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 relative to 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. Most plasma in most fusion reactors (such as Magnetic mirrors, tokamaks and Stellarators) 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.
Both the Polywell and the high beta fusion reactor pre-suppose 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 providing (1) x-ray and (2) flux loop measurements that the diamagnetic effect will impact the external field.
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).
In February 2013, Lockheed Martin Skunk Works announced a new compact fusion machine, the high beta fusion reactor, 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."Mirror Systems: Fuel Cycles, loss reduction and energy recovery" by Richard F. Post, BNES Nuclear fusion reactor conferences at Culham laboratory, September 1969. 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.Park, Jaeyoung (12 June 2014). SPECIAL PLASMA SEMINAR: Measurement of Enhanced Cusp Confinement at High Beta (Speech). Plasma Physics Seminar. Department of Physics & Astronomy, University of California, Irvine: Energy Matter Conversion Corp (EMC2). This is an improvement over the simpler magnetic mirror. 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. In 1955, Harold Grad theorized that a high-beta plasma pressure combined with a cusped magnetic field would improve plasma confinement. A diamagnetic plasma rejects the external fields and plugs the cusps. This system would be a much better trap.
Cusped confinement was explored theoreticallymagnetohydrodynamic stability, j Berkowitz, h grad, p/376 and experimentally.review paper, m g Haines, nuclear fusion, 17 4(1977) 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.
Most experiments on polywells involve low-beta plasma regimes (where β < 1), where the plasma pressure is weak compared to the magnetic pressure. Several models describe magnetic trapping in polywells. 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.
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, As cited by Todd H. Rider in "A general critique of inertial-electrostatic confinement fusion systems", Phys. Plasmas 2 (6), June 1995. Rider specifically stated that "Bussard has revived an idea originally suggested by Lavrent'ev". 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 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. 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.Lawson, J. D. (December 1955). Some Criteria for a Power producing thermonuclear reactor (PDF) (Technical report). Atomic Energy Research Establishment, Harwell, Berkshire, U. K. A.E.R.E. GP/R 1807. 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.
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. 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. Electron trapping has been measured in polywells with Langmuir probes.
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. 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. 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.
Models of energy distribution
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.E. V. Shun'ko. "Langmuir Probe in Theory and Practice". Universal Publishers, Boca Raton, Fl. 2008. p. 243. . From this signal, the energy distribution can be calculated. The energy distribution both drives and is driven by several physical rates, 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: 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; 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 the ion distribution is shown in Figure 5.