A pinch (or: Bennett pinch LOC 60-12766. (after Willard Harrison Bennett), electromagnetic pinch, magnetic pinch, pinch effect, or plasma pinch.) is the compression of an electrically conducting filament by magnetic forces, or a device that does such. The conductor is usually a plasma, but could also be a solid or liquid metal. Pinches were the first type of device used for experiments in controlled nuclear fusion power.
Pinches occur naturally in electrical discharges such as lightning bolts, planetary auroras, current sheets, and solar flares.
Basic mechanism
Types
Pinches exist in nature and in laboratories. Pinches differ in their geometry and operating forces. These include: Uncontrolled – Any time an electric current moves in large amounts (e.g., lightning, arcs, sparks, discharges) a magnetic force can pull together plasma. This can be insufficient for fusion. Sheet pinch – An astrophysical effect, this arises from vast sheets of charged particles. Z-pinch – The current runs down the axis, or walls, of a cylinder while the magnetic field is azimuthal Theta pinch – The magnetic field runs down the axis of a cylinder, while the electric field is in the azimuthal direction (also called a thetatron) Screw pinch – A combination of a Z-pinch and theta pinch (also called a stabilized Z-pinch, or θ-Z pinch)See "MHD Equilibria" in Introduction to Plasma Physics by I.H.Hutchinson (2001) Reversed field pinch or toroidal pinch – This is a Z-pinch arranged in the shape of a torus. The plasma has an internal magnetic field. As distance increases from the center of this ring, the magnetic field reverses direction. Inverse pinch – An early fusion concept, this device consisted of a rod surrounded by plasma. Current traveled through the plasma and returned along the center rod. This geometry was slightly different than a z-pinch in that the conductor was in the center, not the sides. Cylindrical pinch Orthogonal pinch effect Ware pinch – A pinch that occurs inside a Tokamak plasma, when particles inside the banana orbit condense together. Magnetized liner inertial fusion (MagLIF) – A Z-pinch of preheated, premagnetized fuel inside a metal liner, which could lead to ignition and practical fusion energy with a larger pulsed-power driver.
Common behavior Pinches may become unstable. They radiate energy across the whole electromagnetic spectrum including radio waves, microwaves, infrared, x-rays, gamma rays, synchrotron radiation,Peratt, A.L., "Synchrotron radiation from pinched particle beams", (1998) Plasma Physics: VII Lawpp 97: Proceedings of the 1997 Latin American Workshop on Plasma Physics, Edited by Pablo Martin, Julio Puerta, Pablo Martmn, with reference to Meierovich, B. E., "Electromagnetic collapse. Problems of stability, emission of radiation and evolution of a dense pinch" (1984) Physics Reports, Volume 104, Issue 5, p. 259-346. and visible light. They also produce neutrons, as a product of fusion.
Applications and devices Pinches are used to generate X-rays and the intense magnetic fields generated are used in electromagnetic forming of metals. They also have applications in particle beams including particle beam weapons,Andre Gsponer, "Physics of high-intensity high-energy particle beam propagation in open air and outer-space plasmas" (2004) https://arxiv.org/abs/physics/0409157 astrophysics studiesPeratt, Anthony L., "The role of particle beams and electrical currents in the plasma universe" (1988) Laser and Particle Beams (ISSN 0263-0346), vol. 6, Aug. 1988, p. 471-491. and it has been proposed to use them in space propulsion."Z-Pinch Pulsed Plasma Propulsion Technology Development" Final Report Advanced Concepts Office (ED04) Marshall Space Flight Center October 8, 2010, Tara Polsgrove, Et Al. A number of large pinch machines have been built to study fusion power; here are several:
MAGPIE A Z-pinch at Imperial College. This dumps a large amount of current across a wire. Under these conditions, the wire becomes plasma and compresses to produce fusion.http://dorland.pp.ph.ic.ac.uk/magpie/?page_id=239 "Wire Arrays Z-Pinch" accessed: 3-27-2015 Z Pulsed Power Facility at Sandia National Laboratories. ZETA device in Culham, England Madison Symmetric Torus at the University of Wisconsin, Madison Reversed-Field eXperiment in Italy. Dense plasma focus in New Jersey University of Nevada, Reno (USA) Cornell University (USA) University of Michigan (USA) University of California, San Diego (USA) University of Washington (USA) Ruhr University (Germany) École Polytechnique (France) Weizmann Institute of Science (Israel) Universidad Autónoma Metropolitana (Mexico). Zap Energy Inc. (USA)
Crushing cans with the pinch effect
Many high-voltage electronics enthusiasts make their own crude electromagnetic forming devices. They use pulsed power techniques to produce a theta pinch able to crush an aluminium soft drink can using the Lorentz forces created when large currents are induced in the can by the strong magnetic field of the primary coil.
An electromagnetic aluminium can crusher consists of four main components: a high-voltage DC power supply, which provides a source of electrical energy, a large energy discharge capacitor to accumulate the electrical energy, a high voltage switch or spark gap, and a robust coil (capable of surviving high magnetic pressure) through which the stored electrical energy can be quickly discharged in order to generate a correspondingly strong pinching magnetic field (see diagram below).
In practice, such a device is somewhat more sophisticated than the schematic diagram suggests, including electrical components that control the current in order to maximize the resulting pinch, and to ensure that the device works safely. For more details, see the notes.Examples of electromagnetic pinch can crushers can be found at (a) Bob LaPointe's site on High Voltage Devices and Experiments (b) Tristran's Electromagnetic Can Crusher (including schematic) (c) Sam Borros's Solid State Can Crusher
History
The first creation of a Z-pinch in the laboratory may have occurred in 1790 in Holland when Martinus van Marum created an explosion by discharging 100 Leyden jars into a wire.van Marum M 1790 Proc. 4th Int. Conf. on Dense Z-Pinches (Vancouver 1997) (Am. Inst. Phys. Woodbury, New York, 1997) Frontispiece and p ii The phenomenon was not understood until 1905, when Pollock and BarracloughPollock J A and Barraclough S (1905) Proc. R. Soc. New South Wales 39 131 investigated a compressed and distorted length of copper tube from a lightning rod after it had been struck by lightning. Their analysis showed that the forces due to the interaction of the large current flow with its own magnetic field could have caused the compression and distortion.R. S. Pease, "The Electromagnetic Pinch: From Pollock to the Joint European Torus", "Pollock Memorial Lecture for 1984 delivered at the University of Sydney, 28 November, 1984" A similar, and apparently independent, theoretical analysis of the pinch effect in liquid metals was published by Northrup in 1907. The next major development was the publication in 1934 of an analysis of the radial pressure balance in a static Z-pinch by Bennett (see the following section for details).
Thereafter, the experimental and theoretical progress on pinches was driven by fusion power research. In their article on the "Wire-array Z-pinch: a powerful x-ray source for ICF", M G Haines et al., wrote on the "Early history of Z-pinches". In 1946 Thompson and Blackman submitted a patent for a fusion reactor based on a toroidal Z-pinch with an additional vertical magnetic field. But in 1954 Kruskal and Schwarzschild published their theory of MHD instabilities in a Z-pinch. In 1956, Kurchatov gave his famous Harwell lecture showing nonthermal neutrons and the presence of m = 0 and m = 1 instabilities in a deuterium pinch.Kurchatov I V (1957) J. Nucl. Energy 4 193 In 1957 Pease and BraginskiiBraginskii S I 1957 Zh. Eksp. Teor. Fiz 33 645Braginskii S I 1958 Sov. Phys.—JETP 6 494 independently predicted radiative collapse in a Z-pinch under pressure balance when in hydrogen the current exceeds 1.4 MA. (The viscous rather than resistive dissipation of magnetic energy discussed above and inHaines M G et al. 2005 Phys. Rev. Lett.. submitted; see also EPS Conf. on Plasma Physics 2004 (London, UK) paper 73 would however prevent radiative collapse).
In 1958, the world's first controlled thermonuclear fusion experiment was accomplished using a theta-pinch machine named Scylla I at the Los Alamos National Laboratory. A cylinder full of deuterium was converted into a plasma and compressed to 15 million degrees Celsius under a theta-pinch effect. Lastly, at Imperial College in 1960, led by R Latham, the Plateau–Rayleigh instability was shown, and its growth rate measured in a dynamic Z-pinch.
Equilibrium analysis
One dimension In plasma physics three pinch geometries are commonly studied: the θ-pinch, the Z-pinch, and the screw pinch. These are cylindrically shaped. The cylinder is symmetric in the axial (z) direction and the azimuthal (θ) directions. The one-dimensional pinches are named for the direction the current travels.
The θ-pinch
The θ-pinch has a magnetic field directed in the z direction and a large diamagnetic current directed in the θ direction. Using Ampère's circuital law (discarding the displacement term)
Since B is only a function of r we can simplify this to
So J points in the θ direction.
Thus, the equilibrium condition () for the θ-pinch reads:
θ-pinches tend to be resistant to plasma instabilities; This is due in part to Alfvén's theorem (also known as the frozen-in flux theorem).
The Z-pinch
The Z-pinch has a magnetic field in the θ direction and a current J flowing in the z direction. Again, by electrostatic Ampère's law,
Thus, the equilibrium condition, , for the Z-pinch reads:
Although Z-pinches satisfy the MHD equilibrium condition, this is an unstable equilibrium, resulting in various instabilies such as the m = 0 instability ('sausage'), m = 1 instability ('kink'), and various other higher order instabilities.Bellan, P. Fundamentals of Plasma Physics
The screw pinch The screw pinch is an effort to combine the stability aspects of the θ-pinch and the confinement aspects of the Z-pinch. Referring once again to Ampère's law,
But this time, the B field has a θ component and a z component
So this time J has a component in the z direction and a component in the θ direction.
Finally, the equilibrium condition () for the screw pinch reads:
The screw pinch via colliding optical vortices The screw pinch might be produced in laser plasma by colliding optical vortices of ultrashort duration.A.Yu.Okulov. "Laser singular Theta-pinch", Phys.Lett.A, v.374, 4523-4527, (2010) For this purpose optical vortices should be phase-conjugated.Optical phase conjugation and electromagnetic momenta
The magnetic field distribution is given here again via Ampère's law:
Two dimensions
A common problem with one-dimensional pinches is the end losses. Most of the motion of particles is along the magnetic field. With the θ-pinch and the screw-pinch, this leads particles out of the end of the machine very quickly, leading to a loss of mass and energy. Along with this problem, the Z-pinch has major stability problems. Though particles can be reflected to some extent with magnetic mirrors, even these allow many particles to pass. A common method of beating these end losses, is to bend the cylinder around into a torus. Unfortunately this breaks θ symmetry, as paths on the inner portion (inboard side) of the torus are shorter than similar paths on the outer portion (outboard side). Thus, a new theory is needed. This gives rise to the famous Grad–Shafranov equation. Numerical solutions to the Grad–Shafranov equation have also yielded some equilibria, most notably that of the reversed field pinch.
Three dimensions