break-even are that the fuel must be sufficiently hot,dense, and confined for long enough. For the most promising fuel, an equimolar deuterium-tritium (D-T)
mixture near its optimal ion temperature of about 14 keV, these requirements are captured by the socalled ‘triple product’ ݊ ܶ ߬, where n is the density of ions, T is the ion temperature, and W is a measure of
the energy confinement time (discussed in detail below). Then the scientific break-even condition is:݊ ܶ ߬ ൎ 3 × 10ଶଵ keV s/mଷ,1

S. Le Pape, et al., "Fusion energy output greater than the kinetic energy of an imploding shell at the National
Ignition Facility." Physical Review Letters 120, 245003 (2018).

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where temperature is measured in keV (1 keV = 1.2 × 107 K), time in seconds, and density in ions/m3. One
can go to higher density for shorter time, or lower density for longer time—but any combination of theseparameters that crosses the scientific break-even condition has proven extraordinarily difficult to achieve
under controlled conditions. At ion temperatures below 10 keV the condition on the density-time productis much more demanding; T must approach 10 keV to be “in the ballgame” at all.

2.1 The Space between ITER and NIF
At present, there are two main approaches toward achieving controlled thermonuclear fusion. In
Magnetic Confinement Fusion (MCF), a hot plasma is kept away from the reactor walls by a confining
magnetic field. Although many geometries of MCF devices have been explored, the most common
geometry today is the tokamak, a toroidal configuration with a predominantly toroidal magnetic field.
Tokamaks typically operate at an ion density of ~1014/cm3.
The flagship tokamak program is the international collaboration on ITER, under construction in
France. It is projected to cost approximately $25B, more than twice the initial budget, and to commence
D-T fusion operation around the year 2035, more than a decade behind the original schedule. The
Department of Energy (DOE) Office of Fusion Energy Sciences (OFES) budget is $564M (2019) for plasma
fusion research, of which $432M is for domestic research and $132M goes to ITER. 2,3
The second main approach to controlled fusion is Inertial Confinement Fusion (ICF), in which amillimeter-size capsule is compressed via an intense laser pulse to a density of ~1026/cm3, corresponding
to ~300 times the density of water. In the US, ICF research is focused at the National Ignition Facility (NIF)
at Lawrence Livermore National Lab. Controlled fusion experiments at NIF recently passed the milestoneof producing thermonuclear energy (54 kJ) greater than the mechanical kinetic energy in the imploding
liner (21 kJ). This energy output is still far smaller than the optical energy used to compress the shell (1.5
MJ), and the NIF is not considered as a prototype for a future power plant. The NIF program total costhas been approximately $3.3B, and is sponsored by the National Nuclear Security Administration (NNSA)
within the DOE. The mission of NIF is primarily national security (stockpile stewardship), with ICF only oneof several programs at the facility. The total budget for the Inertial Confinement Fusion and High Yield
program is $545M (2019) of which $344M is for NIF. 4 Of the NIF budget, approximately $80M is for
ignition research. In 2013 the National Research Council produced a detailed study of the prospects for
ICF energy production. 5
The two mainline approaches, MCF and ICF, are dramatically different in many ways. Apart froma factor of ~1012 in maximal fuel density, they also differ in timescale: MCF systems operate quasistatically, with runs lasting from tens of seconds to minutes, while ICF operates in a pulsed mode, withmaximal compression lasting ~150 ps. 6 MCF is performed in the presence of a strong magnetic field (5.32https://aries.pppl.gov/FPA/fpn18-38.shtml
https://science.energy.gov/~/media/budget/pdf/sc-budget-request-to-congress/fy2019/FY_2019_SC_FES_Cong_Budget.pdf
4
https://aries.pppl.gov/FPA/fpn18-38.shtml
5
National Research Council. An Assessment of the Prospects for Inertial Fusion Energy. National Academies Press,
2013.
6
S. Le Pape, et al. "Fusion energy output greater than the kinetic energy of an imploding shell at the National
Ignition Facility." Physical Review Letters 120, 245003 (2018)
3

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T at ITER), while ICF is performed without externally applied fields. The fuel chamber for MCF is a
substantial portion of the device--at ITER, the reaction chamber torus is 6.5 m in inner cross-sectional
width. In ICF the fuel is a small pellet ~1 mm in diameter, the evacuated “target chamber” is 10 m indiameter, and the rest of the apparatus is the size of three football fields.
Despite the dramatic differences in physical parameters, MCF and ICF have two features incommon: they are extremely expensive, and they have not yet “worked”, in the sense of reachingscientific break-even. Why are the systems so expensive? To a zeroth approximation, it is because they
are very large. Why are they so large? In MCF
the torus must be large enough that losses atthe surface do not dissipate heat faster thanfusion reactions can replenish the heat in thebulk. Thus surface-to-volume arguments set
the size. In ICF, the target is tiny, and the sizeof the machine is dominated by the laser
required to precisely deliver the compressive
impulse of ~2 MJ in 7.5 ns (momentarily
exceedingworldwideprimary
power
consumption).
The existence of physically plausible,
but technically challenging, approaches tocontrolled fusion at densities differing by afactor of ~1012 raises the question: are there
Figure 3. US government expenditures on fusion
other viable approaches at intermediate
research. ALPHA expenditure on MIF research wasdensities? If so, might they be less technically$30M ($26M in 2009 constant dollars). Data from:demanding, and hence less expensive?
https://aries.pppl.gov/FPA/OFESbudget.html
Fig. 3 shows US expenditures on fusion
research. Of the ICF budget, approximately 15% is directed toward ignition research. 7 The cumulative
ALPHA program to explore magneto-inertial fusion (MIF) had a total budget of $30M. 8 Earlier DOE
expenditures on MIF were of comparable magnitude. This graph is the basis for Finding 2: MIF research
is immature, as it has received ~1% the funding of MCF and ICF.

2.2 A Brief History of ‘Alternative’ Approaches
Nuclear fusion research has a long history. It was hypothesized as the energy source of stars in the
1920’s; that fusion reactions produced energy was demonstrated in the laboratory in the 1930’s; it waslargely put aside, but not forgotten, during World War II; fission-driven uncontrolled fusion reactions were
demonstrated by the so-called “hydrogen bomb” in 1952 by the United States; and efforts to produce
controlled fusion reactions in the laboratory began in earnest in the US, the UK and the USSR in the early
1950’s. Unfortunately, controlled fusion at the level of energy break-even remains elusive.

7
8

https://sites.nationalacademies.org/cs/groups/bpasite/documents/webpage/bpa_088736.pptx
https://aries.pppl.gov/FPA/OFESbudget.html

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In contrast, the development of nuclear fission was amazingly rapid. After its startling discovery
in 1938, nuclear reactors using neutron-induced fission chain reactions began operating four years later,nuclear fission weapons arrived after three more years, and the first nuclear power plants appeared
during the 1950s.
Why is fusion so much harder than fission? The principal problem is that a fusion reaction involves
two positively charged low atomic number atomic nuclei that come together and “fuse” despite theirelectrostatic (“Coulomb”) repulsion, requiring the nuclei to approach each other with very high relative
velocity. By contrast, fission involves reactions between a neutral particle—a neutron—and heavy atomic
nuclei. Thanks to the lack of Coulomb repulsion, some heavy nuclei (called “fissile” nuclei) are sosusceptible to fission reactions that a low energy (“room temperature”) neutron can induce the reaction,
driven by the binding energy of the added neutron—not by the kinetic energy of the neutron. Since thefissions release more neutrons, a chain reaction can be produced and sustained in a reactor by assemblyof a “critical mass”, i.e., enough fissile nuclei to sustain the reaction chain despite losses from the finite
reactor volume. Fusion, by contrast, requires assembly of a certain mass of fuel, heating it to hightemperatures (> 107 K so as to have high relative energies when the nuclei collide), and maintaining it atadequate density to have enough fusion reactions occur that the original input energy investment isrecovered.
The hydrogen bomb demonstrated fission-driven, uncontrolled “inertial confinement fusion”(ICF) in 1952, so named because no confinement method other than the physical size and the inertia of
the hot fuel was used to confine it. A laser-driven controlled ICF program was initiated in the US soon after
the pulsed laser was invented in 1960. 910 Likewise, the magnetic confinement fusion (MCF) programs
addressing controlled fusion in the US, the UK and the USSR were initiated in secrecy. In the US, this was
because they were “born classified” according to the Atomic Energy Act of 1954 11. Recognizing thedifficulty of achieving MCF early on, first the USSR and then the UK and the US, declassified MCF researchin the late 1950’s and scientists in other countries began such research. Most MCF configurations that are
being considered today were already conceived by 1960, including tokamaks, stellarators, z-pinches andfield-reversed configurations. 12 Inertial Confinement Fusion research in the US was partially declassified
in the 1970s (direct-drive ICF) and fully declassified in 1994.
Initially, researchers in ICF hoped that tightly focused laser beams at total energies far less than
1 MJ could trigger fusion by imploding tiny fuel capsules; however experiments showed that laser energy
deposition became highly inefficient due to laser-plasma instabilities, which reflected most of the incident
energy backwards, and hot electron generation, which preheated the fuel and reduced achievable
density. Controlling these effects required larger capsules and more powerful lasers at shorter
wavelengths. Later it was found that hydrodynamic instabilities hindered capsules from imploding to highconvergence ratios, requiring still more powerful lasers. This led to the construction of the National
Ignition Facility (NIF), a 1.8 MJ (at 351 nm wavelength), 192-beam laser facility at the Lawrence Livermore
9 J. H. Nuckolls, “Early Steps Toward Inertial Confinement Fusion Energy (IFE) (1952 to 1962)”, UCRL-ID-131075,

LLNL (1998).
10 T. H. Maiman, “Stimulated Optical Radiation in Ruby,” Nature 187, 494 (1960).
11 https://www.nrc.gov/about-nrc/governing-laws.html#aea-1954
12 http://www-fusion-magnetique.cea.fr/gb/fusion/histoire/site_historique.htm

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National Laboratory. Progress toward ignition, operationally defined as achieving 1 MJ or more fusion
yield, continues to be challenged by hydrodynamic instabilities and other non-linear physics phenomena
involving the intense laser beams inside the indirect drive target. Only recently have laser shots on the
NIF produced fusion energy greater than the kinetic energy in the imploding capsule (and still far less thanthe electromagnetic energy in the laser beam). 13
In the 1970s, national and international MCF programs were also optimistic that a commercially
viable fusion reactor could be designed and built by the year 2000, despite unexplained deficits in theenergy and particle confinement times. The leading device at the time for pursuing scientific breakevenin the 1970s was the tokamak, which led a majority of MCF program funding to be allocated to tokamaks
in the 1980s. Alternative concepts were eliminated, despite widespread contemporaneous argumentsthat field-reversed configurations (FRCs) or devices called spheromaks could be more commercially viable
reactors than tokamaks if confinement and heating issues could be solved.
Over the past 30 years, considerable theoretical, computational and experimental efforts haveidentified the instabilities that limited confinement in tokamaks. Through experience with many tokamak
designs, the MCF community developed empirical scaling relationships that predicted that achieving
scientific break-even with the magnet technology of the mid-1990s would require an ITER-sized machine.
While most MCF resources worldwide shifted to ITER, subsequent developments in high-TC
superconducting magnet technology raised hopes that a high-field Tokamak much smaller than ITER mightachieve scientific break-even in a shorter time and at lower cost. 14 The question of commercial viabilityof a tokamak as a fusion reactor remains.
Thus, in recent years, alternative approaches to MCF that might enable lower cost development
are being pursued, many of which involve the compact toroid configuration, i.e. a toroidal plasma that
does not require a magnetic coil running through its center. The Spheromak and the field-reversed
configuration (FRC) are two special cases of the compact toroid. Most of these projects are privately
funded.
In the 1940’s, Fermi in the U.S. and Sakharov in the Soviet Union independently realized that amagnetic field could reduce cross-field losses of particles and energy in a fusion plasma. 15 Research on
magneto-inertial fusion (MIF) proceeded independently in the two countries until the end of the Cold
War. In the West, Linhart and coworkers performed the first MIF experiments in 1962, identifying manyof the key concepts that persist to this day. 16 At the end of the Cold War, Russian and American
researchers compared achievements, and a Russian approach called MAGO emerged as the most13

S. Le Pape, et al., "Fusion energy output greater than the kinetic energy of an imploding shell at the National
Ignition Facility." Physical Review Letters 120, 245003 (2018).
14
Greenwald, M., et al. "The High-Field Path to Practical Fusion Energy."
http://sites.nationalacademies.org/cs/groups/bpasite/documents/webpage/bpa_185099.pdf
15
I. R. Lindemuth, et al., “Magnetic-Compression/Magnetized-Target Fusion (MAGO/MTF): A marriage of inertial
and magnetic confinement.” No. LA-UR-96-3939; CONF-961005-14. Los Alamos National Lab., (1996).
16
J. G. Linhart, et al., “Amplification of magnetic fields and heating of plasma by a collapsing metallic shell.”
Euratom-CNEN, Frascati, Italy, 1962.

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18 December 2018advanced alternative project 17,18 at least by the criterion of neutron production. MAGO involved
compression of a magnetized plasma by a collapsing metal liner, similar in concept to the ongoing MagLIF
project at Sandia.
Figure 4 shows a taxonomy of approaches to controlled thermonuclear fusion. The overall
impression is that many diverse approaches have been tried. None has succeeded (yet), but few havebeen conclusively ruled unworkable. The present study is restricted to thermonuclear approaches; i.e.,
where the distribution of ion velocities is (approximately) governed by a Maxwell-Boltzmann distribution
with a well-defined temperature. Even within the MIF domain, there is a wide diversity of approaches, as
we will explore below.

Figure 4. Approaches to controlled
fusion. Thermonuclear approaches
maintain an approximately MaxwellBoltzmann velocity distribution,
permitting each ion to undergo many
Coulomb scattering events prior to afusion reaction. MIF approaches areshaded in blue. Approaches unlikely
to reach scientific break-even are
shaded in grey. Image adapted fromS. Hsu, LANL.

We also note the possibility of non-thermal approaches, wherein the kinetic energy does notfollow a Boltzmann distribution. These assume a strongly anisotropic ion velocity distribution. Beams
readily put most of the input energy into the reaction coordinate. The challenge is that un-productive
collisions (Coulomb scattering) randomize the velocity vectors, quickly evolving the system toward
thermal equilibrium. The goal is to attain a high enough rate of productive collisions to compensate forthe wasted input energy from elastic scattering and bremsstrahlung losses. Whether such a goal is17 I. R. Lindemuth, et al., “Target Plasma Formation for Magnetic Compression/Magnetized Target Fusion”,

Physical Review Letters 75, 1953 (1995).
18 P. Sheehey, et al.,”Computational and Experimental Investigation of Magnetized Target Fusion”, CONF-

9606116—56, LANL (1996), and references cited therein.

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18 December 2018attainable has been the subject of debate 19,20,21 One large-scale commercial effort (TAE) uses non-thermal
ions.
Although peaceful energy production is the most prominent stated goal of alternative fusion
projects, arms control experts have pointed to conceivable military applications of pure fusion, such as
small-yield weapons 22. In a 1998 declassification decision, the U.S. DOE stated that “the U.S. does nothave and is not developing a pure fusion weapon and no credible design for a pure fusion weapon resulted
from the DOE investment”. 23 The Comprehensive Nuclear-Test-Ban Treaty, which bans “nuclear
explosions”, does not specifically address pure fusion. The U.S. has signed but not ratified that treaty, yetobserves its provisions; the US position is that ICF is allowed. If fusion power is eventually achieved, thearms-control implications will be non-negligible but likely manageable to an extent similar to that offission power through the IAEA and international treaties. 24

2.3 Fusion in the Energy Landscape
Fusion energy has long held a special mystique in science and in popular culture as a technologythat would be utterly transformative, if only it could be made to work. The prospect of a virtuallyinexhaustible fuel source was especially compelling in the 1950s to ‘70s after the finiteness of fossil fuels
had been recognized (either through finite supply or the deleterious effects of combustion). This
motivation declined with revised estimates of fossil fuel and uranium reserves, which have increased
dramatically over earlier estimates; and declined further with the emergence of affordable andinexhaustible renewable resources.
Today’s strategic outlook is not defined by fuel scarcity, but by overall system cost, environmental
impact, and operational constraints that limit a technology's ability to produce on a flexible schedule thatmeets electricity demand. There is no fundamental shortage of primary energy resources to motivate thedevelopment of fusion per se. Moreover, existing technologies can meet demand with substantial
margins, and a mixture of technologies can be dispatched according to their economic merit to reduce
the system cost to below that of any individual technology.
For fusion energy to become commercially viable and relevant in the current context, fusion must
not only work within this system, but it must be better than some existing technology in one or moredimensions. Those dimensions include the effective levelized cost of generation (present value of the total
cost of building and operating a power plant over an assumed lifetime and duty factor, divided by energy

19

T. H. Rider, "Fundamental limitations on plasma fusion systems not in thermodynamic equilibrium." Physics ofPlasmas 4, 1039-1046 (1997).
20
N. Rostoker, A. Qerushi, and M. Binderbauer. "Colliding beam fusion reactors." Journal of Fusion Energy 22, 83-92(2003).
21
N. Rostoker, M. W. Binderbauer, and H. J. Monkhorst. "Colliding beam fusion reactor." Science 278, 1419-1422(1997).
22
S. L. Jones and F. von Hippel, "The Question of Pure Fusion Explosions under the CTBT" (pdf). Science and Global
Security 7: 129–150. (1998) doi:10.1080/08929889808426452.
23
Department of Energy, “RESTRICTED DATA DECLASSIFICATION DECISIONS, 1946 TO THE PRESENT (RDD-8) ” page90, https://fas.org/sgp/othergov/doe/rdd-8.pdf (2002).
24National Academies, Assessment of Inertial Confinement Fusion Targets, chapter 3 (2013).

11

JSR-18-Task-011 - FUSION

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production), operational flexibility, environmental and proliferation impact, and non-technical factors
such as public acceptance, aesthetics, or prestige.
The U.S. Grid Context: Assuming the main product of fusion reactors to be electric, not thermal,energy (which other studies have assessed to be a good assumption 25), their economics must be
considered in the context of electric grid operations and electricity markets. This context is rapidly
evolving; the character of the U.S. grid by the time commercial fusion reactors could come online is open
to broad speculation, and will be influenced by yet-to-be-made regulatory decisions. Segmented gridswith a predominance of local generation, storage and controllable loads, which could render large
baseload generators obsolete even if they provide bulk energy at lowest cost, are not out of the question.
As of 2018, conventional coal plants are becoming uneconomical to operate and new nuclear plants are
becoming uneconomical to construct in the face of competition from natural gas generation that is both
inexpensive and highly flexible.
Some designers of next-generation fission reactors now favor smaller, more modular and flexible
units in the hope that factory manufacture might reduce the cost of construction through economies ofscale, and lower finance rates (arising from a lower fraction of the utility’s total capitalization being at risk)
will reduce the cost of financing reactors. The success of this strategy remains to be shown, however, and
it is too early to say whether a similar strategy could be adopted for fusion.
As energy production includes a greater component of intermittent renewable resources, suchgrid-specific qualities of generation as dispatchability, ramp rates, and response times are becoming
increasingly valuable properties, enabling technologies to compete on terms that go beyond cost perkilowatt-hour. For example, generators sell grid services such as load following or frequency regulationthat require them to vary their power output at specific rates (on the order of MW per minute) and withspecific response times (on the order of seconds to minutes), where the revenue from these ancillary
services can match or even exceed the profit from energy sales in certain specialized markets. 26 Simply
put, flexibility of operation matters. Flexibility favors technologies with low capital investment, so thatcosts can be decreased when demand is low.
In the United States, natural gas is by a significant margin the lowest cost way to accommodate
the intermittency of renewable generation, followed by electricity storage. The role of natural gas may
eventually have to decrease, however, if carbon-abatement policies are successful in bringing emissions
to well below 50% of current levels. 27 In such a world, there may be opportunities for fission and fusion
to compete with storage for offsetting intermittency. Under a scenario that forbids carbon emission fromnatural gas, higher prices may have to be tolerated as a matter of policy, permitting fission and fusion
technologies to enter the market even at currently speculated prices. Nevertheless, this means that even

25MIT Energy Initiative, The Future of Nuclear Energy in a Carbon-Constrained World, September 2018. pp. 27, 75ff,

and Appendix F.
26 B. Kirby, Ancillary Services: Technical and Commercial Insights. White Paper prepared for Wärtsilä, 2007.
http://www.consultkirby.com/files/Ancillary_Services_-_Technical_And_Commercial_Insights_EXT_.pdf (accessed
Sep 6, 2018).
27 National Security Implications of the U.S. Nuclear Industry and its Position in the Global Market, JASON Technical
Report, JSR-17-07, Appendix B (2018).

12

JSR-18-Task-011 - FUSION

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if all scientific and engineering challenges are overcome and fusion reactors can be built at projected costs,
their business case will ultimately depend on climate-policy choices that have yet to be negotiated in the
U.S. political system.
In 2017, the wholesale electricity price in the United States was $34/MWh, or $0.034/kWh. This
reflects the average marginal cost of production (influenced by tax credits and other factors) and favors
existing production technologies with the lowest absolute marginal cost. This is not a good estimate for
new construction, however, as capital costs influence investment decisions. A better long-term forecast
may be had by considering the projected levelized cost of new generation with which fusion mustcompete. Table 1 gives the U.S. Energy Information Administration’s forecast for the levelized costs ofgeneration resources entering service in 2040, suggesting a wholesale price of approximately $0.05/kWh,assuming no stringent constraints on CO2 emissions.
Fusion energy at 5¢/kWh? Let us consider
Table 1. Levelized cost estimate for electricity
a world in which $0.05/kWh is the maximum pricegeneration resources entering service in 2040
that a future fusion plant will be able to charge for(2017 dollars).
Numbers reflect wholesale
capacity-weighted average prices without tax
grid electricity (with the caveats that regulatory
credits. Nuclear estimate is for 2022 (no 2040
decisions may increase this number; and there
estimate available) Source: Tables B1 and 1b of
may be geographic locations or special
https://www.eia.gov/outlooks/aeo/pdf/
circumstances in which the value of electricity is
Modality
Levelized cost/kWhmuch higher). We can estimate maximum costs forelectricity (2017 ¢US)a viable plant as that where revenue just covers
the plant’s construction costs, interest, fixed
Natural gas
5.0
operating cost, fuel, maintenance, and waste
combined cycle
disposal fees. We shall see that even with
Solar photovoltaic
4.4
reasonably optimistic assumptions on the
Onshore Wind
5.6
engineering, the economics will be challenging.
Advanced Fission
9.3
The literature on fusion energy generally
assumes capital cost for reactor construction as
the main driver, expecting intrinsic fuel costs to be negligible. Overnight construction cost (construction
cost neglecting financing cost during construction) by itself is insufficient information. Build time andinterest are key factors that plant design will attempt to address but cannot entirely control, and overall
project costs remain highly vulnerable to delays. Operation and maintenance costs also harbor significant
uncertainties. Examples include the periodic replacement of components exposed to high-energy
neutrons, and regulatory requirements for handling tritium inventories and low-level waste from
activated materials.
Let us consider financing costs alone, since these are easily quantified. The analysis below uses
reasonable assumptions based on currently contemplated MIF technologies, and is primarily intended toillustrate that deviations from one or more of these assumptions will be needed to make an economically
viable power plant. A 30-year loan at 7% annual interest incurs a financing cost of approximately $9/hr
per $million (M) of loan. To cover financing alone, a power plant must sell a time-average excess electric13

JSR-18-Task-011 - FUSION

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power at $0.05/kWh of at least:ܲ௘௟௘௖௧௥௜௖ >180 kWୣ$M financing

or equivalently have overnight capital costs of less than $5.55/We.
Cost of a notional power plant: The ALPHA project sponsored calculation of cost estimates for
MIF power plants. The estimates were performed in a collaboration between Bechtel National, Woodruff
Scientific, and Decysive Systems (hereafter the `Bechtel Report’) and considered reactor cores comprisedof four prospective MIF technologies: Stabilized Liner Compressor, Plasma Jet Driven Magneto-Inertial
Fusion, Staged Z-Pinch, and Shear Flow Stabilized Z-Pinch. 28 These technologies were also among thosebriefed to JASON.
For a nominal reactor of 150 MWe, the Bechtel report estimated plant costs to range from $0.7 to$1.93Bn, with a mean estimated overnight capital cost of $1.32Bn. The authors of the Bechtel reportcorrectly emphasized that these estimates are notional, at best, considering that the underlying physics
has not yet been demonstrated in the relevant regimes. Taking these estimates at face value, in the simple
JASON financing model above, financing costs alone on $0.83Bn would consume 100% of the revenue
from a 150 MWe plant that operated at 100% duty cycle.
Here we give a condensed summary of the estimates in the Bechtel report to illustrate thedependence on key parameters. Consider a nominal pulsed fusion reactor constructed at a cost of $1B,
with 500 MJ nuclear yield per shot (at the upper end of the range typically considered for MIF). Typicalthermal-to-electrical conversion efficiencies are ~40%, yielding 200 MJ electrical energy (MJe) per shot.
Some of this energy must be recirculated to power the next shot. Assuming a scientific gain of 20, the
500 MJ nuclear yield will require 25 MJ energy input into the fuel. Assuming conversion of electricalenergy into fuel energy at 50% efficiency, we must divert 50 MJe to sustain the reaction, i.e. one quarterof the electricity production is recirculated just to keep the plant running. This estimate leaves 150 MJe
to sell, or 41.4 kWhe. At $0.05/kWhe, this estimate gives $2.07 of electricity per shot. This fact is known
as the ‘kopek’ problem, a Russian reference to the tiny revenue available from a single fusion shot. If theplant continually produces 1 shot/s, then it will produce 150 MWe and a revenue of $7,500/hr. This
revenue would be insufficient to cover the financing costs of $9,000/hr.
The hypothetical Bechtel-like plant has an overnight capital cost of $1B/150 MWe = $6.67/We. For
comparison, natural gas power plants have an overnight cost $1/We, solar photovoltaic $1.7/We, and wind28

Conceptual Cost Study for a Fusion Power Plant Based on Four Technologies from the DOE ARPA-E ALPHA
Program, Bechtel National, Inc. Report No. 26029-000-30R-G01G-00001 Feb. 2017
woodruffscientific.com/pdf/ARPAE_Costing_Report_2017.pdf (accessed Oct. 21, 2018).

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JSR-18-Task-011 - FUSION

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$1.5/We. 29 The last fission construction project in the US, the Vogtle Electric Generating Plant in Georgia,
is in jeopardy due to cost overruns to > $25B, or $10/We. 30
Intermittent operation in the context of renewables would hurt the economics of the notional
plant. Capital cost-dominated energy sources such as fusion are more sensitive to intermittent operations
than are fuel cost-dominated energy sources such as natural gas. These crude estimates demonstrate thechallenging economics posed by the combination of natural gas and renewables: reactors are expensive
and existing alternatives are cheap.
Response of commercial fusion enterprises: The proponents of the commercial fusion efforts
are, of course, aware of these economic challenges. To mitigate, they seek to maximize the efficiency
with which fusion energy is either converted to salable electricity or recycled to power the next shot.
Enhancements in these efficiencies would increase the ratio of electrical output to fusion yield, decreasing
overall capital costs.
In a D-T fusion reaction, 20% of the energy is released in alpha particles, and 80% in neutrons.
The Helion device seeks to capture the energy from alpha particles in a direct-to-electrical conversion
process, bypassing the inefficiencies of a thermal cycle for this portion of the energy. The Helion systemprovides the bulk of the plasma compression through a ramped magnetic field. They seek to recapture
the magnetic energy in each shot via an inductive loop, further decreasing the quantity of electrical energythat must be recycled to recharge the capacitors for the next shot.
In the General Fusion device, the compression is driven by a collapsing molten Pb liner, rotated athigh speed to form a central cavity. The design seeks to conserve the translational and rotational kinetic
energy in the Pb from shot to shot, minimizing the amount of energy that must flow through a lossy
thermal-electrical-mechanical loop to pump the molten Pb. Furthermore, the gas pistons that compress
the molten Pb are pressurized via direct gas heating with the hot Pb efflux, again avoiding a lossy thermalelectrical-mechanical loop. These innovations seek to minimize the portion of electrical power whichmust be recirculated to operate the reactor.
These examples illustrate that economic viability will require innovations in the power harvesting
and cycling aspects of the plant, not just the fusion core. Whether the engineering innovations will be
sufficient to reach economic break-even (assuming the central reaction can be made to work at all)remains to be seen. Finally, there are niche applications in which the advantages of avoiding ahydrocarbon fuel supply chain might justify generation at much more than 5¢/kWh.
Non-U.S. grid: The economics of electric power production can be substantially different in othercountries with different government policies; and where access to natural gas and renewables may belimited. For instance, the Chinese government reports that fission plants are being built for ~$2.4/We in

29 U.S. EIA, “Cost and Performance Characteristics of New Generating Technologies,” Annual Energy Outlook 2018,

Feb. 2018, Table 8.2. https://www.eia.gov/outlooks/aeo/assumptions/pdf/table_8.2.pdf
Russell Gold, “Growing Opposition Threatens Completion of Last U.S. Nuclear Plant,” Wall Street Journal, 20
Sept. 2018, https://www.wsj.com/articles/growing-opposition-threatens-completion-of-last-u-s-nuclear-plant1537447935
30

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China, less than a quarter the cost in the U.S.. 31 Where a technology is invented, where it is manufactured,
and where it is deployed are manifestly three different questions. It is possible, perhaps even likely, thata fusion power plant will be demonstrated outside of the U.S., and that the largest fusion power
deployment will also happen in some other country. In such a scenario, the U.S. might still benefit bymanufacturing the technology; and by supporting transitions away from fossil fuels in other countries.
The meaning of ‘cost’: At present, the science and engineering of fusion in any density regime
entail too many profound uncertainties to support credible cost estimates for hypothetical commercial
reactors. The scope of this study refers explicitly to ‘low-cost’ fusion, so we briefly discuss that modifier.
A possible interpretation of ‘low-cost’ is ‘drastically less expensive and more convenient than allalternatives,’ akin to the romanticized view of limitless energy “too cheap to meter” that would transformsociety. Such a condition seems both unlikely to be met, and unnecessary for fusion technology to be
worth an investment.
An alternative interpretation of ‘low-cost’ is ‘plausibly within the broad cost range of alternatives,’
subject to learning and economies of scale. This does not guarantee ‘preferable’ or ‘competitive.’ The
simple estimates above suggest that fusion reactors might be considered theoretically ‘low-cost’ at thesame time as being uncompetitive with other electric generation resources.
A third interpretation of ‘low-cost’ is ‘substantially less expensive than MCF or ICF to reachscientific break-even in a device configuration which could plausibly be further engineered into a power
plant’. This definition takes the desirability of developing a fusion energy technology as a given, justified
by the existence of substantial ongoing investments in MCF. The question, then, is “Does MIF get us tothe most proximate milestone more economically and perhaps faster than the alternatives—ICF or MCF?”
This is the interpretation we use in this Report.

2.4 Why Now?
Linhart et al. first described the physics underlying MIF in the Western literature in 1962. 32
Lindemuth and Kirkpatrick 33 advanced theoretical arguments in 1983 that MIF could reach break-evenunder less stringent conditions than MCF or ICF. The theoretical arguments underpinning MIF have beendeveloped over the past 35 years and are summarized in a monograph by Garanin and Reinovsky. 34 There
has been a recent surge in interest in MIF research, including a Summer 2018 IAEA-sponsored workshop
on Fusion Enterprise 35, interest from venture capitalists 36, and of course the ALPHA program. What new
information or technologies drive this interest?

31

World Nuclear Association, China Country Profile (updated Aug. 2018): http://www.worldnuclear.org/information-library/country-profiles/countries-a-f/china-nuclear-power.aspx
32
J. G. Linhart, H. Knoepfel, and C. Gourian. Amplification of magnetic fields and heating of plasma by a collapsing
metallic shell. Euratom-CNEN, Frascati, Italy, 1962.
33
I. R. Lindemuth and R. C. Kirkpatrick. "Parameter space for magnetized fuel targets in inertial confinement
fusion." Nuclear Fusion 23, 263 (1983).
34
S. F. Garanin and R. E. Reinovsky. Physical Processes in the MAGO/MFT Systems. No. LA-UR-13-29094. Los
Alamos National Lab.(LANL), Los Alamos, NM (2015).
35
https://nucleus.iaea.org/sites/fusionportal/Pages/Enterprises/2018/General-Info.aspx
36
http://issues.org/32-2/whats-the-big-idea/

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Scientific breakthrough: On the scientific front, in 2014 the MagLIF project demonstrated fusionrelevant conditions, including a temperature of 3 keV and strong magnetic confinement. 37 These ‘proofof-concept’ results catalyzed public and private interest in the MIF approach.
Technological advances: We identified three primary technology drivers of recent progress:
1) Computation. Many MIF concepts involve heterogeneous, dynamically varying magnetic fields,
large gradients in density, temperature, and pressure, and heterogeneous boundaries between
plasma and liner. Recent advances in computational power promise to enable simulations tounderstand and optimize these complex experiments.
2) Power electronics. MIF experiments require delivery of high-energy pulsed power over ns to ms
timescales. These requirements demand high-energy-density capacitor and solid-state, highcurrent, high-voltage switching technologies. Recent advances in Linear Transformer Driver (LTD)technology have decreased the cost and improved the performance of stored-power electricalsystems. 38 A single LTD ‘brick’ can deliver ~1 MA at ~100 kV over ~100 ns, corresponding to apeak power of ~1011 W and a delivered energy of 104 J.
3) High-speed servo controls. Several MIF concepts involve precisely timed launching of liner
material from multiple directions—either liquid Pb liners or high-Z plasma jets—while others
require precise relative timing of multiple current pulses. The ability to control precisely thestrength and timing of high-energy sources is critical to maintaining the symmetry needed forhigh-compression implosions. Advances in 3D printing and high-speed, high-power controls
facilitate implementation of these designs.
While the latter two technological advances might seem minor, the briefers made clear that all threecapabilities are essential to current progress. We note that similar factors were identified in a 1996 joint
report between the US and Russian MTF/MAGO teams, who wrote, “it is only in light of recent
advancements in plasma formation techniques, implosion-system drivers, plasma diagnostics, and largescale numerical simulation capabilities that the prospects for fusion ignition using this approach can beevaluated.” 39

37

M. R. Gomez et al. "Experimental demonstration of fusion-relevant conditions in magnetized liner inertial
fusion." Physical review letters 113, 155003 (2014).
38
A. A. Kim, et al., "Development and tests of fast 1-MA linear transformer driver stages." Physical Review Special
Topics - Accelerators and Beams 12, 050402 (2009).
39
I. R. Lindemuth, et al., “Magnetic-Compression/Magnetized-Target Fusion (MAGO/MTF): A marriage of inertial
and magnetic confinement.” No. LA-UR-96-3939; CONF-961005-14. Los Alamos National Lab., (1996).

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3 PHYSICS BACKGROUND
The energy contained in atomic nuclei can be tapped either by splitting a heavy nucleus into
smaller ones (fission) or combining two small nuclei into a larger one (fusion). Fission (aka nuclear power)
is a well-developed energy technology supplying 11% of the world’s electricity 40, as well as propulsion forsubmarines and naval surface ships. Fusion, although common in the cosmos (it powers the stars), has so
far found meaningful terrestrial application only in nuclear weapons. Achieving sustained and controlled
fusion reactions would open the door to a new source of energy with intriguing advantages relative toexisting sources.
3.1 Cross Sections
If two nuclei are to fuse, they must be brought to a separation r ~ several femtometers (1 fm = 1015
meter), the characteristic size of light nuclei. The energy required to do that (the Coulomb barrier, U)
is given by‫ି ݎ‬ଵܼଵ ܼଶ ݁ ଶ
= 450 keV ܼଵ ܼଶ ቀ
ቁ
ܷ=
‫ݎ‬
3 fm
where Z1,2 are the atomic numbers of the fusion
nuclei. While the coulomb barrier is easily
surmounted by an accelerator beam, energy
applications involve thermonuclear fusion,
where the nuclei collide due to their thermal
motion in a hot plasma. Here the energies arenecessarily much lower (a temperature of
1.2×107 K is only 1 keV), so that if the nuclei are
to fuse, they must tunnel quantum mechanicallythorough the Coulomb barrier (Fig. 5). These
considerations imply that lighter nuclei (a morequantal system that tunnels more readily),smaller atomic numbers (lower coulomb Figure 5. When nuclei collide and reach the classicalturning point (RC), there is a finite probability that thebarrier), and higher temperatures (more relative motion will tunnel through the Coulomb barrierenergetic collisions) will optimize the rate of and fuse.
thermonuclear fusion.

40

http://www.world-nuclear.org/information-library/current-and-future-generation/nuclear-power-in-the-worldtoday.aspx

19JSR-18-Task-011 - FUSION

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Table 2. Energetics of low-Z reactions considered for fusion energy in MeV.
D+D

T(1.011) + p(3.022)

D+D

3

He(0.820) + n(2.449)

p+T3+HQí

D+T

4+H  Q 

T+T

4

He + 2n + 11.332

D + 3He

4+H  S 

T + 3He

4+HQS

T + 3He

4

He(4.800) + D(9.520)

He + 3He

4

3+HS

There are several possibilities for reactions among the isotopes of hydrogen and helium. 41 In Table 2, p
and n are proton and neutron, respectively, D = 2H (deuteron), and T = 3H (triton). The numbers represent
energy in MeV. The highlighted D + T reaction is favored in energy production schemes due to its large
cross section (see below). There are other, minor reaction branches among these reactants, for example
D + D ї 4He + ੘ (24 MeV), which proceeds at a rate some 107 times smaller than the branches shown.
The reaction p + p їнĞ+ + Qe, which is the dominant process in the Sun, has far too low a rate to bepractical on Earth.
The DT reaction has several drawbacks. One is that 80% of the energy produced is carried by a
14.4 MeV neutron, which cannot be confined by a magnetic field, is highly penetrating (a 5 cm range insteel), and induces long-lived radioactivity as well as embrittlement in surrounding materials (bycomparison, fission neutrons have energies around 2 MeV). Replacement of reactor walls will increase
operating costs, cause down-time, and require handling low-level radioactive waste. A second drawbackof the DT reaction is that tritium is radioactive, undergoing a beta decay to 3He with a half-life of 12.3
years. As a result, the tritium fuel is not found in nature (unlike deuterium, which is 0.016% of naturalhydrogen), but must be continuously produced (“bred”) during reactor operation, usually by the 6Li + n Æ4
He + T reaction.
The multiple problems engendered by neutrons have led to consideration of aneutronic reactions
3such as He + 3He ї 4He + 2p + 12.86 MeV, and 11B + p ї 3 4He + 8.7 MeV. While the first suffers fromboth a low reaction rate (only 10-3 that of DT at a temperature of 100 keV) and a relative rarity of 3He innature (only 0.000137% of terrestrial Helium), some have considered 11B + p a promising candidate (11B is
80.1% of natural Boron), though the kinetics of this reaction are less favorable than the alternatives (seebelow).
Nuclear reaction rates are characterized by the cross section, V, which expresses the probabilityof reaction in terms of an equivalent target area presented to the approaching particle. The cross section

41 http://www.kayelaby.npl.co.uk/atomic_and_nuclear_physics/4_7/4_7_4.html

20JSR-18-Task-011 - FUSION

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depends upon the speed of the collision (e.g., collisions at a higher energy will more easily tunnel throughthe Coulomb barrier); it is conventionally measured in units of barns (1 barn = 10-24 cm2). Cross sections
for reactions at thermonuclear energies are dominated by the quantum penetration of the Coulomb
barrier, and so have the formܵ(‫ି )ܧ‬ோ/ாభ/మߪ=݁‫ܧ‬where E is the center-of-mass energy of the collision, S(E) is a nuclear structure factor which in mostcases varies slowly with energy (for a non-resonant reaction), and
ଶ௠

௠

ଵ/ଶ

ܴ = ܼଵ ܼଶ ߨ݁ ଶ ට ԰మ = 31.39 keVଵ/ଶ ܼଵ ܼଶ ቀଵ ୅୑୙ቁ,where m = m1m2/(m1 + m2) is the reduced mass of the collision. R characterizes the strength of the
Coulomb barrier in the reaction.
Figure 6 gives energy-dependent cross sections for reactions of interest. Table 3 shows
approximate values of S and R for some common reactions, neglecting the energy dependence of S(E). 42
In some reactions, such p11B, sharp resonances in S(E) contribute substantially to the cross section.
Energy-dependent interpolation formulas for S(E) for common reactions are in Ref. 43. DT has the largest
cross section at thermonuclear energies both because of the low atomic numbers involved and becauseof a resonance in the compound nucleus 5He.
Table 3: Cross section parameters for some fusion reactions
ReactionS(barns-keV)

R(keV1/2)

D–Dp
D–Dn
D–T
T–T
D–3He
T–3He
3
He–3He



9821


2422
5500

31.39
31.39

38.41




42

E. G. Adelberger, et al. "Solar fusion cross sections." Reviews of Modern Physics 70, 1265 (1998).
H.-S. Bosch and G. M. Hale. "Improved formulas for fusion cross-sections and thermal reactivities." Nuclear
Fusion 32, 611 (1992)
43

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JSR-18-Task-011 - FUSION

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Figure 6. Fusion cross sections. A) Cross sections of common fusion reactions as a function of center-of-mass kinetic
energy. The p-p reaction, which dominates in the Sun, has too low a cross section to be useful on Earth, due to theparticipation of the Weak interaction. B) Comparison of Coulomb and fusion cross sections for the D-T reaction. At
all energies, Coulomb scattering is more likely than fusion. D-T data from [Bosch, H-S., and G. M. Hale. "Improved
formulas for fusion cross-sections and thermal reactivities." Nuclear fusion 32.4 (1992): 611.]. The parameter ln /was set to 10.

Fusion reactions compete with non-productive Coulomb scattering, which can cause loss ofparticles and energy from the plasma. The Coulomb scattering cross-section decreases as kinetic energy
increases because the classical Coulomb turning radius scales as 1/E. Integrating over the differential
cross-section yields an effective Coulomb cross-section:ߨ݁ ସ ܼ௔ଶ ܼ௕ଶ
ߪ஼ =
ln Ȧ
ଶ
‫ܧ‬௖௠
where the parameter Ȧ = 12ߨ݊ߣଷ஽ , n is the particle density and OD is the Debye shielding length. /accounts for shielding of long-range electrostatic forces in the plasma. The parameter ln Ȧ varies by lessthan a factor of 3 for plasmas of interest in fusion research 44 (Table 4).
The ratio of Coulomb scattering to fusion events is given by the ratio of their cross-sections, eachplotted in Fig. 6. This ratio is an important dimensionless parameter of a fusion system. It is a function oftemperature, but only a weak function of density: both Coulomb scattering and fusion rates areproportional to n2 leading to a cancellation in their ratio, but the Coulomb logarithm introduces anadditional weak n dependence into VC>

44

F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (1984), Ch. 5.6, p. 169.

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Table 4. Coulomb shielding parameters for some fusion-relevant plasmas.

3.2 Reaction Rates
For a DT reaction, the rate (fusions per unit volume per second) is Ȟ = ݊஽ ݊ ் ‫ۄݒߪۃ‬, where n is thenumber density of reactants and <ʍv> is the velocity-weighted average of the cross section over the
Maxwellian distribution of (relative) velocities. Thus, for a plasma at temperature Tஶ‫ ~ ۄݒߪۃ‬න ݀‫ି ݁)ܧ(ܵ ܧ‬ா/் ݁ ିோ/ாభ/మ଴

where the integral is over E, the relative energy of the collision. If one neglects the energy dependence
ଵ/ଷோ் ଶ/ଷா‫כ‬ோమor ൎ ቀ ቁ . For the DT reaction, R = 34.37 keV1/2,்ସ்
ଶ

of S(E), then the integrand peaks at ‫ כ ܧ‬ൎ ቀ ቁ

so at T = 10 keV, E*/T ൎ 3.1, implying that most reactions occur in the extreme tail of the Maxwellian
distribution (i.e., only the very fastest particles participate). Inclusion of S(E) in the integrand shifts thisresult to E*/T = 3.5. Representative reaction rates are shown in Fig. 7.

3.3 Thermodynamics
For the DT reaction, the energy released is 'U = 17.6 MeV per reaction. This energy is equivalent
to 3.4×108 MJ/kg of DT fuel. For comparison, burning of methane releases 55 MJ/kg fuel. The power
density (power per unit volume) of a fusion reaction is ܲ = nୈ n୘ ‫ ۄݒߪۃ‬οܷ. To achieve scientific breakeven, the power released must exceed the power supplied to assemble the fuel. The latter can be
estimated by ܷ௜௡௧ /߬ா , where Uint is the internal thermal energy in the plasma, and WE is the energyଷଶdissipation time. The internal energy is well described by a simple ideal gas model, with ܶ of energy per
particle (where T is measured in energy units). In a neutral plasma ݊௘௟௘௖௧௥௢௡ = ݊௜௢௡ , and if one assumes
all species have the same temperature, then for the DT reaction, ܷ௜௡௧ = 3 ܶ ݊௜௢௡ .
ଵଶAssuming a 1:1 mixture of D and T (so ݊஽ = ݊ ் = ݊௜௢௡ ), then the break-even condition
becomes:12 ܶοܷ ‫ۄݒߪۃ‬In MCF systems where the maximum pressure is relatively constant (set by the maximum magnetic field),then it is customary to multiply both sides of the above expression by T, yielding:
12 ܶ ଶ
݊ܶ߬ா ൒οܷ ‫ۄݒߪۃ‬
݊߬ா ൒

23

JSR-18-Task-011 - FUSION

18 December 2018
்మ

By the ideal gas law, the quantity n T is the pressure. The quantity ‫ۃ‬ఙ௩‫ ۄ‬has a minimum around T = 14 keV,and substituting this value, leads to the Lawson criterion, ݊߬ா ܶ ൒ 3 × 10ଶଵ keV s/mଷ. Fig. 7 shows that
this expression is approximate, valid for DT only at T = 14 keV. Higher or lower temperatures require ahigher value for the triple product.
At thermonuclear temperatures (T < 100 keV), DT has the largest reaction rate by two orders ofmagnitude and hence is the favored candidate for most approaches to fusion energy. The p11B reaction
has been considered as an aneutronic alternative to DT. Despite the large charge product (Z = 5 for boron),its rate of energy production per ion ('U × <ʍv>) is within an order of magnitude of DT at temperatures
above 150 keV (Fig. 7). A resonance in the compound 12C system helps here, although the hightemperatures are much more challenging than those required for DT. The presence of 5 electrons per B
atom doubles the heat capacity of the p11B plasma relative to DT, assuming electrons and ions are at thesame temperature. Thus twice as much energy must be delivered to p11B relative to DT to reach the same
temperature.

Figure 7. Thermodynamics of fusion reactions. A) Reactivity (reaction rate per particle) of thecommonly studied fusion reactions. At temperatures < 100 keV, the DT reaction is most favorable,
but at temperatures > 100 keV the p11B reaction becomes comparable. B) Triple product to achievescientific break-even as a function of temperature. For the DT reaction, the optimal temperature is
14 keV.

3.4 Dissipation
Minimizing energy loss to the ambient environment is the primary challenge in every controlled
fusion experiment. Energy is lost through photons, neutrons, and charged particles (electrons and ions).
Neutrons escape freely and charged particle loss is described by the confinement time (which is different
for the reactants than for the energetic charged products of the reactions).

24

JSR-18-Task-011 - FUSION

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Loss through photons is primarily via Bremsstrahlung radiation produced by electron-ion
collisions. The radiative power dissipation is:ଵ/ଶܲ஻ ~ܶ௘ ݊௘ଵܼ௜ଶ ݊௜ ݊௘ଶଶ[ܸ݁]෍ ݊௜ ܼ௜ =ܶ௘
[7.69 × 10ଵ଼ ݉ିଷ ]ଶ௜௢௡௦Figure 7A shows that for temperatures < 10 keV, the DT reactivity grows approximately as T4,
whereas the Bremsstrahlung power only grows as T1/2. Both quantities scale as n2, so their ratio isinsensitive to density. For low-Z plasmas (e.g. DT), Bremsstrahlung radiation becomes insignificant relative
to fusion power at temperatures above 4 keV. However, the Z2 dependence imposes severe requirementson plasma purity. For instance, several MIF concepts contemplate using a Pb (Z = 82) liner to compress
the plasma. Pb impurities at a concentration of ~10-4 relative to the fuel will approximately double theBremsstrahlung rate.
While most analyses of MIF concepts havefocused on minimizing transport of fuel nuclei to thereactor walls, we note that transport of high-Z liner
atoms into the fuel is a potentially serious problem
that has received inadequate attention.
For solid and liquid liners, the problem of linerfuel mix can be divided into two parts: 1) ejection of
atoms from the liner surface; and 2) transport of theseions through the magnetized fuel. Fig. 8 shows theequilibrium density of Pb atoms in the vapor phase as
a function of the surface temperature of molten Pb(melting temperature 601 K). This vapor pressure
places a lower bound on the Pb density in the vapor Figure 8. Equilibrium vapor pressure of leadphase during a MIF experiment with a Pb liner. During as a function of temperature.
fuel compression, the Pb surface may be heated byplasma-wall collisions and by Joule heating from induced electric currents; and Pb atoms may be sputtered
off the surface by high-energy neutrons and ions escaping from the plasma. Characterization of theseeffects will require an experimental program to study liner-plasma interactions. The results of theseexperiments should be the joint distribution of velocities and ionization states of atoms exiting the liner
surface when in contact with the plasma under realistic conditions.
Liner-atom transport is also a complex process. Initially, neutral liner atoms will be able topenetrate the plasma without deflection by magnetic fields. As the evaporated or sputtered liner atoms
heat, they will increase in both velocity and ionization state, while also affecting plasma parameters via
Bremsstrahlung cooling. An improved understanding of this transport will be critical for mitigating
technical risk in Pb liner-based approaches; and perhaps in other approaches with high-Z liners as well.
This understanding will likely require a combination of experimental and computational work.
In addition to Bremsstrahlung radiative losses, high-Z impurities have another route to cool
plasmas in pulsed systems: initially neutral liner atoms will absorb energy from the plasma as they heat25

JSR-18-Task-011 - FUSION

18 December 2018ଷ
ଶand ionize. The nth electron to be ionized from a liner atom will absorb ‫ܫ‬ா௡ + ݇஻ ܶ of energy from theଷplasma, where ‫ܫ‬ா௡ is the nth ionization energy and ଶ ݇஻ ܶ reflects the translational kinetic energy after
ionization.

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4 MIF PHYSICS••••

A magnetic field can drive four distinct processes in a plasma
Suppress transport of particles and energy across field lines;
Confine and compresses the plasma: increase pressure and keep particles off reactor walls;
Enhance D deposition to facilitate self-heating and sustained burn;
Suppress some instabilities.

To achieve each of these benefits of a magnetic field imposes different design constraints. MIF devices
can, in principle, benefit from all four mechanisms. In some MIF concepts the bulk of the mechanicalcompression comes from a collapsing liner, rather than from a magnetic field.

4.1 Size Scaling: Why ITER is Big and NIF Targets are Small
In any fusion scheme, one wishes to maximize the number of collisions that a particle undergoes
before it exits the plasma, to maximize the likelihood of fusion. This simple principle leads to very different
implications in MCF vs. ICF.
The low density (limited by the confining magnetic stress) and comparatively large gyroradiiof MCF plasma requires large dimensions to minimize particle loss. The rate of loss is a function of thedimensionless parameter R/rg, where rg ~ 1/B is the gyroradius. Thus an important figure of merit for
tokamak designs is the parameter B R. The magnetic field in ITER is limited by the critical field ofsuperconducting coils of the mid-1990s to 5.3 T. Improvements in high TC superconducting magnets haveincreased the attainable magnetic field to ~12 T, enabling a corresponding down-scaling of Tokamak
dimensions, and presumably costs. This scaling underlies the SPARC Tokamak effort. 45
In ICF, the likelihood of an ion reacting is proportional to the column density, ߩ௙ ܴ௙ , where ߩ௙ isthe final density and Rf is the final radius after compression. The density scales as ߩ௙ = ߩ௜ ܴ௜ଷ /ܴ௙ଷ, so thecolumn density scales as ߩ௜ ܴ௜ଷ /ܴ௙ଶ. The upper limit on the initial density is set by material constraints:
cryogenic solid hydrogen has a density of n ~ 5 × 1022/cm3 at ambient pressure. The upper limit on the
product ߩ௜ ܴ௜ଷ is set by the available impulsive energy: 3kBT of energy must be delivered per ion to heat
the fuel. Given these constraints, to maximize the column density one should minimize Rf, which is why
ICF targets are small, compression is fast, and the convergence ratio (ܴ௜ /ܴ௙ ) is as large as possible(nominally 30).

4.2 Elements of a MIF system
MIF lies between the limits of MCF and ICF. Most MIF research falls into the density range n =10 – 1023 cm-3, a factor of 105. Not surprisingly, diverse approaches have been explored to cover such a
broad range in final density. This diversity is a striking feature of current MIF research: whereas the MCF
and ICF communities have, by financial necessity, each focused most effort on a single design, there was
18

45

Greenwald, M., et al. "The High-Field Path to Practical Fusion Energy." Commonwealth Fusion Systems White
Paper, http://sites.nationalacademies.org/cs/groups/bpasite/documents/webpage/bpa_184790.pdf (accessed 15
Oct. 2018)27

JSR-18-Task-011 - FUSION

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not a clear front-runner among the 8 MIF projects briefed to JASON. This diversity reflects the early stageof the technology: most projects have not progressed to a level of development where the likely physicaland engineering constraints apply. Here we review briefly the recent progress and current status of MIF
efforts.
Generically, a MIF system requires a source of magnetized plasma and a means to compress theplasma. For the magnetic field to suppress heat loss, the field lines must either form closed loops entirely
within the plasma, or the geometry should be cylindrical with an axial magnetic field with an aspect ratio>> 60, so that electron transport along field lines does not exceed cross-field ion transport. All DT MIF
schemes aim for a temperature of T ~10 keV, so the scientific break-even constraints on the final plasma
density and confinement time are inversely related: at n = 1018 cm-3, the confinement time must exceed
߬ா > 300 Ɋs; at n = 1023 cm-3, the confinement time must exceed ߬ா > 3 ns.
Within these broad constraints, there are many options for plasma and liner (Figure 9). In the
Marshall gun configuration, a radial current between a central and surrounding conductor produces a࢐ × ࡮ force on the plasma (as in a rail gun), causing plasma to eject through a nozzle, carrying acircumferential magnetic field along with it. In the approaches of General Fusion and Hyperjet Fusion, theplasma detaches from the gun, forming a stable configuration with a toroidal magnetic field. In the FuZE
apparatus, the plasma reconnects with a conducting wall perpendicular to the axis of symmetry, forming
a cylindrical Z-pinch configuration (axial current, circumferential magnetic field).

Figure 9. Ingredients of a MIF system. Many combinations of magnetized plasma and compression
scheme are possible (though not all possibilities are practical). Only a subset of the plausible approaches
has been tried.
An alternative approach is to use conventional coils to apply a magnetic field to a target prior toionization, and then to use a laser pulse to ionize and pre-heat the plasma. This approach, used in the
MagLIF and Omega experiments, works best in the high-density regime, where the fuel is sufficiently

28

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compact to be efficiently ionized by a focused laser pulse. The field lines are axially oriented and not
closed in these geometries, so these require a very high aspect-ratio cylindrical compression.
The third approach to plasma formation in MIF is to produce a ‘field-reversed configuration’ (FRC).
A cylindrical plasma is formed with an axial magnetic field. A rapid reversal of the applied magnetic field
causes the field lines to close on themselves. Helion and Compact Fusion Systems have both proposed
devices in which two FRCs are formed and then collided with each other to form an initially heated plasma.
The means of compression in MIF are also remarkably diverse, encompassing high-Z solid, liquid,and gas liners, and also purely electromagnetic drives. In the MagLIF system, a solid cylindrical can iscaused to implode via an axial current pulse. These solid liners have the merit of having high inertia, andhence the ability to drive high compression; but the liners are destroyed in the process and it is hard to
imagine how this configuration could solve the ‘kopek problem’.
Compact Fusion Systems and General Fusion both propose to use collapsing liquid Pb liners.
These liners are rotated quickly about the axis of symmetry to form a cylindrically symmetrical cavity, andthen rapidly imploded by gas pistons to collapse on the plasma. As with the solid liners, the liquid liner
has high inertia and so can drive strong compression; but in contrast to the solid liners, the liquid liner isregenerated with each cycle, offering the hope of a rapid repetition rate. The liquid Pb liner approachalso addresses the issue of neutron damage to solid reactor walls. The Pb, if carrying 6Li, also provides a
substrate for breeding tritium, a necessary step in any self-sustaining DT fusion reactor.
The primary concerns with the liquid Pb liner are (a) whether the material can maintain adequate
symmetry throughout the collapse, and (b) whether Pb ions will mix with, and quench, the plasma. The
molten Pb fluid flow has been predicted to remain laminar and cylindrically symmetrical during the௩మcollapse, 46 stabilized by centrifugal forces provided that ‫ݎ‬ሷ െ ഇ < 0, where r is the inner radius of the liner௥and vT is the component of the velocity in the direction of rotation. Scaled experiments have supported
this prediction. 47 But whether this stability will persist to fusion-relevant conditions remains to be seen.
A sufficiently high gas pressure (e.g. driven by D heating) or magnetic pressure during stall and reexpansion could cause sufficient outward radial acceleration to violate the stability condition.
Furthermore, the predictions of stability only apply about the rotation axis. In the orthogonal dimension
the flow might not be stable, particularly near the poles in the case of a spherical collapse.
Liner-fuel mix could arise during a compression, as described above. Additionally, the intense
energy released during a successful shot would be sufficient to vaporize the Pb surface (Appendix D),
possibly terminating the reaction early either via liner-fuel mix or by disrupting the electric currents in theliner needed to maintain confinement. This vapor must be removed almost entirely from the chamberprior to the next shot, possibly limiting the repetition rate.
A secondary concern with the liquid Pb liner systems is to what extent the kinetic energy in the
Pb can be recaptured after each shot to power the next shot. Commercial viability of these systems relies
on efficient recapture, to minimize the amount of electrical energy that must be diverted to prepare the46

D. L. Book, and P. J. Turchi. "Dynamics of rotationally stabilized implosions of compressible cylindrical liquid
shells." Physics of Fluids 22, 68-78 (1979).
47
P. J. Turchi, et al., "Rotational stabilization of an imploding liquid cylinder." Physical Review Letters 36, 1546
(1976).

29

JSR-18-Task-011 - FUSION

18 December 2018next shot. JASON is not aware of an analysis of the post-shot liner dynamics. There are concerns both at
the inner surface (will the surface remain Rayleigh-Taylor stable?) and at the outer surface (how will thegas pistons be re-charged without disrupting the rotational flow of the liner?).
Gaseous (plasma) liners have also been considered in the Hyperjet Fusion and MIFTI systems.
Hyperjet proposes to use plasma guns to drive a high speed (> 50 km/s) and approximately sphericallysymmetric collapse of a Xe plasma around a magnetized DT plasma target. MIFTI proposes to drive a Zpinch current through a cylindrical high-Z noble gas liner, causing collapse on a cylindrical target (“staged
Z-pinch”). The liner initially heats the target through shock heating, and then further heats the target
adiabatically, in a geometry broadly similar to the MagLIF experiment. The merit of the gaseous approachis that there are no mechanical moving parts, giving the promise of high repetition rate and reliability.
The first solid wall can be several meters from the reaction, decreasing neutron flux and associateddamage.
The primary concerns with this approach are (a) whether the symmetry of the implosion can be
maintained, (b) whether the high-Z liner will mix with the fuel, (c) the efficiency with which the linertransfers its kinetic energy to the fuel (since none of the liner kinetic energy is recaptured), and (d) how
residual liner atoms will be removed from the chamber to prepare for the next shot. Whereas gaseousPb atoms will stick upon collision with the (comparatively) cold liquid Pb wall, inert Xe atoms can beremoved from the chamber only by mechanical pumping. JASON recommends estimating the time toevacuate the chamber post-shot (given a sufficient efflux aperture), as this time limits the ultimate
repetition rate. A recent analysis cast doubt on the viability of the staged Z-pinch approach. 48
Finally, several approaches have contemplated purely electromagnetic compression. The FuZE
system uses an axial current through the plasma to drive a compressive ࢐ × ࡮ force. This ‘Z-pinch’
geometry was long-considered unworkable due to the emergence of multiple instabilities in the plasma(‘sausage’ and ‘kink’ instabilities). However, the FuZE team showed that these instabilities were
suppressed in the presence of a radial shear in the axial flow velocity. By setting up a system in which theelectric current simultaneously drove the Z-pinch and the shear flow, the FuZE team has argued that thisapproach will maintain stability up to fusion break-even conditions. The Helion system uses a large singleturn coil to produce a pulsed axial magnetic field that compresses the FRC-magnetized fuel. The purely
electromagnetic approaches avoid issues of liner contamination and moving parts. The main challengewith these is whether they can simultaneously achieve sufficiently high compression while maintaining
plasma stability. Table 5 gives the geometries and key physical parameters of some fusion approaches.

48 I. R. Lindemuth, M. R. Weis, and W. L. Atchison. "The staged z-pinch as a potential high gain fusion energy

source: An independent review, a negative conclusion." Physics of Plasmas 25, 102707 (2018).

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JSR-18-Task-011 - FUSION

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Table 5. Approaches to controlled fusion ranked by final density. ITER and NIF are included as thelimiting cases. Temperature, density, and radius are reported at maximum compression. WE is theenergy confinement time at maximum compression. Entries in blue represent data on integrated
prototype systems. Other entries represent goal parameters.

Experiment Plasma
configuration
ITER
TokamakHelionColliding FRCs

FuZE

Z-pinchCompact
FusionSystems
MIFTI

Colliding FRCs

Hyperjet
FusionLANLMagLIF onZ
MagLIF on
Omega
NIF

Z-pinch withaxial magnetic
field
Spheroidal

Axial magnetic
field and laser
heating
Axial magnetic
field and laser
heating
Spherical

Final B(T)
5
8
40

Final R
(cm)
240
6
6

Shear-stabilized 2E+17
Z-pinch
1E+20
Liquid Pb
1.4E+18
blanket

8.5
50
130

0.3
<0.1
3.4

5E-06
5E-06
Data notavailable

Staged noble
gas Z-pinch

3.5E+20

200

0.14

2E-09

High-Z plasma
jets

5E+21

300

0.5

1E-06

Z-pinch in a
metal can

1E+23

14000

0.006

2.5E-09

4.5E+23

14000

0.008

2.5E-09

Laser directdrive

2.75E+23

10000

0.001

3E-10

laser indirectdrive

2.5E+2503.5E-03

1.5E-10Compression
none
Pulsed B field

31

density(ions/cm3)
1E+14
8E+16
3E+17

WE (s)
3.6
4E-05
1E-03

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5 RECENT ADVANCES IN ALPHA PROJECTS AND ELSEWHERE
5.1 Progress along Key Metrics
Figure 10 summarizes recent progress in the MIF projects in parameter space (triple product vs.
temperature) and Figure 11 shows the same data as a function of time, with future projections included.
Figure 10A gives the illusion that we are ‘almost there’: many fusion efforts show a steady march
toward the break-even condition. Why have so many efforts gotten so close, but not reached break-even?
The truth is that no efforts are close to break-even: the proximity is an artifact of the logarithmic axes.
Fig. 10B shows the same data on a linear scale. The closest MIF effort, MagLIF, must either increase nTW
by a factor of 2, or increase temperature by a factor of 1.5 to reach scientific break-even. The next-closest
effort, at the LLE/Omega system, must increase temperature by a factor of 3 and density by a factor of
2.5 to reach scientific break-even. No other MIF project is within two orders of magnitude of scientificbreak-even. To the extent that input energy scales with temperature, and that costs scale with input
energy for a given technology, substantial financial investments would be required to upgrade the nearbreak-even systems to achieve that goal.

Figure 10. MIF efforts toward scientific break-even (blue curve). Tokamak programs (JET) and the NIF are included forcomparison. A) Experimental results plotted on a log-log scale, as is customary. B) Same data plotted on a linear scale,
highlighting the distance between most MIF programs and scientific break-even conditions.

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5.2 Examples from Select Projects
Here we describe recent progress in two MIF projects to illustrate the challenges andopportunities.

n T W (1020 keV s/m3)

MagLIF: One ALPHA-supported project, MagLIF at Sandia, differs from the others in that it iscarried out exclusively at a National Laboratory, and so benefits from previous Federal investment in alarge pulsed-power driver, the ZR machine (the Z-machine after a refurbishment of the pulsed powersystem in 2006/7). Fusion research began at Sandia in the 1970s and has been pursued on a sequence ofseveral increasingly powerful pulsed-power machines, measured for example by peak current, now up to
22 MA on today’s ZR. Several approaches to fusion have been pursued, including particle beams and Zpinches, the latter through both indirect drive and, later, direct drive of a target containing fuel. Sandia
researchers believe that break-even would be achievable on a new pulsed-power machine several times
more powerful than ZR.
As the MIF effort closest to
NIF
scientific break-even, the MagLIF
102
SPARC FuZE MagLIF IT
Break-even @ T = 14 keVproject has a unique potential to101
inform the other MIF projects.
MIFTI
LLE/OMEGAGA
A
Sandia should publish its open results
Hyperjet100
on MagLIF for the benefit of theentire fusion community; JASON
10-1
recommends that the backlog of
Helionunpublished results be published10-2
expeditiously. JASON notes that
TAE
10-3
many studies on MagLIF could inform
other MIF efforts, without requiring
10-4
substantial upgrades to ZR. For
instance, studies of cross-field
2010 2012 2014 2016 2018 2020 2022 2024 2026 2028
transport in the MagLIF plasmas
FuturePast
Year
could inform other efforts that
Figure 11. MIF progress vs. time toward scientific break-even. Filled
produce plasmas with comparable
symbols represent past results, empty symbols represent future
parameters (FuZE, MIFTI, HyperJet). projections. Tokamak programs (ITER, SPARC) and the NIF are included
MagLIF experiments with Pb liners for comparison. The indicated break-even condition is specific to T =could yield important information on 14 keV. MagLIF did not achieve break-even despite crossing thisthreshold in triple product because MagLIF was too cold.
Pb cross-field transport, which could
inform the efforts that propose to use a collapsing liquid Pb wall (General Fusion, Compact Fusion
Systems).
Sandia has developed an impressive suite of diagnostics on ZR, many of which might apply toother fusion projects, and sharing should be encouraged. As well, Sandia along with LLNL and LANL havegreat expertise in simulation codes, some of which has been shared with the wider community; such
sharing should be further encouraged.
JASON recommends that proposals to increase the power at ZR and at the LLE not be justified
solely on the basis of reaching scientific break-even. Reaching this condition, for its own sake, carries little34

JSR-18-Task-011 - FUSION

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value. JASON assesses that the solid liner MagLIF approach is unlikely to be scalable to a low-cost, highrepetition-rate system, as needed for a power plant. Thus the value in MagLIF is in the physics learned,
and disseminated to the community. Upgrades in power at MagLIF should be justified by the new physics
to be learned; and weighed against the physics that could be learned by exploring different geometries,
liner materials, diagnostics, or other experimental parameters with the current power level.
Shear-stabilized Z-pinch (FuZE): The FuZE program is notable as a primarily academic effort thathas achieved substantial progress in neutron production in recent years. While Z-pinch approaches tofusion have been considered since the 1950s 49, early efforts were limited by instabilities. The key insightunderlying the FuZE program was that at a sufficiently high laminar shear rate, the peaks and troughs of
emergent instabilities would be mixed together. If the mixing of peaks and troughs exceeds the instability
growth rate, then the instabilities would be quenched. 50 This theoretical prediction has been borne out
by experiments that have increased the triple product 30-fold in the last three years. One of the further
merits of this system is that as a purely electromagnetic compression system, it is capable of running at~50 shots/day, enabling rapid explorations of parameter space and providing a path to sufficient
repetition rate to be used in a practical power generating capacity.

5.3 Classification by Dimensionless Parameters
We wish to identify important dimensionless parameters that characterize the local properties ofa MIF plasma. There are two such parameters. The first is the ratio of the Coulomb mean-free-path (mfp)ɉi of the ions to the cyclotron radius rg. The Coulomb MFP is:ߣ௜ =(4ߨ߳଴ ܶ)ଶߨ݊݁ ସ ܼ ସ ln Ȧ

The ratio ߣ௜ /‫ݎ‬௚ is called the ‘collisionality’, and is large in MCF and small in ICF. When the collisionality islarge, the transport properties of the plasma are anisotropic, whereas when it is small, the transport isapproximately isotropic.
The second important parameter is the ratio of the plasma pressure, ݊௧௢௧ ܶ, (or equivalently theenergy density in the kinetic energy of plasma particles) to the magnetic pressure, ‫ܤ‬ଶ /2ߤ଴ in SI units (orequivalently the energy density in the magnetic field). The ratioߚ=

2 ߤ଴ ݊ܶ
‫ܤ‬ଶ

is small for MCF and large for ICF. For large Ⱦ the role of the magnetic fields can be largely ignored in thehydrodynamics, while for small Ⱦseen in, e.g., tokamaks, they play a dominant role.

49

J. L. Tuck, Method and apparatus for producing neutrons and other radiations. U.S. Patent No. 3,037,921. 5 Jun.

1962.
50

U. Shumlak, et al. "Increasing plasma parameters using sheared flow stabilization of a Z-pinch." Physics ofPlasmas 24, 055702 (2017).

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In Table 6, we list a sampling of the current approaches to fusion, ranging from the low-density,
magnetically confined regime (as in the ITER facility) to the high-density, inertially confined regime,
indicated with the NIF experiment. In the pulsed approaches where the density and the magnetic fieldstrength evolve as a power of the convergence ratio, we use the target endpoint quantities that areimportant for confinement and breakeven goals in these experiments. We note that the data combines
experimental data (MagLIF, NIF) with projections of future results (all others).
For the estimates in the table, we take the ion and electron densities and temperatures to beequal to the plasma density ni = ne = n, and temperature Ti = Te = T, respectively and set the latter to
10 keV. We also assume a hydrogen plasma (D-T mixture) and set the atomic charge to be Z = 1 and the
Coulomb logarithm ln / to 12.
Table 6. Dimensionless parameters of fusion efforts. Parameters are approximate and are drawn fromliterature sources and communications with the project leads. Entries in blue represent data, otherentries are projections. Parameter definitions: ni: ions density at maximal compression. B: magnetic field(Tesla) at maximal compression. R: plasma radius (along smallest dimension if not spherical) at maximal
compression. E: ratio of thermal to magnetic pressure. Oi: ion mean-free path. ɘc,i: angular cyclotron
frequency of ions. ɋi: frequency of Coulomb scattering events for ions. ri: cyclotron radius. The last column
gives the ratio of gyrofrequency to collision frequency for ions.
Experiment density
ri/Rɘc,iȀɋi
ɉi/R
Final
Final
Final T E
(ions/cm3) B (T)R (cm) (keV) 
ITER
Helion

1E+14
8E+16
3E+17

5
8
40

240
6
6

8
2
10

0.013
0.95
0.95

3.4E03 1.7E-03 2.0E06
11
0.021
500
71
9.5E-03 7.5E03

FuZE

2E+17
1E+20
1.4E+18

8.5
N.D.
130

0.3
<0.1
3.4

1
10
22

1
N.D.
0.73

21
13
130

0.28
76
N.D.
N.D.
7.7E-03 1.7E04

3.5E+20

200

0.14

4.5

16

0.53

0.055

9.7

5E+21

300

0.5

10

224

0.051

0.015

3.4

1E+23

14000 0.006

2.5

0.5

0.013

0.014

0.98

4.5E+2314000 0.008

10

9.3

0.036

0.020

1.75

MagLIF on
Omega

2.75E+23

10000 0.001

2.9

3.2

0.041

0.13

0.32

NIF

2.5E+25

0

4.5

>> 1

3E-04

>> 1

<< 1

Compact
FusionSystems
MIFTI
Hyperjet
FusionLANLMagLIF on Z

3.50E0336

JSR-18-Task-011 - FUSION

18 December 2018

In addition to the local parameters, there are several dimensionless parameters that capture
aspects of the overall geometry. Geometry is critical in determining loss rates (surface-to-volume ratio)
and also in governing onset of instabilities. The most fundamental parameter is N, the mean number of
Coulomb collisions a particle undergoes before it either exits the plasma or the plasma cools by adiabatic
expansion.

Figure 12. Fusion efforts arranged by dimensionless parameters. Empty circles represent
projections, filled circles represent data. Parameters are approximate and are drawn fromliterature sources and communications with the project leads.

37

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FUNDAMENTAL TECHNOLOGY NEEDS TO ADVANCE SMALL-SCALEFUSION RESEARCH

6.1 Computational Modeling of Experiments in the MIF Regime
Why Computations? Computational modeling has been crucial for designing, interpreting, andscaling fusion experiments. High fidelity models can help with performing parameter scans for optimizing
experimental setup as well as for scalability studies. When interpreting experimental results thatincorporate numerous physical effects, computational modeling allows numerical investigations ofspecific concepts that can help isolate individual effects. Verifying computational models against
experimental results can lead to a deeper understanding of the microphysics that contribute to fusion
experiments.
Computational modeling is also used frequently for planning purposes. Models can lead to thedevelopment of advanced approaches for improved control. Predictive modeling improves extrapolations
from regimes currently tested to different system parameters and help reduce risks. Finally, because
numerical experiments are cheaper and faster than physical ones, they can help with the continued lowcost training of future scientists.
Reaping these benefits requires computational tools that can faithfully reproduce the outcomesof physical experiments. This is a worthwhile but challenging task, for the reasons discussed below.
Modeling approaches in different regimes. In the low-density tokamak regime, the mean-freepath is many times the system size R and hydrodynamic approaches are not applicable. Instead, codesthat solve for motions of individual particles, such as particle-in-cell (PIC) and gyrokinetic codes are
utilized.
In the opposite, inertial confinement, regime, the mean-free-path is much smaller than othercharacteristics lengths in the system (i.e., system size and the ion gyro radius) and the fluid approximation
is appropriate. Here, hydrodynamic codes are widely used.
By definition, the magneto-inertial fusion (MIF) regime falls between these two extremes in bothof these key parameters but the various approaches themselves span a significant range in density and Ⱦ,
as can be seen in Table 6. Because of that, the selection of the appropriate computational tools and theirapplications depend sensitively on the details (i.e., whether a particular setup is closer to magnetic orinertial confinement). In general, the global properties of the plasma generated in MIF experiments
typically require magnetohydrodynamic (MHD) approaches to model. In this regime, the fluid
approximation holds but the magnetic field has dynamical effects on the plasma.
Further considerations within the MHD regime are related to the dissipative effects in the plasma.
Ideal MHD equations neglect any dissipative effects such as resistivity and viscosity, resulting in hyperbolic
equations, which are more tractable computationally. However, there are numerous non-ideal effects
such as (anisotropic) resistivity, viscosity, anisotropic thermal conduction, and separate ion and electron
temperatures, some of which can be captured by the generalized Ohm’s law and can be added as extra
terms to the MHD equations.

39JSR-18-Task-011 - FUSION

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As an example, anisotropies in the dissipation terms can be characterized by considering the ratiosof the cyclotron frequencies to the Coulomb collision frequencies for the ions and the electrons. The
cyclotron frequency for the ions can be expressed as୆ୋ୫ɘୡ,୧ = 9.6 × 10ଷ ቀ ቁ ቀ ౦ ቁ Z rad s ିଵ୫౟and is scaled by the relevant mass ratio for the electrons. The collision frequency ɋi is simply the ratio of
the thermal speed to the mean-free-path. The last two columns of Table 6 show this ratio for the ions andelectrons evaluated for the parameters of the various experiments. The setups for which these ratios areη1 need to account for anisotropic dissipation terms. When such terms are added, the mathematicalcharacter of the equations change to parabolic, significantly increasing the computational complexity.
In practice, the distinctions are not as clear cut and hybrid approaches are also employed toappropriately cover the landscape. For example, a fluid (MHD) approach might be sufficient to model thebulk of the plasma but small-scale plasma instabilities might require one to accurately capture particle
distributions and resistivities (through, e.g., a PIC code) to account for heat transport. Furthermore, formany experimental setups, there are large gradients in density within the plasma cavity and large
evolution of the parameters from the initial setup to the point of ignition that are not captured by thetypical values shown in Table 6. In devices with solid or liquid liners, one must include dynamics acrossinterfaces with dramatically different atomic numbers and weights. At the plasma-liner interface, there
can be near-discontinuities in physical parameters and dynamical regimes, requiring very fine meshing.
These factors often necessitate a combination of approaches to cover the entire range of physicalconditions.
In addition to modeling the plasma, the transport of neutrons through the experimental cavity isneeded to track yields and energy losses. While the radiation energy density is low compared to thermal
and magnetic energies, some approaches also require an accounting for the transport of energy throughradiation, such as when high-Z impurities mix into the plasma and enhance Bremsstrahlung radiation.
Though radiation does not account for a significant portion of energy loss from an unmagnetized plasma,
radiation may become a substantial source of wall heating in the presence of strong magnetic fields.
Dimensionality in models. Two geometries are employed in the codes to capture the geometryof the plasma: cylindrical and spherical. Even though the global symmetries would in principle allow thecodes to be simplified to a 2D geometry, the instabilities and small-scale fluctuations that play importantroles in the fusion problem necessitate working in 3D, making the computations expensive. During the
implosion and ignition, the domain shrinks by the compression factor C ‫ ؠ‬Ri/Rf. Depending on thegeometry, quantities of interest such as density and temperature scale as third or second powers of C.
Handling these changes requires moving mesh/adaptive approaches.
Community needs. JASON surveyed the MIF community to determine computational bottlenecks
and needs. Uniformly, the responses indicated that there are simulations the groups would find helpful
to run, but cannot. The stated reasons behind this were:
1. Lack of software that can capture all the required physics (indicating the need for codedevelopment);40

JSR-18-Task-011 - FUSION

18 December 2018

2. Lack of expertise to set up and run the appropriate simulations (indicating the need to cultivate andhire talent in this field);
3. Lack of computing resources, especially outside of national labs (indicating that ALPHA-like
programs should consider providing awards on high-performance computing along with grants);
with #1 and #2 having a larger impact than #3. The inaccessibility of codes (e.g., because they are classified
or proprietary) was mentioned by some respondents but was not a dominant concern; though it was notapparent whether all respondents knew about the capabilities of classified codes.
Other computationally intensive fields have adopted creative strategies advance the state of theart. The MIF community could draw inspiration from these approaches. Examples include:
x Competitions. Fusion physics is an exciting area with the possibility to recruit widespread talent
in the development of advanced software. Contests have driven significant progress in softwaredevelopment in other fields. Examples include the Critical Assessment of Protein Structure
Prediction (CASP),51 and the DARPA Grand Challenge for self-driving cars. 52 These annualcompetitions have helped benchmark progress in the field, and serve a recruiting and training
function as well. The competition meetings provide a platform for seeding collaborations andexchanging information. In the context of MIF research, one could select a challenging problem(e.g., a collapsing, inhomogeneous, magnetized plasma), and challenge teams to simulate anexperimental result. Pairing software and hardware development, as in the DARPA Grand
Challenge, could further advance the field.
x Distributed Computing. Many computationally intensive fields have developed distributed
computing ‘screensavers’ which use idle computing power over the internet, e.g. in protein
folding simulations (folding@home) and in the Search for Extraterrestrial Intelligence(SETI@home). More recently, the availability of computing power for rent on platforms such as
Amazon Web Services gives access to nearly arbitrary computing power without requiring major
capital investments. Efforts should be made to adapt MIF simulations to these platforms.

6.2 Instabilities and Loss Mechanisms
A common feature of all historical efforts at controlled fusion has been that instabilities made theproblem harder than initially thought. Under conditions far from break-even, simple scaling rules
governed the relation between energy inputs and final density, temperature, and confinement time. But
as energy inputs grew, plasma parameters deviated below expectations. There is no reason to think that
MIF experiments will be immune from these generic features of highly compressed plasmas.
Plasma instabilities can be divided roughly into two classes: fluid and kinetic. In a fluid instability
the plasma can be described by macroscopic thermodynamic variables (electron and ion temperatures,densities and velocities of each species) that are continuous functions of space. The local distributionfunctions are equilibrium (Maxwellian). Hydrodynamic and magnetohydrodynamic instabilities (kink,sausage, Rayleigh-Taylor, Kelvin-Helmholtz, etc.) are examples of fluid instabilities. In a kinetic instability
the local distribution function is non-equilibrium, and this local deviation from equilibrium provides the5152

http://predictioncenter.org/
http://archive.darpa.mil/grandchallenge/

41

JSR-18-Task-011 - FUSION

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free energy that drives the instability. Familiar examples are the "two stream" or "ion-acoustic"
instabilities that occur when a beam of particles penetrates a plasma, or when there is a relative electronion drift.
While the complete zoology of plasma instabilities is too large to review, we note some genericfeatures of instabilities that will apply to MIF experiments.
1) The characteristic rate of instability growth is typically much greater than any macroscopic
rate (nuclear reaction or collisional energy loss) of the plasma. For magnetohydrodynamic
instability it is an Alfven wave frequency, while for a kinetic instability it is a weighted
geometric mean of the plasma and gyro frequencies. When the growth rate is negative, themode of concern remains at small amplitude. When its growth rate turns positive, even if its
suitably nondimensionalized growth rate is small, it grows and saturates rapidly. Saturation
typically occurs at large enough amplitude to disrupt the plasma or to produce
catastrophically rapid loss of plasma particles or energy. Experiments give little or no warningof instabilities until they occur. This feature of instabilities urges caution in simple scaling
extrapolations.
2) Geometry matters. MIF experiments have a wide diversity of geometries, and there is noconsensus on which are superior. The arguments for most MIF concepts motivate thegeometry from simple scaling considerations, but those arguments might miss important
instabilities, which often depend on plasma aspect ratio or topology.
The analysis of plasma parameters above focused solely on local variables (temperature, density,
magnetic field strength), and global geometry. But instabilities in a fluid are often driven by gradients inphysical parameters (e.g., the onset of instability in Rayleigh-Benard convection, depends on a
combination of material parameters, temperature gradient, and overall geometry). The possibly relevant
gradients in MIF include gradients in:x Temperaturex Density
x Flow velocity
x Magnetic fieldx Electric fieldx Composition
In the parameter space of MIF, the stability of plasmas under gradients in these quantities has
been inadequately studied. While one often worries about gradients driving instabilities, they can have astabilizing effect too. Magnetic shear has been used to stabilize tokamak plasmas. 53 Under somecircumstances, shear flows can also suppress turbulence and transport, by mixing regions with oppositely
directed motion before these motions can grow to substantial amplitude. 54 This principle has been used

53

E. J. Strait, et al., “Enhanced confinement and stability in DIII-D discharges with reversed magnetic shear.”Physical Review Letters 75, 4421 (1995).
54
P. W. Terry, Suppression of turbulence and transport by sheared flow. Reviews of Modern Physics 72, 109 (2000).

42JSR-18-Task-011 - FUSION

18 December 2018

to good effect in stabilizing a Z-pinch geometry, 5556 which had been long discarded due to susceptibility
to instabilities.
Growth of asymmetries. Imperfections in the initial symmetry of a fusion target can seed thegrowth of instabilities, or can become amplified during compression and lead to energy loss even in theabsence of a formal instability. In tokamaks, the boundary conditions are set by the tokamak walls andthe magnetic coils. These are precisely engineered prior to plasma formation. In ICF experiments, theinitial conditions (hohlraum geometry, capsule symmetry) are precisely engineered prior to each shot.
Despite these efforts, slight asymmetries in ICF targets have been a major challenge at NIF. 57 In most MIF
approaches, neither the boundary conditions nor initial conditions are well defined: a dynamically
evolving magnetized plasma is compressed by a dynamically evolving collapsing liner. The challenges of
establishing sufficient initial symmetry to attain a homogeneous compression merit further study.
Loss mechanisms. Simple scaling arguments may miss important energy and particle loss
mechanisms that decrease the energy confinement times in MIF plasmas. In MCF tokamaks, energy loss
is primarily through particle transport to the edges of the confining magnetic field. Since cooling is at thesurface, there is a motivation to minimize the surface-to-volume ratio by making the plasma large. In ICF,
the plasma cools by adiabatic expansion in the bulk, and the rate of expansion sets the energy
confinement time. In the intermediate MIF regimes the plasma will cool both via surface evaporation andvia bulk expansion. The combined influence of these two mechanisms requires further study.
Finally, the physics of plasma-liner interactions is an area of technical risk and interest for MIF
research. In all MIF approaches with physical liners, the liner comes into direct contact with the plasma.
In MIF, the compression is slower than in ICF, giving more time for liner to mix into the plasma, where it
can quench the fusion reaction. In the research reviewed by JASON, liner mix was primarily treated as anempirical variable. Development of theoretical principles and experimental knowhow to minimize liner
mix would be beneficial. Recent ICF results at NIF benefited from a thin carbon film deposited on theinside of the hohlraum. 58 We suggest studies of multi-layer liners where a low-Z material provides somestandoff from a high-Z pusher.
A further concern with ultimate high repetition rate power systems will be removal of high-Z
contaminants from preceding shots.

55

U. Shumlak, et al., Increasing plasma parameters using sheared flow stabilization of a Z-pinch. Physics of Plasmas
24, 055702 (2017).
56
Y. Zhang, et al., "Sustained neutron production from a sheared-flow stabilized Z-pinch." arXiv:1806.05894 (2018).
57
V. A. Thomas and R. J. Kares. "Drive asymmetry and the origin of turbulence in an ICF implosion." Physical Review
Letters 109, 075004 (2012).
58
S. Le Pape, et al., "Fusion energy output greater than the kinetic energy of an imploding shell at the National
Ignition Facility." Physical Review Letters 120, 245003 (2018).

43

JSR-18-Task-011 - FUSION

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6.3 Diagnostics
Diagnostics play an essential role in all the alternative approaches JASON was briefed on. They
include:
x
x
x
x
x

x

Measurements of currents and magnetic fields; these are essential for any approach involving
magnetized plasmas, and relatively straightforward.
Optical or UV imaging. Straightforward (if opacity allows) and often helpful.
Point measurements of plasma densities and temperatures at ~100 eV and above. Difficult tocarry out, especially of density, but key to understanding the success of compression.
X-ray imaging of plasmas at temperatures at ~100 eV and above. Difficult, but key tounderstanding instabilities. Time-dependent imaging is especially valuable if achievable.
X-ray spectroscopy. Difficult but valuable.
Neutron output is the “proof of the pudding” but difficult to measure well. A most important
issue is whether the neutrons are produced by nuclear reactions in a thermal plasma (as isessential for break-even), or by in-flight reactions of beam nuclei or superthermal nuclei. To
distinguish, neutron time-of-flight measurements over long distances are needed, with large-area
detectors.

There is a need to develop highly sensitive diagnostic systems to monitor fusion reactor
performance that operate with sufficient speed that information can be fed back into reactor
performance. This is most obviously of value for reactors that run continuously, as the plasma status could
be monitored and adjusted with input from the diagnostic systems. However, even reactors that function
on a punctuated fashion with repetitive fusion shots could benefit from diagnostic feedback systems.
Imperfections in a preceding shot could help inform reactor adjustments for the subsequent shot.
Advanced measurement and feedback systems could be used to tame some instability modes.

44JSR-18-Task-011 - FUSION

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7 NON-ENERGY APPLICATIONS
7.1 Spacecraft propulsion
NASA asked JASON to consider whether novel schemes for achieving compact, low-cost fusion
power, such as those supported by the ARPA-E ALPHA program, might be adapted to the needs ofspacecraft power or propulsion. Among the obvious advantages of controlled fusion for NASA’s missionare:x high fuel energy density, and therefore a high payload fraction if used to achieve high specificimpulse for interplanetary flight;
x relatively low levels of radioactivity at launch from Earth compared to fission fuels
A further potential advantage suggested by Dr. Ronald Litchford in his brief to JASON is reduced exposure
to solar energetic particles and cosmic rays resulting from shorter mission durations. But this must bebalanced against exposure to radiation from the nuclear reactions on board.
Regarding the first advantage listed above, the theoretical energy density of deuterium-tritiumĨƵƐŝŽŶ;ŚĞƌĞĂĨƚĞƌ͞dĨƵƐŝŽŶ͟ͿŝƐɻDT уϯпϭϬ14 J/kg, or 0.0037 c2, as compared to 1.6×107 J/kg for chemical
combustion of hydrogen and oxygen. This is, however, only four times larger than the theoretical energy
density of 235U fission, 8.3×1013 J/kg = 0.00093 c2, and whereas fission reactors—even space reactors—are
essentially a solved problem, the same cannot be said of fusion reactors.
These theoretical estimates neglect the ancillary mass of shielding, radiators (to reject heat),pumps, pipes, turbines, and structural materials needed by an actual power or propulsion system (the“balance of plant”). Nor do they allow for thermodynamic losses in the conversion of heat from thenuclear reactions to mechanical or electrical work (Carnot efficiencies).

Figure 13. HOPE spacecraft design.

45JSR-18-Task-011 - FUSION

18 December 2018

7.1.1 Comments on a conceptual design for a fusion-propelled spacecraft
A NASA technical report by Adams et al. presents notional designs of spacecraft for manned
missions beyond the orbit of Mars. 59 By way of example, they detail a 654-day round-trip between Callisto(the outermost Galilean moon of Jupiter) and the L1 point of the Earth-Sun system. Their fiducial design(Fig. 13) combines magnetized-target fusion (hereafter “MTF”) for propulsion with fission for electrical
power. It has a total mass of 645 metric tonnes (T), of which 164 T is payload—the crew, their quarters,
associated consumables, etc. The “dry” mass of the MTF propulsion system is 116 T; about half of this isshielding to protect the crew from fusion neutrons. The propellant, 106 T, is ordinary hydrogen (1H); theŵĂƐƐŽĨdĂŶĚĨƵĞůŝƐƌĞƉŽƌƚĞĚƚŽďĞϭͬϭϳŽĨƚŚŝƐ;уϲdͿ͘/ĨƚŚĞĨƵĞůǁĞƌĞďƵƌŶĞĚĐŽŵƉůĞƚĞůǇĂŶĚŝƚƐenergy converted entirely to the kinetic energy of the exhaust, the specific impulse 60 would be Isp уϭϳ;ϮɻDT)1/2 уϮ͘ϲпϭϬ6 s. Since the reported specific impulse is only Isp = 70,400 s, the net efficiency of the proposedƉƌŽƉƵůƐŝŽŶƐǇƐƚĞŵŝƐчϯйŝŶƚĞƌŵƐŽĨƚŚƌƵƐƚ͕ĂŶĚƚŚĞƐƋƵĂƌĞŽĨƚŚŝƐŝŶƚĞƌŵƐŽĨĞŶĞƌŐǇ͘WĂƌƚŽĨƚhe loss isdue to neutrons, which carry off 3/4 of the energy of the DT reaction but provide negligible net thrust. 61
The rest of the discrepancy is presumably explained by incomplete burning of the fuel.
And yet this design is optimistic. The proposed MTF propulsion design involves injecting andcompressing a magnetized field-reversed configuration (FRC) via plasma jets that are not distributed overa full sphere, in order to leave some solid angle free for the products to escape as exhaust and provide
direct thrust (Fig. 14). It is far from clear that an FRC plasma can be stably compressed sufficiently toachieve fusion even in a more symmetrical configuration, as might be attempted for a terrestrial MTF
power plant, let alone with the less symmetrical arrangement proposed for this thruster. Among otherconcerns, the hydrogen liner has lower molecular weight than the DT and DD fuel, so that if all of theseplasmas have the same entropy (i.e., the same pressures at a common temperature), then the interface
between the fuel and the liner will be Rayleigh-Taylor unstable when the latter accelerates the former.

59ǤǤ,Ǥ,“  -  

ǳǡ  -2003-ʹͳʹ͸ͻͳǡǡʹͲͲ͵Ǥ
60   ǯ ǣI‫ؠ‬V/gْ.
61  ǡ

ǡ.

46 

JSR-18-Task-011 - FUSION

18 December 2018


Figure 14.Distribution of plasma guns in the conceptual design of a fusion thruster. These guns inject DT
plasma followed by an ordinary hydrogen (1 ) “liner” to compress the fuel and also add to the propellant
mass. The gray rings in the lower panel carry current to create a magnetic nozzle that deflects and expels
the expanding exhaust gases.


JASON does not wish to seem overly critical of the document by Adams et al. 62. Notwithstanding the
optimism concerning the fusion thruster, the overall design is admirably detailed and very instructive in
illustrating the various energy losses, added weight, and complexities of a thoroughly engineered
spacecraft design. For example, the design includes a 2 MW (thermal) fast spectrum fission reactor to
supply 375 kW of electrical power via a Rankine cycle heat engine; thus the overall energy efficiency ofthe power system is 19%. The total mass of the power system is 71,370 kg, of which 90% is shielding(tungsten and lithium hydride covering a full sphere around the reactor), while 2% is for radiators, pumps,
pipes, and fluid (NaK) in the heat-rejection system. It is instructive to compare this to the 100 kg initial
mass in 235U fuel (of which only 3.8%, or 0.005% of the total mass of the power system, is actually burned
during the reactor’s 50,000-hour life).
7.1.2 General physical and economic considerations
Energy densities of fuels: As the notional design discussed above illustrates, it is misleading tocompare the energy densities of fission and fusion directly, since most of the mass of a practical nuclear
spacecraft propulsion or power system would constitute structures and systems other than the fuel itself.
But for what it’s worth, the theoretical energy density of DT fuel is only four times larger than that of 235U.
For terrestrial commercial power production, the availability and cost of nuclear fuels, whether for fission
or fusion, as well as the nature and mass of radioactive waste products, will probably be more important
than the theoretical energy density. But the weight attached to these factors will probably be different

62 ǤǤ,Ǥ,“  -    -2003-ʹͳʹ͸ͻͳǡǡʹͲͲ͵Ǥ

47Ǥ”JSR-18-Task-011 - FUSION

18 December 2018

for spacecraft dedicated to exploration, whether manned or unmanned. Exploration of deep space is not
yet a commercial venture, although it may lead to commercial enterprises eventually. For the foreseeable
future, a more important economic consideration for spaceflight is the total mass that must be launchedfrom the Earth’s surface (probably by chemical rockets: see below) in order to deliver a given payload tothe destination (and return the crew to Earth, in the case of a manned mission).
Shielding: Shielding is an important or even dominant part of the mass of a nuclear power plant.
In a previous but unpublished study, 63 JASON suggested that a fission reactor be placed on a separate
spacecraft from the crew quarters (or other sensitive payload), and that the two be connected by longcables or microwave beams for power transmission. For the purposes of the following discussion,
however, we will assume that the reactor and the crew are separated by R = 100 m, which might bepossible on a single spacecraft. The MTF thruster in the notional design discussed above would have aƚŚĞƌŵĂůƉŽǁĞƌWуϮ'tth. If this were produced entirely by DT fusion 64, the unshielded fluence of prompt
neutrons would beȰሶ =୔ൎ 3 × 10ଵଵ ܲீௐ ܴଶିଶ neutrons cmିଶ sିଵସ ஠ ୖమ ×ଵସ.ଵ ெ௘௏where PGW is the thermal power in gigawatts, and R2 the distance from the reactor divided by 100 meters.
This corresponds to a radiation dose of 65
‫ = ܪ‬5 × 10ଽ ܲீௐ ܴଶିଶ Sv yr ିଵ .
The reactor shielding must reduce the dose to ‫ ׽‬ϭ^ǀǇƌоϭ͕ǁŚŝĐŚŝƐĂƚůĞĂƐƚƚĞŶƚŝŵĞƐƚŚĞƌĞĐŽŵŵĞŶĚĞĚ
safe dosage for humans, but comparable to the unshielded dosage rate from cosmic rays and solar
energetic particles outside the Earth’s atmosphere. We presume that the crew quarters will haveadditional shielding sufficient to deal with the cosmic rays. 66
Suppose the shielding is composed of lithium hydride (LiH), using the less common isotope 6Li
because of its huge cross section for absorbing low-energy neutrons and breeding tritium [6Li(Ŷ͕ɲ)t]: ʍу150(En/1eV)о1/2 barn for En ч10 keV.67 The cross-sections of 6Li and 1H for 14-MeV neutrons are 0.69 barn(almost entirely elastic) and 1.45 barn (67% elastic), respectively, 68 so a grammage of 125 g/cm2 of thehydride, corresponding to a thickness of 1.73 m at room temperature, is needed to decrease the fluenceof the fast neutrons by a factor 10о10. Since they lose about a third of their energy in each elastic collision,
63“Interplanetary Travel: Nuclear Propulsion Prospects.” JASON Technical Report, JSR-01-0752, 2001.

64

In fact, the design calls for a combination of DT and DD fusion, in unstated proportions.
J. D. Cossairt and K. Vaziri. “Neutron dose per fluence and weighting factors for use at high energy accelerators.”
Health Physics 96, 617–628 (2009)66
The grammage in shielding required to block charged particle such as cosmic rays may differ from what is required
to block the same fluence in neutrons, depending on the shielding material. On the other hand, inasmuch as theshielding must reduce the neutron fluence by a factor ш1010, only a 10% increase in the thickness and mass of theshielding would be needed to decrease the dosage by another order of magnitude.
67
D. Steiner and M. Tobias. “Cross-section sensitivity of tritium breeding in a fusion reactor blanket: effects ofuncertainties in 6Li, 7Li, and 93Nb.” Nuclear Fusion 14,153 (1974).
68
H. M. Fisher. A Nuclear Cross Section Data Handbook. LANL, 1989.
65

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and since ‫ ׽‬ln(1010)2 у ϰϲ ƐĐĂƚƚĞƌŝŶŐƐ ĂƌĞ ŶĞĞĚĞĚ ƚŽ ƌĂŶĚŽŵ-walk across the shielding, the scatteredneutrons will be moderated down to thermal energies and captured by the 6Li.
The total mass of this shielding depends upon the area that needs to be covered. The MTF thruster
envisaged by Adams et al. is 13 meters in diameter; if all of this needed to be shielded by a disk of thesame diameter, the mass would be 166 T (about a quarter of the mass of the spacecraft). However, in MTF
fusion, the neutrons are released when the target is maximally compressed and therefore much smaller
than the reaction chamber; if it could be assured that the target were always close to the spacecraft axis
when it burned, a considerably smaller disk diameter and mass would be sufficient to shield the forward
sections of the spacecraft from the neutron flux. In fact, the design uses a tank of H2O 2.3 m in diameterand 5.5 m long, with mass 37 T, to shield the thruster; this is 25 mean-free-paths thick, approximately thesame as for our lithium hydride.
Suppose one were to dispense with the MTF drive (which one does not yet know how to build) infavor of a scaled-up fission reactor to be used for propulsion as well as power. As noted above, there
would be only a modest penalty in fuel mass, but what about shielding? For the same power level, theneutron fluence of 2369U would be somewhat lower than for DT fusion.5 Fission also produces gamma rays:
approximately 15 MeV per fission if both prompt and delayed gamma rays (the latter from beta decays offission products) are counted. The quality factor, or biological harm per unit energy absorbed in the body,is an order of magnitude smaller than for fast neutrons. So we may assume conservatively that therequired attenuation factor for fission gamma rays is comparable to that for DT-fusion neutrons at thesame power level. Gamma rays with energies of 1-2 MeV are hardest to stop since, especially in a highatomic-number shielding material, photoelectric cross sections rise rapidly toward lower photon energies,
and pair-production cross sections at higher energies. The mass attenuation coefficient length is about
0.05 cmо2 gо1 at 1.5 MeV in most materials, 70 so ‫׽‬0.46 kg cmо2 of shielding would be required for 23
attenuation lengths.
The total mass of shielding depends of course on the area that must be covered. Here fission
reactors are at a disadvantage compared to MTF fusion ones: the active volume is much larger. Suppose
for example a total thermal energy of ER = 1GWth yr must be produced at a burnup fraction of 3.8%: therequired mass of 235U is about 10 T (104 kg), and the corresponding volume would be 2.6 m3 assuming a
20% volume filling fraction for the fuel. This could be accommodated in a cylinder of approximately 1 m
radius and equal height. If shielding needs to be applied only in the direction of the payload, the required
mass would be ‫׽‬13 T, scaling approximately as [ER/(1GWth yr)]2/3. So at this “design point,” the mass offuel plus shielding is 23 T, to which would have to be added the mass of the reactor vessel and control
rods, cooling fluids, pumps, turbines, and radiators to make a full power system; and electrically powered
thrusters for propulsion. Assuming conversion of thermal to electrical power with 25% efficiency, themass-to-electrical pŽǁĞƌƌĂƚŝŽǁŽƵůĚƚŚĞƌĞĨŽƌĞďĞш1 kg/kWe. Although it has not yet launched a space
reactor (the Soviets and Russians have), NASA and collaborators at the national labs have designed several

69

Each fission releases 202.5MeV and 2.5neutrons, but one is of these is used to sustain the chain reacton, hence
there is effectively 135MeV of thermal power per neutron produced, as compared to 17.4 MeV for DT fusion.
70
D. R. McCalister. “Gamma Ray Attenuation Properties of Common Shielding Materials.” Technical Report, PG
Research Foundation, Inc., 2013.

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space reactors and even built some prototypes, most recently the kilopower reactor. 71 Some NASA
employees, at least, project that reactor+shielding masses as low as 10 kg/kWe and suitable for manned
missions could be achieved within 10 years, and 2 kg/kWe within 30. 72 This is in line with the lower boundestimated here, but it seems that there is a long way to go technologically.

7.2 Stockpile Stewardship
Could progress toward low-cost MIF also support the National Nuclear Security Administration (NNSA)
mission? Fusion-for-energy research coexists with the stockpile stewardship activities on the NIF at
Livermore and on the ZR machine at Sandia. The physical parameters of MIF plasma are unlike those in afusion weapon, so the plasma itself is unlikely to be useful to NNSA. However, JASON identified two ways
in which progress toward MIF could support the NNSA mission.

7.2.1 Pulsed neutron generation
Neutron sources are a powerful tool for studying material properties, and in pulsed mode can beused for energy-resolved mapping (via time-of-flight measurements) and for stroboscopic imaging. The
potential for an ICF system to provide a pulsed neutron source that is orders of magnitude brighter thancurrent sources has been previously explored. 73
All MIF systems operate in a pulsed mode and therefore make pulses of neutrons. If all the matter
involved is plasma (excluding machines in which plasma is compressed by liquids or solids) then thesepulses will have the same duration as the period of peak plasma temperature and density. Table 5 gives
the radius and lifetime at maximum compression for the MIF approaches studied by JASON. In
combination with the yield, these parameters determine the fluence of the neutron source. For example,
a 140 MJ D-T thermonuclear yield would produce 5×1019 neutrons at 14.1 MeV. For comparison, theattributes of different neutron sources are reviewed in Ref. 74. Neutron yields from small plasma focus
devices are 109 DD neutrons, or 5×1010 DT neutrons if an equimolar DT gas fill is used 75. Larger plasma
focuses produce yields as high as 1013 DD neutrons, or 5×1014 DT neutrons 76. Large spallation neutron
sources have been built at Argonne (Intense Pulsed Neutron Source, decommissioned in 2008) and Oak
Ridge (Spallation Neutron Source) national laboratories with neutron fluences of ~4 × 1016 n cm-2 s-1. A
MIF-based source would have ~100-fold higher fluence, but would also have longer pulse durations dueto the slower implosion compared to ICF.

71

M. A. Gibson, S. R. Oleson, D. I. Poston, and P. McClure. “NASA’s kilopower reactor development and the path tohigher power missions.” In 2017 IEEE Aerospace Conference, pages 1–14, March 2017.
72
M. Houts. “Space Reactor Design Overview.” ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20150021391.pdf,
2015. retrieved 6/24/2018.
73
A. Taylor, et al. "A route to the brightest possible neutron source?" Science 315 1092-1095 (2007).
74
L. J. Perkins, et al. "The investigation of high intensity laser driven micro neutron sources for fusion materials
research at high fluence." Nuclear fusion 40, 1 (2000).
75
R. Verma, et al., "Development and characterization of a high yield transportable pulsed neutron source withefficient and compact pulsed power system." Review of Scientific Instruments 87, 095102 (2016).
76
A. Bernard, et al. "The dense plasma focus—A high intensity neutron source." Nuclear Instruments and Methods
145, 191-218 (1977).

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We suggest two applications:
1. Simulation of hostile environments produced by nearby exo-atmospheric nuclear explosions.
Depending on the mixture of D and T used, one could simulate any desired ratio of higher energy (14MeV) and lower energy (2.45 MeV) neutrons. At comparatively low neutron fluences the validity ofneutron transport calculations in complex structures could be tested. At higher neutron yield (oneproposal has suggested yields as high as 5×1019 neutrons) the fluences of real hostile environments
might be simulated, fully testing calculations of effects.
2. Measurement of neutron scattering cross-sections, including partial inelastic cross-sections. A
short-pulse monoenergetic source would enable precise determination of the energy of scatteredneutrons from their post-scattering times of flight. A suitably triggered high neutron-flux system
could also be used for neutron imaging of dynamics processes, such as might occur during an
explosion.
Neutron scattering is used in a wide variety of other material science applications, including studies ofbattery technology, protein dynamics, and catalysis, and thus a MIF-based pulsed neutron source wouldfind broad utility.

7.2.2 Tritium production
Tritium in thermonuclear weapons must be restocked to compensate for radioactive decay (half-life 12.3
years). Publicly available information puts this demand at 2.2 kg/year for the ~10,000 weapons in the U.S.
arsenal, 77 but there is serious concern about the robustness of the US tritium supply. 78
A 40 MWth DT fusion reactor would consume ~2.2 kg tritium/year. For any reactor to be selfsustaining, it must breed at least as much tritium as it consumes. A 2011 JASON report analyzed in detail
tritium breeding in a prospective fusion reactor, and concluded, “A 2.5 GWth, 1 GWe fusion plant with[tritium breeding ratio] TBR = 1.10 and 33% efficiency for converting heat to electrical energy, would
produce about 17 kg yо1 of tritium beyond the 170 kg needed to replace what must be burnt.” 79 At$0.05/kWhe, the value of the electricity from this notional plant would be $4.4×108 yr-1. The current
market cost of tritium is ~US$30,000/g, implying a value of $5.1×108 yr-1 for the excess tritium.
While the prices of tritium and its decay product 3He would certainly change in the face of such a
dramatic increase in supply, the above estimates show that tritium production could be an important
contribution to the economics of any future MIF reactor, and that emergence of MIF reactors could have
implications for stockpile stewardship.

77

https://ieer.org/resource/reports/tritium-environmental-health-budgetary-strategic-effects/#(11) (accessed 30
Oct. 2018)78https://www.defensenews.com/opinion/commentary/2017/03/06/commentary-the-looming-crisis-for-ustritium-production/ (accessed 30 Oct. 2018)
79
JASON report JSR-11-345, “Tritium” (2011), https://fas.org/irp/agency/dod/jason/tritium.pdf

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8 MORE BANG FOR THE BUCK: COST-DRIVERS FOR MIF DEVELOPMENT
JASON was tasked: “As applicable, assess the additional time, funds, and/or specific technicalinvestments necessary to realize low-cost magneto-inertial fusion.“ There are multiple steps along theway to “realize low-cost magneto-inertial fusion,” principally:
x
x
x
x
x

Concept exploration and computational modeling (current status of all projects)
Break-even-equivalent conditions with D-D fuelReaction and transport studies with D-D fuel doped with T
D-T proof-of-concept
Reactor prototype

To inform this analysis, we surveyed briefers on their capital and operating budgets, and on theirwish lists for future resource allocation (See Appendix C for survey questions). Several themes emerged:
x

x

x

x

x

At the present levels of ALPHA support (< $5M over three years), teams mostly work on individualcomponents; or if a facility is already in place then the teams worked on incremental advances ofpre-existing concepts. Continued funding at this level could support computational analyses thatmight help winnow the field of potential approaches, e.g. Ref. 80.
The power sources themselves are a substantial, but not dominant part of the hardware costs.
Typical estimates for pulsed electric power are ~$1/J, and MIF systems will require at least 10 MJ
per shot for scientific break-even, and several tens of MJ/shot to approach powerplant-relevant
gain. Estimates of minimum input energy are necessarily uncertain because for most approaches
these estimates extrapolate across orders of magnitude in density and temperature (Fig. 10).
Most published costing estimates for MIF focus on the hardware: the requirements for stored
energy (in MCF-like devices) or impulsive peak power (in ICF-like devices). Our briefers indicatedthat 60-75% of their costs are for personnel, including ~20% for simulations. The hardware is only
~1/3 of the cost.
Most MIF teams estimated that to test a new integrated concept in a D-D scale model would
require ~$25 – 50M over 3 years. The projects that have reached closest to break-even-equivalentconditions had the highest cost estimates (>> $100M) to reach these conditions, while someprojects in the early experimentation and planning stages estimated costs as low as $10M to reachbreak-even-equivalent conditions. JASON assesses that the cost estimates on the upper end of
the range (>> $100M) are more realistic as they reflect the view of the most experienced teams.
Cost extrapolations across orders of magnitude in conditions are unreliable.
All briefers estimated that costs to reach scientific break-even with D-T fuel would exceed $100M;
some estimated that the costs would be several $100M. While this is ‘low cost’ compared to NIF
and ITER, it implies that unless there is a dramatic expansion in MIF research funding, there will
not be federal funds available for many teams to attempt this goal. The major commercial fusion
efforts all have projected costs > $450M to reach a scientific break-even D-T prototype.

80

I. R. Lindemuth, M. R. Weis, and W. L. Atchison. "The staged z-pinch as a potential high gain fusion energy
source: An independent review, a negative conclusion." Physics of Plasmas 25, 102707 (2018).

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Apart from MagLIF, no team has come close to scientific break-even conditions in a D-D MIF device. JASON
assesses that it is too early to pick a `winning horse’ in the push toward scientific break-even conditions,as the critical barriers in most approaches have not yet been identified. Common concerns, among thebriefers and JASONs were: (1) plasma instabilities under MIF-relevant conditions and (2) liner-fuel mix (aswell as removing residual liner during pulsed-mode operation in an eventual power plant). Numerical andexperimental studies of these topics should be supported to develop an understanding of thefundamental requirements and constraints of MIF research. From an engineering standpoint, a recurrent
theme was the need for lower cost pulsed power sources, which would need to operate at 1 Hz or fasterin an eventual power plant.
JASON further recommends that a push toward scientific break-even should not be pursued for
its own sake. Rather, research should focus on identifying the key technical risks for each approach, andeither mitigating the risks or abandoning the approach. The configurations of the most advanced
experiments, MagLIF on Z and Omega, are not suitable for power production, so further research on thesefacilities should focus on identifying and mitigating barriers to progress in the techniques that could
plausibly be suitable for power production. This research does not necessarily require pushing to higher݊ ܶ ߬. Rather, it could include studies of different liner materials, magnetic field configurations, orcompression geometries.
Another recurring theme was the benefit of having access to expertise in simulation, plasma
physics, and diagnostics; as well as access to physical tools for these activities (high-performancecomputing, pulsed power supplies, and measurement equipment). The national laboratories have these
intellectual and physical resources in abundance. Several of the commercial and academic briefers
suggested ways to help MIF efforts benefit from these resources. Leveraging the national laboratories
would also help minimize redundancy of effort and equipment between MIF efforts. The Advanced Small
Modular Reactor Program 81 and the Gateway for Accelerated Innovation in Nuclear 82 program were heldup as models for possible future MIF efforts. Another creative idea was a federally funded externshipprogram for National Laboratory scientists to work in academic or commercial efforts.
As the Federal Government considers its portfolio management approach to MIF, it is worth
revisiting projections from a 1976 study from the Energy Research and Development Administration (thepredecessor of DOE). 83 Fig. 15 shows projected time to reach a functioning MCF reactor as a function of
investment. JASON has overlaid the actual expenditures on MCF and ICF in 1976 dollars, showing that thepredictions of the 1976 study were remarkably prescient. JASON cautions against programmatic support
that is sufficient to keep existing efforts ongoing, but is insufficient to conclusively validate or refute MIF
concepts.

81

https://www.energy.gov/ne/nuclear-reactor-technologies/small-modular-nuclear-reactors
gain.inl.gov
83
S. O. Dean, “Fusion power by magnetic confinement,” ERDA 76/110/1 UC-20,
https://fire.pppl.gov/us_fusion_plan_1976.pdf
82

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Figure 15. 1976 ERDA projections of routes to MCF fusion energy and historical fusion funding in 1976
dollars.

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9 COMMERCIALIZING FUSION
Large-scale deployment of fusion power in the US must involve commercialization, as the great
bulk of generation capacity is in private hands. Although fusion is still at the “talking dog” stage (It doesn’t
matter what the dog says; it’s remarkable if it can talk at all!), there is growing private-sector interest incommercializing fusion power.

9.1 The Ecosystem for Private Fusion Companies
Private investment exceeds public funding for MIF by a factor of ~10. Several private companies,
some founded as early as two decades ago, have received substantial private investments to pursue theconstruction of commercially successful fusion reactors. JASON used open source information (newsarticles, corporate press releases, investor press releases) to evaluate the amounts and sources of funding
received by the existing commercial fusion ventures (Fig. 16). The two oldest companies, TAE Technologies(formerly Tri Alpha Energy; > $600 M) and General Fusion (~$95 M), have secured the vast majority of theprivate funds invested in commercial ventures pursuing the development of high-energy fusion
reactors. 84,85 Public research programs must thus account for this economic context.

Figure 16. Total investments
received by existing commercial
thermonuclear fusion companies.
Values were converted into $ (US)when necessary. Inset: data from themain graph plotted on a log10 scale,excluding companies with no private
investment.

Private companies are performing cutting-edge research. The scale of private investment meansthat some private efforts are further along than academic, and by some measures, national laboratory,
teams. Federal investment should thus support these efforts, provided that the federal support leads todurable and publicly disseminated learning. Federal support can come in forms other than direct grantfunding, such as sabbatical programs for National Lab personnel in private companies; and access totechnical expertise, computational resources, and diagnostic equipment at National Labs.

84
85

https://www.geekwire.com/2018/tae-technologies-pushes-plasma-machine-new-high-fusion-frontier/https://www.geekwire.com/2018/commercial-fusion-ventures-learn-lessons-engineering-expectations/57

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Private R&D is often proprietary. Many components are shared between the different MIF
approaches (e.g. pulsed power systems, plasma jets, diagnostics). Most commercial fusion endeavors are
pursuing research only on key subsystems, or are building small-scale test reactors. Thus there isopportunity for mutual learning which should not be damped by premature competition. Federal support(of private, academic, and National Lab teams) should be contingent upon public dissemination of results
to the greatest extent possible. Support for workshops and conferences provides a low-cost means toencourage information sharing. In other industries, e.g. Pharma, federal support has been used tocatalyze formation of pre-competitive public-private consortia to address challenges that are beyond thecapabilities of individual private enterprises, e.g. 86 Similar opportunities exist in MIF.
Private enterprise is fluid. Given the large costs and long timescales to reach a commercial fusion
reactor, one can expect that there will be mergers, acquisitions, and failures in the private efforts; andthat the failures may be driven by non-technical factors. These considerations further underscore theimportance of supporting durable knowledge production in the private efforts.
The timescale to reach commercial fusion exceeds the 7 to 10-year timescale of many venture
capital funds, suggesting that some investors’ interests may not align with long-term goals. Such investors
may be motivated to achieve key milestones that lead to an increase in perceived value and liquidity,
regardless of whether these milestones genuinely advance the effort; others may redirect resources
toward ancillary uses of fusion technologies (e.g. particle-beams for materials processing and medical
applications.) Federal support for commercial MIF efforts should thus focus on building a solid foundationof technical work that will apply to multiple efforts.
In a recent article, 87 one major VC supporter of fusion R&D (Venrock) clearly details their rationale
for funding an endeavor that is considered to be a much longer term investment than normal. Other
investors, such as sovereign wealth funds, can accommodate the necessary decadal timescales.
Investors vary in sophistication. Fusion is sufficiently complex that many investors will not beable to perform adequate technical diligence on novel approaches. For instance, a cold fusion company
called Industrial Heat recently attracted substantial investment (~$42 M),88 despite being based on adiscredited approach. Backlash from unsuccessful efforts or over-inflated claims can damage the wholeindustry. Federal investment should support the establishment of industry standards and independent
verification of fusion-related claims. For instance, diverse definitions of ‘scientific break-even’ are incommon use, leading to ambiguous claims. Adoption of standard diagnostics e.g. for neutron production,
will help facilitate quantitative comparisons between approaches.
Investors often flock together. A corollary to the challenge of independently verifying technicalmerits of a MIF effort is the impulse to `bet on a winning horse’ and to invest in the perceived front-runnerof the moment. This impulse can drive an instability in the investment ecosystem, concentrating
resources in projects that are not necessarily the best long-term prospects. This private dynamic mirrors
the dynamic in federal support, e.g. concentrated MCF research on tokomaks, possibly to the exclusion ofother viable approaches.
86

Volkow, N.D., and Collins, F.S. "The role of science in addressing the opioid crisis." New England Journal of
Medicine 377.4, 391-394 (2017).
87
http://issues.org/32-2/whats-the-big-idea/
88
https://ftalphaville.ft.com/2016/11/25/2180322/so-neil-woodford-invested-in-a-cold-fusion-company/

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Just as JASON advises against concentrating federal resources too early in the technology
development, JASON also advises against federal funding strategies that could trigger private
concentration of investment. ALPHA funding has the greatest positive impact on the smallest commercial
entrants. Indeed, ARPA-E grant support appears to be an important source of funding for three of thenewest representatives (Helion; MIFTI; NumerEX) of this small but ambitious community. Since fusionrelevant conditions are still a distant hope for all commercial efforts, JASON recommends that alltechnically plausible efforts be supported for as long as possible (with an emphasis on identifying failuremodes). By ensuring rigorous technical review and adherence to community-wide standards, ARPA-E has
the opportunity, through its funding decisions, to provide unbiased validation that investors can use in
their decision-making.
A recurring theme from the commercial efforts was the challenge of finding appropriately trained
employees. Individual careers will likely span many commercial efforts, so investment in fusion-related
workforce development is likely one of the highest-impact opportunities.

9.2 Commercialization Challenges
As discussed in Chapter 2, the economics of electricity generation are complicated. A simple
figure such as a projected levelized cost of energy from a particular plant design is insufficient to predictthe commercial viability and adoption of that technology. Additional challenges are:
x

x

x

x

x

89

Fusion must not only work, but must be better: There is no fundamental shortage of primary energy
resources that might motivate a search for a new fuel source. Further, there are many generating
technologies and generators on the grid and the value of electricity to the end-user is independent of
how it is generated. For fusion to be commercially viable, not only does it have to “work”, but it mustbe “better” than the alternatives in one or more dimensions. Among those are operational flexibility,
reliability, environmental impact, proliferation impact, the balance of capital/operating costs, andnon-technical factors such as public acceptance, aesthetics, or technological prestige.
Utilities are technically conservative: The primary goal of private utilities is to make a profit, whilethat of public utilities is to serve their customers reliably at the lowest cost. Technological innovation
is a low priority.
Large investments are involved: Like fission, fusion is expected to be capital intensive (fission iscurrently some $6-8/Watt overnight cost, compared to NGCC, which can be less than $1/Watt). As aresult, investments are long-term, with attendant risks and low (utility-level) rates of return.
Fusion technology will be regulated because of the safety aspects of tritium, neutrons, and activatedmaterials. Further, as the neutrons from a fusion facility could also be used to create weapons-usable
materials (e.g., breeding 239Pu by adding 238U to the blanket), non-proliferation considerations will
favor Federal, if not international, regulation.
US electricity demand is projected to be growing slowly through 2040 relative to historical norms,
with electricity intensity falling in all sectors due to efficiency improvements. 89 Additions to generating
capacity are projected to average some 15 GW per year through 2040, with the mix evolving due tohttps://www.eia.gov/outlooks/aeo/pdf/0383(2017).pdf

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JSR-18-Task-011 - FUSIONx

18 December 2018changes in taxation and regulation. Growth in electric vehicle adoption introduces uncertainty, but
accounts for a relatively small contribution in the EIA projections (ca. 1 million annual EV sales by2030) that would not substantially change the overall demand outlook even if doubled. In contrast,electricity demand and generating capacity additions are expected to continue growing strongly in
non-OECD countries. For that reason, as well as a less-restrictive regulatory environment, it is likelythat the first power-producing fusion plant, if one is ever built, will be located outside of the US.
The periphery of the grid is evolving most rapidly. This evolution is driven by declining costs ofphotovoltaics, electric vehicles and energy storage, along with the capability of power electronics andinformation technology to coordinate and control distributed resources and loads. Microgrids canassure power quality and reliability with less dependence on central generation and transmission
resources, increasingly within economic reach. The role of the electric utility itself is evolving, withnew actors such as “prosumers” and aggregators taking the regulatory and policy stage. California ismandating Zero Net Energy residential construction as of 2020. This context calls into question theoverall size of the bulk power generation market in which fusion would aim to compete.

This multiplicity of challenges means that some form of government support will be required to enable
commercial deployment of fusion power even after demonstration of technical feasibility.

9.3 Lessons from Fission
It is useful to consider what happened in the case of nuclear power, 90 the first time thegovernment tried to catalyze deployment of a novel, capital-intensive generating technology. The current
challenges faced by the U.S. nuclear industry suggest that Federal support of fission development could
have been better managed.
Following the creation of the first man-made reactor by Fermi et al. in late 1941, reactors weredeveloped and used in the Manhattan Project to produce plutonium for nuclear weapons. The Atomic
Energy Act of 1946 set civilian nuclear energy as a federal policy goal and enabled power reactor progress
via Atomic Energy Commission (AEC) support, culminating in the first order for a privately-financed fullscale commercial reactor at Oyster Creek, whose construction began in 1964. Simultaneously, the US
government was pursuing nuclear reactors for naval propulsion beginning in the late 1940s, culminatingin the launch of the USS Nautilus submarine in late 1954. There are today some 100 nuclear reactors
producing 19% of US electricity and in 2017, 81 U.S. naval ships 91 (11 aircraft carriers and 70 submarines– 18 SSBN/SSGN and 52 SSN) were powered by 92 reactor cores.
The US government took a number of important steps to facilitate the development anddeployment of nuclear power in the early years. Quoting from the report, these included:x Atomic Energy Acts of 1946 and 1954: The AEA of 1946 established the AEC and set federal policy forcivilian use of nuclear energy, including the explicit use of nuclear power for commercial reactors,
however retained significant federal control over access to fissile materials, research data, and90

https://www.energy.gov/sites/prod/files/2017/01/f34/Innovation%20Pathway%20Study-U.S.%20Commercial%20Nuclear%20Power.pdf
91
http://www.world-nuclear.org/information-library/non-power-nuclear-applications/transport/nuclear-poweredships.aspx60JSR-18-Task-011 - FUSION

x

x

x

18 December 2018

intellectual property. The AEA amendments of 1954 loosened these restrictions and directed AEC tobegin licensing privately-owned power plants.
AEC R&D: AEC R&D policies, programs, and funding created the basic scientific understanding of how
to build a uranium-fueled fission reactor, control the reaction, and extract usable heat that could be
used to generate electricity. After the 1954 AEA amendments, the Civilian Application Program (CAP)
enabled the transfer of AEC and DoD research to private sector companies for use in commercial
development of reactors.
AEC Demonstration Programs: Following the AEA amendments of 1954, AEC implemented the Power
Reactor Demonstration Program (PRDP) to encourage utilities to partner with prospective NSSS
manufacturers and AEC in order to gain crucial construction and operational experience. The PRDP
played a significant role in identifying the commercial readiness of various reactor technologies andprovided GE and Westinghouse with sufficient confidence to offer commercial reactors.
Price-Anderson Act: The 1957 law was intended to reduce liability risks associated with commercial
nuclear power plants by setting a maximum liability for plant owners in case of accidents, above which
the federal government would pay damages. The act was intended to temporarily address the inabilityof utilities to obtain insurance, however it has been continually extended and updated.

There are, however, several crucial differences between today’s fusion situation and the earlyfission situation:xxx

Reactor progress was, and continued to be, driven by national security needs (nuclear weapons,
naval propulsion), and later national prestige. Civilian nuclear power was a spin-off of those otherefforts, which had very different design constraints.
Reactors had already been demonstrated when the push to commercial power began.
Some of the reactor technologies and most of the fuel technologies were closely held by the US
government.

9.4 Lessons from Wind and Solar
The commercial evolution of wind and solar electric power generation technologies is anotherpoint of comparison. As with nuclear fission and fusion, these renewable resources offer a primary energy
supply that is practically unlimited and that would remain viable under severe constraints on carbon
emissions. And likewise, the development and deployment of renewable resources has been driven by
governmental policy and incentives. Federal investment in wind and solar R&D was most significant during
the earlier development stages, although substantially smaller than R&D funding for fossil and nuclear
energy over the past seven decades, as shown in Figure 17. 92

92

Corrie Clark, Renewable Energy R&D Funding History: A Comparison with Funding for Nuclear Energy, Fossil
Energy, Energy Efficiency, and Electric Systems R&D. Congressional Research Service Report RS22858, June 2018.
https://fas.org/sgp/crs/misc/RS22858.pdf

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Figure 17. Fiscal Year R&D Funding of DOE Energy Technologies, from Clark/CRS 2018.
Subsidies now largely consist of production tax credits on a path toward phase-out, with a marked
drop since 2013.93 Other incentives for wind and solar deployment include renewable portfolio standards
at the State level. In 2016, wind accounted for 5.6% of electric energy generation in the U.S. and solar
thermal and photovoltaic ca. 1.3%. 94 As of early 2018, wind contributed ca. 8% to U.S. electricity
generation, 95 with an installed capacity of 90 GW 96. Installed nuclear had a roughly similar capacity, but
contributed more (~19%) of U.S. grid electricity due to the higher duty cycle of nuclear plants vs. wind.
Wind and solar power are only now playing a transformative role in global energy, after a long
history of serving in niche applications and finally being tailored for mass markets through additional
decades of R&D. Aerodynamic lift has been understood for many centuries of sailing, and wind electricity
generation was demonstrated in the 1880s. The photovoltaic effect was observed in the 19th century, andPV cells have been used for space applications since the 1950s. Solar thermal power uses well-understood93

Direct Financial Interventions and Subsidies in Energy in Fiscal Year 2016. U.S. Energy Information
Administration, April 2018. https://www.eia.gov/analysis/requests/subsidy/pdf/subsidy.pdf
94
https://www.eia.gov/electricity/annual/html/epa_01_01.html . Note that solar generation is difficult to estimate
both due to annual growth in the tens of percent, and the large contribution from customer-owned rooftop
photovoltaics that are not captured by electricity sales data.
95
https://www.eia.gov/totalenergy/data/monthly/pdf/sec7_6.pdf
96American Wind Energy Association U.S. Wind Industry Second Quarter 2018 Market Reporthttps://www.awea.org/2018-market-reports62JSR-18-Task-011 - FUSION

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thermodynamics much like a fossil-fuel plant. The interesting and important innovations for all of thesetechnologies have centered on fine points: marginal improvements in performance and practicality
through clever design and new materials, but not the application of new principles from a little understoodbranch of physics. Efficiencies were increased by single digits at a time, over many iterations. This home
stretch of development and commercialization has taken longer than many in the industry anticipated: acommon joke held that photovoltaics are exactly seven years from being cost-effective – and have been
so for decades. Though the pattern finally broke for renewables, the analogous joke for fusion, where thetime constant is closer to 30 years, gives one pause.
Arguably, the history of alternative energy commercialization – for renewables as well as nuclear– can only be understood within a political-economic context that accounts for industry lobbying, public
opinion, and other forces beyond the purview of engineering economics or scientific forecasting. For
example, a budding industry of wind electricity generation on U.S. farms in the 1930s was stalled by rural
electrification, a highly subsidized effort to provide equal access to a reliable grid. The simple, general
lesson is just how much stands between scientific demonstration and a successful commercial product.
Some specific observations:x Technological progress benefits from iterations along a learning curve. This is helped by smallerscale, repeatable units of hardware.
x Manufacturing economies of scale are important. This also favors smaller, repeatable units.
Nevertheless, optimal unit scale is not obvious from the outset. The history of wind power
development has seen trend reversals, first toward larger, then smaller, then larger machines withnew design solutions for problems associated with large diameter rotors. Photovoltaics, aparadigm of modular technology, are being deployed in large commercial arrays often comprisingtens of thousands of modules.
x Like the nuclear industry, the manufacturing of wind and solar generation technology is global:
China produced 70% of PV modules in 2017, North America 3.7%. 97 The two leading producers ofwind turbines are European. 98 The policy question of what R&D strategy the U.S. should pursue
with respect to energy technology is linked to the question of what international role the U.S.
wishes to play.
x The deployment of renewable generation has not followed a straight path of engineeringeconomic cost minimization. On the one hand, some technically promising opportunities to
exploit lowest-cost resources such as offshore wind and solar power in fragile deserts have been
put aside due to environmental concerns and “not-in-my-backyard” opposition; being “green”
does not guarantee easy project siting. On the other hand, rooftop PV is a popular favorite,
despite generally higher per-kW cost than centralized solar power plants, owing at least in part toqualities such as aesthetics and cultural symbolism.
In sum, the path to a viable commercial fusion power plant, if it exists, may hold many surprises.

97
98

https://www.ise.fraunhofer.de/content/dam/ise/de/documents/publications/studies/Photovoltaics-Report.pdf
https://www.windpowermonthly.com/article/1445638/top-ten-turbine-makers-2017

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10 FINDINGS AND RECOMMENDATIONS
The findings of this study are summarized below.
1. Magneto-Inertial Fusion (MIF) is a physically plausible approach to studying controlled thermonuclear
fusion in a region of parameter space that is less explored than Inertial Confinement Fusion (ICF) or
Magnetic Confinement Fusion (MCF).
2. MIF research is immature. Despite having received ~1% the funding of MCF and ICF, MIF experiments
have made rapid progress in recent years toward break-even conditions, and some (e.g. MagLIF) arewithin a factor of 10 of ‘scientific break-even’.
3. There are many plausible and distinct approaches to MIF. Some early projects supported by the
ALPHA program are showing rapid progress in critical physical parameters and have not yet reachedinsurmountable obstacles. As in ICF and MCF, instabilities may make scientific break-even MIF morechallenging than simple scaling estimates suggest.
4. ALPHA program support for development of broadly applicable technologies has accelerated progressof multiple efforts. All MIF approaches would benefit from improved understanding of plasma
instabilities and liner-plasma interactions, better computational tools, and improved diagnostics.
5. While scaling from current experiments is uncertain, it is likely that reaching scientific break-even witha single MIF prototype will cost at least several $100M and possibly much more. Considerably larger
expenditures would be required to go from scientific breakeven to a demonstration power plant; andeven more from a demo to a production capability.
6. Given the immaturity of the technologies, the future ability of fusion-generated electricity to meetcommercial constraints cannot be usefully assessed. Rapidly developing infrastructures for natural
gas and renewable energy sources and storage will compete with any future commercial fusion
efforts. Nevertheless, there is a small but growing private-sector community investing in and pursuingcommercial fusion projects.
7. The pursuit of MIF could lead to valuable spinoff technologies, and to non-power fusion applications,with broad civilian and military import. Some approaches have low enough mass to be candidates forspace propulsion, but it is too early to impose the relevant design constraints (low weight, low thermal
dissipation) on ongoing research.
8. MIF research could productively absorb a significantly higher level of funding than the $10M/yr of the
ALPHA program.
These findings lead to the following recommendations:
1. MIF activities should be supported by an investment in basic research to:a. study plasma instabilities and transport under MIF conditions, andb. study plasma-liner interactions.
2. The National Laboratories should contribute their unclassified state-of-the-art simulation codes tocollaborations with academic and commercial efforts, and support training of qualified users.
3. Targeted technology development programs should focus on development of components, including
plasma guns (high Z and low Z), pulsed power and electronics, diagnostics, and advanced magnets andmaterials.
4. The near-term goal should be scientific break-even (thermonuclear energy out > mechanical +electromagnetic energy into the fuel) in a system which plausibly scales to a commercial plant. Until

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18 December 2018that goal is achieved, set aside questions of neutron economy (tritium breeding) or balance of plant.
Pursue system integration only insofar as it is needed to demonstrate scientific break-even.
5. Explore pulsed neutron sources and space propulsion as motivating applications with different
constraints than grid electricity. Efforts in these speculative directions should supplement, notreplace, basic MIF research.
6. Support all promising approaches for as long as possible. Do not concentrate all resources on early
front-runners.

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APPENDIX A: Statement of Work (SOW)
BackgroundIn 2014 the Advanced Research Projects Agency, Energy (ARPA-E) announced a funding opportunity
announcement known as Accelerating Low-cost Plasma Heating and Assembly (ALPHA) 99. The stated goalof the ALPHA program was to:
Develop and demonstrate low-cost tools to aid in the development of fusion power, witha focus on approaches to produce thermonuclear plasmas in the final density range of1018-1023 ions/cm3. The program goal is to create a toolset that will allow a significant
reduction in facilities costs for fusion development and to enable rapid learning through ahigh shot rate at a low cost-per-shot.
Scope
Alternative approaches to fusion (for energy, propulsion, or security) that are distinct from the mainline
approaches of (a) short-ƉƵůƐĞŝŶĞƌƚŝĂůĨƵƐŝŽŶ;ĚĞŶƐŝƚǇшϭϬ23 ions/cm3, as at the National Ignition Facility)or (b) long-ƉƵůƐĞ͕ ŵĂŐŶĞƚŝĐĂůůǇ ĐŽŶĨŝŶĞĚ ĨƵƐŝŽŶ ;ĚĞŶƐŝƚǇ ч ϭϬ18 ions/cm3, as in the multinational ITER
project).
The ALPHA program kicked off in fall 2015 and is scheduled to wrap-up in late 2018. As the ALPHA programapproaches completion, have the nine ALPHA teams realized the goals of ALPHA? What have we learned?
Which additional challenges remain for the ALPHA teams and the larger magneto-inertial fusion
community? What’s needed next?
Objectives
1. Survey the progress of magneto-inertial fusion teams both inside and outside of ALPHA toward
their stated goals.
2. Assess the progress of ALPHA and non-ALPHA magneto-inertial fusion teams toward realizing lowcost fusion.
3. As applicable, assess the additional time, funds, and/or specific technical investments necessary
to realize low-cost magneto-inertial fusion. Particular topics of interest include scientificallycredible opportunities to cost-effectively reduce technical and schedule risk in pursuit of fusion
applications.

99

https://arpa-e-foa.energy.gov/Default.aspx?Search=alpha&SearchType=#FoaId4c902711-2bf4-409d-bd468d9c57ed83d1

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APPENDIX B: Briefings

In addition to these on-site briefings, four study participants made a 4-hour visit to the DIII-D Tokamak
on the General Atomics Campus on Monday June 18, and six study participants made a 2-hour site visit
to the Tri Alpha Energy facility in Foothill Ranch, CA on Friday, June 29.

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APPENDIX C: Briefer Questionnaire
Instructions: Please fill the table with the years of critical milestones, going back no further than 5 years,
and going forward no further than 5 years (enter as many rows as you wish). Please ignore any irrelevant
fields. For the highlighted fields, please enter parameters at maximum compression.

Year

E

Shot Material
rate consumed per
shot, including
vessel etc. (g)Input
energy per
shot

B
InitialGeometry
initial temperature (sphere or(T)(eV)
cylinder)B (T) Temperature R (cm) BR (G cm)(keV)

Lawsontime (s)Confinement
time (s)Convergence
ratio

Densityrho
R(ions/cm^3) (g/cm^2)

Neutron yield (#)(specify whether
DD or DT)

Names of any
software packages
used in simulations

Comments

Costing questions:
Approximately how much money have you spent to-date on your system? If you used substantial
repurposed items or in-kind contributions, please include estimates of their value.
What were the main categories of expenses and approximately how much went to each (e.g. pulsed
power system; magnets; simulations; personnel; etc.).
What would you spend the additional money on if you had an extra $1M? $10M? $100M?
What areas of federal support, in your opinion, would best accelerate progress toward MIF break-even?

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APPENDIX D: Evaporation of Liquid Pb Liners by High-flux Neutrons
Some magneto-inertial fusion proposals involve cylindrical or spherical liners of Pb or Pb-Li alloy tocompress the plasma and (if 6Li is alloyed with the Pb) breed tritium. Here we estimate the maximum
neutron fluence that can be tolerated without boiling the liner.
We have been unable to find values for the latent heat of evaporation of Pb-Li alloys (otherthermodynamic data for Pb-Li eutectics may be found in Ref. 100. The Pb partial vapor pressure is given
in Fig. 8. Raoult's law overestimates the Li partial vapor pressure of the Pb-Li eutectic by a factor of
1400, 101 indicating strong chemical binding of Li to Pb. We will consider only Pb (the eutectic is 84.3% Pb
by atomic composition and 99.3% by mass), treating the alloy as if it were pure Pb. Pure Pb is less volatile
than pure Li, so this is a conservative approximation.
Consider a cylindrical fusion reactor of length l and neutron energy yield Y (e.g. modeled after theCompact Fusion Systems design). The maximum radius at which the liner vaporizes isܻߪா ܰ஺
ܻ/݈‫ݎ‬௠௔௫ ==ൎ 26 cm௩௔௣
2ߨ݈ ο‫ܪ‬
5 MJ/cmwhere VE ൎ 10 b is the energy deposition cross-section 102 for 208Pb and analogous references for the othermajor isotopes 206Pb and 207Pb, NA is Avogadro's Number and 'Hvap = 1.78 kJ/mole is the latent heat ofvaporization of Pb. We have neglected the enthalpy required to heat Pb to its (pressure-dependent)
boiling point and the temperature dependence of 'Hvap, rather roughly equated the inelastic cross-section
to the energy-deposition cross-section, and have ignored the complexity of neutron scattering and energy
degradation. The former approximations are not large, but the final approximation likely introduces afactor of two uncertainty into the result.

௒
ହ ୑୎
ൎ
may be roughly appropriate for an actual power௟ୡ୫

generating reactor; experiments and even useful neutron sources may involve values smaller by orders ofmagnitude.
Any liner material closer to the plasma than rmax will boil, introducing a large quantity of neutral
Pb and Li vapor into the experimental chamber in addition to that evaporated (without boiling) from theinner surface of the liner.
The Pb boils at the temperature where its vapor pressure matches the pressure inside the liquid
Pb. At a depth d below the surface, the pressure in the liquid Pb is ܲ = ݃௘௙௙ ߩ݀, where geff is the
combination of gravitational and centripetal acceleration of the lead and U is the density. When thereactor cavity is fully expanded with initial radius ri, the initial centripetal acceleration must be gi > g to
avoid collapse under Earth’s gravity. As the liner collapses to final radius rf, conservation of angularmomentum implies that its linear velocity grows. The centripetal acceleration scales as

௚೐೑೑
௚೔
3

௥

ଷ

= ൬௥ ೔ ൰ .
೑

4Thus for convergence ratios of 10 – 20, the final centripetal acceleration will be immense: 10 – 10 g. At
100

E.M. De Les Valls, , et al. "Lead–lithium eutectic material database for nuclear fusion technology." Journal of
nuclear materials 376, 353-357 (2008).
101
N. J. Hoffman, A. Darnell, and J. A. Blink. “Properties of lead-lithium solutions.” No. UCRL-84273; CONF-8010119. (1980).
102 t2.lanl.gov/nis/data/endf/endfvii.1-n-pdf/pb208.pdf

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a depth d = 1 cm from its surface (the neutron energy deposition has a characteristic depth of about 4 cm)
the liquid Pb will have a pressure P = 106 – 107 Pa and will vaporize at a temperature > 3000 K. Neutral Pb
vapor would flow freely across magnetic field lines into the plasma, where it would be quickly ionized bycharge exchange with plasma ions or by UV radiation. At this density it would quench any thermonuclear
plasma by its rapid bremsstrahlung, bound-free and bound-bound radiation. The extent of liner
penetration will depend on the rate at which the Pb atoms are heated and ionized as they intermingle
with the fuel. 103
Vaporization of the inner Pb surface will also disrupt the electrical currents which are responsible
for maintaining the intense magnetic field in the plasma.

103

P. J. Turchi, S. D. Frese, and M. H. Frese. "Stabilized Liner Compressor For Low-Cost Controlled Fusion:
Progress And Issues." 2017 IEEE International Conference on Plasma Science (ICOPS). IEEE, (2017).

74

JASON STUDY ON THE PROSPECTS FOR LOW-COST FUSION DEVELOPMENT
ARPA-E is grateful to JASON for conducting this study and for their insightful findings and recommendations.
Here, we provide commentary related to their finding #6: “Given the immaturity of the technologies, the future
ability of fusion-generated electricity to meet commercial constraints cannot be usefully assessed…” This is afair statement given the large uncertainties in the state of the technology and in the future needs of the U.S. andworld electricity markets. However, in the view of ARPA-E, some of the analysis in Sec. 2.3 (Fusion in the
Energy Landscape) does not adequately capture the full range of potential outcomes for either the technology
or for the market needs.
Section 2.3 includes some analysis based upon a maximum levelized-cost-of-electricity (LCOE) of $0.05/kWh,which is drawn from the current estimate for natural gas combined cycle (NGCC) electricity generation, andleads to a rough estimate of a maximum allowable overnight capital cost of $5.55/W. This is compared against
a notional $6.67/W fusion power plant from the referenced Bechtel cost study. However, the latter, which
examined the cost drivers for four fusion-core concepts applied to a 150-MW point design, was intended to
identify the main cost levers, not to arrive at accurate, absolute capital cost estimates for a future fusion plant.
In fact, the study was based upon costing models for nuclear fission plants that are already known to be well
above costs being achieved in other parts of the world. For example, Korea has repeatedly shown that presentgeneration fission plants can be built for roughly $2/W. Thus, conclusions drawn based on capital cost estimatesfrom the Bechtel study could be overly pessimistic.
From the standpoint of market needs, a benchmark of NGCC in the current context of the U.S. grid does notadequately capture global markets and/or market segments where fusion might be first adopted, or the futureneeds of the electric grid. Benefits of fusion that do not factor into such an analysis include:-

minimal carbon emissions-

geographic siting flexibility, with a small footprint, including near dense population centers-seasonal stability, high dispatchability, and potential load-following capability-

a practically inexhaustible fuel supply with minimal need for new transportation/delivery infrastructure.

In fairness, NGCC does address some of these considerations as well, but these features are not well capturedby the $0.05/kWh LCOE figure. The JASON study does note that there are applications that can justify electricity
costs well above the notional $0.05/kWh, and that the likely largest market for fusion energy may not be in the
U.S. In addition, the study acknowledges that there are certain markets within the U.S. where there are income
streams for ancillary services that can meet or even exceed the value of selling baseload electricity. Thesecaveats serve to remind us that directly comparing early estimates for fusion-plant capital costs with income
based on current U.S. LCOE projections for NGCC is too restrictive to assess the future market attractivenessof fusion power.
Beyond the specific details of the cost analysis, the JASON report highlights the importance of including cost
analyses in assessing the potential real-world impact of fusion (or any energy technology). This is a message
that ARPA-E appreciates, and we hope that the fusion R&D community will embrace this attitude as it continues
to make progress.