Pinch (plasma physics)

[7] Pinches occur naturally in electrical discharges such as lightning bolts,[8] planetary auroras,[9] current sheets,[10] and solar flares.

[30] A number of large pinch machines have been built to study fusion power; here are several: Many high-voltage electronics enthusiasts make their own crude electromagnetic forming devices.

[32][33][34] 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.

[37] 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.

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.

[40] A similar, and apparently independent, theoretical analysis of the pinch effect in liquid metals was published by Northrup in 1907.

[41] The next major development was the publication in 1934 of an analysis of the radial pressure balance in a static Z-pinch by Bennett[42] (see the following section for details).

[43] 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.

[7] 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.

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.

[54] The magnetic field distribution is given here again via Ampère's law: A common problem with one-dimensional pinches is the end losses.

Numerical solutions to the Grad–Shafranov equation have also yielded some equilibria, most notably that of the reversed field pinch.

As the current flows through its own magnetic field, a pinch is generated with an inward radial force density of j x B.

The generalized Bennett relation considers a current-carrying magnetic-field-aligned cylindrical plasma pinch undergoing rotation at angular frequency ω.

Along the axis of the plasma cylinder flows a current density jz, resulting in an azimuthal magnetic field Βφ.

The Carlqvist relation can be illustrated (see right), showing the total current (I) versus the number of particles per unit length (N) in a Bennett pinch.

The plasma temperature is quite cold (Ti = Te = Tn = 20 K), containing mainly hydrogen with a mean particle mass 3×10−27 kg.

Carlqvist further notes that by using the relations above, and a derivative, it is possible to describe the Bennett pinch, the Jeans criterion (for gravitational instability,[60] in one and two dimensions), force-free magnetic fields, gravitationally balanced magnetic pressures, and continuous transitions between these states.

A fictionalized pinch-generating device was used in Ocean's Eleven, where it was used to disrupt Las Vegas's power grid just long enough for the characters to begin their heist.

This is a basic explanation of how a pinch works. ( 1 ) Pinches apply a high voltage and current across a tube. This tube is filled with a gas, typically a fusion fuel such as deuterium. If the product of the voltage & the charge is higher than the ionization energy of the gas the gas ionizes. ( 2 ) Current jumps across this gap. ( 3 ) The current makes a magnetic field which is perpendicular to the current. This magnetic field pulls the material together. ( 4 ) These atoms can get close enough to fuse.
An example of a man-made pinch. Here Z-pinches constrain a plasma inside filaments of electrical discharge from a Tesla coil
The MagLIF concept, a combination of a Z-pinch and a laser beam
Model of the kink modes that form inside a pinch
Model of the kink modes that form inside a pinch
Pinched aluminium can, produced via a pulsed magnetic field created by rapidly discharging 2 kilojoules from a high voltage capacitor bank into a 3-turn coil of heavy gauge wire.
Electromagnetic pinch "can crusher": schematic diagram
The Institute of Electrical and Electronics Engineers emblem shows the basic features of an azimuthal magnetic pinch. [ 38 ]
A sketch of the θ-pinch equilibrium. The z-directed magnetic field corresponds to a θ-directed plasma current.
A sketch of the Z-pinch equilibrium. A θ-directed magnetic field corresponds to a z-directed plasma current.
A toroidal coordinate system in common use in plasma physics.
The red arrow denotes the poloidal direction (θ)
The blue arrow denotes the toroidal direction (φ)
A stream of water pinching into droplets has been suggested as an analogy to the electromagnetic pinch. [ 56 ] Gravity accelerates free-falling water which causes the water column to constrict. Surface tension breaks the narrowing water column into droplets (not shown, see Plateau–Rayleigh instability ). This is analogous to the magnetic field suggested as the cause of pinching in bead lightning. [ 57 ] The morphology (shape) is similar to the so-called sausage instability in plasma.
The generalized Bennett relation considers a current-carrying magnetic-field-aligned cylindrical plasma pinch undergoing rotation at angular frequency ω
The Bennett pinch showing the total current (I) versus the number of particles per unit length (N). The chart illustrates four physically distinct regions. The plasma temperature is 20 K, the mean particle mass 3×10 −27 kg, and ΔW Bz is the excess magnetic energy per unit length due to the axial magnetic field B z . The plasma is assumed to be non-rotational, and the kinetic pressure at the edges is much smaller than inside.