To build a fusion rocket we first need to “ignite” the reaction, which is what this article will cover. We will dive into what fusion ignition is, the broad methods that are used to try and achieve it, and related concepts that try to push outside of the normal fusion nomenclature.

Ignition and Other Important Definitions

Just like in fission, the goal in fusion is typically to achieve a chain reaction. Ideally we would like to just put in the energy needed to get to fusion conditions and then let the energy of the reaction carry things from there. The definition of fusion ignition, burning plasma, gain, and a wide variety of other terms varies according to who you are asking and how much grant money they need. As such we are going to run with the following definitions.

Ignition: The point in which the fusion plasma is primarily self-heating rather than relying on external sources of heat. In steady state schemes there may still be some heating energy put in, while in pulsed schemes ignition is the point where the reaction rapidly runs away similar to the combustion event in a car engine. 

Scientific Break-even: The point where the fusion reactor outputs equal or more FUSION ENERGY than is put into the fuel.

Engineering Break-even: The point where the fusion reactor puts out more USABLE ENERGY than is put into the fuel. This is often taken as electrical energy but for rocketry we could also consider total energy or thermal energy.

Gain: The amount past Engineering Break-even (and sometimes Scientific Break-even) that the fusion reactor reaches. This can be reported for either continuous or pulsed systems with the same numbers.

There are other relevant terms that we are going to ignore as it gets far too complicated far too quickly and it won’t help this article.

There are a couple of important takeaways here. The first is that fusion ignition is a VERY important mile-stone to reach. Without reaching ignition our reactor would have to continuously heat the fuel up. Now at first glance this seems fine as each fusion reaction produces thousands of times more energy than is needed to heat it. However, it is important to remember that heating is not 100% efficient and all of the fusion fuel we heat up won’t necessarily react. Thus in an effort to get a lot more energy out then we put in (aka high gain) we need to reach ignition. Interestingly enough you can come up with plenty of fusion schemes that can reach scientific break-even without reaching ignition. They would struggle to reach engineering break-even though, which makes these schemes fringe at best. To make a really good fusion rocket we not only need to get engineering break-even but typically want extremely high gains so that we can get the maximum benefit out of the fusion fuel. Without high gains the fusion rocket/reactor will require large amounts of circulating electricity to sustain itself which will require lots of heavy equipment. This eats into the thrust to weight ratio and can end up making a rocket that performs more like an ion drive and less like a Heinlein style torch drive.

——- Exciting Side Note——–

Excitingly enough humanity reached fusion ignition and scientific break-even (without the benefit of a nuclear fission weapon) in 2021! The National Ignition Facility (NIF) achieved 1.3 MJ of fusion energy out of a shot in August. The pellet is heated by ~200 kJ of x-ray energy that is generated by ~2 MJ of laser energy generated by even more electrical energy… No fusion reactors quite yet, but just reaching this point is a pretty amazing step! There is still a long ways to go, but the ability to study an ignited plasma in the lab can’t be understated. This is the point where we “lit the fire” for fusion and although a working “engine” is a long ways off, we have now taken the first step down the path.

——- End Side Note ———-

It is important to note that all of this discussion hinges on the idea of a thermalized plasma. This means that the ions and electrons are roughly at the same temperature and that we have a distribution of energies that follows a classic Maxwell-Boltzmann distribution (give or take). A Maxwell-Boltzmann distribution (see Fig 1.) is the classic temperature distribution for gases and plasmas, and is the stable state for these materials to be in.

Maxwell-Boltzmann Distribution for Fusion Plasma (https://www.hep.phy.cam.ac.uk/~chpotter/particleandnuclearphysics/Lecture_16_FissionFusion.pdf)

 There are more fringe fusion schemes (such as Farnsworth fusors) that attempt to operate in a non-thermal regime. Non-thermal fusion can potentially side step all sorts of issues IF it can be made to work. There is a lot to be said about all of this, but needless to say it is not an easy thing to do and we will only be talking about thermal fusion for the rest of the article.

The Lawson Criterion and the Triple Product

The Lawson criterion is a way to discuss fusion concepts and how close to ignition they are. It is a simple energy balance (energy in vs energy out) and just takes radiation losses into account. This can then be extended into a concept called the Triple Product that takes radiation losses, fusion cross-section, plasma heating and plasma confinement time into account. This much better value is used as a point of comparison between fusion reactors and can even be extended to advanced fuels. The triple product value for the “easiest” fusion fuel (deuterium-tritium or DT) is 3×10^21 keV-sec/m^3 at about 14 keV. This value can also be translated into about 5 atm-sec at 14 keV. So this means we need to maintain about 5 atmospheres of plasma pressure for 1 second at 14 keV temperature. Although that sounds easy, it REALLY is not! A lot of progress has been made over the decades and below is a plot of various fusion machines and how close they are (or will be) to ignition of DT as seen in Figure 2.

Triple Product vs Year for Various Fusion Projects (Wetzel, S., Hsu, S.C., Progress toward fusion energy breakeven and gain as measured against the Lawson criterion, https://arxiv.org/pdf/2105.10954.pdf)

Fusion Ignition Schemes

There are broadly three types of fusion ignition schemes that are used to try and heat fusion fuel up to the insane temperatures needed AND confine it long enough to do the job. Magnetic confinement fusion (MCF) utilizes extremely powerful magnets to confine a very hot and low density plasma. Inertial confinement fusion (ICF) relies on a powerful external force (lasers, particle beams or even a fission bomb) to violently compress the fuel to very high densities and confine it with shear inertia. Magneto-inertial confinement fusion (MICF) sits in-between the two extremes of MCF and ICF in density, temperature and confinement time, and utilizes both inertial confinement and magnetic fields.

 

Magnetic Confinement Fusion (MCF)

Magnetic confinement is probably the most well known fusion confinement method out there. The basic concept is to construct some sort of magnetic trap or “bottle” that can hold the plasma long enough for sustained nuclear fusion to take place. This works because the individual components of a plasma (ions and electrons) are charged and respond to the presence of magnetic fields. The hard part is making a magnetic bottle that can hold on to hot enough plasma long enough to matter! Plasma is a famously slippery material and magnetic bottles tend to be a bit leakier than your average glass water bottle. Dr.Robert L. Hirsch (a prolific fusion scientist) once said magnetic confinement is “like trying to hold Jello with rubber bands”.

Magnetic confinement fusion tends to have a couple of key characteristics. The confinement time tends to be long (on the order of seconds) no matter if the machine is pulsed or not, the ignition temperatures tend to be high ( typically >25 keV or ~2.9E8 Kelvin is the operating temperature for DT fuel), and the fuel densities tend to be low (far less than even air and more of what we would call “hot vacuum”). These machines also tend to be quite large and because large magnets are required, tend to have very low specific powers. This doesn’t mean they are inherently useless for rocketry, but it does limit their utility and puts MCF rocket designs more into the realm of ion drives (although self powered ion drives). 

There are a wide variety of MCF configurations, but there are a couple of broad types that mostly cover the field: tokamaks, stellarators, magnetic mirrors, and field-reverse configurations (FRCs). Tokamaks are far and above the most common MFC machine today and are the classic fusion donut that we all know and love (Fig 3). 

Tokamak (https://www.energy.gov/science/doe-explainstokamaks)

Tokamaks currently operate in pulsed configurations, but long term there is hope to operate them in steady state. They are currently the most successful MFC machine ever made and steady progress is being made on the construction of the largest tokamak in history known as ITER. This machine is expected to finally hit fusion ignition in an MCF device.

 

Stellarators are an older toroidal confinement technology that was first developed in Princeton in the 1950’s. They fell out of favour when tokamaks first started showing promise, but have had a recent comeback in the 21rst Century. Stellarators operate in steady state configuration and require extremely complicated magnets, but do offer very stable fusion plasma.




Stellerator (https://www.sciencemag.org/news/2015/10/bizarre-reactor-might-save-nuclear-fusion)

Magnetic mirrors are arguably the oldest MCF device and are most likely what leaps to mind when one hears “magnetic bottle”. They also fell out of favor once tokamaks started showing promise and still do not have much support to this day. Mirror machines typically operate in steady state configurations and were one of the first fusion rockets considered.




Magnetic Mirror (Grubb, D P. Plasma potential formation and measurement in TMX-U and MFTF-B. United States: N. p., 1984. Web.)

Field-reverse configuration (FRC) is another old concept that fell out of favor but is making a comeback (primarily in the private sector). This concept is almost like a mix of a magnetic mirror and a tokamak in terms of plasma confinement, but relies heavily on plasma currents rather than external magnets. Current machines all operate in pulsed mode, but future plans include continuous operation. FRC’s have been considered for use as fusion rockets and as a potential way to burn advanced fusion fuels like DHe3.




TAE Field Reverse Configuration (https://www.pnas.org/content/117/4/1824)

Inertial Confinement Fusion (ICF)

Inertial confinement fusion is unique in that it is the only fusion ignition technique that we know works. The theory is there for the other techniques, and plenty of experimental evidence is there to back them up, but only ICF has actually lit a fusion chain reaction. Of course the way this was accomplished was by using the power of a fission explosive to compress and heat the fusion fuel. It sure counts as fusion ignition, but may not be the best for most applications! The big challenge in ICF is trying to find the smallest amount of fusion fuel that can be ignited and to do so without using fission as the power source (or “driver” in fusion speak). ICF typically involves pulse timeframes on the order of nanoseconds, densities several times that of lead, and “low” ignition temperatures on the order of 4-6 keV. In theory ICF reactors have quite impressive specific power and many fusion rocket designs use some form of ICF.

 

The premise behind ICF is similar to that of a diesel engine. Some external source of power is used to compress fusion fuel to extreme densities and pressures. While doing so the fuel becomes extremely hot and this combination of high pressure and heat can cross the Lawson criterion and reach fusion ignition. The fuel is only confined by it’s own inertia (i.e. the name) and will undergo a very rapid fusion chain reaction and explode outwards. A new mass of fuel (often a pellet of frozen fuel) is inserted and the “engine” is fired again. The advantage of this sort of method is that no attempt needs to be made to confine a burning plasma for human relevant time scales, and thus many instabilities can be side-stepped. The drivers (i.e. the power source doing confinement) can also be kept far away from the neutron spewing fusion plasma, which allows them to have longer lifetimes compared to the magnets in MCF. 

 

Aside from nuclear weapon based drivers (which I won’t dive into here) there are three primary methods of compressing fusion fuel for ICF: lasers, particle beams and pulsed magnetic fields. All three of these methods can be used in either “direct drive” or “indirect drive” for compression of fusion fuel. Direct drive is where the driver directly impacts and compresses the fusion fuel, while indirect drive uses the drivers to generate x-rays which then ablate and compress the target. Indirect drive is related to the compression method used in nuclear weapons, thus it is often studied for stockpile stewardship reasons as well as fusion energy.

 

Laser Driven Inertial Confinement Schemes (Moses, E., Ignition on the National Ignition Facility: A path towards inertial fusion energy, Sept. 2009, Nuclear Fusion 49(10), DOI: 10.1088/0029-5515/49/10/104022)

In the case of beam (laser or particle) direct drive and all forms of indirect drive, the compression is accomplished with ablation. The outer shell of the target is heated by the beams or x-rays and then begins to ablate away (see Fig 3). Due to Newton’s 3rd Law the rest of the fuel will begin to fly inwards during this ablation. What we have essentially created is an ablation driven rocket! The largest laser ICF facility in the world (the National Ignition Facility at Lawrence Livermore National Labs) has achieved compression velocities in excess of 400 km/sec, pressures over 1 TPa, and temperatures of ~4 keV! They have also seen the very beginning of alpha multiplication and could potentially reach fusion ignition if we are lucky (see above note about how this was done recently)! The facility was originally designed to reach fusion ignition around 2012, but well… fusion is hard! 

 

In the case of pulsed magnetic field direct drive, this technique is so closely related (and arguably is a better fit) to the next section and I will address it there.

 

Magneto-Inertial Confinement Fusion (MICF)

Magneto-inertial confinement fusion (MICF or sometimes called MIF) is the concept that is currently most in vogue, although the idea is incredibly old and arguably the first fusion concept ever tried! MICF schemes are always pulsed and rely on a combination of magnetic fields and inertial confinement to achieve fusion ignition. These concepts typically have longer pulses than ICF (micro to milliseconds), intermediate densities between ICF and MCF (density of air up to low density solids typically), and intermediate ignition temperatures on the order of ~10-20 keV.

 

The basic concept is that a magnetic field is pulsed extremely hard as well as potentially some other external driver. The combination of magnetic compression and confinement, as well as some other form of compression and/or heat then creates the correct conditions for fusion ignition. There are a LOT of very varied MICF concepts out there, but a couple of notable ones are Magnetic Linear Inertial Fusion (Mag-LIF), Shear-Flow Stabilized Z-pinch (SFS Z-pinch), and Plasma Linear Fusion (PLF). General Fusion is a rather well known fusion start-up that is also working on a form of MICF, although not one with much potential for space propulsion applications.

 

Interestingly enough the Z-pinch was one of the first fusion confinement schemes ever attempted. It is a very natural confinement concept because it is so simple and elegant. All that is needed is a large pulse of current through a gas and then you naturally get what is known as a “pinch” where the current collapses on itself. This compresses the already heated gas (now a plasma) and then fusion! Well that was the hope before a wide variety of plasma instabilities popped up that sucked energy from the pinch and seemed to kill the concept. Several decades later, more innovative versions of Z-pinches seem to be one of the most promising fusion concepts out there, especially for rocketry! One of the largest fusion research machines in the world, called “the Z machine”, even uses Z-pinches to generate incredibly promising fusion explosions.

 

Z-Machine at Sandia National Labs (https://www.sandia.gov/z-machine/)

References and Further Reading

  1. Atzeni, S., & Meyer-ter-Vehn, J. (2009). The physics of inertial fusion: Beam plasma interaction, hydrodynamics, hot dense matter. Oxford, U.K.: Oxford University Press.
  2. Ivy Mike, 1 November 1952 – first full-scale THERMONUCLEAR test. (n.d.). Retrieved February 12, 2021, from https://www.ctbto.org/specials/testing-times/1-november-1952-ivy-mike
  3. Moses, E. I. (2009). Ignition on the National Ignition Facility: A Path towards Inertial Fusion Energy. Nuclear Fusion, 49(10), 104022. https://doi.org/10.1088/0029-5515/49/10/104022

  4. Wurzel, S., Hsu, S.C., Progress toward fusion energy breakeven and gain as measured against the Lawson criterion, October 2021, arXiv:2105.10954v3
  5. Harms, A. A. (2010). Principles of Fusion Energy: An Introduction to Fusion Energy for students of Science and Engineering. World Scientific.

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