Afusion energy gain factor, usually expressed with the symbolQ, is the ratio offusion power produced in anuclear fusion reactor to the power required to maintain theplasma insteady state. The condition ofQ = 1, when the power being released by the fusion reactions is equal to the required heating power, is referred to asbreakeven, or in some sources,scientific breakeven.

The energy given off by the fusion reactions may be captured within the fuel, leading toself-heating. Most fusion reactions release at least some of their energy in a form that cannot be captured within the plasma, so a system atQ = 1 will cool without external heating. With typical fuels, self-heating in fusion reactors is not expected to match the external sources until at leastQ ≈ 5. IfQ increases past this point, increasing self-heating eventually removes the need for external heating. At this point the reaction becomes self-sustaining, a condition calledignition, and is generally regarded as highly desirable for practical reactor designs. Ignition corresponds to infiniteQ.^[1]

Over time, several related terms have entered the fusion lexicon. Energy that is not captured within the fuel can be captured externally to produce electricity. That electricity can be used to heat the plasma to operational temperatures. A system that is self-powered in this way is referred to as running atengineering breakeven. Operating above engineering breakeven, a machine would produce more electricity than it uses and could sell that excess. One that sells enough electricity to cover its operating costs is sometimes known aseconomic breakeven. Additionally, fusion fuels, especiallytritium, are very expensive, so many experiments run on various test gasses likehydrogen ordeuterium. A reactor running on these fuels that reaches the conditions for breakeven if tritium was introduced is said to be atextrapolated breakeven.

The current record for highestQ in atokamak (as recorded during actual D-T fusion) was set byJET atQ = 0.67 in 1997. The record forQ_ext (the theoretical Q value of D-T fusion as extrapolated from D-D results) in a tokamak is held byJT-60, withQ_ext = 1.25, slightly besting JET's earlierQ_ext = 1.14. In December 2022, theNational Ignition Facility, or NIF, aninertial confinement facility, reachedQ = 1.54 with a 3.15 MJ output from a 2.05 MJ laser heating.^[2] NIF achieved ignition seven times. The highest gain as of 2025^[update] of Q = 4.13 yielded 8.6 MJ from 2.08 MJ of laser energy.^[3][4]

Q^[a] is simply the comparison of thepower being released by the fusion reactions in a reactor,P_fus, to the constant heating power being supplied,P_heat, in normal operating conditions. For those designs that do not run in the steady state, but are instead pulsed, the same calculation can be made by summing all of the fusion energy produced inP_fus and all of the energy expended producing the pulse inP_heat.^[b] However, there are several definitions of breakeven that consider additional power losses.

In 1955,John Lawson was the first to explore the energy balance mechanisms in detail, initially in classified works but published openly in a now-famous 1957 paper. In this paper he considered and refined work by earlier researchers, notablyHans Thirring,Peter Thonemann, and a review article byRichard Post. Expanding on all of these, Lawson's paper made detailed predictions for the amount of power that would be lost through various mechanisms, and compared that to the energy needed to sustain the reaction.^[5] This balance is today known as theLawson criterion.

In a successful fusion reactor design, the fusion reactions generate an amount of power designatedP_fus.^[c] Some amount of this energy,P_loss, is lost through a variety of mechanisms, mostly convection of the fuel to the walls of the reactor chamber and various forms of radiation that cannot be captured to generate power. In order to keep the reaction going, the system has to provide heating to make up for these losses, whereP_loss =P_heat to maintain thermal equilibrium.^[6]

The most basic definition ofbreakeven is whenQ = 1,^[d] that is,P_fus =P_heat.

Over time, new types of fusion devices were proposed with different operating systems. Of particular note is the concept ofinertial confinement fusion, or ICF. The magnetic approaches, MCF for short, are generally designed to operate in the (quasi) steady state. That is, the plasma is maintained in fusion conditions for time scales much longer than the fusion reactions, on the order of seconds or minutes. The goal is to allow most of the fuel time to undergo a fusion reaction. In contrast, ICF reactions last only for a time on the order of dozens of fusion reactions, and instead attempt to ensure the conditions are such that the much of fuel will undergo fusion even in this very short time span. To do so, ICF devices compress the fuel to extreme conditions, where the self-heating reactions occur very rapidly.^[7]

In an MCF device, the initial plasma is set up and maintained by large magnets, which in modernsuperconducting devices requires very little energy to run. Once set up, the steady state is maintained by injecting heat into the plasma with a variety of devices. These devices represent the vast majority of the energy needed to keep the system running. They are also relatively efficient, with perhaps as much as half of the electricity fed into them ending up as energy in the plasma. For this reason,P_heat in the steady state is something fairly close to all of the energy being fed into the reactor, and the efficiency of the heating systems is generally ignored. When the total efficiency is considered then it is generally not part of the calculation ofQ, but instead included in the calculation of engineering breakeven,Q_eng (see below).

In contrast, in ICF devices the energy needed to create the required conditions is enormous, and the devices that do so, typicallylasers, are extremely inefficient, about 1%.^[8] If one used a similar definition ofP_heat, that is all the energy being fed into the system, then ICF devices are extremely inefficient. For instance, the NIF uses over 400 MJ (0.11 MWh) of electrical energy to produce an output of 3.15 MJ (0.00088 MWh), a ratio of 127 to 1. In contrast to MCF, this energy has to be supplied to spark every reaction, not just get the system up and running.^[9][10]

ICF proponents point out that alternative "drivers" could be used that would improve this ratio at least ten times. If one is attempting to understand improvements in the performance of an ICF system, then it is not the performance of the drivers that is interesting, but the performance of the fusion process itself. Thus, it is typical to defineP_heat for ICF devices as the amount of driver energy actually hitting the fuel, about 2 MJ (0.56 kWh) in the case of NIF. Using this definition ofP_heat, one arrives at aQ of 1.5. This is, ultimately, the same definition as the one used in MCF, but the upstream losses are smaller in those systems and no distinction is needed.

To make this distinction clear, modern works often refer to this definition asscientific breakeven,Q_sci or sometimesQ_plasma, to contrast it with similar terms.^[11][12]

Since the 1950s, most commercial fusion reactor designs have been based on a mix ofdeuterium andtritium as their primary fuel; other fuels have attractive features but are much harder to ignite. As tritium is radioactive, highlybioactive, and highly mobile, it represents a significant safety concern and adds to the cost of designing and operating such a reactor.^[13]

In order to lower costs, many experimental machines are designed to run on test fuels of hydrogen or deuterium alone, leaving out the tritium. In this case, the termextrapolated breakeven,Q_ext, is used to define the expected performance of the machine running on D-T fuel based on the performance when running on hydrogen or deuterium alone.^[14]

The records for extrapolated breakeven are slightly higher than the records for scientific breakeven. Both JET and JT-60 have reached values around 1.25 (see below for details) while running on D-D fuel. When running on D-T, only possible in JET, the maximum performance is about half the extrapolated value.^[15]

Another related term,engineering breakeven, denotedQ_E,Q_eng orQ_total depending on the source, considers the need to extract the energy from the reactor, turn that into electrical energy, and feed some of that back into the heating system.^[14] This closed loop sending electricity from the fusion back into the heating system is known asrecirculation. In this case, the basic definition changes by adding additional terms to theP_fus side to consider the efficiencies of these processes.^[16]

D-T reactions release most of their energy asneutrons and a smaller amount as charged particles likealpha particles. Neutrons are electrically neutral and will travel out of any plasma before they can deposit energy back into it. This means that only the charged particles from the reactions can be captured within the fuel mass and give rise to self-heating. If the fraction of the energy being released in the charged particles isf_ch, then the power in these particles isP_ch =f_chP_fus. If this self-heating process is perfect, that is, all ofP_ch is captured in the fuel, that means the power available for generating electricity is the power that is not released in that form, or (1 − f_ch)P_fus.^[17]

In the case of neutrons carrying most of the practical energy, as is the case in the D-T fuel, this neutron energy is normally captured in a "blanket" oflithium that produces more tritium that is used to fuel the reactor. Due to variousexothermic andendothermic reactions, the blanket may have a power gain factor M_R. M_R is typically on the order of 1.1 to 1.3, meaning it produces a small amount of energy as well. The net result, the total amount of energy released to the environment and thus available for energy production, is referred to asP_R, the net power output of the reactor.^[17]

The blanket is then cooled and thecooling fluid used in aheat exchanger driving conventionalsteam turbines and generators. That electricity is then fed back into the heating system.^[17] Each of these steps in the generation chain has an efficiency to consider. In the case of the plasma heating systems,${\displaystyle {\eta }_{heat}}$ is on the order of 60 to 70%, while modern generator systems based on theRankine cycle have${\displaystyle {\eta }_{elec}}$ around 35 to 40%. Combining these we get a net efficiency of the power conversion loop as a whole,${\displaystyle {\eta }_{NPC}}$, of around 0.20 to 0.25. That is, about 20 to 25% of${\displaystyle P_R}$ can be recirculated.^[17]

Thus, the fusion energy gain factor required to reach engineering breakeven is defined as:^[18]$${\displaystyle Q_E\equiv \frac{P_{\text{fus}}}{P_{\text{heat}}}=\frac{1}{{\eta }_{\text{heat}}\cdot f_{\text{recirc}}\cdot {\eta }_{\text{elec}}\cdot (1-f_{\text{ch}})}}$$

To understand how${\displaystyle Q_E}$ is used, consider a reactor operating at 20 MW andQ = 2.Q = 2 at 20 MW implies thatP_heat is 10 MW. Of that original 20 MW about 20% is alphas, so assuming complete capture, 4 MW ofP_heat is self-supplied. We need a total of 10 MW of heating and get 4 of that through alphas, so we need another 6 MW of power. Of the original 20 MW of output, 4 MW are left in the fuel, so we have 16 MW of net output. UsingM_R of 1.15 for the blanket, we getP_R about 18.4 MW. Assuming a good${\displaystyle {\eta }_{NPC}}$ of 0.25, that requires 24 MWP_R, so a reactor atQ = 2 cannot reach engineering breakeven. AtQ = 4 one needs 5 MW of heating, 4 of which come from the fusion, leaving 1 MW of external power required, which can easily be generated by the 18.4 MW net output. Thus for this theoretical design theQ_E is between 2 and 4.

Considering real-world losses and efficiencies, Q values between 5 and 8 are typically listed for magnetic confinement devices to reach${\displaystyle Q_E=1}$,^[17] while inertial devices have dramatically lower values for${\displaystyle {\eta }_{\text{heat}}}$ and thus require much higher Q values, on the order of 50 to 100.^[19]

As the temperature of the plasma increases, the rate of fusion reactions grows rapidly, and with it, the rate of self-heating. In contrast, non-capturable energy losses like x-rays do not grow at the same rate. Thus, in overall terms, the self-heating process becomes more efficient as the temperature increases, and less energy is needed from external sources to keep it hot.^[20]

EventuallyP_heat reaches zero, that is, all of the energy needed to keep the plasma at the operational temperature is being supplied by self-heating, and the amount of external energy that needs to be added drops to zero. This point is known asignition. In the case of D-T fuel, where only 20% of the energy is released as alphas that give rise to self-heating, this cannot occur until the plasma is releasing at least five times the power needed to keep it at its working temperature.^[20]

Ignition, by definition, corresponds to an infiniteQ, but it does not mean thatf_recirc drops to zero as the other power sinks in the system, like the magnets and cooling systems, still need to be powered. Generally, however, these are much smaller than the energy in the heaters, and require a much smallerf_recirc. More importantly, this number is more likely to be near-constant, meaning that further improvements in plasma performance will result in more energy that can be directly used for commercial generation, as opposed to recirculation.^[21]

The final definition of breakeven iscommercial breakeven, which occurs when the economic value of any net electricity left over after recirculation is enough to pay for the reactor and all processes to gather and transportreactants, such astritium anddeuterium, to the reactor.^[14] This value depends both on the reactor'scapital cost and any financing costs related to that, itsoperating costs including fuel and maintenance, and thespot price of electrical power.^[14][22]

Commercial breakeven relies on factors outside the technology of the reactor itself, and it is possible that even a reactor with a fully ignited plasma operating well beyond engineering breakeven will not generate enough electricity rapidly enough to pay for itself.^[23] Whether any of the mainline concepts likeITER can reach this goal is being debated in the field. A large reason for these debates is the current lack of technology and the lack of interest and funding in the area in its current stage.^[24] Scientists have only just reached the point in the fusion process where they are having a positive energy gain, meaning the energy produced is marginally more than the energy required to initiate the fusion process.^[25] Nuclear physicists are sure that there is a maximum amount of energy that can be harnessed from fusion reactions but the maximum amount is currently unknown.^[26] With enough investment, it is possible to increase the Q and create a definite increase in the energy and profits but that doesn’t mean that it is enough to reach the commercial breakeven.^[27]

Most fusion reactor designs being studied as of 2017^[update] are based on the D-T reaction, as this is by far the easiest to ignite, and is energy-dense.^[28] This reaction gives off most of its energy in the form of a single highly energetic neutron, and only 20% of the energy in the form of an alpha. Thus, for the D-T reaction,f_ch = 0.2. This means that self-heating does not become equal to the external heating until at leastQ = 5.^[20]

Efficiency values depend on design details but may be in the range ofη_heat = 0.7 (70%) andη_elec = 0.4 (40%). The purpose of a fusion reactor is to produce power, not to recirculate it, so a practical reactor must havef_recirc = 0.2 approximately. Lower would be better but will be hard to achieve. Using these values we find for a practical reactorQ = 22.^[29]

Many early fusion devices operated for microseconds, using some sort of pulsed power source to feed theirmagnetic confinement system while using the compression from the confinement as the heating source. Lawson defined breakeven in this context as the total energy released by the entire reaction cycle compared to the total energy supplied to the machine during the same cycle.^[15][29]

Over time, as performance increased by orders of magnitude, the reaction times have extended from microseconds to seconds, andITER is designed to haveshots that run for several minutes. In this case, the definition of "the entire reaction cycle" becomes blurred. In the case of an ignited plasma, for instance, P_heat may be quite high while the system is being set up, and then drop to zero when it is fully developed, so one may be tempted to pick an instant in time when it is operating at its best to determine a high, or infinite,Q. A better solution in these cases is to use the original Lawson definition averaged over the reaction to produce a similar value as the original definition.^[15]

There is an additional complication. During the heating phase when the system is being brought up to operational conditions, some of the energy released by the fusion reactions will be used to heat the surrounding fuel, and thus not be released to the environment. This is no longer true when the plasma reaches its operational temperature and enters thermal equilibrium. Thus, if one averages over the entire cycle, this energy will be included as part of the heating term, that is, some of the energy that was captured for heating would otherwise have been released in P_fus and is therefore not indicative of an operationalQ.^[15]

Operators of the JET reactor argued that this input should be removed from the total:$${\displaystyle Q^{\ast }\equiv \frac{P_{\text{fus}}}{P_{\text{heat}}-P_{\text{temp}}}}$$where:$${\displaystyle P_{\text{temp}}=\frac{dWp}{dt}}$$

That is,P_temp is the power applied to raise the internal energy of the plasma. It is this definition that was used when reporting JET's record 0.67 value.^[15]

Some debate over this definition continues. In 1998, the operators of theJT-60 claimed to have reachedQ = 1.25 running on D-D fuel, thus reaching extrapolated breakeven. This measurement was based on the JET definition of Q*. Using this definition, JET had also reached extrapolated breakeven some time earlier.^[30] If one considers the energy balance in these conditions, and the analysis of previous machines, it is argued the original definition should be used, and thus both machines remain well below break-even of any sort.^[15]

Lawrence Livermore National Laboratory (LLNL), the leader in ICF research, uses the modifiedQ that definesP_heat as the energy delivered by the driver to the capsule, as opposed to the energy put into the driver by an external power source. This definition produces much higherQ values, and changes the definition of breakeven to beP_fus /P_laser = 1. On occasion, they referred to this definition as "scientific breakeven".^[31][32] This term was not universally used; other groups adopted the redefinition ofQ but continued to refer toP_fus =P_laser simply as breakeven.^[33]

On 7 October 2013, LLNL announced that roughly one week earlier, on 29 September, it had achieved scientific breakeven in theNational Ignition Facility (NIF).^[34][35][36] In this experiment,P_fus was approximately 14 kJ, while the laser output was 1.8 MJ. By their previous definition, this would be aQ of 0.0077. For this press release, they re-definedQ once again, this time equatingP_heat to be only the amount of energy delivered to "the hottest portion of the fuel", calculating that only 10 kJ of the original laser energy reached the part of the fuel that was undergoing fusion reactions. This release has been heavily criticized in the field.^[37][38]

On 17 August 2021, the NIF announced that in early August 2021, an experiment had achieved aQ value of 0.7, producing 1.35 MJ of energy from a fuel capsule by focusing 1.9 MJ of laser energy on the capsule. The result was an eight-fold increase over any prior energy output.^[39]

On 13 December 2022, theUnited States Department of Energy announced that NIF had exceeded the previously elusiveQ ≥ 1 milestone on 5 December 2022. This was achieved by producing 3.15 MJ after delivering 2.05 MJ to the target, for an equivalentQ of 1.54.^[40][41]

• Entler, Slavomir (June 2015). "Engineering Breakeven".Journal of Fusion Energy.34 (3):513–518.Bibcode:2015JFuE...34..513E.doi:10.1007/s10894-014-9830-2.S2CID 189913715.
• Lawson, John (1957). "Some Criteria for a Power Producing Thermonuclear Reactor".Proceedings of the Physical Society, Section B.70 (6):6–10.Bibcode:1957PPSB...70....6L.doi:10.1088/0370-1301/70/1/303.
• Meade, Dale (October 1997).Q, Break-even and the nτE Diagram for Transient Fusion Plasmas. 17th IEEE/NPSS Symposium on Fusion Engineering.
• McCracken, Garry; Stott, Peter (2005).Fusion. Academic Press.ISBN 9780123846563.

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