# MSNW fusion rocket

Happy Cosmonautics Day! After reading the post “Under the auspices of NASA build a fusion space engine” , I decided to find more information about this project. Next, I want to talk about what this engine is and how it works.

To begin with, a small introduction to what thermonuclear fuel is and how it can be used.

#### Thermonuclear fuel

Energy can be obtained by breaking large unstable atoms into smaller pieces, or by merging two or more small atoms into one large one. In all cases, if you weigh the initial atoms and compare them with the weight of the result, you can find that the resulting mass will be less. This phenomenon is known as a mass defect and represents the amount of matter converted into energy. Everyone knows that `e = mc^2`, but not everyone knows how large `c`(the speed of light in vacuum ) is a large number, and squared it becomes just very large. Accordingly, even a microscopic amount of matter becomes capable of producing an impressive amount of energy.

According to the Convention, 1 amu ( atomic unit of mass ) = 931.494028MeV .

Example.
DT synthesis begins with an atom of deuterium and tritium and ends with a helium-4 atom and a neutron. Initial mass 2.013553 + 3.015500 = 5.029053. Final mass 4.001506 + 1.008665 = 5.010171. Subtracting the second from the first, we find that the mass defect is 0.018882. Multiplying by 931.494028 we find the received energy equal to 17.58847 MeV.

Note, fusion generates energy as more and more atoms merge, until they grow to such an extent that they become iron atoms. After this, the fusion of heavy atoms begins to consume more energy than it produces.

##### Particles

SymbolTitleWeight
pProton ionized hydrogen1.007276
nNeutron1.008665
1 HHydrogen-1, ordinary hydrogen1.007940
DDeuterium, hydrogen-22.013553
TTritium, hydrogen-33.015500
3 HeThe famous helium-33.014932
4 HeHelium-4, ordinary helium4.001506
6 LiLithium 6
7 LiLithium 7, regular lithium
11 BBor-11, ordinary boron11.00931

This table gives symbols for various particles that can be used as thermonuclear fuel. Particle masses are given in case you want to calculate the mass defect for the reactions below and be surprised at the amount of energy received.

The half-life of tritium is only 12.32 years, which makes it difficult to use in space, since after twelve years it will half break up into helium-3. That is why there are no natural deposits of tritium. Most tritium-based reactor designs rely on tritium generators. They are usually liquid lithium tanks surrounding the reactor. Lithium absorbs neutrons and transmutes into fresh tritium and helium-4.

The famous helium-3, which is often called the economic motive for space exploration, unfortunately, is not as good as one might assume. Firstly, it is absent on Earth, which makes it difficult to mine. Some enthusiasts want to mine it on the moon without specifying, its concentration there is very small. To produce just tons of helium-3, 100 million tons of lunar regolith must be processed. Alternatively, it can be produced in factories, but this requires a large number of neutrons. In general terms, you need to get tritium and wait until it decays. Huge amounts of helium-3 are available in the atmosphere of Saturn and Uranus, but the corresponding infrastructure is needed for its extraction from there. The concentration of helium-3 in their atmospheres can reach ten parts per million, which is much better than on the moon.

##### Thermonuclear reactions

ReactionMeV / reactionTJ / kg1 TW burningKLWithout neutronExhaust
D + T4 He + n17.6 MeV339.72 TJ / kg0.002944 g / s18.7% c
D + DT + 1 H4.03 MeV97.23 TJ / kg0.01028 g / sthirty4.3% c
3 He + n3.27 MeV78.90 TJ / kg0.01267 g / s4.2% c
p + 11 B3 × 4 He8.7 MeV69.97 TJ / kg0.01429 g / s500Yes4.5% c
D + 3 He4 He + p18.3 MeV353.23 TJ / kg0.002831 g / s168.9% c
3 He + 3 He4 He + 2 × p12.9 MeV207.50 TJ / kg0.004819 g / s?Yes 6.8% c
n + 6 LiT + 4 He
n + 7 LiT + 4 He + n
p + p + p + p4 He26.73 MeV644.93 TJ / kg0.001551 g / sMany11.7% c

The Reaction column lists the initial and final reaction products. The MeV / reaction column shows how much energy is released as a result of one reaction in MeV. The column TJ / kg shows how many terajoules (10 12 ) of energy will be released as a result of burning a kilogram of fuel. For comparison, 1 kiloton of TNT ≈ 4.1840 TJ. In one TW combustion specified as grams of fuel needed to burn every second for 1 TW thermal energy. Column KL indicates the Lawson criteria for this reaction. Without neutrontalks about whether the reaction produces neutrons or not. It should be noted that even if neutrons do not appear in the reaction, they can still be formed as a result of side reactions. And the Exhaust column gives an idea of ​​the theoretically maximum velocity of the expiration of combustion products as a percentage of the speed of light. It is assumed that all the energy obtained during the reaction is converted into kinetic energy of the movement of the reaction products.

There are quite a few thermonuclear reactions, but only a small number of them are suitable for use as energy sources for rocket engines. You can read about restrictions here . Of all the candidates, the most simple to use are reactions with a low Lawson criterionby which one can judge the complexity of the onset and maintenance of the reaction. If the reaction produces only charged particles, then this can be considered a big plus, since it becomes possible to convert them into electricity directly, without an intermediary in the form of heat.

It is also desirable that the reaction does not produce neutrons, since they are not only hazardous radiation, but also tend to weaken structural materials and transmute engine parts into radioactive elements . Unless, of course, there is a need to use neutrons to produce tritium.

D + 3 Hethe reaction is especially interesting for use in rocket engines, since its products are only charged particles, which makes it possible to directly control them using a magnetic nozzle.

From the table it can be seen that there are various reactions that look promising for use in space and on Earth. Note that the D + D reaction has two possible results and, accordingly, two rows in the table. Each result has a 50% probability. The two reactions with lithium do not produce energy and are used to produce tritium, as mentioned above.

The DT reaction is relatively easy to initiate, as indicated by the low Lawson test, but it consumes tritium with a short half-life. Hydrogen boricthe reaction (a proton is an ionized hydrogen atom) has the advantage that it does not produce neutrons, but it is very difficult to ignite. Helium-3 + helium-3 is also neutron-free, but helium-3 is difficult to mine. Apparently because of this, information on the Lawson criterion for this reaction could not be found.

The proton-proton reaction takes place on the sun. The problem is the greatest Lawson criteria from the entire table. It is almost impossible to make four protons merge; it’s easier to use an existing star to get energy.

The two reactions with lithium do not produce any energy and are usually used to produce tritium.

#### Fusion rocket engine

Based on the publication of Mission Design Architecture for the Fusion Driven Rocket. Pancotti, A., Slough, J. Kirtley, D. et al. AIAA Joint Propulsion Conference (2012) .

##### Introduction

This article describes, at first glance, another way to use thermonuclear energy to carry out fast manned space flights. Previous efforts on this path have failed, for the most part due to the following two reasons. Firstly, they were based on the design of fusion reactors. The straightforward application of the approaches used in reactors leads to systems with colossal masses and problems with energy removal. With a detailed analysis for the most compact TOKMAK concept, a spherical torus, the mass of the ship exited around 4,000 tons. The maximum mass for launching into a low reference orbit using chemical rockets should not exceed 200 tons.

The second reason is that, in fact, all previous propulsion systems required complex reactions that produced, for the most part, charged particles. This was necessary to reduce energy losses through neutrons. The most promising were D- 3 He and P- 11 B. But these reactions required much higher plasma temperatures and were orders of magnitude more difficult to achieve than DT synthesis, which is much more accessible and is considered as the only candidate for use on Earth. Being less profitable, however, they require a huge amount of energy to maintain combustion, making them not much better than alternative fission reactions.

It is necessary to rethink past ideas about how to use thermonuclear energy in space propulsion systems. Let's see what gives chemical rocket engines such benefits. The main reason is that the energy obtained from the chemical reaction of combustion can be either large or small, if desired. From 13 GW for a heavy Atlas launch vehicle, up to 130 kW for a car. It is worth noting that at lower energy, combustion is more efficient, since it is possible to increase the temperature without worrying about the need for intensive heat dissipation and thermal damage that may occur during prolonged continuous operation.

As tests of atomic and hydrogen bombs have shown, burning nuclear fuel can produce energy many orders of magnitude greater than the same Atlas. The problem is how to control the release of nuclear energy to obtain the characteristics needed for space missions: a torch of several megawatts, low specific gravity `α`(~ 1 kg / kW) at a high specific impulse`Isp` (> 20,000 m / s). It turned out that, at least for nuclear fission, there is no possibility of scaling down to the required energy scale, since a certain critical mass (critical configuration) is required to start a self-sustaining reaction. As a result, projects using nuclear fission reactions, such as Orion, usually produced millions of tons of thrust, which is only suitable for spaceships with a mass of 107 kg and above.

Fortunately, the scale of thermonuclear reactions can be much smaller and methods such as Magneto Inertial Fusion (Mango-Inertial Thermonuclear Fusion, MIF) can produce large amounts of energy from nuclear material in systems that may be suitable for space propulsion systems in size. weight, power and cost.

##### Physics engine

The engine is based on the principle of three-dimensional implosion (blast compression) of a metal foil around a FRC plasmoid ( Field-reversed configuration - field with a reversed configuration) using a magnetic field. This is necessary to achieve the conditions necessary for starting the synthesis, such as high temperature and pressure. This approach to starting the reaction is a kind of inertial synthesis. In order to roughly understand how it works, you can take a look at inertial controlled thermonuclear fusion(Inertial Confinement Fusion - ICF). ICF synthesis is achieved using three-dimensional implosion of a spherical capsule with millimeter-sized cryogenic fuel. Implosion occurs due to the explosive evaporation of the capsule body, after its heating with the help of laser beams, electrons, or ions. The heated outer layer of the capsule explodes in the outer direction, which produces a counteracting force that accelerates the rest of the capsule material inward, compressing it. Also, shock waves appear, moving inside the target. A sufficiently powerful set of shock waves can compress and heat the fuel in the center so much that a thermonuclear reaction begins. This method assumes that the inertia of a small capsule is enough to hold the plasma long enough to so that all fuel reacts and produces a useful yield of G ~ 200 or more (G = synthesis energy / plasma energy). The ICF approach has been pursued by the National Nuclear Security Administration (NNSA) for decades, as it is a kind of miniature fusion bomb. Due to its small size and mass, the capsule should be heated to the synthesis temperature within nanoseconds. It turned out that the most promising solution to this problem is an array of high-power pulsed lasers focused on a capsule with DT fuel. the capsule should be heated to the synthesis temperature within nanoseconds. It turned out that the most promising solution to this problem is an array of high-power pulsed lasers focused on a capsule with DT fuel. the capsule should be heated to the synthesis temperature within nanoseconds. It turned out that the most promising solution to this problem is an array of high-power pulsed lasers focused on a capsule with DT fuel.

The National Ignition Facility (NIF) at the Livermore National Laboratory conducts experiments on laser implosion of thermonuclear fuel capsules, but attempts have so far not been very successful.

However, for use in space, other approaches are needed. This means that the use of huge laser systems will have to be abandoned. Heavy ions and crimped metal shells are the two most promising technologies. Regardless of the method, the compression should be uniform, strong and carried out with great accuracy, which can lead to large, high voltage and very expensive systems. In the mid-nineties, it was found that the presence of a strong magnetic field significantly suppresses the transfer of heat in the target, which reduces the implosion power needed to compress the target and start synthesis in it. Long before the thermal energy of the plasma is dissipated, a metal shell can be used for direct compression. So we can increase the fusion time, thanks to the bounding metal shell. The shell can be compressed using explosives as well as using a magnetic field. It was shown that if the implosion of the shell around the magnetized target was completely three-dimensional, then energy amplification can be obtained on a small scale with a kinetic energy of the shell of up to 1 MJ.

At that time there was no known way to achieve all this in practice. But in 2000 it was shown that for a sufficiently magnetized target plasma, thermonuclear combustion can begin even when the restriction `ρ⋅R > 0.1 г/см``2`(R is the radius of the target, ρ is the density of the target) is not fulfilled. Burning has become possible for as long as `B⋅R > 60 Тл⋅см`(B - magnetic induction). Therefore, combustion can be obtained at a much lower pressure than in ICF. The final element necessary for effective use in space remains the method of converting the released energy into thrust while maintaining a high specific impulse.

Schematic representation of the process of inductive implosion of FRC plasmoid by a metal insert.(a) Thin metal hoops begin to move at such a speed and in such a direction that they compress the plasmoid in the throat of the nozzle. A FRC plasmoid acting as a target is fired at the engine chamber. (b) The FRC plasmoid is held by a longitudinal magnetic field from contact with the walls of the chamber as it travels to the nozzle throat. (c) Liner segments compress the FRC plasmoid, whereby conditions are reached for initiating a thermonuclear reaction. (d) Under the influence of alpha particles and neutrons obtained as a result of a thermonuclear reaction, the liner evaporates and turns into an ionized plasma, which expands along a diverging magnetic field. This leads to direct generation of electricity, thanks to the back EMF, and directional traction from the outflow of plasma from the magnetic nozzle.

It was clear that the conditions for initiating a thermonuclear reaction could be achieved on a small scale due to the kinetic energy of a massive metal insert aimed at compressing the plasma in the target to a high density and temperature. But to translate this into reality, it was necessary to answer the following questions:
1. How to do this without huge magnetic coils?
2. How to make it effective and repeatable?
3. How to create a suitable plasmoid used as a target?
4. How to convert fusion energy into directional thrust?

The key to answering all of these four questions may be studies of magnetic three-dimensional compression of metal rings around the FRC target to obtain a thermonuclear reaction, recently conducted at MSNW. A logical continuation of these studies is the method that uses these metal rings not only to achieve the necessary conditions for starting combustion, but also to directly create reactive thrust. To answer the first two questions, it is necessary to achieve high installation efficiency and achieve “stand-off” - the ability to protect the structure and fuel from the energy released by the reaction. The converging motion of metal rings can be achieved using inductance, for which they need to be placed along the inner surface of cylindrical or conical wedge-shaped coils. This solves problems with both efficiency and stand-off. The metal insert can be located up to a meter from the target. Moreover, the coils can be isolated both physically and electrically. Drive efficiency can be extremely high, since the coils in it are an inductive element in a simple oscillatory circuit, where the resistance loss is extremely small compared with the transmitted energy. Using even such simple elements as an array of diodes, any magnetic energy not transferred to the liner can be returned back to the charger after the shell is ejected through the nozzle after the first half of the cycle.

Even considering that the magnetic field inside the metal ring is initially relatively small, there is sufficient leakage of magnetic flux during acceleration of the ring inward, so that, at the peak of compression, the longitudinal magnetic field locked inside the now much thinner ring can reach 600 Tc. Now this field is even more than what is needed to compress the FRC and start a thermonuclear reaction with a significant useful yield.

The next problem was the creation of magnetized plasma for use as a target. To use the system in space, a small installation mass is required. The system with the smallest mass in which a thermonuclear reaction can be achieved, and the only one applicable in this case, uses compact toroidal plasmoids, usually called reversed-configuration fields (FRC). The biggest advantage of using plasma with closed magnetic field lines is its very high`β`(plasma / magnetic pressure ratio) and the possibility of its direct movement and compression to start the reaction. In all versions of thermonuclear reactors, only the FRC plasmoid has a linear geometry and is limited due to the closed field. Moreover, FRCs have already shown their ability to travel long distances and the ability to survive compression to the size and density needed to start synthesis. FRC have already been created with an internal field satisfying the B дляR ratio for starting combustion at the peak of compression.

For a liner nominal convergence rate of 3 km / s, FRC with a radius of 0.2 m, which is typical for this device, will be fully compressed in 67 μs, which is only part of the total lifetime of such an FRC (~ 1 ms).

To answer the fourth question, a fairly straightforward approach was developed to convert the energy of a thermonuclear reaction into thrust. As indicated above, a thin metal liner with an inductive drive is used to compress the plasma. After completing radial and longitudinal compression, this insert takes the form of a thick (r> 5 cm) shell, which behaves as a protective wall and absorbs almost all the energy of both the reaction and plasma during thermonuclear combustion. After that, heated to an ultra-high temperature, the ionized metal begins to expand rapidly inside the diverging field of the magnetic nozzle, which converts the plasma energy into reactive thrust. It is also possible to obtain electricity due to the back EMF induced in the conical coil due to compression of the stream. Worth noting

##### Flight to Mars

Next, data from presentation 1 and presentation 2 are taken .

I want to note that when it comes to space flights, the main indicator becomes Δv - the increment of speed (m / s or km / s). It is a measure of the amount of “effort” that is needed to move from one trajectory to another, when performing an orbital maneuver. For a spacecraft, there are no such concepts as fuel supply, maximum distance, or maximum speed, there is only Δv. The maximum Δv of the ship can be represented as the increment of speed that it will receive, having consumed all the fuel. It is important to know that a “mission” can be characterized according to which Δv is required to complete it. For example, the rise from the Earth,the Goman trajectory to Mars and landing on it requires a budget Δv of 18 km / s. If the ship has a margin Δv greater than or equal to Δv mission, then he can complete this mission.

In order to find out Δv of a ship, one can use the Tsiolkovsky formula .

where:
V is the final (after the generation of all fuel) the speed of the aircraft (m / s);
I is the specific impulse of the rocket engine (the ratio of engine thrust to second fuel mass flow rate, the velocity of the working fluid from the nozzle, m / s);
M 1 - the initial mass of the aircraft (payload + apparatus design + fuel, kg);
M 2- final mass of the aircraft (payload + design, kg).

A very important conclusion follows from this, which may not be very obvious at first glance. If Δv of the mission is less, or equal to the specific impulse, then the relative mass of the ship is large and it becomes possible to transport a larger payload. However, if Δv of the mission is greater than the specific impulse, the relative mass begins to decrease exponentially, making the ship a huge tank with fuel with a tiny payload. Actually, precisely because of this, interplanetary flights using conventional chemical engines are very difficult.

Plan for a 210-day flight to Mars and back.

###### 90-day mission to Mars (ΔV = 13.5 km / s)

Goal: Better payload to total weight ratio.
Benefits:
• No need for additional transport missions
• Simplified mission architecture
• The ability to bring all stocks in one mission
• Low cost mission
• The ability to start a mission after a single launch from Earth

###### 30-day mission to Mars (ΔV = 40.9 km / s)

Goal: the fastest mission.
Benefits:
• Low risk
• Apollo-type mission architecture
• The key to regular visits to Mars
• Development of technologies necessary for the conquest of deep space

Parameter (with a useful yield of a thermonuclear reaction equal to 200)90 days30 days
Exhaust power (MW)2.633
Solar Power (kW)27350
Specific impulse (s)51405140
Specific Mass (kg / kW)4.30.38
Initial mass (tons)90153
Отношение полезной нагрузки к общей массе65%36%

В настоящее время NASA занимается разработкой системы космических запусков (Space Launch System, SLS) — сверхтяжёлой ракеты-носителя, способной выводить на низкую опорную орбиту от 70 до 130 тонн полезной нагрузки. Это делает возможной начала 90-дневной миссии к Марсу уже после одного запуска подобной ракеты-носителя.

Обе миссии имеют возможность непосредственной отмены и возврата на Землю.

###### Ключевые параметры миссии

Допущения, касающиеся топлива
Расходы на ионизацию материала вкладыша75 МДж/кг
Эффективность передачи энергии вкладышу (оставшаяся энергия возвращается обратно в конденсаторы)50%
Эффективность преобразования в тягу ηt90%
Масса вкладыша (соответствует коэффициенту усиления от 50 до 500)от 0,28 до 0,41 кг
Фактор воспламенения5
Safety factor (G F = G F (calc.) / 2)2
Mission Assumptions
Mass of the Martian module (according to Design Reference Architecture 5.0)61 t
• Inhabited area31 t
• Returnable capsule16 t
• descent system14 t
Relative mass of capacitors (it also includes the necessary wiring)1 j / g
The relative mass of solar panels200 W / kg
Structural factor (tanks, structure, radiators, etc.)10%
Full fuel braking, aerodynamic braking not used
Ship design
Structure (fairings, power structures, communication channels, ACS, batteries)6.6 t
Lithium retention system0.1 t
Plasma Generation and Injection System0.2 t
Fuel supply mechanism1.2 t
Capacitor banks1.8 t
Liner compression coils0.3 t
Wiring and power electronics1.8 t
Solar panels (180 kW at 200 W / kg)1.5 t
Thermal control system1.3 t
Magnetic nozzle0.2 t
Ship mass15 t
The mass of the Martian module61 t
Lithium working fluid57 t
total weight133 t

Judging by the research plan, the pulse repetition rate will be higher than 0.1 Hz. If we take into account that the specific impulse is 51400 m / s, and the working fluid mass is 0.37 kg per pulse, then we can calculate the impulse p = mv = 19018 kg · m / s. According to the law of conservation of momentum, the speed of the ship will increase by p / M = 19018/133000 = 0.14 m / s. If we take the nozzle radius of 1 m, then the expanding gases will press on it in the region of t = r / v = 1/51400 = 0.00002 s. Therefore, the acceleration will be in the region a = dv / dt = 0.14 / 0.00002 = 7000 m / s 2 . Obviously, either shock absorbers will be used, as in the Daedalus project , or some other technical solutions for smoothing the momentum.