Editing Stellarator (section)

== Concepts ==
=== Requirements for fusion ===
Heating a gas increases the energy of the particles within it, so by heating a gas into hundreds of millions of degrees, the majority of the particles within it reach the energy required to fuse. 

According to the [[Maxwell–Boltzmann distribution]], some of the particles will reach the required energies at much lower average temperatures. Because the energy released by the fusion reaction is much greater than what it takes to start it, even a small number of reactions can heat surrounding fuel until it fuses as well. In 1944, [[Enrico Fermi]] calculated the D–T reaction would be self-sustaining at about {{val|50000000|u=K}}.{{sfn|Asimov|1972|p=123}}

Materials heated beyond a few tens of thousand degrees ionize into their [[electron]]s and [[atomic nucleus|nuclei]], producing a gas-like [[state of matter]] known as [[plasma (physics)|plasma]]. According to the [[ideal gas law]], like any hot gas, plasma has an internal [[pressure]] and thus wants to expand.{{sfn|Bishop|1958|p=7}} For a fusion reactor, the challenge is to keep the plasma contained. In a magnetic field, the electrons and nuclei orbit around the magnetic field lines, confining them to the area defined by the field.{{sfn|Thomson|1958|p=12}}{{sfn|Bishop|1958|p=17}}

=== Magnetic confinement ===
A simple confinement system can be made by placing a tube inside the open core of a [[solenoid]]. The tube can be evacuated and then filled with the requisite gas and heated until it becomes a plasma. The plasma naturally wants to expand outwards to the walls of the tube, as well as move along it, towards the ends. The solenoid creates magnetic field lines running down the center of the tube, and the plasma particles orbit these lines, preventing their motion towards the sides. Unfortunately, this arrangement would not confine the plasma along the ''length'' of the tube, and the plasma would be free to flow out the ends.{{sfn|Spitzer|1958}}

The obvious solution to this problem is to bend the tube around into a [[torus]] (a ring or donut) shape.{{sfn|Spitzer|1958}} Motion towards the sides remains constrained as before, and while the particles remain free to move along the lines, in this case, they will simply circulate around the long axis of the tube. But, as Fermi pointed out,{{efn|[[Andrei Sakharov]] also came to the same conclusion as Fermi as early as 1950, but his paper on the topic was not known in the west until 1958.{{sfn|Furth|1981|p=275}}}} when the solenoid is bent into a ring, the electrical windings would be closer together on the inside than the outside. This would lead to an uneven field across the tube, and the fuel will slowly drift out of the center. Since the electrons and ions would drift in opposite directions, this would lead to a charge separation and electrostatic forces that would eventually overwhelm the magnetic force. Some additional force needs to counteract this drift, providing long-term ''confinement''.{{sfn|Bromberg|1982|p=16}}{{sfn|Spitzer|1958}}

=== Stellarator concept ===
Spitzer's key concept in the stellarator design is that the drift that Fermi noted could be canceled out through the physical arrangement of the vacuum tube. In a torus, particles on the inside edge of the tube, where the field was stronger, would drift up, while those on the outside would drift down (or vice versa). However, if the particle were made to alternate between the inside and outside of the tube, the drifts would alternate between up and down and would cancel out. The cancellation is not perfect, leaving some net drift, but basic calculations suggested drift would be lowered enough to confine plasma long enough to heat it sufficiently.{{sfn|Spitzer|1958|p=181}}

Spitzer's suggestion for doing this was simple. Instead of a normal torus, the device would essentially be cut in half to produce two half-tori. They would then be joined with two straight sections between the open ends. The key was that they were connected to alternate ends so that the right half of one of the tori was connected to the left of the other. The resulting design resembled a figure-8 when viewed from above. Because the straight tubes could not pass through each other, the design did not lie flat, the tori at either end had to be tilted. This meant the drift cancellation was further reduced, but again, calculations suggested the system would work.{{sfn|Spitzer|1958|pp=182-183}}

To understand how the system works to counteract drift, consider the path of a single particle in the system starting in one of the straight sections. If that particle is perfectly centered in the tube, it will travel down the center into one of the half-tori, exit into the center of the next tube, and so on. This particle will complete a loop around the entire reactor without leaving the center. Now consider another particle traveling parallel to the first, but initially located near the inside wall of the tube. In this case, it will enter the ''outside'' edge of the half-torus and begin to drift down. It exits that section and enters the second straight section, still on the outside edge of that tube. However, because the tubes are crossed, when it reaches the second half-torus it enters it on the ''inside'' edge. As it travels through this section it drifts back up.{{sfn|Spitzer|1958|p=183}}

This effect would reduce one of the primary causes of drift in the machine, but there were others to consider as well. Although the ions and electrons in the plasma would both circle the magnetic lines, they would do so in opposite directions, and at very high rotational speeds. This leads to the possibility of collisions between particles circling different lines of force as they circulate through the reactor, which due to purely geometric reasons, causes the fuel to slowly drift outward. This process eventually causes the fuel to either collide with the structure or cause a large charge separation between the ions and electrons. Spitzer introduced the concept of a ''divertor'', a magnet placed around the tube that pulled off the very outer layer of the plasma. This would remove the ions before they drifted too far and hit the walls. It would also remove any heavier elements in the plasma.{{sfn|Spitzer|1958|p=188}}

Using classical calculations the rate of diffusion through collisions was low enough that it would be much lower than the drift due to uneven fields in a normal toroid. But earlier studies of magnetically confined plasmas in 1949 demonstrated much higher losses and became known as [[Bohm diffusion]]. Spitzer spent considerable effort considering this issue and concluded that the anomalous rate being seen by Bohm was due to instability in the plasma, which he believed could be addressed.<ref>{{cite journal |last1=Spitzer |first1=L. |year=1960 |title=Particle Diffusion across a Magnetic Field |journal=Physics of Fluids |volume=3 |issue=4 |pages=659–651 |bibcode=1960PhFl....3..659S |doi=10.1063/1.1706104}}</ref>

=== Alternative designs ===
One of the major concerns for the original stellarator concept is that the magnetic fields in the system will only properly confine a particle of a given mass traveling at a given speed. Particles traveling faster or slower will not circulate in the desired fashion. Particles with very low speeds (corresponding to low temperatures) are not confined and can drift out to the tube walls. Those with too much energy may hit the outside walls of the curved sections. To address these concerns, Spitzer introduced the concept of a ''divertor'' that would connect to one of the straight sections. This was essentially a [[mass spectrometer]] that would remove particles that were moving too fast or too slow for proper confinement.{{sfn|Spitzer|1958|p=188}}

The physical limitation that the two straight sections cannot intersect means that the rotational transform within the loop is not a perfect 180 degrees, but typically closer to 135 degrees. This led to alternate designs in an effort to get the angle closer to 180. An early attempt was built into the Stellarator B-2, which placed both curved sections flat in relation to the ground, but at different heights. The formerly straight sections had additional curves inserted, two sections of about 45 degrees, so they now formed extended S-shapes. This allowed them to route around each other while being perfectly symmetrical in terms of angles.

A better solution to the need to rotate the particles was introduced in the Stellarator B-64 and B-65. These eliminated the cross-over and flattened the device into an oval, or as they referred to it, a racetrack. The rotation of the particles was introduced by placing a new set of magnetic coils on the half-torus on either end, the ''corkscrew windings''. The field from these coils mixes with the original confinement fields to produce a mixed field that rotates the lines of force through 180 degrees. This made the mechanical design of the reactor much simpler, but in practice, it was found that the mixed field was very difficult to produce in a perfectly symmetrical fashion.

Modern stellarator designs generally use a more complex series of magnets to produce a single shaped field. This generally looks like a twisted ribbon. Differences between the designs generally come down to how the magnets are arranged to produce the field, and the exact arrangement of the resulting field. A wide variety of layouts have been designed and some of these have been tested.

=== Heating ===
Unlike the [[z-pinch]] or tokamak, the stellarator has no induced electrical current within the plasma – at a macroscopic level, the plasma is neutral and unmoving, in spite of the individual particles within it rapidly circulating. In pinch machines, the current itself is one of the primary methods of heating the plasma. In the stellarator, no such natural heating source is present.

Early stellarator designs used a system similar to those in the pinch devices to provide the initial heating to bring the gas to plasma temperatures. This consisted of a single set of windings from a [[transformer]], with the plasma itself forming the secondary set. When energized with a pulse of current, the particles in the region are rapidly energized and begin to move. This brings additional gas into the region, quickly ionizing the entire mass of gas. This concept was referred to as ''ohmic heating'' because it relied on the resistance of the gas to create heat, in a fashion not unlike a conventional [[electric heating|resistance heater]]. As the temperature of the gas increases, the conductivity of the plasma improves. This makes the ohmic heating process less and less effective, and this system is limited to temperatures of about 1 million kelvins.{{sfn|Spitzer|1958|p=187}}

To heat the plasma to higher temperatures, Spitzer proposed a second heat source, the ''magnetic pumping'' system. This consisted of radio-frequency source fed through a coil spread along the vacuum chamber. The frequency is chosen to be similar to the natural frequency of the particles around the magnetic lines of force, the ''[[cyclotron frequency]]''. This causes the particles in the area to gain energy, which causes them to orbit in a wider radius. Since other particles are orbiting their own lines nearby, at a macroscopic level, this change in energy appears as an increase in pressure.{{sfn|Spitzer|1958|p=188}} According to the [[ideal gas law]], this results in an increase in temperature. Like ohmic heating, this process also becomes less efficient as the temperature increases, but is still capable of creating very high temperatures. When the frequency is deliberately set close to that of the ion circulation, this is known as ''ion-cyclotron resonance heating'',{{sfn|Spitzer|1958|p=189}} although this term was not widely used at the time.

=== Inherent problems ===
Work on the then-new tokamak concept in the early 1970s, notably by [[Tihiro Ohkawa]] at [[General Atomics]], suggested that toroids with smaller ''[[aspect ratio]]s'' and non-circular plasmas would have much-improved performance.{{sfn|Bromberg|1982|p=164}} The aspect ratio is the comparison of the radius of the device as a whole to the radius of the cross-section of the vacuum tube. An ideal reactor would have no hole in the center, minimizing the aspect ratio. The modern [[spherical tokamak]] takes this to its practical limit, reducing the center hole to a single metal post, elongating the cross-section of the tubing vertically, producing an overall shape that is nearly spherical and has a ratio less than 2. The [[Mega Ampere Spherical Tokamak|MAST]] device in the UK, among the most powerful of these designs, has a ratio of 1.3.<ref>{{cite conference |url=https://www.researchgate.net/publication/260451493 |title= The upgrade to the Mega Amp Spherical Tokamak |last1= Stork |first1=Derek |last2= Meyer |first2= Hendrik |date= January 2010 |publisher= |book-title= |pages= |location=Daejon |conference= Proceedings of the 23rd International Conference on Fusion Energy |id=}}</ref>

Stellarators generally require complex magnets to generate the desired field. In early examples, this was often in the form of several different sets of magnets stacked. While modern designs combine these together, the resulting designs often require significant room around them. This limits the size of the inner radius to something much larger than seen in modern tokamaks, so they have relatively large aspect ratios. For instance, W7-X has an aspect ratio of 10,<ref>{{cite journal |first=Friedrich |last=Wagner |journal=Europhysics News |date=1995 |pages=3–5 |title=The W7-X Stellarator Project|volume=26 |issue=1 |doi=10.1051/epn/19952601003 |bibcode=1995ENews..26....3W |url=https://www.europhysicsnews.org/articles/epn/pdf/1995/01/epn19952601p3.pdf|doi-access=free }}</ref> which leads to a very large overall size. There are some new layouts that aim to reduce the aspect ratio, but these remain untested {{asof|2023|lc=yes}} and the reduction is still nowhere near the level seen in modern tokamaks.{{sfn|Landreman|Boozer|2017|p=1}}

In a production design, the magnets would need to be protected from the 14.1&nbsp;MeV [[neutron]]s being produced by the fusion reactions. This is normally accomplished through the use of a [[breeding blanket]], a layer of material containing large amounts of [[lithium]]. In order to capture most of the neutrons, the blanket has to be about 1 to 1.5 meters thick, which moves the magnets away from the plasma and therefore requires them to be more powerful than those on experimental machines where they line the outside of the vacuum chamber directly. This is normally addressed by scaling the machine up to extremely large sizes, such that the ~10&nbsp;centimetre separation found in smaller machines is linearly scaled to about 1 meter. This has the effect of making the machine much larger, growing to impractical sizes.{{sfn|Landreman|Boozer|2017|p=1}} Designs with smaller aspect ratios, which scale more rapidly, would address this effect to some degree, but designs of such systems, like ARIES-CS, are enormous, about 8 meters in radius with a relatively high aspect ratio of about 4.6.<ref>{{cite journal |journal=Fusion Science and Technology |first=F. |last= Najmabadi |date=2008 |volume=54 |issue=3 |title=The ARIES-CS Compact Stellarator Fusion Power Plant |pages=655–672 |url=https://www.tandfonline.com/doi/abs/10.13182/FST54-655 |doi=10.13182/FST54-655|bibcode=2008FuST...54..655N |s2cid=8620401 |url-access=subscription }}</ref>

The stellarator's complex magnets combine together to produce the desired field shape. This demands extremely tight positioning tolerances which drive up construction costs. It was this problem that led to the cancellation of the US's [[National Compact Stellarator Experiment]], or NCSX, which was an experimental low-aspect design with a ratio of 4.4. To work properly, the maximum deviation in placement across the entire machine was {{val|1.5|u=mm}}. As it was assembled this was found to be impossible to achieve, even the natural sagging of the components over time was more than the allowed limit. Construction was cancelled in 2008, throwing the future of the PPPL into doubt.<ref name=Orbach2008>{{cite web |url=http://ncsx.pppl.gov//DOE_NCSX_052208.pdf |title=Future of the Princeton Plasma Physics Laboratory (PPPL), Statement by Dr. Raymond L. Orbach, Under Secretary for Science and Director, Office of Science, U.S. Department of Energy |date=22 May 2008}}</ref>

Finally, stellarator designs are expected to leak around 5% of the generated [[alpha particle]]s, increasing stress on the plasma-facing components of a reactor.{{sfn|Landreman|Boozer|2017|p=2}}