Afield-reversed configuration (FRC) is a type ofplasma device studied as a means of producingnuclear fusion. It confines a plasma on closed magneticfield lines without a central penetration.^[1][2] In an FRC, the plasma has the form of a self-stable torus, similar to asmoke ring.

FRCs are closely related to another self-stablemagnetic confinement fusion device, thespheromak. Both are considered part of thecompact toroid class of fusion devices. FRCs normally have a plasma that is more elongated than spheromaks, having the overall shape of a hollowed out sausage rather than the roughly spherical spheromak.

FRCs were a major area of research in the 1960s and into the 1970s, but had problems scaling up into practicalfusion triple products (target combinations of density, temperature and confinement time). Interest returned in the 1990s and as of 2019^[update], FRCs were an active research area.

The FRC was first observed in laboratories in the late 1950s duringtheta pinch experiments with a reversed background magnetic field.^[3] The original idea was attributed to the Greek scientist and engineerNicholas C. Christofilos who developed the concept of E-layers for theAstron fusion reactor.^[4]

The first studies were at theUnited States Naval Research Laboratory (NRL) in the 1960s. Considerable data were collected, with over 600 published papers.^[5] Almost all research was conducted duringProject Sherwood atLos Alamos National Laboratory (LANL) from 1975 to 1990,^[6] and during 18 years at the Redmond Plasma Physics Laboratory of theUniversity of Washington,^[7] with the larges experiment (LSX).^[8]

Later research was at theAir Force Research Laboratory (AFRL),^[9] the Fusion Technology Institute (FTI) of theUniversity of Wisconsin-Madison,^[10]Princeton Plasma Physics Laboratory,^[11] and theUniversity of California, Irvine.^[12]

Private companies now study FRCs for electricity generation, includingGeneral Fusion,TAE Technologies, andHelion Energy.^[13]

The Electrodeless Lorentz Force Thruster (ELF) developed by MSNW was an attempt to design a space propulsion device.^[14] ELF was a candidate inNASA's NextSTEP advanced electric propulsion program, along with the X-3 Nested-Channel Hall Thruster andVASIMR^[15] before MSNW dissolved.

The primary application is for fusion power generation.

The FRC is also considered fordeep space exploration, not only as a possible nuclear energy source, but as means of accelerating a propellant to high levels ofspecific impulse (I_sp) forelectrically powered spaceships andfusion rockets, with interest expressed byNASA.^{[16][17][18][19][20]}

Producing fusion power by confining the plasma with magnetic fields is most effective if the field lines do not penetrate solid surfaces but close on themselves into circles or toroidal surfaces. The mainline confinement concepts oftokamak andstellarator do this in a toroidal chamber, which allows a great deal of control over the magnetic configuration, but requires a very complex construction. The field-reversed configuration offers an alternative in that the field lines are closed, providing good confinement, but the chamber is cylindrical, allowing simpler, easier construction and maintenance.^[21]

Field-reversed configurations andspheromaks are together known ascompact toroids.Spheromaks and FRC differ in that a spheromak has an extra toroidal field. This toroidal field can run along the same or opposite direction as the spinning plasma.^[22] In the spheromak the strength of thetoroidal magnetic field is similar to that of thepoloidal field. By contrast, the FRC has little to no toroidal field component and is confined solely by a poloidal field. The lack of a toroidal field means that the FRC has nomagnetic helicity and that it has ahigh beta. The high beta makes the FRC attractive as afusion reactor and well-suited toaneutronic fuels because of the low required magnetic field. Spheromaks haveβ ≈ 0.1 whereas a typical FRC hasβ ≈ 1.^[23][24]

In modern FRC experiments, the plasma current that reverses the magnetic field can be induced in a variety of ways.

When a field-reversed configuration is formed using thetheta-pinch (or inductive electric field) method, a cylindrical coil first produces an axial magnetic field. Then the gas is pre-ionized, which "freezes in" the bias field from amagnetohydrodynamic standpoint, finally the axial field is reversed, hence "field-reversed configuration." At the ends, reconnection of the bias field and the main field occurs, producing closed field lines. The main field is raised further, compressing and heating the plasma and providing a vacuum field between the plasma and the wall.^[25]

Neutral beams are known to drive current inTokamaks^[26] by directly injecting charged particles. FRCs can also be formed, sustained, and heated by application of neutral beams.^[24][27] In such experiments, as above, a cylindrical coil produces a uniform axial magnetic field and gas is introduced and ionized, creating a background plasma. Neutral particles are then injected into the plasma. They ionize and the heavier, positively-charged particles form a current ring which reverses the magnetic field.

Spheromaks are FRC-like configurations with finite toroidal magnetic field. FRCs have been formed through the merging of spheromaks of opposite and canceling toroidal field.^[28]

Rotating magnetic fields have also been used to drive current.^[29] In such experiments, as above, gas is ionized and an axial magnetic field is produced. A rotating magnetic field is produced by external magnetic coils perpendicular to the axis of the machine, and the direction of this field is rotated about the axis. When the rotation frequency is between the ion and electron gyro-frequencies, the electrons in the plasma co-rotate with the magnetic field (are "dragged"), producing current and reversing the magnetic field. More recently, so-called odd parity rotating magnetic fields^[30][31] have been used to preserve the closed topology of the FRC. It was analytically shown that at a very high critical threshold magnitude of 'odd parity' rotating magnetic field, the axisymmetric equilibrium magnetic field lines loses closure and fundamentally changes field topology.^[31]

FRCs contain an important and uncommon feature: a "magnetic null," or circular line on which the magnetic field is zero. This is necessarily the case, as inside the null the magnetic field points one direction and outside the null the magnetic field points the opposite direction. Particles far from the null trace closed cyclotron orbits as in other magnetic fusion geometries. Particles which cross the null, however, trace notcyclotron or circular orbits butbetatron or figure-eight-like orbits,^[32] as the orbit's curvature changes direction when it crosses the magnetic null.

Because the particle's orbits are not cyclotron, models of plasma behavior based on cyclotron motion likemagnetohydrodynamics (MHD) are inapplicable in the region around the null. The size of this region is related to the s-parameter,^[33] or the ratio of the distance between the null and separatrix, and the thermal ion gyroradius. At high-s, most particles do not cross the null and this effect is negligible. At low-s, ~2, this effect dominates and the FRC is said to be "kinetic" rather than "MHD."

At low s-parameter, most ions inside an FRC follow largebetatronorbits (their averagegyroradius is about half the size of the plasma) which are typical inaccelerator physics rather thanplasma physics. These FRCs are very stable because the plasma is not dominated by usual small gyroradius particles like otherthermodynamic equilibrium ornonthermal plasmas. Its behavior is not described by classicalmagnetohydrodynamics, hence there are noAlfvén waves and almost noMHD instabilities despite their theoretical prediction,^{[citation needed]} and it avoids the typical "anomalous transport", i.e. processes in which excess loss ofparticles orenergy occurs.^[34][35][36]

As of 2000^[update], several remaining instabilities are being studied:

• Thetilt and shift modes. Those instabilities can be mitigated by either including a passive stabilizing conductor, or by forming veryoblate plasmas (i.e. very elongated plasmas),^[37] or by creating a self-generated toroidal field.^[38] The tilt mode has also been stabilized in FRC experiments by increasing the ion gyroradii.^[33]
• Themagnetorotational instability. This mode causes a rotating elliptical distortion of the plasma boundary, and can destroy the FRC when the distorted plasma comes in contact with the confinement chamber.^[39] Successful stabilization methods include the use of a quadrupole stabilizing field,^[40][41] and the effects of a rotating magnetic field (RMF).^[42][43]

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Field-reversed configuration devices have been considered for spacecraft propulsion. By angling the walls of the device outward, the plasmoid can be accelerated in the axial direction and out of the device, generating thrust.

• Google techtalks:Nuclear Fusion: Clean Power for the Next Hundred Centuries
• University of Washington" FRC Introduction"

• Magnetic confinement fusion

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