LOW

. A vacuum toroidal field has been superimposed on a spheromak by means of an axial conductor. It has been observed that the resulting configuration corresponds to a tokamak with limiting low aspect ratio, i.e. a spherical torus with aspect ratio 1.1. The corresponding spheromak is unstable to n = 1 tilt and shift modes, but this tokamak configuration is found to be globally stable without additional passive stabilization.

ABSTRACT. A vacuum toroidal field has been superimposed on a spheromak by means of an axial conductor. It has been observed that the resulting configuration corresponds to a tokamak with limiting low aspect ratio, i.e. a spherical torus with aspect ratio 1.1. The corresponding spheromak is unstable to n = 1 tilt and shift modes, but this tokamak configuration is found to be globally stable without additional passive stabilization.
At present, toroidal magnetic fusion devices of the tokamak type show the most advanced confinement properties. Scaling considerations from MHD equilibrium and ballooning calculations [1] suggest that higher plasma pressures can be sustained at comparable magnetic field strength if the aspect ratio can be made smaller. The ultimate low aspect ratio limit of a toroidal device is attained in a compact toroid where both toroidal and poloidal magnetic fields are sustained by corresponding plasma currents, i.e. a spheromak with no external toroidal field. In the present experiments the toroidal and poloidal plasma currents are created 'non-inductively' (in the sense of a singly connected plasma without external flux linkage through the centre). Therefore, no transformer along the symmetry axis nor toroidal field coils are needed. This technical advantage may be maintained in future quasi-static experiments if current drive by helicity injection continues to prove feasible. Since the poloidal current density in the spherical plasma varies smoothly, there LETTERS is no 1/r toroidal field profile as in the tokamak. However, if we allow for an external axial current by insertion of an axial conductor into a spheromak, we obtain the configuration termed 'spherical torus' by Peng [2]. Depending on the strength of the current along the central conductor, we can expect a gradual transition from the strongly paramagnetic spheromak toroidal field profile to a tokamak-like field profile.
Peng [2] and Peng and Strickler [3] have discussed the spherical torus plasma and its possible advantages compared with the standard tokamak. The basic feature of the spherical torus is that at very low aspect ratio the strong increase of the toroidal field near the symmetry axis and the paramagnetism allow a much larger plasma current to be driven than in a usual tokamak, without the q-value decreasing below unity. In fact, the toroidal and poloidal fields can become comparable in magnitude. In this case, j3 t , the ratio of plasma pressure to toroidal magnetic field pressure, can amount to more than 20% when an analytical scaling as obtained for MHD stability [4] is applied to the data of the Heidelberg Spheromak Experiment (HSE). This high beta value is similar to the one found experimentally in genuine spheromaks (where q < 1), both in the PS experiments [5] and in the HSE.
To our knowledge, this report is on the first experimental realization of such a spherical torus configuration at an aspect ratio of 1.1 in a high current density plasma. A short initial communication was given in Ref. [6]. We note that related studies at low fields are under way in rotamaks [7].
To produce a spherical torus, we have equipped the HSE with an axial conductor. The experimental device and previous results pertaining to the usual spheromak operation as well as to doubly toroidal configurations have been described elsewhere [6,8,9].
For the purpose of the present studies the experiment was operated with an energy input of 30 kJ. Approximately spherical to slightly oblate plasmas with up to 30 cm diameter were formed. For the present initial studies of the spherical torus we used a standard fill pressure of 2 x 10 21 m~3 deuterium atom density and, as the only diagnostics, two internal magnetic probe arrays, which gave information on the radial profile of all three components of the magnetic field by simultaneous measurements at ten radial positions. Axial scans were performed on a shot-to-shot basis.
The axial conductor inserted into the HSE is located along the symmetry axis passing through the whole length of the plasma (Fig. 1). It consists of a hollow copper rod of 1.5 cm diameter and can be used in three operational modes: (a) The conductor is shielded electrically from the plasma along its whole length by a complete quartz envelope; (b) additionally, an external current circuit is connected to the conductor (the return current is passed through rods symmetrically placed along the outside of the vacuum vessel); and (c) the rod is equipped only with quartz sleeves that provide the necessary insulation against the end plates of the vessel; otherwise it is bare.
In this way, it is possible (a) to insulate the conductor from the plasma and to keep it floating (no current passing along it); (b) to pass an external current along the insulated conductor; and (c) to expose the rod to the plasma without an external current drive, whereby part of the poloidal plasma current can be led into the rod.
The current drive formation proceeds according to the spheromak 0-z pinch scenario [10] in a vacuum vessel of 1 m length and 15 cm inner radius. Solenoidal coils with a radius of 17.5 cm are located outside the vessel. Annular electrode rings protrude at r = 11 cm from the end plates into the vessel; the electrode tips are located at z = ±40 cm (z = 0 being the symmetry plane of the device). After creating an axial bias field by a set of two solenoidal coils at z = ± 11 cm, the axial current is initiated within the plasma via the electrode rings. Shortly after initiation of the axial current (1-4 /xs) the axial main field (opposite in direction to the bias field) is applied by a separate set of coils placed at z = ±25 cm. During the rise of the axial current the plasma follows approximately the F-0 trajectory [11] along a sequence of equilibria with increasing radial eigenvalues [6].
The current rises to a maximum of about 180-200 kA in 12 /xs. The pinch is sufficiently slow to avoid strong compressional effects. With the axial conductor, no significant differences between this configuration and the standard spheromak formation are observed. By this technique, toroids are established with typical magnetic field amplitudes of 0.3-0.6 T.
If the conductor is currentless and shielded against the plasma (case (a)) the plasma currents will form the standard magnetic field configuration of a spheromak [8], which is well known to be unstable against n = 1 modes. In the present setup, with the shape of the toroid being almost spherical, a combined tilt and shift mode destroys the configuration within a few microseconds, irrespective of the insertion of the axial rod (case (a)).
To pass an axial current along the rod during the formation and equilibrium phases of the spheromak (case (b)), we use a slow capacitor bank that can supply currents up to 26 kA parallel to the poloidal plasma current inside the magnetic axis, i.e. up to about 14% of its peak value. (If the current is applied in reversed direction, the poloidal flux is sharply reduced.) At low superimposed currents (less than 7% of the peak plasma current) the toroid becomes unstable, as in case (a). However, with increasing external axial current the onset of n = 1 modes is found to be delayed. With a current of more than 24 kA passing through the insulated conductor, the plasma configuration is almost completely stable; there are, however, deviations from symmetry and slow motions of the plasma.
The third experimental modification (case (c)), which we now discuss in more detail, was performed by removing the insulating quartz tube (only the insulation against the end plates was maintained). Generally, highly symmetric and stable plasmas were obtained. Again, the maximum axial current passing through the annular electrodes was 180 kA.  shows the temporal development of the externally applied current and the current measured within the axial rod at the symmetry plane. It can be seen that rather late during the z-pinch phase, about one-third of the plasma current flows into the central conductor and then decays with about the same time constant as the total plasma current. From the field profiles of the established plasma configuration we can infer that the axial current of the conductor returns mainly beyond the separatrix, through the outside plasma and possibly along the inner side of the walls. Measurements of the external current (through the I z circuit) by Rogowski coils show that the current in the axial rod must be closed within the vacuum vessel. (If there remains a residual external current -due to non-ideal crowbar performance -we find that the toroid is rather insensitive to the direction of this current.) Figure 3 shows the measured radial profiles of the magnetic field in the symmetry plane at t = 24 /xs (indicated by an arrow in Fig. 2). The poloidal field (and flux) pattern is almost unchanged with respect to a simple spheromak-like equilibrium (indicated by broken lines on the right-hand side), but the toroidal field is highly enhanced near the symmetry axis. Figure 4 shows the axial field profiles (for B z at r = 1.5 cm, for B tor at r = 7.5 cm, the latter demonstrating the paramagnetism). Experimentally, there is a shift of the symmetry centre 1.7 cm to the right. This is possibly due to asymmetries in the end plates of the device. For comparison, Fig. 4  approximately sinusoidal dependence on z and have also been shifted by 1.7 cm to match the experimental asymmetry. As a consequence, the q-profile of the confined plasma is changed drastically from that of the normal spheromak (i.e. q^^ axis < q sep aratrix)-The absolute value is everywhere slightly above q = 1, increasing to q > 5 at the separatrix. Hence, while there is low shear in the bulk of the plasma, towards the separatrix there is a much higher shear than in the normal spheromak (and also the large aspect ratio tokamak) equilibrium. In fact, the q-profile is close to the one anticipated from Peng's calculations for the spherical torus.
As a certain basis for comparison, we use an approximate analytical model, assume straight cylindrical boundary conditions and solve the equilibrium equation, with I = 1,^ + Ioandp = * = C.rJ.dlilr) + C 2 rY,(|I,|r) -Po r 2 /I] -VI, (1) where Ji and Y, are Bessel functions of the first and second kind, C, and C 2 are constants of integration, and Io is the current passing along the axial conductor. Of course, this equilibrium is applicable -if at allonly in the symmetry plane of the investigated configuration, since here the first derivative with respect to z vanishes and the second one contributes only to the amplitude and not to the shape of the profiles (in a separable situation). In any case, when we compare the experimental profiles with this crude model (with C) matched by the conductor radius, I, and Io taken from a plot of the poloidal current versus poloidal flux, and C 2 taken from a least-squares fit to the radial toroidal field profile) we find good agreement (Fig. 3, solid  lines). Also, the similarity with the profiles of Peng and Strickler is evident (Fig. 5 of Ref. [3], left-hand side graph). We note especially the strong paramagnetism as a remnant of the ideal spheromak equilibrium (the vacuum field contribution is indicated by the broken curve on the left-hand side of our Fig. 3).
In cases (b) and (c) the established spherical torus persists for about 42 /xs. Some shots show field reversal times up to 55 [is. The magnetic energy content is about 600 J and hence is a factor of two to three above the magnetic energy content of a corresponding spheromak. Although we did not measure the plasma parameters, we can conclude from the decay time (using Spitzer resistivity) and from Thomson scattering on related spheromaks [8] that the electron temperature near the magnetic axis will be about 15-20 eV. This is in reasonable agreement with one-dimensional transport calculations which show that a few per cent of low-z impurities make the transport radiation dominated. While higher ion temperatures can be anticipated in a pinch-like formation, we do not expect to have a significant difference between electron and ion temperatures during the later decay phase.
The excellent global stability of the toroid with the central axial current in case (c) shoud be noted. While line tying might contribute to this stability, case (b) demonstrates that the toroidal field itself has a strong stabilizing influence. We believe that the stability and symmetry of the toroid would be further enhanced in case (b) if the external current could be increased to beyond 26 kA. We can infer from the temporal traces of the magnetic signals taken at various r-and z-positions that the magnetic fluctuation level under the present resistive conditions is not significant.
In summary, we have created a spherical torus by non-inductive current drive. The equilibrium found is very similar to the one expected by Peng and Strickler [3] and shows comparable toroidal and poloidal field amplitudes. Preliminary beta studies indicate average values of around 20%. Thus, regarding energetics, the equilibrium is as favourable as that of a spheromak. The complete removal of the global n = 1 modes in case (c), irrespective of the time varying eigenvalue, makes this plasma interesting for further study.