The polywell is a proposed design for a fusion reactor using an electric and magnetic field to heat ions to fusion conditions.

The design is related to the fusor, the high beta fusion reactor, the magnetic mirror, and the biconic cusp. A set of electromagnets generates a magnetic field that traps electrons. This creates a negative voltage, which attracts positive ions. As the ions accelerate towards the negative center, their kinetic energy rises. Ions that collide at high enough energies can fuse.

Mechanism

Fusor Heating

A Farnsworth-Hirsch fusor consists of two wire cages, one inside the other, often referred to as grids, that are placed inside a vacuum chamber. The outer cage has a positive voltage versus the inner cage. A fuel, typically, deuterium gas, is injected into this chamber. It is heated past its ionization temperature, making positive ions. The ions are positive and move towards the negative inner cage. Those that miss the wires of the inner cage fly through the center of the device at high speeds and can fly out the other side of the inner cage. As the ions move outward, a Coulomb force impels them back towards the center. Over time, a core of ionized gas can form inside the inner cage. Ions pass back and forth through the core until they strike either the grid or another nucleus. Most nucleus strikes do not result in fusion. Grid strikes can raise the temperature of the grid as well as eroding it. These strikes conduct mass and energy away from the plasma, as well as spall off metal ions into the gas, which cools it.

In fusors, the potential well is made with a wire cage. Because most of the ions and electrons fall onto the cage, fusors suffer from high conduction losses. Hence, no fusor has come close to energy break-even.

Diamagnetic Plasma Trapping

The Polywell is attempting to hold a diamagnetic plasma - a material which rejects the outside magnetic fields created by the electromagnets. This kind of behavior is not normal for fusing plasmas.

• Most plasma in most fusion reactors (such as Magnetic mirrors, tokamaks and Stellerators) are considered magnetized. A Magnetized plasma occurs when the external field is so strong that it completely penetrates and controls the plasma, such that the material behavior is dominated by the external field.
• Some fusion plasmas are self-magnetized (such as field-reversed configurations, or Dynomaks) all of which can create their own weak magnetic fields through the formation of loops of plasma currents and other structures.

But both the Polywell and the high beta fusion reactor are pre-supposes that the plasma self-generated field is so strong that it will reject the outside field. Bussard later called this type of confinement the Wiffle-Ball. This analogy was used to describe electron trapping inside the field. Marbles can be trapped inside a Wiffle ball, a hollow, perforated sphere; if marbles are put inside, they can roll and sometimes escape through the holes in the sphere. The magnetic topology of a high-beta polywell acts similarly with electrons. In June 2014 EMC2 published a preprint^[3] providing (1) x-ray and (2) flux loop measurements that the diamagnetic effect will impact the external field.

This figure shows the development of the proposed "wiffle ball" confinement concept. Three rows of figures are shown: the magnetic field, the electron motion and the plasma density inside the polywell. (A) The field is the superposition of six rings in a box. In the center is a null point - a zone of no magnetic field.^[4] The plasma is magnetized, meaning that the plasma and magnetic field intermix. (B) As plasma is injected, the density rises. (C) As the plasma density rises, the plasma becomes more diamagnetic, causing it to reject the outside magnetic field. As the plasma presses outwards, the density of the surrounding magnetic field rises. This tightens the corkscrewing motion of the particles outsides the center. A sharp boundary is formed.^[3] A current is predicted^[5][6] to form on this boundary. (D) If the pressures find equilibrium at a beta of one, this determines the shape of the plasma cloud. (E) In the center, there is no magnetic field from the rings. This means that its motion inside the field free radius should be relatively straight or ballistic.^[4]

According to Bussard, typical cusp leakage rate is such that an electron makes 5 to 8 passes before escaping through a cusp in a standard mirror confinement biconic cusp; 10 to 60 passes in a polywell under mirror confinement (low beta) that he called cusp confinement; and several thousand passes in Wiffle-Ball confinement (high beta).^[7][8]

In February 2013, Lockheed Martin Skunk Works announced a new compact fusion machine, the high beta fusion reactor,^[9][10] that may be related to the biconic cusp and the polywell, and working at β = 1.

Other Trapping Mechanisms

Magnetic mirror

Magnetic mirror dominates in low beta designs. Both ions and electrons are reflected from high to low density fields. This is known as the magnetic mirror effect.^[11] The polywell's rings are arranged so the densest fields are on the outside, trapping electrons in the center. This can trap particles at low beta values.

Cusp confinement

In high beta conditions, the machine may operate with cusp confinement.^[12] This is an improvement over the simpler magnetic mirror.^[13] The MaGrid has six point cusps, each located in the middle of a ring; and two highly modified line cusps, linking the eight corner cusps located at cube vertices. The key is that these two line cusps are much narrower than the single line cusp in magnetic mirror machines, so the net losses are less. The two line cusps losses are similar to or lower than the six face-centered point cusps.^[14] In 1955, Harold Grad theorized that a high-beta plasma pressure combined with a cusped magnetic field would improve plasma confinement.^[5] A diamagnetic plasma rejects the external fields and plugs the cusps. This system would be a much better trap.

Cusped confinement was explored theoretically^[6] and experimentally.^[15] However, most cusped experiments failed and disappeared from national programs by 1980.

Beta in Magnetic Traps

Magnetic fields exert a pressure on the plasma. Beta is the ratio of plasma pressure to the magnetic field strength. It can be defined separately for electrons and ions. The polywell concerns itself only for the electron beta, whereas the ion beta is of greater interest within Tokamak and other neutral-plasma machines. The two vary by a very large ratio, because of the enormous difference in mass between an electron and any ion. Typically, in other devices the electron beta is neglected, as the ion beta determines more important plasma parameters. This is a significant point of confusion for scientists more familiar with more 'conventional' fusion plasma physics.

Note that for the electron beta, only the electron number density and temperature are used, as both of these, but especially the latter, can vary significantly from the ion parameters at the same location.

${\displaystyle \beta _{e}={\frac {p}{p_{mag}}}={\frac {n_{e}k_{B}T_{e}}{(B^{2}/2\mu _{0})}}}$^[16]

Most experiments on polywells involve low-beta plasma regimes (where β < 1),^[17] where the plasma pressure is weak compared to the magnetic pressure. Several models describe magnetic trapping in polywells.^{[citation needed]} Tests indicated that plasma confinement is enhanced in a magnetic cusp configuration when β (plasma pressure/magnetic field pressure) is of order unity. This enhancement is required for a fusion power reactor based on cusp confinement to be feasible.^[18]

Design

The main problem with the fusor is that the inner cage conducts away too much energy and mass. The solution, suggested by Robert Bussard and Oleg Lavrentiev,^[19] was to replace the negative cage with a "virtual cathode" made of a cloud of electrons.

A polywell consists of several parts. These are put inside a vacuum chamber^[20]

• A set of positively charged electromagnet coils arranged in a polyhedron. The most common arrangement is a six sided cube. The six magnetic poles are pointing in the same direction toward the center. The magnetic field vanishes at the center by symmetry, creating a null point.
• Electron guns facing ring axis. These shoot electrons into the center of the ring structure. Once inside, the electrons are confined by the magnetic fields. This has been measured in polywells using Langmuir probes.^[21][22][4] Electrons that have enough energy to escape through the magnetic cusps can be re-attracted to the positive rings. They can slow down and return to the inside of the rings along the cusps. This reduces conduction losses, and improves the overall performance of the machine.^[23] The electrons act as a negative voltage drop attracting positive ions. This is a virtual cathode.
• Gas puffers at corner. Gas is puffed inside the rings where it ionizes at the electron cloud. As ions fall down the potential well, the electric field works on them, heating it to fusion conditions. The ions build up speed. They can slam together in the center and fuse. Ions are electrostatically confined raising the density and increasing the fusion rate.

The magnetic energy density required to confine electrons is far smaller than that required to directly confine ions, as is done in other fusion projects such as ITER.^[21][24][25]

Other behavior

Single-electron motion

As an electron enters a magnetic field, it feels a Lorentz force and corkscrews. The radius of this motion is the gyroradius. As it moves it loses some energy as x-rays, every time it changes speed. The electron spins faster and tighter in denser fields, as it enters the MaGrid. Inside the MaGrid, single electrons travel straight through the null point, due to their infinite gyroradius in regions of no magnetic field. Next, they head towards the edges of the MaGrid field and corkscrew tighter along the denser magnetic field lines.^[17][26] This is typical electron cyclotron resonance motion. Their gyroradius shrinks and when they hit a dense magnetic field they can be reflected using the magnetic mirror effect.^[27][28][29] Electron trapping has been measured in polywells with Langmuir probes.^[21][22][4]

The polywell attempts to confine the ions and electrons through two different means, borrowed from fusors and magnetic mirrors. The electrons are easier to confine magnetically because they have so much less mass than the ions.^[30] The machine confines ions using an electric field in the same way a fusor confines the ions: in the polywell, the ions are attracted to the negative electron cloud in the center. In the fusor, they are attracted to a negative wire cage in the center.

Plasma recirculation

Plasma recirculation would significantly improve the function of these machines. It has been argued that efficient recirculation is the only way they can be viable.^[31][32] Electrons or ions move through the device without striking a surface, reducing conduction losses. Bussard stressed this; specifically emphasizing that electrons need to move through all cusps of the machine.^[33][34]

Models of energy distribution

As of 2015^[update] it had not been determined conclusively what the ion or electron energy distribution is. The energy distribution of the plasma can be measured using a Langmuir probe. This probe absorbs charge from the plasma as its voltage changes, making an I-V Curve.^[36] From this signal, the energy distribution can be calculated. The energy distribution both drives and is driven by several physical rates,^[31] the electron and ion loss rate, the rate of energy loss by radiation, the fusion rate and the rate of non-fusion collisions. The collision rate may vary greatly across the system:^{[citation needed]}

• At the edge: where ions are slow and the electrons are fast.
• At the center: where ions are fast and electrons are slow.

Critics claimed that both the electrons and ion populations have bell curve distribution;^[31] that the plasma is thermalized. The justification given is that the longer the electrons and ions move inside the polywell, the more interactions they undergo leading to thermalization. This model for^[31] the ion distribution is shown in Figure 5.

Supporters modeled a nonthermal plasma.^[33] The justification is the high amount of scattering in the device center.^[37] Without a magnetic field, electrons scatter in this region. They claimed that this scattering leads to a monoenergetic distribution, like the one shown in Figure 6. This argument is supported by 2 dimensional particle-in-cell simulations.^[37] Bussard argued that constant electron injection would have the same effect.^[20] Such a distribution would help maintain a negative voltage in the center, improving performance.^[20]

Considerations for net power

Fuel type

Nuclear fusion refers to nuclear reactions that combine lighter nuclei to become heavier nuclei. All chemical elements can be fused; for elements with fewer protons than iron, this process changes mass into energy that can potentially be captured to provide fusion power.

The probability of a fusion reaction occurring is controlled by the cross section of the fuel,^[38] which is in turn a function of its temperature. The easiest nuclei to fuse are deuterium and tritium. Their fusion occurs when the ions reach 4 keV (kiloelectronvolts), or about 45 million kelvins. The Polywell would achieve this by accelerating an ion with a charge of 1 down a 4,000 volt electric field. The high cost, short half-life and radioactivity of tritium make it difficult to work with.

The second easiest reaction is to fuse deuterium with itself. Because of its low cost, deuterium is commonly used by Fusor amateurs. Bussard's polywell experiments were performed using this fuel. Fusion of deuterium or tritium produces a fast neutron, and therefore produces radioactive waste. Bussard's choice was to fuse boron-11 with protons; this reaction is aneutronic (does not produce neutrons). An advantage of p-¹¹B as a fusion fuel is that the primary reactor output would be energetic alpha particles, which can be directly converted to electricity at high efficiency using direct energy conversion. Direct conversion has achieved a 48% power efficiency^[39] against 80–90% theoretical efficiency.^[11]

Lawson criterion

The energy generated by fusion inside a hot plasma cloud can be found with the following equation:^[40]

${\displaystyle P_{\text{fusion}}=n_{A}n_{B}\langle \sigma v_{A,B}\rangle E_{\text{fusion}}}$

where:

• ${\displaystyle P_{\text{fusion}}}$ is the fusion power density (energy per time per volume),
• n is the number density of species A or B (particles per volume),
• ${\displaystyle \langle \sigma v_{A,B}\rangle }$ is the product of the collision cross-section σ (which depends on the relative velocity) and the relative velocity of the two species v, averaged over all the particle velocities in the system.

Energy varies with temperature, density, collision speed and fuel. To reach net power production, reactions must occur rapidly enough to make up for energy losses. Plasma clouds lose energy through conduction and radiation.^[40] Conduction is when ions, electrons or neutrals touch a surface and escape. Energy is lost with the particle. Radiation is when energy escapes as light. Radiation increases with temperature. To get net power from fusion, these losses must be overcome. This leads to an equation for power output.

Net Power = Efficiency × (Fusion − Radiation Loss − Conduction Loss)

• Net Power — power output
• Efficiency — fraction of energy needed to drive the device and convert it to electricity.
• Fusion — energy generated by the fusion reactions.
• Radiation — energy lost as light, leaving the plasma.
• Conduction — energy lost, as mass leaves the plasma.

Lawson used this equation to estimate conditions for net power^[40] based on a Maxwellian cloud.^[40] Zdroj:https://en.wikipedia.org?pojem=Polywell
Text je dostupný za podmienok Creative Commons Attribution/Share-Alike License 3.0 Unported; prípadne za ďalších podmienok. Podrobnejšie informácie nájdete na stránke Podmienky použitia.