The structure of the n = 1 mode in the SPHEX spheromak, which plays a central role in relaxation during sustainment, is investigated by analysing the measured voltage fluctuations in the central plasma column. By combining these results with a suitably defined helical magnetic flux function, the mode is found to be due to a rotating helical distortion of the open linked flux. We propose that the distortion is due to a saturated current-driven kink mode of the open flux tube. The prolongation of this 'helical column' on its return around the outside of the closed flux is found to be strongly asymmetric. Previously published measurements of the Poynting flux and µ-profile are re-analysed in the light of these results, and implications for the mechanism of relaxation and non-inductive current drive are discussed.

We describe the design and operation of the SPHEX spheromak device and present an overview of its behaviour. The plasma is formed by ejection from a magnetized Marshall gun, and can be sustained as long as the gun is energized. The plasma is divided into the annulus comprising the closed toroidal flux, linked with the open flux forming the central column. The column current is driven directly by the central gun electrode, and the toroidal current in the annulus is driven indirectly by a mechanism associated with a coherent n = 1 oscillation of the column. The configuration exemplifies the operation of the process of relaxation to a state of minimum magnetic energy, which leads to magnetic configurations similar to those observed; to sustain these configurations requires some mechanism of toroidal current drive. Associated with this is the amplification of the poloidal flux, which is typically a factor of about five larger than the flux generated by the gun solenoid; the constancy (to a first approximation) of this factor plays a controlling role in spheromak behaviour. In standard operating conditions there is a 'hard' limit, set by the solenoid flux, on the current carried by the column; any current driven by the external circuit above this apparently does not emerge from the gun. Evidence is presented that the column current is carried largely (>50%) by accelerated ions with energy up to the gun voltage (≈500 V for a typical gun current of 60 kA). These ions are poorly magnetized and can escape across the magnetic field to the wall, a likely mechanism for the observed 'loss' of current. Hydrogen is the normal operating gas: other gases (D 2 and He) have been used, but the current drive is found to be less effective than in H 2 , with lower toroidal current maintained in the annulus.

We present measurements of the magnetohydrodynamic ''dynamo" due to correlated fluctuations of velocity and magnetic field in the SPHEX spheromak. We show that there are both single-mode and turbulent dynamo processes present, although the single-mode process is in this case an "antidynamo" opposing the externally applied electric field. The size of the turbulent dynamo at the magnetic axis is close to that required to drive the toroidal current there.

The spheromak device SPHEX has been modified by adding a current-carrying rod along the geometric axis, providing a preexisting toroidal field. We show that plasma can be successfully injected into such a field from a helicity source; the field assists plasma ejection from the gun and improves the coupling between gun and plasma, so that T^., Ti, and the toroidal current all increase with rod current. The mechanism of plasma sustainment appears to be the same as that of the spheromak. These results represent a step towards the achievement of steady-state tokamak operation.PACS numbers: 52.55.Hc SPHEX is a gun-injected spheromak device similar to the Compact Toroid Experiment (CTX) [1] at the Los Alamos National Laboratory; it is described in the preceding Letter [2], which presents results suggesting the outline of a relaxation mechanism involving a largescale coherent mode of oscillation which, we believe, drives the toroidal current in the plasma.In this paper we describe the modification of SPHEX in which the plasma is injected into a pre-existing toroidal field. This is generated by a current-carrying rod placed along the geometric axis of both the gun and the flux conserver (see Fig. 1 of Ref. [2]). This configuration was suggested by results from the Heidelberg HSE experiment [3]; a similar scheme has been proposed [4] to sustain a tokamak discharge by helicity injection. Our results (presented briefly in Ref.[5]) show for the first time that a coaxial helicity source can form and sustain a plasma in an externally generated toroidal field; although it is not clear that our configuration can properly be described as a tokamak, our results suggest that sustainment in a tokamak regime may be possible.In an ideal spheromak configuration the toroidal field vanishes at the wall but the safety factor q does not [6]; in fact, in a closed spheromak it varies by < 20% over the radius. We expected that because of the tight aspect ratio and strong toroidicity, the addition of toroidal field might lead to a significant shear even at modest rod currents. We have therefore studied numerically the effects of toroidal field on force-free equilibria described by VxB=/iB, both for constant p (the relaxed state [7]) and for p =='p^,+c\i//y/o, where if/ is the poloidal flux coordinate, y/G is the gun solenoid flux, and p^ is the value of p at the wall. This form has been used to describe spheromak equilibria in CTX [8]; with j/^ = 0 at the wall, a driven spheromak has <: < 0, the relaxed state r=0, and a decaying plasma c > 0 [8]. Solutions are obtained [9] by the SOR (successive over-relaxation) method applied to the corresponding Grad-Shafranov equation (linearized when p is not a constant). We have so far studied the driven or relaxed cases, c :< 0.We first consider spheromaklike solutions with IR =0. Figure 1 (a) shows a typical set of flux surfaces. Since this system has flux entering and leaving through the electrodes, it includes a separatrix dividing the field into regions of *'short open flux,'' *'long open flux,'' and...

No abstract

It is shown that thcse two models are closely related. The "Tangled Discharge Model" (TDM) necessarily involves a non-vanishing ( t x b), the so-called "dynamo" effect, while the effective functioning of this term in the "Dynamo" models is shown to require a stochastic magnetic field structure. There is no inconsistency between thiscanclusionand the fact that the fully-relaxedstatemay be described by analytical forms such as the "Bessel Function Madcl" which apparently contain good Rur surfdces. The TDM is not

We have used a probe containing both a Rogowski coil and a magnetic pick-up coil to measure both the current density and the fl value in the plasma of the SPHEX spheromak. The results are broadly in agreement with previous measurements but give much better spatial resolution; they reveal a discontinuity at the interface between the 'central column' and 'annulus' regions of the plasma. In the annulus, the range of values of fl spans the spheromak eigenvalue as expected from theory. When the spheromak current drive is terminated by shorting the Marshall gun, the current density at the magnetic axis initially rises to a maximum before decaying, and fi continues to rise towards the eigenvalue. These results are interpreted as showing that the relaxation process continues to operate in the decaying plasma.

Force-free equilibrium magnetic fields in tight-aspect-ratio toroidal configurations are investigated. The study is mainly directed to modelling field configurations in the 'rodomak', a modification to the SPHEX gun-injected spheromak in which a current-carrying rod is inserted along the geometric axis. A family of analytical relaxed states (V x B = p.8, p constant) is presented for a torus of rectangular cross section, with boundary conditions allowing for flux embedded in the walls, representing the gun. Numerically calculated fields in SPHEX geometry, with p profiles relevant to the driven phase of operation, are also given. The dependence of the field conligwations and global quantities such as energy, helicity and toroidal current on the controlling parameters (gun flux, gun current and rod current) and geometry is discussed.