Fusion-based rocket propulsion remains our best current option to deliver substantial probe payloads to the nearest stars quickly. Project Icarus was founded by members of the British Interplanetary Society (BIS) and Tau Zero Foundation in 2009. It is now a joint effort by the BIS and Icarus Interstellar to build on BIS Project Daedalus using the knowledge and technology developed in the 30-40 years since that first thorough design study for an interstellar probe. Here our Principium deputy editor considers one of the more advanced designs within the Icarus Programme - the Z-Pinch propelled Firefly Icarus craft.

**A Review Paper based on the ‘Firefly Icarus’ Design**

*Patrick J Mahon*

### Abstract

If we are to launch unmanned probes that can reach and explore the nearest stars within a human lifetime, we will need to develop new propulsion technologies enabling much higher velocities than are possible at present. Nuclear fusion is one of the leading options, but it has yet to be achieved sustainably at a commercial scale.

Many different engineering approaches have been proposed for using nuclear fusion to propel a spacecraft. One such approach is Z-Pinch fusion, where a high current is driven through a plasma, compressing it sufficiently to initiate nuclear fusion. This is one of the approaches that has been explored recently by the Firefly team of the Project Icarus Study Group, led by Robert Freeland and Michel Lamontagne. Project Icarus follows-up Project Daedalus, the British Interplanetary Society’s 1978 design for an interstellar probe.

This review paper, written at a technical level suitable for beginning undergraduates, considers in outline the physics and engineering of Z-Pinch fusion, and illustrates how this might work in practice through a case study of the ‘Firefly Icarus’ spacecraft design.

### 1. INTRODUCTION

The stars above us have interested humans in myriad different ways since the dawn of civilisation. However, a specific interest in the *astrophysics* of the universe beyond our own solar system seems particularly acute at present. This is partly due to the wealth of new science being done by space agencies around the world. For example, recent astronomical observations from the Kepler space telescope [1] have shown that many stars have planets in orbit around them, potentially including Proxima Centauri, our nearest star. If we want to know more, do we need to be able to master interstellar flight, so we can send probes to explore these distant stellar systems?

#### 1.1. The justification for interstellar travel

Some will argue that we shouldn’t try to send probes. After all, aren’t we getting more than enough data from space-based telescopes? It’s certainly true that our study of the stars has been revolutionised over recent years by observations from such instruments as Kepler, the Hubble Space Telescope and many others. However, remote observation does have its limitations. For example, our knowledge of the dwarf planet Pluto was increased by an order of magnitude by the New Horizons probe’s flyby of the planet in July 2015. We can do a lot of science from *here*, but to answer some key questions, we will need to go *there*.

#### 1.2. The main challenge to interstellar travel

The main problem with ‘going there’ is that the stars are an extremely long way away. Our nearest star, Proxima Centauri, is some 4.3 light years away from Earth. This is equal to 269,000 Astronomical Units, or AU, where 1 AU equals the average distance between the Earth and our own Sun (roughly 150,000 km). A quick calculation will show you that there are 63,240 AU in one light year; multiplying this by 4.3 gives you the answer above. To compare, Pluto orbits the Sun at an average distance of just under 40 AU – so our *nearest* star is around 7,000 times as far away as our solar system’s *most distant* (dwarf) planet!

How long would it take for a probe to reach Proxima? The fastest spacecraft our species has yet produced is the Voyager 1 probe, launched in 1977 to survey Jupiter and Saturn. It left our solar system in 2012 and is currently travelling at 17 km/s (3.6 AU/year) [2]. If Voyager 1 was pointing towards Proxima, it would take some 74,000 years to get there.

That’s clearly not a useful timeframe from the point of view of human scientists waiting for their results. Realistically, if a space probe is going to provide useful returns, it needs to do so within a reasonable human timeframe of decades or, at most, a century. To be clear, we’re therefore talking about flight durations roughly 1,000 times shorter than it would take Voyager 1 to get to Proxima Centauri. Since time = distance/speed, we are going to have to find ways to accelerate probes to speeds three orders of magnitude higher than we can achieve today. Will that be easy or hard? The answer comes from a Russian space scientist born over 150 years ago.

#### 1.3. The Tsiolkovsky Ideal Rocket Equation

Konstantin Tsiolkovsky was a schoolteacher who made great contributions to aerospace engineering in his spare time [3]. In 1903, Tsiolkovsky published the equation that now bears his name [4]. This shows how the final velocity that a rocket can reach is related to the velocity of its exhaust gases, the mass of fuel and oxidiser, and the mass of the spacecraft. The equation is derived in Box 1, and the final result is:

\[\Delta V = v_e \ln\left(\dfrac{m_0}{m_f}\right)\]

- where \(\Delta V\) (‘delta-V’) is the change in the rocket’s velocity, \(v_e\) is the velocity of the exhaust gases, \(m_0\) is the initial, and \(m_f\) the final, mass of the rocket, so that \(m_0 - m_f\) is the mass of the fuel plus oxidiser used to accelerate the rocket.

#### Box 1: Deriving the Tsiolkovsky Ideal Rocket Equation

Consider the rocket illustrated in Figure 1. At time \(t = 0\), the spacecraft’s momentum (measured in the rest frame) is

\[(m + \Delta m ) v\]

After an infinitesimal time period \(\Delta t\), the momentum has changed to

\[m (v + \Delta v) + \Delta m (v - v_e )\]

Conservation of momentum enables us to equate these two terms. Expanding and simplifying, we reach

\[m \Delta v = \Delta m v_e\]

If we then multiply through by \(\Delta t / \Delta t\), and take the limit as \(\Delta t\) tends to zero (noting that in the limit, \(dm = – \Delta m\), as a positive \(\Delta m\) reduces \(m\)) and then integrate over the duration of the rocket firing, we obtain

\[\Delta V= -v_e \int \dfrac{1}{m}\dfrac{dm}{dt}\]

or

\[\Delta V = v_e \ln{\left(\dfrac{m_0}{m_f}\right)}\]

As Table 1 below demonstrates, the presence of the natural logarithm in the equation means that achieving a delta-V much greater than about three times the exhaust velocity is largely impractical, as the mass ratio (\(m_0 / m_f\)) becomes so high (above twenty) that the rocket would be near impossible to build, as it would consist almost entirely of fuel and oxidiser. At the extreme, to achieve a delta-V five times the exhaust velocity would require that the fuel and oxidiser weigh nearly 150 times as much as the payload and rocket structure. Building a rocket structure light enough to achieve this mass ratio, whilst remaining strong enough not to collapse under the weight of the fuel, would be extremely challenging, if not impossible.

\(\Delta V / v_e\) | \(m_0 / m_f\) | \((m_0 - m_f) / m_f\) |
---|---|---|

1 | 2.718 | 1.718 |

2 | 7.389 | 6.389 |

3 | 20.09 | 19.09 |

4 | 54.60 | 53.60 |

5 | 148.4 | 147.4 |

Table 1: Implications of Tsiolkovsky’s Ideal Rocket Equation

In practical terms, a mass ratio of around 20 is a reasonable upper limit on what can normally be achieved. To take an example, for the Saturn V rocket which took men to the Moon, the lift-off mass (including fuel) was 2.8 million kilograms, of which 2.6 million kilograms was fuel and oxidiser. The non-fuel mass (\(m_f\)) was 220,000 kilograms [5]. The mass ratio was thus around 12.7.

What the Tsiolkovsky rocket equation demonstrates is that, for a given choice of fuel, with a given exhaust velocity, achieving a final velocity for the rocket of much more than around three times that exhaust velocity is essentially impractical. Now, the most energetic chemical fuel used today is hydrogen-oxygen, which produces an exhaust velocity of around 4,400 m/s (9,900 mph). Realistically, therefore, a rocket burning hydrogen and oxygen can accelerate to a final velocity of around 13,200 m/s (29,700 mph). This is sufficient to get us into Earth orbit (17,500 mph) or even to the Moon (25,000 mph). But it is equal to 0.0044% of the speed of light. At that speed it would take us 98,000 years to reach Proxima Centauri.

Application of Tsiolkovsky’s Ideal Rocket Equation therefore demonstrates that chemical fuels are not suitable for interstellar travel via rocket within reasonable human timeframes of a few decades to a century, as the velocity of the exhaust products is far too low. What can we do instead?

#### 1.4. Alternatives to chemical rockets

Many alternatives to chemical propulsion have been proposed in the interstellar travel literature – see, for example, [6], [7]. A brief list might include solar or laser sails, ion engines, nuclear fission-powered rockets, the Bussard ramjet and the antimatter rocket. However, almost all of these technologies have one or more drawbacks (typically either acceleration or thrust levels) which rule them out of contention for our present purposes, where we want near-term technologies that can achieve a mission duration of no more than a century.

Laser sails, which do not have to carry their own fuel on board and thus have the significant advantage of not being subject to the constraints of Tsiolkovsky’s Ideal Rocket Equation, provide one potential option for sub-century travel to nearby star systems, and are under active investigation by such organisations as Breakthrough Starshot [8]. However, it is not immediately clear how a laser sail would decelerate into orbit when it arrived at its target – which is one of the constraints we will observe here (see section 2.4 below).

The most promising technology left on the table if laser sails are ruled out is, for many interstellar proponents, nuclear fusion.

### 2. NUCLEAR FUSION

#### 2.1. Introduction to nuclear fusion

A detailed discussion of the physics of nuclear processes is outside the scope of this article. For those interested, a good treatment can be found in [9]. However, in brief, Einstein’s famous equation \(E = mc^2\) tells us that energy and mass are interchangeable, with very small amounts of mass being equivalent to very large amounts of energy, due to the conversion factor \(c^2\) (roughly \(9 \times 10^{16}\), or ninety thousand trillion): total conversion of one kilogram of mass would create 90,000 TJ (terajoules) of energy, equivalent to over two-thirds of the energy produced by the UK’s largest power plant, Drax, in a whole year.

There are two different ways in which this energy can be harnessed usefully: nuclear fission, and nuclear fusion.

Nuclear fission is the process where an unstable heavy atomic nucleus, such as Uranium-235, decays into two lighter nuclei. This leads to a small reduction in overall mass, which is converted into energy that can be used peacefully in a nuclear power plant, or as the basis for a nuclear bomb. Nuclear fission is a tried and tested technology that has been used for both purposes for over fifty years.

On the other hand, nuclear fusion is the process where two light nuclei are brought together at sufficiently high temperatures and pressures, and for a sufficiently long time, that they are able to overcome the strong repulsive force between them and fuse together, forming a heavier nucleus. This process again leads to a small reduction in total mass, releasing energy. Many different nuclei can potentially be brought together in a fusion reaction, and this choice is vital as it determines what the fusion products are and how easy they are to use afterwards, whether for energy production or propulsion. The simplest example of relevance to spaceflight consists of the fusion of two nuclei of deuterium (an isotope of hydrogen consisting of one proton and one neutron). Half the time, the fusion reaction forms tritium (another isotope of hydrogen, this time comprising one proton and two neutrons) plus a proton; alternatively, it forms helium-3 and a neutron. In either case, the reaction products carry away the energy produced by the small reduction in overall mass.

Nuclear fusion is the process which powers all the stars in the Universe, so it is tried and tested on a stellar scale. However, humanity has not yet managed to create a self-sustaining fusion reaction here on Earth which produces more energy than is needed to keep it going. Intensive research is being undertaken by several international collaborations, including one based at the Joint European Torus (JET) facility at the Culham Centre for Fusion Energy in Oxford, and the ITER (Latin "The Way") facility currently being constructed in southern France and due to become operational in 2025.

At the high temperatures required to enable fusion (typically tens of millions of degrees Kelvin), the fuel takes the form of an ionised plasma, with the positive nuclei separated from their atomic electrons. The key performance metric used to describe a fusion reaction is the so-called triple product, obtained by multiplying together the plasma density \(n\), the plasma temperature \(T\), and the confinement time \(\tau\). This triple product must exceed a minimum value for fusion to be self-sustaining.

#### 2.2. Approaches to achieving nuclear fusion

There are two broad engineering approaches to achieving nuclear fusion in the laboratory:

**Magnetic Confinement Fusion (MCF)**uses magnetic fields to confine the charged plasma, typically (although not always) within a ring doughnut-like toroidal container. The magnetic fields are necessary to ensure that the plasma does not touch the sides of the containment vessel, since at the temperatures required to initiate fusion any contact would lead to melting of the container and loss of containment of the plasma.**Inertial Confinement Fusion (ICF)**instead focuses powerful lasers onto a small pellet of the fusion fuel, such that the energy from the lasers heats and compresses the fuel, leading at the centre of the pellet to temperatures and pressures sufficient to initiate nuclear fusion.

Each of these approaches to fusion has been incorporated into detailed designs for an interstellar spacecraft: Project Daedalus and a range of designs in Project Icarus.

#### 2.3. Project Daedalus

In the early 1970s, the BIS set up Project Daedalus to establish whether interstellar travel was practically feasible, or just the stuff of science fiction. The outcome of this ground-breaking volunteer-led project was a 1978 design [10] for an Inertial Confinement Fusion-powered unmanned starship that would send a 450-tonne scientific payload on a flyby mission past Barnard’s Star, some 5.9 light years away and, at that time, seen as the most promising nearby star for scientific study.

#### 2.4. Project Icarus

Project Icarus is a collaboration between the members of the British Interplanetary Society and Icarus Interstellar. It began in 2009 with the idea of updating the Project Daedalus design to take account of three decades of technological progress. The project has several specific goals of direct relevance to this article [11], [12]:

- The design must use ‘current or near-future technology’;
- The propulsion system must be ‘mainly fusion-based’;
- The vessel must reach its destination within one hundred years of its launch; and
- The mission is to fully decelerate a 150-tonne scientific payload into orbit around Alpha Centauri.

Given constraints (c) and (d) – of accelerating to reach, and then decelerating into orbit around, a destination 4.3 light years away within a century – this immediately gives us a minimum delta-V over the journey of 8.6% of the speed of light. We will need to check at the end of this article whether this constraint has been met.

One of the spacecraft designs that has been studied in detail by the Project Icarus Study Group is the ‘Firefly Icarus’ which is powered by a particular type of Magnetic Confinement Fusion known as Z-Pinch fusion [13]. It is this design that we will focus on in the rest of this article. To understand how it works, we first need some background on the concept of a Z-Pinch.

#### Box 2: Fleming’s right-hand and left-hand rules

Fleming’s ‘right-hand rule’ tells you the direction of the magnetic field generated by a (positive) current (eg in an electric wire, or a plasma).

Simply curl your right hand into a ‘thumbs-up’ sign, and point the thumb in the direction of the current. Your curled fingers indicate the direction of the magnetic field induced by the current – showing, for example, that the field curls around the current in an anti-clockwise direction if the current is travelling towards you.

Fleming’s ‘left-hand rule’ tells you the direction of the force generated by a (positive) current moving in a magnetic field. This time, hold out the thumb, first finger and second finger of your left hand, all at right angles to each other. Align your **F**irst **F**inger with the direction of the magnetic **F**ield, and your se**C**ond finger with the direction of the **C**urrent. Your thu**M**b will then point in the direction of **M**otion due to the induced force.

The size of this force is then given by Ampère’s law: \(\mathbf{F} = \mathbf{j} \times \mathbf{B}\) , where \(\mathbf{j}\) is the current vector, \(\mathbf{B}\) is the magnetic field vector, \(\mathbf{F}\) is the force vector, and \(\times\) is the vector product operator.

### 3. THE Z-PINCH

A Z-Pinch occurs naturally when a large current passes through any medium. As shown in Figure 2 and described in more detail in Box 2, the current gives rise to a magnetic field in line with Fleming’s ‘right-hand rule’, and the magnetic field in turn generates an inward force on the current in line with his ‘left hand rule’.

In the case of a Z-Pinch, this leads to a pinch force which squeezes the current inwards. A naturally occurring example of this phenomenon is lightning, where the electrical discharge from cloud to ground ionises the air, creating a plasma, and then pinches it, producing both the visible lightning and the audible thunder.

The next question to answer is how much the current gets pinched by the magnetic field, and what the equilibrium condition is for such a situation.

#### 3.1. Deriving the Bennett Pinch Relation

The equilibrium condition is determined by the Bennett Pinch Relation, first derived by Willard Harrison Bennett in 1934 [14], and re-derived in Box 3, by equating the magnetic pressure inwards to the outwards pressure of the hot plasma. The result is:

\[(1+Z) N k T = \frac{\mu_0 I^2}{8 \pi}\]

What this tells us is that the higher the plasma current, \(I\), the higher the product of the plasma density (\(N\)) and temperature (\(T\)) at equilibrium. Recalling from section 2.1 that these are two of the three factors which feature in the fusion triple product, we can see how a Z-Pinch of sufficiently high strength, running continuously for long enough, could conceivably create the right conditions to initiate nuclear fusion.

#### 3.2 Practical problems with using a Z-Pinch to initiate fusion

Following Bennett’s pioneering work, research on the use of a Z-Pinch to initiate fusion continued until the 1950s, when Kruskal and Schwarzschild published a paper describing potential instabilities in Z-Pinch plasmas [15]. This posed some serious questions for the viability of Z-Pinch fusion, and research on it stalled for forty years, until Uri Shumlak published a paper in the late 1990s, suggesting that these instabilities could be overcome through sheared axial flows (where adjacent layers of the plasma move parallel to each other, but at different speeds) of sufficiently high speed [16]. It is Shumlak’s research that led the Project Icarus Study Group to consider Z-Pinch Fusion as a possible propulsion technology.

#### Box 3: Deriving the Bennett Pinch Relation

We derive the equilibrium condition for a Z-Pinch by equating the inward magnetic pressure (from Maxwell’s equations) to the outward plasma pressure (from the Ideal Gas Law) for a cylinder of arbitrary radius \(r\) and length \(L\).

At equilibrium, the inwards force \(\mathbf{F}\), squeezing the plasma together, is balanced by the pressure of the hot plasma trying to expand outwards. Since pressure = force/area, at a general radius \(r\) from the central axis, we have:

\[\text{Magnetic field strength inwards} = H = \frac{I}{2\pi r} \qquad \text{(from Ampère's law)}\]

\[\text{Inward force due to this magnetic field} = |\mathbf{F}| = |\mathbf{j} \times \mathbf{B}| = \mu_0 |\mathbf{j} \times \mathbf{H}| = \frac{\mu_0 I^2}{2\pi r}\]

\[\text{Outwards force at radius } r = \text{pressure} \times \text{area} = 2\pi r p\]

But the plasma pressure \(p\) is given by the Ideal Gas Law, \(pV = NRT\), which can equivalently be written as \(p = nkT\), where \(n =\) gas density (no. of gas particles per unit volume), \(k =\) Boltzmann’s constant, and \(T =\) temperature). Equating the inward and outward forces at equilibrium, we have:

\[F_{\text{in}} = \frac{\mu_0 I^2}{2\pi r}\]

\[F_{\text{out}} = 2\pi r p = 2\pi r nkT\]

\[\frac{\mu_0 I^2}{2\pi r} = 2\pi r nkT\]

\[\frac{\mu_0 I^2}{4\pi^2 r^2} = nkT\]

Finally, we convert \(n\) (the plasma ‘gas’ density per unit volume) into \(N\) (plasma density per unit length). Now, if a volume of radius \(r\) and length \(L\) contains \(X\) gas particles, then by simple geometry, \(X = n \pi r^2 L = N L\). Substituting \(N\) for \(n\), and noting that each ion in the plasma is accompanied by \(Z\) electrons (where \(Z\) is the atomic number), we finally have:

\[(1+Z) NkT = \frac{\mu_0 I^2}{8\pi}\]

### 4. Z-PINCH FUSION

Having established that a Z-Pinch can compress a plasma and raise its temperature, we now explore what happens if the conditions are extreme enough to initiate fusion. The mathematics of a fusing plasma in a Z-Pinch are complex, so I will simply reproduce two key results from [13] here.

#### 4.1. Plasma temperature

As fusion proceeds, the plasma heats up and new energetic ion species are created. The equilibrium plasma temperature \(T_p\) is given by:

\[T_p = \dfrac{\mu_0 I^2}{8 \pi Ne (1 + Z_p)}\]

Where \(Z_p = \frac{1}{N} \sum_i N_i Z_i\) is the weighted average atomic number of the various ions in the plasma. If the current \(I\) stays constant, the only way that \(T_p\) can increase is if \(N\), the linear number density of the various ion species, decreases. This happens both because fusion, as the name suggests, takes two ions and joins them into one, halving their number density, and also because the speed of the ions through the pinch region increases, again reducing the number of them per unit length (ie their linear number density).

#### 4.2. Exhaust velocity

The velocity of the exhaust leaving the fusion engine is given by:

\[V_{ex} = \left(\dfrac{2 P_{ex}}{dm / dt}\right)^{1/2}\]

Where \(P_{ex}\) is the power remaining in the exhaust plume, once the various power losses (which include the power needed to accelerate, heat and compress the plasma, and the losses due to Bremsstrahlung radiation – explained in section 5.2) are taken into account, while \(dm / dt\) is the mass flow rate through the engine.

Using these equations, plus expressions for other relevant physical quantities including the radius of the Z-Pinch during fusion, the fusion reaction rate, and the mass flow rate, [13] models the performance of the Z-Pinch fusion engine, leading to the results presented in section 6 below.

### 5. PRACTICAL ISSUES

Any spacecraft, whatever its propulsion system, needs to be carefully designed to ensure that it will function effectively in the unforgiving environment of space. The general details of spacecraft design are outside the scope of this article; a good introduction can be found in [17].

However, the use of a Z-pinch fusion engine creates several specific engineering challenges for the spacecraft. In this section, we briefly outline the practical issues that will need to be overcome, drawing heavily on [13], where more detail can be found. In broad terms, they fall into three categories: (a) energy management; (b) radiation management; and (c) the consequences of these for spacecraft design.

#### 5.1. Energy management

A Z-Pinch fusion drive requires a large electrical current to compress the plasma to a sufficiently high density to enable fusion. Freeland and Lamontagne calculate that the electrical system needs to supply 5 MA at 235 kV, implying a power of \(P = I \times V = 1175 \text{ GW}\). This is roughly one-third of the power consumption of the entire United States in 2005. The current itself is more than an order of magnitude larger than the highest current we can presently produce.

This creates three distinct energy management issues: (i) recapture of the energy from the fusion products in the exhaust plume; (ii) startup power; and (iii) cooling.

##### 5.1.1. Energy recapture

Given their magnitude, we cannot expect to generate the required power levels in the usual way from a power plant onboard the spacecraft. The only realistic source of this power is by recapturing some of the surplus energy generated by the fusion reactor. This would be done by removing energy from the charged particles in the exhaust and feeding it back into the power system.

##### 5.1.2. Startup power

Clearly, we cannot recapture energy from the fusion engine’s exhaust plume before the engine has started. We therefore need a separate source of power to start the engine up. This will be provided by a set of capacitors which are charged up using the ship’s primary power source, which in the Firefly design is a compact fission reactor.

##### 5.1.3. Cooling

The need to reject excess heat is an issue for any spacecraft, given that the insulating properties of the vacuum of space mean that this heat cannot escape through conduction or convection, leaving radiation as the only option. For a spacecraft whose propulsion system relies on huge electrical currents to drive nuclear fusion, this problem is particularly acute.

As set out in the next sub-section, the spacecraft is designed so that most of the potentially damaging high energy radiation created in the fusion reaction can escape directly into space. This reduces the cooling requirements significantly. However, it is still necessary to cool several key parts of the ship, including the electrodes carrying power to the Z-Pinch drive, the magnetic nozzle which focuses the charged particles in the exhaust, and the support structure around the fusion engine.

To achieve the necessary level of cooling efficiency, Freeland and Lamontagne have chosen a phase-change radiator using Beryllium as the working fluid. This creates its own problems, since Beryllium has a high boiling point (2,743 Kelvin) and is extremely toxic to humans, but it has the advantage that Beryllium has the highest heat of vaporisation per unit mass of any element, at 33.0 MJ/kg, minimising the mass of working fluid needed to deal with a given heat load.

The working fluid is pumped through those elements of the ship that need cooling, where it changes from a liquid into a gas, then runs through pipes made from zirconium carbide (which can not only withstand the high temperatures involved, but also has a low probability of absorbing any passing neutrons and is resistant to radiation damage) and is fed to carbon-carbon radiators, where the Beryllium gas turns back into a liquid as the excess heat is radiated away into space.

#### 5.2. Radiation management

The Firefly Icarus engine is powered by the fusion of deuterium with deuterium. The choice of fuel was motivated by Project Icarus’s terms of reference, and in particular the wish to be able to produce all the propellant on Earth (in comparison to the Project Daedalus engine, which required helium-3 mined from the atmosphere of Jupiter), as this significantly advances the timeframe within which the mission might become technically feasible.

However, the choice of D-D fusion leads to the creation of large amounts of radiation, including highly energetic neutrons which cannot be directed using electric or magnetic fields. In addition, the extreme conditions in the pinch region lead to the emission of Bremsstrahlung radiation in X-ray wavelengths. Since the pinch region is essentially a one-dimensional line, the neutrons and X-rays are effectively emitted cylindrically outwards.

This radiation flux is of such high energy that the inclusion of comprehensive shielding against it would be prohibitively expensive in mass terms. Instead, the Firefly designers have taken the opposite approach, designing the spacecraft so that the fusion engine is located as far as possible away from the payload and other radiation-sensitive parts of the ship. The design then allows the radiated neutrons and X-rays to escape into space without irradiating other parts of the ship. Shielding is then only required in the small area directly between the engine and the rest of the ship’s structure.

#### 5.3. Spacecraft design

Figure 3 is a schematic of the Firefly Icarus spacecraft design, illustrating how the various subsystems described above are integrated into the vehicle. Further details can be found in [13].

### 6. SUMMARY AND CONCLUSIONS

This paper briefly explains why chemical rockets are not up to the challenge of sending spacecraft to the stars in a reasonable timeframe, and why nuclear fusion is one of the leading alternatives. It summarises the logic behind the choice of Z-pinch fusion as the preferred propulsion technology for the Firefly Icarus interstellar spacecraft. Following an optimisation exercise, the Project Icarus Study Group have settled on a spacecraft with the following key design features [13]:

- Length = 750 metres
- Dry mass = 2,200 tonnes. This breaks down as follows:
- radiators (1,600 t);
- shielding (160 t);
- payload (150 t);
- miscellaneous structure (130 t);
- magnetic nozzle/energy recapture (110 t); and
- reactors (50 t).

- Wet mass = 23,550 tonnes. This includes:
- Dry mass (2,200 t);
- Fuel tanks plus pressurant (350 t); and
- Fuel (21,000 t).

- Exhaust velocity \(v_e =\) 12,000 km/s (= 4% of the speed of light)
- Specific Impulse (Isp) \(= v_e / g =\) 1,200,000 seconds
- Thrust = 600 kN

It’s worth noting at this point that since \(v_e\) is 4% of the speed of light, the constraint set out in section 2.4 above, that the Firefly Icarus propulsion system be able to achieve a delta-V of at least 8.6% of \(c\), should easily be satisfied, since according to the Tsiolkovsky equation, that only requires a mass ratio of \((m_0 / m_f) = \exp{(\Delta V / v_e)} = 8.58\), which is well within current capabilities.

The spacecraft could be constructed in Earth orbit, or alternatively at one of the Earth-Moon Lagrange points. The dry mass could be launched into Low Earth Orbit (LEO) on 17 of NASA’s planned Space Launch System rockets (Block 2) or 20 Saturn Vs, so this aspect of the project is feasible with proven or near future launch capabilities [13]. The proposed mission profile would be as follows:

- the completed vehicle is towed to the far side of the Moon;
- it ignites its engines there (to avoid any radiation concerns back on Earth);
- it reaches 4.7% \(c\) after 10 years;
- it cruises at that velocity for 85 years;
- the spacecraft then turns through 180 degrees and fires the engine again for 5 years to decelerate it; and
- Finally, the spacecraft enters into orbit around Alpha Centauri after 100 years.

#### 6.1. Areas for further study

Although the Z-Pinch fusion engine proposed for the Firefly Icarus spacecraft design is based on current or near-future technology, there remain several theoretical and practical issues which will require further study before the design can be said to be fully worked up. The three main challenges, as discussed by Freeland in [18], are:

**Energy recapture.**As explained in section 5.1.1 above, the only realistic way to provide a Z-Pinch fusion engine with sufficient power to operate continuously is by recapturing energy from the jet of fusion products as they exit the engine. Research is needed on the best technology for achieving this.**Plasma stability.**As discussed in section 3.2 above, a Z-Pinch is subject to plasma instabilities which can potentially be overcome through a sufficiently rapid sheared axial flow. The Firefly Icarus engine design assumes that this is true in practice as well as theory, so that once fusion is initiated, the plasma remains stable indefinitely. This is currently being tested on a small scale by Uri Shumlak [19], but can only be fully verified experimentally by running a Z-Pinch fusion engine continuously – which requires a solution to the energy recapture problem discussed above.**Theoretical analysis.**The mathematical analysis of a Z-Pinch which was briefly presented in sections 3 and 4 above is not strictly applicable to a Z-Pinch once fusion occurs, as the analysis assumes adiabatic compression (ie compression where there is no gain or loss of heat). This is a valid assumption for the experimental tests of non-fusing Z-Pinches which have been carried out to date. It is not, however, valid for a continuous fusing plasma. A proper theoretical analysis will need to be developed in due course to support further experimental work.

#### 6.2. Conclusion

This paper hopefully demonstrates that although sending an unmanned probe to our nearest star is a highly ambitious undertaking, it is feasible with present day or near-term technologies. Just as importantly, I hope I have shown that the central issues involved are amenable to analysis by the average science undergraduate.

If this article has whetted your appetite for interstellar spacecraft design, I would encourage you to follow up the references (particularly [13]), read relevant books (eg [6], [7]) and consider attending one of i4is’s Starship Engineer courses (see [20] for details). Finally, I would strongly recommend that you obtain a copy of the Project Daedalus report ([10], available from the BIS in an attractive hardback reprint edition), and the Project Icarus final report [21] upon publication.

### ACKNOWLEDGEMENTS

Particular thanks are due to Robert Freeland II and Michel Lamontagne, as the inspiration for this article comes from their excellent 2015 JBIS paper summarising the Firefly Icarus concept; I have drawn heavily on that paper and some of Michel’s images within it here. Robert and Michel have also both been extremely generous with their help during the preparation of this article.

Thanks are also due to the members of the Project Icarus Study Group, especially Project Leader Rob Swinney, for allowing this article to be published ahead of the Project Icarus final report. I should additionally acknowledge helpful discussions with Principium editor John Davies, and with my son Andrew Mahon, a maths undergraduate who proved a willing and able test subject.

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#### About Patrick Mahon

Patrick is a physicist working in the waste and recycling sector. He is a long-committed space enthusiast who enjoys the challenges of interstellar science and technology presented by i4is. He is a regular contributor to Principium and is its Deputy Editor.