G. J. Marklin

Experimental determination of the conservation of magnetic helicity from the balance between source and spheromak

The conjecture that magnetic helicity (linked flux) is conserved in magnetized plasmas for time scales that are short compared to the resistive diffusion time is experimentally tested in the CTX spheromak [Phys. Rev. Lett. 45, 1264 (1980); 51, 39 (1983); Nucl. Fusion 24, 267 (1984)]. Helicity is created electrostatically by current drawn from electrodes. The magnetized plasma then flows into a conducting flux conserver where the energy per helicity of the plasma is minimized and a spheromak is formed on a relaxation time scale of many Alfven times. The magnetic field strength of the equilibrium is subsequently increased and sustained. The amount of helicity created by the magnetized coaxial plasma source, the helicity content of the spheromak equilibrium, and the resistive loss of the helicity are measured to determine the balance of helicity between source and spheromak with a ±16% uncertainty. In CTX the amount of energy that must be rapidly dissipated within the conducting boundary while conserving hel...

The impedance and energy efficiency of a coaxial magnetized plasma source used for spheromak formation and sustainment

Electrostatic (dc) helicity injection has previously been shown to successfully sustain the magnetic fields of spheromaks and tokamaks. The magnitude of the injected magnetic helicity balances (within experimental error) the flux lost by resistive decay of the toroidal equilibrium. Hence the problem of optimizing this current drive scheme involves maximizing the injected helicity (the voltage‐connecting‐flux product) while minimizing the current (which multiplied by the voltage represents the energy input and also possible damage to the electrodes). The impedance (voltage‐to‐current ratio) and energy efficiency of a dc helicity injection experiment are studied on the CTX spheromak [Phys. Fluids 29, 3415 (1986)]. Over several years changes were made in the physical geometry of the coaxial magnetized plasma source as well as changes in the external electrical circuit. The source could be operated over a wide range of external charging voltage (and hence current), applied axial flux, and source gas flow rate...

Energy confinement studies in spheromaks with mesh flux conservers

The paper presents experiments and analysis of energy confinement on the CTX spheromak. Compared to previous published results from 0.4 m radius flux conservers, in a 0.67 m radius mesh flux conserver (with the current density kept constant), the magnetic field increases while the plasma density is kept the same. However, the electron temperature does not rise, and hence βvol drops. The plasma resistivity remains constant (the resistance drops as the size increases), and the energy confinement time stays the same. Plasma energy content results from spheromaks during sustainment by helicity injection are also presented and show confinement equivalent to that during the decay phase. Increased magnetic field in the same size experiment produces very little improvement in electron temperature and a decrease in confinement time. The resistive decay time is found to be empirically independent of the core electron temperature. It is, instead, proportional to the strength of the magnetic field at constant plasma density, while the ratio of magnetic field to decay time depends on plasma density, consistently with ionization breakdown at the edge of the spheromak dominating helicity dissipation. The possible causes of this observed confinement are examined separately in detailed quantitative and qualitative studies. Absolutely calibrated multichord bolometry shows that impurity radiation is not the cause of the low electron temperatures. The particle confinement time has increased with size, but does not show an increase with increasing magnetic field. At the lower βvol of the larger experiment, the particle replacement power cannot explain the unaccounted energy losses. Any important role of pressure driven modes in the CTX energy balance is shown to be inconsistent with the available CTX data. The possibility that rotating coherent current driven kink modes can seriously degrade energy confinement is evaluated and discounted owing to the lack of improvement when the modes are absent. The role of anomalous ion heating is examined, and the available data are presented. Finally, a hypothesis explaining these results is presented, suggestions for future work are made, and the results are summarized.

Progress with energy confinement time in the CTX spheromak

Large improvements in spheromak parameters and new understanding have been obtained from the CTX experiment at Los Alamos [Phys. Rev. Lett. 51, 39 (1983); 61, 2457 (1988)]. In one experiment the global energy confinement time has been increased an order of magnitude over previous experiments to 0.2 msec and the magnetic‐energy decay time increased to 2 msec. These results were achieved in a decaying spheromak by reducing the helicity dissipation in the edge. In another smaller spheromak, record electron temperatures (∼400 eV) and record magnetic field strengths (∼30 kG) have been obtained.

The m=1 helicity source spheromak experiment

In this paper extensive measurements of magnetic equilibrium and source parameters in the m=1 helicity source spheromak experiment are described (previously called the kinked z‐pinch source [Comments Plasma Phys. Control Fusion 9, 161 (1985)]). In the cylindrical entrance region connecting the stabilized z‐pinch helicity source to the spheromak flux conserver, the observed equilibrium configuration is the helical azimuthal m=1 state with no net axial flux. In the flux conserver, the equilibrium is a spheromak (m=0) state with an m=1 distortion. The magnetic equilibria observed are compared to theory. The performance of the source relative to coaxial helicity sources is also examined.

Ion heating and current drive from relaxation in decaying spheromaks in mesh flux conservers

The plasma energy confinement in CTX mesh flux conservers appears to be dominated by relaxation fluctuations which drive current in the resistive plasma edge region. Strong ion heating is expected from these relaxation processes. The paper presents new data, from previously studied decaying discharges, which show impurity oxygen ion Doppler temperatures much above the Thomson scattering electron temperature. In addition, using the standard MHD equilibrium model by Knox et al., and the resistivity model previously described by Fernandez et al., the contribution of relaxation fluctuations to spheromak current drive along the open magnetic field lines at the spheromak edge can be estimated.

Increased particle confinement observed with the use of an external dc bias field in a spheromak experiment

Spheromaks are formed in a mesh flux conserver in the presence of an external dc bias magnetic field. The particle confinement is improved when the spheromak separatrix is put inside the metal mesh by the application of positive bias flux. The spheromaks remain stable to tilt instabilities with ratios of bias‐to‐spheromak flux of up to 47±7%.

Numerical calculation of Mercier beta limits in spheromaks

By iteratively solving the Grad–Shafranov equation and the Mercier criterion, stable pressure profiles may be determined self‐consistently with spheromak equilibria. No assumption is made about the shape of the pressure profile and an individual determination is made for that value of the pressure that drives the plasma marginally stable everywhere. These limits determine the pressure profile that provides the largest 〈β〉vol allowed by Mercier modes. Particular attention is given to the CTX spheromak [Phys. Rev. Lett. 51, 39 (1983)]. The results on spheromak Mercier stability limits leading to 〈β〉vol =1.5% for sustained spheromaks are summarized. In addition, 〈β〉vol =7.0% has been calculated for spheromaks with current holes.

The evolution of a decaying spheromak

The evolution of a low beta spheromak initially in a two‐dimensional stable equilibrium having a constant J/B (the so‐called minimum energy state) is calculated within the context of resistive magnetohydrodynamics. Since the initial equilibrium is stable, the spheromak at first resistively evolves through a sequence of stable quasiequilibria. This phase of the evolution is calculated with a transport code in which the resistivity is assumed to be largest at the wall and lowest at the magnetic axis. Resistive diffusion causes the safety factor q to decrease everywhere while decreasing fastest near the wall. The quasiequilibria through which the spheromak evolves are tested for stability with both an ideal linear stability code and a resistive one. The results of both stability codes are in basic agreement and show that when q drops to below (1)/(2) everywhere the spheromak becomes unstable to an n=2 mode. The agreement of the stability codes implies that the unstable mode is a resistively modified ideal mo...