Pinch (plasma physics) Totally Explained

Everything about Pinch Plasma Physics totally explained

A pinch is the compression of an electrically conducting filament by magnetic forces. The conductor is usually a plasma, but could also be a solid or liquid metal. In a z-pinch, the current is axial (in the z direction in a cylindrical coordinate system) and the magnetic field azimuthal; in a theta-pinch, the current is azimuthal (in the theta direction in cylindrical coordinates) and the magnetic field is axial. The phenomenon may also be referred to as a "Bennett pinch" (after Willard Harrison Bennett), "electromagnetic pinch", "magnetic pinch", "pinch effect" or "plasma pinch".
Pinches occur naturally in electrical discharges such as lightning bolts, the aurora, current sheets, and solar flares. They are also produced in the laboratory, primarily for research into fusion power, but also by hobbyists.

Pinch production and types

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. The phenomenon wasn't understood until 1905, when Pollock and Barraclough 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. A similar, and apparently independent, theoretical analysis of the pinch effect in liquid metals was published by Northrupp 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":
ť In 1946 Thompson and Blackman [43] submitted a patent for a fusion reactor based on a toroidal z-pinch [43] with an additional vertical magnetic field. But in 1954 Kruskal and Schwarzschild [44] 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 [45]. In 1957 Pease [46] and Braginskii [47] 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 in [32] would however prevent radiative collapse). Lastly, at Imperial College in 1960, led by R Latham, the Rayleigh–Taylor (RT) instability was shown, and its growth rate measured in a dynamic z-pinch [48]."

Configurations

One Dimensional configurations

There are three analytic one dimensional configurations generally studied in plasma physics. These are the θ-pinch, the Z-pinch, and the Screw Pinch. All of the classic one dimensional pinches are cylindrically shaped. Symmetry is assumed in the axial (z) direction and in the azimuthal (θ) direction. It is traditional to name a one-dimensional pinch after the direction in which the current travels. The θ-pinch The θ-pinch has a magnetic field traveling in the z direction. Using Ampère's law (discarding the displacement term)

abla 	imes vec + Delta W_k

and is applicable to many space plasmas.
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 chart illustrates four physically distinct regions. The plasma temperature is quite cold (T_i = T_e = T_n = 20 K), containing mainly hydrogen with a mean particle mass 3×10^-27 kg. The thermokinetic energy W_k >> π a² p_k(a). The curves, ΔW_Bz show different amounts of 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. Chart regions: (a) In the top-left region, the pinching force dominates. (b) Towards the bottom, outward kinetic pressures balance inwards magnetic pressure, and the total pressure is constant. (c) To the right of the vertical line ΔW_Bz=0, the magnetic pressures balances the gravitational pressure, and the pinching force is negligible. (d) To the left of the sloping curve ΔW_Bz=0, the gravitational force is negligible. Note that the chart shows a special case of the Carlqvist relation, and if it's replaced by the more general Bennett relation, then the designated regions of the chart are not valid.
Carlqvist further notes that by using the relations above, and a derivative, it's possible to describe the Bennett pinch, the Jean's criterion (for gravitational instability, in one and two dimensions), force-free magnetic fields, gravitationally balanced magnetic pressures, and continuous transitions between these states.

Crushing cans with the pinch effect

Many high-voltage electronics enthusiasts make their own devices using pulsed power techniques to produce a theta pinch capable of crushing an aluminium soft drink can by pressure of strong magnetic field. (Warning! High-voltage electric shocks may be lethal).
   An electromagnetic aluminium can crusher consists of four main components (1) A high voltage DC power supply which provides a source of electrical energy (2) A large energy discharge capacitor to accumulate the electrical energy (3) A high voltage switch or spark gap and (4) 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.
   Sam Barros's can crusher cost about $500, and uses a large SCR and a 900 Volt capacitor bank storing about 3000 Joules of energy. For a very short time, it generates a magnetic field B~5T (250,000 times the strength of the Earth's magnetic field) which has magnetic pressure P ~ 100 atm. Rate of energy conversion (from electric into magnetic and back) in this device is about 22 megawatts.
   (Warning! High-voltage electric shocks may be lethal. Do not attempt to build such a device without proper training and precautions.).

Depictions

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.

Further Information

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