Theta-pinch, or θ-pinch, is a type of fusion power reactor design. The name refers to the configuration of currents used to confine the plasma fuel in the reactor, arranged to run around a cylinder in the direction normally denoted as theta in polar coordinate diagrams. The name was chosen to differentiate it from machines based on the pinch effect that arranged their currents running down the centre of the cylinder; these became known as z-pinch machines, referring to the Z-axis in cartesian coordinates.

Theta-pinch was developed primarily in the United States, mostly at the Los Alamos National Laboratory (LANL) in a series of machines known as Scylla. In 1958, Scylla I was the first machine to clearly demonstrate thermonuclear fusion reactions of deuterium in a controlled manner. It became one of the major lines of fusion research during the 1960s. General Electric and the Naval Research Laboratory also experimented with the concept, and later, many international labs. A series of machines was capped by the Scylla IV which demonstrated temperatures as high as 80 million K, more than enough to sustain a burning plasma. During these runs, Scylla IV produced billions of fusion reactions.

The Scylla machines also demonstrated very poor confinement times, on the order of a few microseconds. It was believed this was due to losses at the ends of the linear tubes. Scyllac (Scylla-closed) was designed to test a toroidal version that would improve confinement a thousandfold. A design mistake led to Scyllac being unable to come anywhere near its desired performance, and the United States Atomic Energy Commission shut the program down in 1977 to focus on the tokamak and magnetic mirror.

Some of the lack of interest in theta since the 1970s is due to a variation of the design known as the field-reversed configuration, or FRC, which has seen significant exploration. In this version, the induced magnetic fields are coaxed to take on a closed form that gives better confinement. The differences are enough that FRCs are considered to be a separate concept. Likewise, theta-pinch is often seen in magnetized target fusion systems, but these also differ significantly from the original concept.

Nuclear fusion occurs when nuclei, protons and neutrons, come close enough together for the nuclear force to pull them together into a single larger nucleus. Opposing this action is the electrostatic force, which causes electrically charged particles with like charges, like protons, to repel each other. To fuse, the particles must be travelling fast enough to overcome this coulomb barrier. The nuclear force increases with the number of nuclei, and the coulomb barrier is lowered when the number of neutrons in the nuclei is maximized, which leads to the fusion rate being maximized for isotopes of lighter elements like hydrogen and helium with extra neutrons.

Using classical electromagnetism, the energies required to overcome the coulomb barrier would be enormous. The calculations changed considerably during the 1920s as physicists explored the new science of quantum mechanics. George Gamow's 1928 paper on quantum tunnelling demonstrated that nuclear reactions could take place at much lower energies than classical theory predicted. Using this new theory, in 1929 Fritz Houtermans and Robert Atkinson demonstrated that expected reaction rates in the core of the sun supported Arthur Eddington's 1920 suggestion that the sun is powered by fusion. In 1934, Mark Oliphant, Paul Harteck and Ernest Rutherford were the first to achieve fusion on Earth, using a particle accelerator to shoot deuterium nuclei into a metal foil containing deuterium, lithium and other elements. This allowed them to measure the nuclear cross section of various fusion reactions, and determined that the deuterium-deuterium reaction occurred at the lowest energy, peaking at about 100,000 electronvolts (100 keV).

This energy corresponds to the average energy of particles in a gas heated to about 10 billion Kelvin (K). Materials heated beyond a few thousand K dissociate into their electrons and nuclei, producing a gas-like state of matter known as plasma. In any gas the particles have a wide range of energies, normally following the Maxwell–Boltzmann statistics. In such a mixture, a small number of particles will have much higher energy than the bulk. This leads to an interesting possibility; even at average temperatures well below 100 keV, some particles within the gas will randomly have enough energy to undergo fusion. Those reactions release huge amounts of energy. If that energy can be captured back into the plasma, it can heat other particles to that energy as well, making the reaction self-sustaining. In 1944, Enrico Fermi calculated this would occur at about 50 million K for a deuterium-tritium fuel.

Taking advantage of this possibility requires the fuel plasma to be held together long enough that these random reactions have time to occur. Like any hot gas, plasma has an internal pressure and thus wants to expand according to the ideal gas law. For a fusion reactor, the problem is keeping the plasma contained against this pressure; any known substance would melt at these temperatures. As it consists of freely moving charged particles, plasma is electrically conductive. This makes it subject to electric and magnetic fields. In a magnetic field, the electrons and nuclei orbit the magnetic field lines. A simple confinement system is a plasma-filled tube placed inside the open core of a solenoid. The plasma naturally wants to expand outwards to the walls of the tube, as well as move along it, towards the ends. The solenoid creates a magnetic field running down the centre of the tube, which the particles will orbit, preventing their motion towards the sides. Unfortunately, this arrangement does not confine the plasma along the length of the tube, and the plasma is free to flow out the ends. For a purely experimental machine, the losses are not necessarily a major problem, but a production system would have to eliminate these end losses.