Exploring Optimization of the Stellarator over Tokamak Fusion Reactors: A Comparative Analysis

Rayan Abdullah Khan, Cambridge Mack, Tenifayo Adedeji & Gabriel Hemetrio de Menezes

August 1, 2024

2360

Abstract

For years, a top priority has been given to a sustainable solution for producing energy without harming the environment. Among many, tokamaks and stellarators are complex fusion reactors capable of producing enormous energy. A tokamak is a fusion reactor employed in the study of nuclear fusion, designed to keep plasma contained using magnetic forces. It features an intricate arrangement of magnetic fields that suspends the plasma, made up of electrically charged particles which have super-heated, within a cylindrical, doughnut-like enclosure, known as a torus. On the other hand, a stellarator (combining the Latin word Stella meaning star, and the English word generator — produced the word Stellarator means it is a generator of stellar energy) is a ring-shaped device designed to generate precise fusion reactions in super-heated plasma, in which the main magnetic fields are created through external coils which are wound and bent into complex helical shapes. By exploring both options, our primary focus is to find out which one is a more viable option given the proper circumstances for producing more energy after reviewing available literature and data. This paper finds that an optimized version of the stellarator can be used for longer periods to achieve a Q-gain factor $>$ 1 implying the reactor can produce energy by modifying various components and aspects of the stellarator and ensuring that the triple product of the stellarator is high enough to meet the requirement for sustainable fusion energy.

Key Words: Nuclear Fusion, Nuclear Energy, Sustainable Energy Production, Q-gain Factor, Stellarator, Tokamak, Wendelstein 7-X Stellarator, Magnetic Confinement, Triple Product, Optimization

Introduction

The use of nuclear energy has been heavily criticized due to the consequences of nuclear meltdowns – the three most famous, Three Mile Island, Chernobyl, and Fukushima-Daiichi- receive heaps of negative attention from the media. Nuclear energy’s contribution to global energy production, at about one-tenth, stakes in comparison to the output of power plants dependent on fossil fuels, which worsen climate change¹. With the current global infrastructure, it is unrealistic for the majority of our energy to come from nuclear fission power plants. Nuclear fusion, however, produces four million times more energy than nuclear fission does². One nuclear fusion power plant is enough to power Earth multiple times and would allow for projects that require more energy than currently possible. However, many scientists often argue whether nuclear fusion is safe or not and how it could be used to produce more energy for a longer period of time.

Figure 1: The increasing trend in CO₂ levels from 1958 onwards³

As of May 2024, the carbon dioxide level in the Earth’s atmosphere was measured to be 427 ppm (parts per million) (Figure 1). This is a staggering increase from 317.45 ppm in 1958. Over the last 200 years, CO₂ concentration has increased by 50 % due to human activities involving the burning of fossil fuels⁴. Since the 1880s, average global temperature has been said to have increased by about 1.1° Celsius (1.9° Fahrenheit) which has resulted in warmer winters and summers (Figure 2). It is now imperative that climate change be mitigated to prevent worsening natural disasters and absurd weather patterns⁵. To lower carbon emissions a shift in energy production is needed. Nuclear fusion may just be the answer to this and further research and implementation is necessary to further this cause as fusion reactors in the past have proved to be inefficient. This is mainly due to the lack of research and sufficient knowledge on fusion itself. Few nations have shown interest in implementing this energy resource due to mixed opinions and a lack of awareness. However, fusion reactors hold promise for a better future.

Figure 2: Global temperature anomaly since the 1880s⁶

Fusion reactors have several merits as a means of producing energy. First, they do not emit CO_2. Fusion mainly produces helium as a product of its process which is neither a greenhouse gas nor harmful to health. Second, they produce more energy. Nuclear fusion produces 4 million times more energy than any fossil fuel and four times that of fission, given that equal amounts of fuel from each source are used. Just this serves as a tantamount to the immense potential of fusion over all other types of energy production. Third, none of them have the risk of running out of fusion fuel. Deuterium-tritium, which is the main fuel used in fusion reactors, is a renewable resource, unlike fission where Uranium-235 is a limited resource and cannot be renewed at will. Deuterium (an isotope of Hydrogen) can be extracted from just water, while tritium itself is reproduced in fusion reactors when the ejected neutrons collide with lithium breeding blankets in the fusion reactors⁷.

Nuclear fusion is safer than nuclear fission. Unlike nuclear fission which uses highly radioactive isotopes like Uranium-235 and produces waste like caesium-137, strontium-90, caesium-134, xenon-133, iodine-133, plutonium-240, etc.,⁸. While nuclear fusion uses deuterium which is superheated⁹. Also, in comparison to fission, fusion is not dependent on a chain reaction which could become uncontrollable if reactors are improperly handled, as the plasma is held together by electromagnetic forces. By stopping the heating drive or changing the magnetic field it can cause subsequent cooling of the plasma in just a matter of seconds. This will have no effects on the outside of the reactor and there will be no nuclear meltdown.

Keeping this in mind, efforts are underway to develop a nuclear fusion reactor that produces more energy than it uses for longer periods of time. However, the demerits of fusion reactors are also very apparent. First, they are expensive. One of the world’s largest fusion reactors, the ITER tokamak will cost its developers about 22 billion dollars. On the other hand, the Wendelstein 7-X stellarator costs around 370 million euros. This is related to the high cost of components used such as the vacuum pumps, the breeding blankets, the wires and magnets. Second, nuclear waste will be a byproduct of these reactors. When the plasma is heated to such high temperatures during deuterium-tritium fusion, neutrons are created. The breeding blanket consisting of lithium slows down the neutrons and acts as a coolant; in the meantime, the neutron radiation has serious consequences. The neutrons slowly cause structural damage to the interior and the fuel assemblies and make the surrounding components radioactive as atoms are knocked out of their normal positions in the lattice structures. Even non-structural parts have the possibility of becoming highly radioactive and this includes the breeding blanket also. Hence, these radioactive substances have to be removed from time to time to prevent further deterioration of fusion components. However, waste from fusion reactors has lower levels of radioactivity compared to fission reactors, they are produced in much larger quantities and hence sheltering waste becomes a huge issue. Third, one can face problems in controlling energy production due to difficulties in plasma confinement. The fusion of deuterium and tritium to produce helium and neutrons requires temperatures surpassing 100 million degrees and very high pressures. From these, two key issues arise the stability of the plasma and how to confine it within the reactor during operation. This is mainly due to plasma turbulence which causes heat to radiate and interfere with the magnetic field lines at the border of the plasma which in turn destabilizes the plasma and hence causes degradation of its effectivity to generate energy¹⁰’¹¹’¹²’¹³.

Generally, energy output is the amount of energy released by a nuclear fusion reactor. Energy input is the amount of energy required to operate the nuclear fusion reactor and keep the Q value or Q-gain factor as it will be referred to from now on is the ratio of energy output to energy input:

$Q = \frac{\text{energy output}}{\text{energy input}}$

Currently, sustainable Q values of nuclear fusion reactors are below a value of 1, meaning that it requires more energy for a reactor to operate than it will produce. For nuclear fusion to be viable, a value Q $>$ 1 must be maintained consistently. For nuclear fusion to eliminate the need for carbon-emitting fuel sources, a Q value significantly greater than one is required. Currently, many methods of achieving fusion exist, all of which differ from one another by the way they confine plasma to produce energy.

Figure 3: Outputted fusion power in megawatts as a function of time. (Reproduced with permission from Keilhacker Source: Keilhacker, 1999. P. 279¹)

After reviewing the available literature, we find several methods of confinement of plasma. One of the newer methods of nuclear fusion is inertial confinement. Over here a laser is focused on a small shell of deuterium-tritium fuel which causes it compressed to 1000 times its liquid density. This only lasts for 10 billionths of a second. This causes the outer layer to explode and additionally creates a compression front which moves inwards into the fuel shell and causes it to heat up. This allows the deuterium-tritium already under immense pressure and heat to release huge amounts of energy which heats the surroundings and thereby initiates a chain reaction. Magneto-inertial fusion method is used for plasma confinement in stellarators, tokamaks and reverse field pinch devices. This method simply uses large powerful magnets to confine large volumes of deuterium-tritium plasma (hundreds of cubic meters) within the fusion reactor. As plasma is ionized, it has ions and electrons and hence follows the magnetic field lines. This helps to separate the plasma which is at 150 million degrees Celsius from the walls of the reactor vessel otherwise, it would slow it down as the fuel particles will lose their heat by conduction and radiation. In a tokamak, the magnetic field in the shape of a torus is created by a series of coils which are evenly spaced within the reactor. While a network of horizontal coils outside the toroidal magnets generates the poloidal magnetic field. Stellarators use helical-shaped coils to create the field lines needed to suspend and confine the plasma. While the Reversed Field Pinch (RFP) is very similar to the tokamak utilizing both toroidal and poloidal structures it has 2 key differences. Firstly, the current is stronger and secondly, the sign of the plasma is reversed at the edge. Hybrid fusion combines fusion and fission. While the plasma at inside the fusion reactor continually emits neutrons these neutrons are absorbed by a subcritical fission reactor which surrounds the plasma fuel. These neutrons start a fission chain reaction as more and more neutrons are released¹⁴.

Two of the most celebrated fusion reactors which hold promise for future implementation are the stellarator and tokamak. Various comparisons can be made between tokamaks and stellarators. Stellarators are more renowned for keeping the plasma stable hence allowing steady-state operation. Plasma turbulence is much lower than tokamaks, hence avoiding disruptions in plasma handling. At the same time, there are fewer Magnetohydrodynamics (MHD) activities. Due to less plasma turbulence, drift-wave modes are much more stable in stellarators and hence more controllable. Additionally, tokamaks may suffer from the isotope effect which does not happen in stellarators. At the same time, since the stellarator is a non-axisymmetric system while the tokamak is an axisymmetric system it can be manufactured from a greater number of possible combinations as the number of degrees of freedom is more. Furthermore, impurity retention in the diverter is much easier in stellarators due to the presence of a stochastic magnetic boundary. On the other hand, tokamaks are of much simpler design and are technically easier to make. It has lesser neoclassical transport while also combining stronger toroidal rotations. The plasma flow in the poloidal direction suffers from less damping effect which is highly effective. In addition, flow-shear is also stronger in tokamaks due to the powerful toroidal rotation of the magnetic field lines within the plasma.

Results

Stellarators have superiority over tokamaks and inertial confinement fusion. Firstly, stellarators have a greater range of flexibility, unlike tokamaks which generally have a fixed design. The helical magnetic field coils can be adjusted to produce different sizes and shapes. Secondly, stellarators consume much less power to confine and sustain the plasma than their tokamak counterparts¹⁵. This is because stellarators do need a power drive to stretch their pulses while tokamaks do which consumes immense amounts of energy. Thus, stellarators can provide electricity much more efficiently to the central grid rather than using electricity itself to sustain the plasma flow. Thirdly, stellarators are renowned for their steady state operation and benefit from a much lower rate of disruptions than tokamaks and laser fusion¹⁶. Unlike the tokamak, a toroidal field does not exist and this stops disruptions in the working of the reactor. The external stellarator field helps to minimize the effects of any disruptions occurring and allows the plasma to remain stable and avoid turbulences. Disruptions mainly arise due to current field lines produced by a toroidal field and since such a component is not present in stellarators, they are more proficient in controlling plasma which is the essence of nuclear reactions. Additionally, in comparison to inertial confinement fusion which allows fusion to occur in pulses, stellarators can work continually reducing the danger of sudden bursts due to accidents in aligning the lasers. Stellarators are also cost-effective albeit they are extremely complex.

Figure 4: Triple Product in m^-3 s keV as a function of peak temperature¹⁷

To undergo fusion, plasmas need to satisfy three requirements: they must attain a high temperature, a critical density, and enough time (Figure 4, 5). Collectively, these elements define the Lawson criterion or the triple product¹⁸. While the most promising stellarator the W7-X has a diameter of 16m, a height of 5m and weighs 725 tons, the ITER (International Thermonuclear Experimental Reactor) weighs a hefty 23000 tons and has a height of 6 times that of the stellarator (30m)¹⁹’²⁰. The sheer size makes manufacturing a tokamak a mammoth task in comparison to the stellarator.

Figure 5: Triple Product (fusion product) record for Wendelstein7-X stellarator²¹

Now, the most important comparison has come to hand which displays stellarator’s potential. In 2018 the fusion product of the stellarator reached well over 6*10²⁶ Celcius m^-3 s at a plasma temperature of just 40 million degrees Celcius (3.447 keV) at particle density of 0.8*10²⁰ particles per cubic meter. This is remarkable when taking into account the smaller size of the stellarator and the lower temperature used. The Wendelstein 7-X stellarator can be operated at temperatures of 130 million degrees Celcius (11.2 keV). At the same time, the divertor has been improved by replacing the graphite tiles by carbon-reinforced carbon components which will be able to make discharges for about 30 minutes (1800 s). In a stellarator, a divertor is tasked with ensuring a thorough removal of ash particles and energy across a broad spectrum of plasma and magnetic conditions. It serves as a protective barrier for the vacuum vessel which separates the outer layer of the plasma from the walls; thus creating a distinct plasma region. For the record break in 2018, the confinement during the production of energy was roughly 2 s. Now triple product is the product of temperature in keV, density of particles and confinement time (Triple Product= Temperature in keV* Density of particles per meter cube* Time in s). Converting 6*10²⁶ Celcius m^-3 s to keV m^-3 s for 2 seconds of confinement time at the conditions stated before gives roughly 5.5152*10²⁰ keV m^-3 s. However, recent developments for the stellarator have uplifted its potential. For a running time of 30 minutes (1800s) at 130 million degrees Celcius, with a particle density of 0.8*10²⁰paricles per cubic meter, the triple product turns out to be approximately 1.6128*10²⁴ keV m^-3 s, which is more than enough for the requirement for D-T power plant to be viable which is shown in Fig No. 4.

Calculation: Triple Product for Optimized stellarator= 11.2 keV * 0.8*10²⁰ m^-3 * 1800 s

= 1.6128*10²⁴ keV m^-3 s

It should be noted that Celsius was first converted to kelvin and then to keV for calculations³.

Figure 6: Fusion Reaction Rate as a Function of Temperature²²

Deuterium-Tritium fuel has been positively identified as being the most efficient fuel for fusion. While the reaction rate of deuterium-deuterium fuel rises consistently the rate of increase per temperature rise decreases and it surpasses deuterium-tritium at temperatures in excess of 10¹⁰ K which is too high a temperature to maintain properly for conventional stellarators (Figure 6). On the contrary, deuterium-tritium fuel achieves a high rate at temperatures less than 10⁹ K, which is a much favored temperature as both electrical costs to feed the reactor and the material cost to build the vacuum chamber will be reduced.

Figure 7: Stellarator Source: Max Planck Institute of Plasma Physics, Germany

The stellarator is its ability to reach a stable plasma state after ignition. While tokamaks are more capable of keeping plasma hot, stellarators are more capable at keeping the plasma stable²³. Also, crucial for a future fusion power plant, it can theoretically run for hours while tokamaks must stop periodically to reset their magnet coils. This is crucial for its promotion and integration into the electrical grid system and for it to be seen as viable by the government and public.

Figure 8: Parts of a Stellarator Source: Max Planck Institute of Plasma Physics, Germany

Due to the various advantages, available scientific works suggest that the stellarator be used more prominently in future projects. More funds should be available from regional and international organizations, especially ITER, to invest more in future research on the stellarator since tokamaks function by operating intermittently caused by pulses. At the same time, 100,000 kilometers or 62,000 miles of superconducting wires are used²³. The ITER fusion reactor weighs 23,000 tons and will cost its 35 member countries 63 billion dollars²⁴’²⁵. Against the backdrop, one could recommend to use a stellarator (Figure 7) which is used for magnetic confinement fusion to produce energy. The stellarator is more cost-effective than the tokamak and the main reason behind is the absence of the transformer. Unlike the tokamak, the stellarator does not require a transformer to induce a magnetic field. The magnetic field inside a stellarator is generated by the help of a single coil system. This removes the need for a transformer as there is no longitudinal net current. Consequently, stellarators are more convenient for continual work. Instead, by twisting the magnets, the helical plasma shape can be produced.

Discussion

The Working Mechanism of Tokamak and Stellarator

Tokamak, is a name of Russian origin which translates to “toroidal chamber with a magnetic coil”²⁶. The tokamak consists of a doughnut-shaped chamber in which the plasma is confined, typically called the torus. The chamber is vacuumed to prevent any form of disruption or contamination. Two isotopes of hydrogen, deuterium and tritium in gaseous form, are injected into the vacuum chamber to be used as fuel for plasma. The hydrogen fuel is then superheated to form plasma which generates energy. The internal component of the tokamak is shielded from this extreme heat by suspending the plasma using magnetic coils. While the toroidal coils surrounding the torus creates the toroidal magnetic field, the central solenoid which is an electromagnet (magnet through which electric current passes) generates a poloidal magnetic field. Both of these fields help in the confinement of plasma. Furthermore, another set of magnetic coils helps in the formation of a further poloidal field on the exterior of the 2 existing fields in order to restrict the plasma in a torus shape. Before the electromagnets are turned on and the hydrogen fuel is inserted, the air is pumped out to create the vacuum essential for plasma formation. Moreover, electric current is induced in the plasma which helps in ionizing the gas particles by stripping negatively charged electrons from the strong attraction of the positively charged nucleus. This is referred to as Ohmic heating. Additionally plasma is also kept hot through auxiliary heating which raises the temperature to operational levels. This is done by neutral beam injection or through high frequency electromagnetic waves. The plasma particles collide with one another and in this chaotic and turbulent environment, the plasma heats up even further reaching temperatures close to 150 million degrees Centigrade²⁷. At such high temperatures, the positively charged plasma particles overcome their natural repulsive forces and combine together to expel large amounts of energy.

A stellarator is a form of nuclear fusion reactor that is created to contain hot plasma by using magnetic fields to maintain a fusion reaction. It varies from the more widespread tokamak design in that it utilizes intricate, twisted magnetic fields to confine the plasma, removing the necessity for a large toroidal current. Hence stellarators do not require a transformer for it to work. A stellarator also uses a magnetic field to suspend the super-heated plasma in the chamber. Unlike the tokamak, the stellarator does not require a central solenoid to stabilize the magnetic fields holding the plasma. The stellarator utilizes a set of external coils which have an intricate helical shape in order to create the magnetic field. Even though they share the same conceptualization of tokamaks by using nested electromagnetic surfaces to confine plasma, a net toroidal current through the plasma is not present in stellarators. Furthermore, they have an added advantage of inherent steady-state operation and do not suffer from disruptions as plasma particles do not wander off course. A stellarator mainly consists of a helical coil which holds the toroidal plasma in place. At the same time, the appropriateness of helical systems in fusion reactors has been doubted from a technical standpoint as they are challenging to manufacture and used near to their technical boundaries: hence, a modular design centered on a collection of single coils is crucial for smooth functioning. Consequently, the modular coils are non-planar as they provide the poloidal magnetic field which further helps in optimization.

Since stellarators always use magnets outside the plasma for suspension they do not suffer from plasma terminating instabilities. At the same time, this helps to remove the requirement for an external current drive or a transformer to stabilize the plasma. Stellarators do not have Ohmic heating as there is no central current. Like the tokamak, plasma heating is achieved by injecting high energy neutral particles into the plasma. This works by generating and speeding up an ion beam outside the containment barrier. The beam is then made neutral through a process known as charge exchange before it is transmitted into the plasma. Upon entering the plasma, the beam is ionized once again and the neutral particles are held in place by the strong magnetic field. The energy from the subsequent collisions is then spread out, leading to an increase in plasma temperature. A stellarator normally possesses a high aspect ratio and does not need costly auxiliary magnets for shaping the magnetic field, coils for controlling plasma position and power supplies for the current drive. Its unconventional design due to the configuration of its coils allows access from every direction. This in turn assists in a more flexible approach for designing the blanket and the shield²⁸.

Based on previous research by International Thermonuclear Experimental Reactor (ITER), Institute of Accelerating Systems and Applications (IASA), and other organizations for nuclear energy, the question is how a nuclear fusion reactor can be designed that not only produces more energy than it consumes and can sustainably operate for longer periods. ITER aims to achieve a value of Q $\geq$ 10 by 2025²⁹. The current world record for sustained plasma is held by 1,056 seconds, or 17 minutes and 36 seconds, by the EAST Tokamak in Hefei, China³⁰.

The tokamak (Figure 9) is one of the devices that can be used for magnetic confinement fusion. It is one of the two most prominent designs that may help us achieve sustainable nuclear fusion power in the future. The electric field which is produced by the transformer directs a current inside the plasma loop, indicated by the red arrows in the diagram below. The poloidal magnetic field produced helps to sustain the plasma material in a loop. By doing so, leakage is prevented and consequently due to the circular shape of the containment a vacuum is created. Apart from that the other magnetic field throughout the length of the reactor is said to be toroidal (like a doughnut; see green horizontal ring). When the Tokamak is operational, it creates helical magnetic field lines³¹. A tokamak has several parts that are required for it to operate.

Figure 9: Tokamak Source: Max Planck Institute of Plasma Physics, Germany

One of the parts is the breeding blanket. It is a layer of lithium that surrounds the torus. When the plasma in the center releases neutrons, it absorbs the energy and prevents any sensitive areas of the reactor from being damaged. This energy powers a steam turbine, providing usable energy³². The neutrons are then reused by reacting with lithium and producing tritium, which is reused as reactor fuel. For the stability of the reactions, it is important to maintain vertical magnetic fields acting on the system. This is done by the poloidal coils, which are large rings encircling the entire torus and usually large structures. The neutrons emitted during deuterium-tritium fusion reaction have an energy of 14.07 MeV.

The equation is as follows: D+T= n (14.07 MeV) + ⁴He (3.52 MeV) where 1 eV= 1.6*10^-19 J³³.

The total number of turns of coils varies according to the size and shape of the reactor and also how it is designed. The number of turns of coils depends on the current strength which holds the plasma. One example the SMART tokamak is one reactor that has 12 coils in series and taking into account that it consists of 4 turns; the total number of turns adds up to 48. On the other hand, the giant ITER tokamak has 18 coils which make up the toroidal field and 6 poloidal coils for the poloidal electromagnet³⁴’³⁵’³⁶.

Central solenoid magnet of tokamak creates the initial magnetic flux change responsible for starting the plasma, generating the plasma current and maintaining the plasma current during the burning. It is composed of six coil packs made of niobium-tin superconducting cable and held by a vertical pre-compression structure³⁷. The temperature at which the plasma state is suitable for operation is 150 million degrees Celsius. The main purpose of the six coil packs of niobium-tin is to act as extremely strong magnets, thereby helping to confine and direct the ionized plasma in the reactor³⁸.

Tokamak also uses a toroidal field magnet which is a hollow circular ring in the shape of a doughnut that has many turns of enameled wire which are wound so close to each other that there is negligible space between the two turns. It is wound around the outside of the tokamak. In the toroidal field magnet, the spiraling mass of wires helping to generate the toroid creating a magnetic field directed in the same bearing as the toroid³¹. To confine and suspend the super-heated plasma so that it does vaporize the components, electromagnets are vital components which include both the toroidal and poloidal magnets. The wires supply current to the magnets which helps to induce the magnetic field. However, an important factor has to be considered and that is resistance to the current. All metal substances, iron, nickel and niobium have electrical resistance due to their characteristic resistivity. This severely affects the strength of the magnetic field as the current flow is reduced and some is lost as heat. Hence tokamaks apply the action of ‘superconductivity’ in their electromagnets. As the mass of wires is connected to virtually every magnetic component, the temperature is reduced to -270 degree C. This is because, at this temperature, the niobium-titanium alloys which are used for the wires in the electromagnets become superconducting. Superconductivity is the phenomenon when the electrical resistance in the wires and electromagnets becomes virtually non-existent which allows the strongest magnetic fields to be generated. At the same time, no additional thermal energy is lost from the magnets or the wires which might otherwise affect performance³⁹.

It should be noted that, magnetic field intensity is defined as the force exerted on one-unit north -pole in a magnetic field⁴⁰. In simple words, it describes how strong or weak a magnetic field is. Furthermore, magnetic induction is defined as the total quantity of magnetic field line of force lines passing through per unit area of a substance

A vacuum chamber of tokamak is mostly a fixed area from which air and other gases are removed by a vacuum pump. During nuclear fusion, huge amounts of tritium and deuterium protons cause a large emission of neutral particles. Without removing these neutral particles, it will be impossible to stop the cooling of plasma³¹. Plasma is cooled in very similar methods in both tokamaks and stellarators. Cooling the super-heated plasma continuously emitting neutrons is as challenging as confining it. To cool the plasma a method known as quenching is used. In general, there are two ways of quenching a reactor. In the first method, large volumes of gas is pumped into the plasma which gradually cools the plasma from the exterior and eventually the inside of the plasma. Sometimes a cryogenically frozen solid can also be used. Another method is inserting diamond shells at very high speeds (hundreds of kilometers per hour) into the interior of plasma which initiates cooling from the inside as opposed to using gas. The diamond immediately vaporizes to create a large chunk of boron which helps in cooling the plasma from the inside to the outside. This is how the cooling and eventual shutdown of both stellarators and tokamaks occur⁴¹.

Methods

To make the stellarator more popular among public opinion against its cousin the tokamak, various prospects for its efficient integration into the electrical grid can be presented. Various improvements can be carried out to further the cause of stellarators. Some of them are⁴²’⁴³.

A) Enhanced coil configuration

In the past, the helical coils of the stellarator were first designed and fitted together according to conventional designs and then plasma properties inside the stellarator were tested. This, which can already be attested, was an inefficient process and would in time turn too costly. Nowadays, advanced computer modelling has helped in manufacturing more accurate coils. Significant enhancements to coil design encapsulated in a revised model known as the COILOPT++ have been utilized to create coil designs that align with a broad maintenance scheme. Integrating specific engineering limitations into the optimization process is crucial in this approach, which has since been adapted to utilize spline representations of the coils instead of Fourier models. In order to handle higher current densities and greater magnetic fields than traditional superconductors, high Tc superconducting tapes can be used. This also allows greater adaptability for cooling systems needed to cool the plasma once the system shuts down and hence will allow a significant reduction of the size of coil windings. This will inevitably bring down the costs and complexity of the whole system. The new conductors also involve further unique benefits for non-axisymmetric plasmas. For instance, the minimum local radius of curvature, often a challenge for stellarator coils, is eased by an increased current density. This eventually allows the use of thinner coils and hence reduces the curvature constraint. Another key factor in the complexity of the stellarator is the fact that the coils require to be positioned relatively near to the plasma compared to the tokamak. This requirement for close proximity of the coils is due to the weakening of the magnetic field as the distance from the coils increases. This also implies that as the distance between the plasma and the coil increases, the deviation of the coils from a flat plane must also increase significantly. This is crucial as a gap is needed between the plasma and the coils for the blanket and neutron shield. The blanket and the neutron shield reduce the strength of the magnetic field as they act as obstructions and also increase the distance. In fact, in the study of the ARIES-CS reactor, the “plasma-coil separation” was remarked as the most critical factor which influenced the size and cost of stellarators. Nevertheless, the maximum distance between the plasma and the coils is directly related to the shape of the plasma. Plasma shapes with concave areas necessitate coils that are very close together, whereas shapes with convex cross-sections allow increased distance of the coils from the plasma chamber. Several new approaches were introduced to magnetic field efficiency, which is known as the efficiency sequence and feasibility sequence. These measures can be utilized to identify efficient shapes which will aid in the “optimization of shape” to reduce the necessity for close plasma coil separation.

B) Divertor design

In a stellarator, a divertor is tasked with ensuring a thorough removal of ash particles and energy across a broad spectrum of plasma and magnetic conditions. It serves as a protective barrier for the vacuum vessel which separates the outer layer of the plasma from the walls; thus creating a distinct plasma region. Consequently, this allows for the majority of the interactions between the plasma and the material to occur near the target plates and the gap between the pumps, without significant altercations to the plasma core. In case of tokamaks, the two-dimensional poloidal divertor provides a clear boundary for the plasma’s private region, which is separated from the main plasma. On the other hand, stellarators with their three-dimensional magnetic structures, necessitate a three-dimensional divertor with a more complex arrangement of connections outside the separatrix and a dynamic or random behavior within the private plasma region.

There are 2 primary approaches to divertor design in modern stellarators: (1) resonant or island diverters, which are found in W7-X example, and (2) non-resonant diverters that leverage the strong plasma shaping characteristic of well-optimized stellarators. Resonant diverters require less space than non-resonant diverters in the plasma chamber but also place the diverter strike points very close to the plasma, which complicates shielding. From a design perspective, the diverter is intricately linked to all aspects of coil geometry, plasma turbulence and the power exhaust for fast particles. To be effective, the design of the divertor must be integrated into the optimization process. The shape of the diverter and, eventually, the diverter chamber deeply influences the vacuum vessel’s shape, which in turn affects coil geometry, the magnetic field and plasma flow. Additionally, several divertor components must be housed within the vacuum vessel, such as all components facing the plasma, cooling ducts, cryo-pumps and possibly additional divertor control coils.

It is essential to include the diverter design in the optimization of stellarators necessitates the incorporation of codes capable of handling diverter heat loads. The most straightforward method is to employ field line tracing with diffusion to model particle trajectories as they approach the divertor plates. This technique has been successfully applied to the modeling of diverter heat loads for the W7-X example giving an optimized configuration.

C) Confining high-energy ions within the vacuum chamber

A functional magnetic fusion reactor will require the ability to hold alpha particles long enough for them to transfer most of their energy to the primary species. Achieving this goal is more difficult for non-axisymmetric designs compared to their axisymmetric counterparts. Axisymmetric ensures the conservation of canonical angular momentum, which means that all particle paths are confined within a specific magnetic field without collisions or turbulence. However, in non-axisymmetric plasmas, the lack of such a conservation law means that particle paths may not always be confined. For thermal particles, the issue is somewhat mitigated by the collision less detrapping that occurs with poloidal ExB drift, but for high-speed particles, this beneficial process is less effective due to a smaller ratio of ExB to parallel speed. The challenge of containing high-speed particles is clearly illustrated in which found that nearly all trapped alpha particles were lost in less than 10-4 to 10-3 seconds in simulations of a conventional (not optimized) l=2 stellarator and of W7-AS. For comparison, the required time to confine alpha particles for typical reactor conditions is estimated to be at least 0.1 seconds. The confinement of high-speed particles in modern optimized designs such as W7-X and NCSX has seen significant improvements over conventional stellarators but remains a key challenge for the concept. Alpha confinement was identified as one of the most significant concerns in the ARIES-CS reactor study. Despite the ARIES design’s success in reducing alpha losses to 5% over a slowing-down time. Neoclassical optimization naturally enhances the confinement of high-speed particles, but the considerations for both thermal and high-speed particle confinement differ. Targets for neoclassical optimization such as the effective helical ripple, are typically based on small particle orbit widths, which is often not the case for high-speed particles. This means that the finite orbit width of particles must be considered. Additionally, alpha particles are frequently found near the magnetic axis, making the effects of finite orbit width particularly significant. Furthermore, neoclassical transport calculations assume a Maxwellian distribution function, whereas the distribution function of fast particles is often far from Maxwellian. While collisions are crucial for neoclassical confinement, they are less relevant for the confinement of high-speed particles, and vice versa for poloidal magnetic drift.

D) Additional Improvements

Ease of maintenance of stellarator magnets for better upkeep.
Building experimental setups to confirm the accuracy of turbulence calculations in stellarators, thereby increasing trust in utilizing turbulence as a key design factor.
Development of instruments and plans for achieving confinement of alpha particles relevant to reactors.
Addressing the issue of materials by incorporating divertor design into the stellarator optimization strategy.

Figure 10: Wendelstein 7-X Stellarator, Source: Max Planck Institute of Plasma Physics, Germany

Moreover, the electromagnet’s temperature can be reduced to as low as -269 Celsius to increase its magnetic superconductivity and contain plasma more efficiently⁴⁴. The magnets need to contain plasma with a precision of 0.001 m or 1 mm or else the fusion will stop⁴⁵. Lowering the temperature closer to absolute zero will strengthen the toroidal and the helical magnetic field and hence will be able to contain the plasma more easily while maintaining the plasma at temperatures of 15 million degrees Celsius⁴⁶. This produces the largest temperature gradients in the known Universe. Using a stellarator, a single glass of seawater can produce as much as a barrel of oil whilst producing no waste or pollution⁴⁷.

At the same time, the goal is to promote the use of tritium atoms which are hydrogen atoms containing 1 proton and 2 neutrons which will make collisions more successful. Though tritium is radioactive, which if leaked into the atmosphere may combine with oxygen to produce radioactive water, its low concentrations mean that it will become diluted⁴⁸. At any one time, our world contains about 20 kilograms of tritium. Most of the available tritium is concentrated in nuclear warheads. Until that is approved, the use of deuterium is recommended as it is both stable and found in abundance in seawater (33 gm/m³)⁴⁹.

The stellarator works without using a transformer and running costs are much lower as a result. Instead of heating the plasma by driving an electric current as plasma being an electrical conductor undergoes heating due to current flowing through as a result of electrical resistance or by high-frequency electromagnetic waves the heating is to be carried out using neutral particles. This is done by using a neutral particle beam injector which makes ions and accelerates them with an electric field.

The ions are made non-charged to avoid interference from the stellarator’s magnetic field. Their significant energy is transferred to the plasma particles through interactions leading to heating. In the design phase, the magnets must be shielded from the 14.1 MeV neutrons generated by the fusion reactions. This is typically done with a breeding blanket, a material layer rich in lithium. To capture most of the neutrons, the blanket must be at least 1 to 1.5 meters thick, which necessitates stronger magnets than those used in experimental setups, which are placed around the vacuum chamber’s exterior. This can be achieved by increasing the size of the machine to extremely large dimensions, such that the ~10-centimeter gap in smaller machines is proportionally reduced to about 1 meter. The intricate configuration of the stellarator’s twisted magnets is crucial for generating the desired magnetic field.

Conclusion

Based on the available scientific works and data at hand, we could suggest that nuclear fusion is more efficient and useful, as it is a clean source of energy that helps humanity to reduce carbon emissions and mitigate the effects of global warming in the future. (20) To achieve this, it was needed in both units (Stellarator and Tokamak) to maintain a Q- gain factor for nuclear reactors bigger than 1 (Q $>$ 1) for longer periods of time in order to achieve sustainability. We saw two possible reactors that could be used for this, Tokamak and Stellarator, and comparing them, it was possible to determine that the Stellarator was the best option, as it provides more stability and can confine the reactions for longer periods. Although there are various benefits, there are still a lot of challenges to face in order to increase the number of stellarators used in the world. It is very hard to build and maintain them, and not every country has the necessary resources to make them. However, it is still important to keep studying and researching these reactions to produce energy.

Acknowledgement

The first draft of this paper is written during Yale Young Global Scholar Program, Session 3: Innovations in Science and Technology, July 16- July 28, 2023, as part of the Capstone Project. Corresponding author: Rayan Abdullah Khan, rayanabdullahkhan2009@gmail.com.

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