B34 Spheromaks

A spheromak reactor has a toroidal configuration not shaped by either material walls or the magnet. In this respect a spheromak is similar to an FRC. Unlike an FRC

though, the poloidal and toroidal field strengths are approximately equal. Spheromak research is reviewed in [Jarboe, 1994].

Spheromaks are relaxed configurations verifying the Taylor minimum energy principle [Taylor, 1976]. According to such a principle, the magnetic configuration relaxes to a state which minimizes the energy U = J dV B2/(2p0) with the constraint of constant helicity K = J* dV A • B, where A is the vector potential and B = V x A the magnetic field (the integral is over the plasma volume). The minimization of U with the constraint K = constant leads to the equation

where A is a global constant. Solution of Equation (B.37) results in a force-free state (J x B = 0). The minimum energy principle has been successfully applied to describe the reversed field pinch equilibrium, a plasma configuration that has several features in common with spheromaks. Note that, strictly speaking, relaxed states by definition have a zero pressure gradient and are therefore irrelevant to plasma confinement. In practice, these configurations depart from a truly relaxed state and have finite pressure gradients.

B.3.4.1 Spheromak formation

Five different schemes are currently employed for spheromak formation: the flux core; the 0-pinch; z-pinch; the coaxial source; the conical 0-pinch; the kinked z-pinch. These schemes are described in [Jarboe, 1994]. Only the coaxial source is reported here since it produces the best-quality spheromaks (toroidal plasma current of 1 MA, peak magnetic field of 3 T, electron temperature of 400 eV, plasma density close to 1020 m-3, and energy confinement time of 0.2ms, for a 10ms pulse). For reference, the layout of the CTX experiment is shown in Figure B.20. The formation sequence is shown in Figure B.21.

The coaxial source is made of a pair of coaxial electrodes. Initially, a magnetic flux penetrates the inner electrode. Gas is injected between the electrodes and ionized to form a plasma which is frozen in the initial magnetic field. The electrode current is increased and, above a certain threshold, plasma and magnetic field are ejected from the source into the flux conserver. After the coaxial current drops below a threshold value, the fields between the source and the spheromak reconnect and an isolated spheromak is formed. The coaxial source can also be used to maintain steady-state conditions in the spheromak configuration that otherwise would decay due to dissipation in the plasma. Note that the whole magnetic configuration, including the toroidal current in the plasmoid, is sustained, although the electric field produced by the gun is in the poloidal direction, namely orthogonal to the driven current. A similar situation arises in the reversed-field pinch system [Bodin and Newton, 1980] where a poloidal current associated with field reversal is maintained by a toroidal electric field. The generation of a magnetic field by the plasma is due to the so-called "dynamo mechanism'', which is typically a turbulent process. The drawback of this process is the generation of stochastic magnetic fields that can substantially reduce the confinement properties of these configurations.

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