Equilibrium and Stability Studies of Plasmas Confined in a Dipole Magnetic Field Using Magnetic Measurements

Abstract

The Levitated Dipole Experiment (LDX) is the first experiment of its kind to use a levitated current ring to confine a plasma in a dipole magnetic field. The plasma is stabilized by compressibility and can theoretically attain a peak beta on the order of unity. Various magnetic sensors have been designed, calibrated, installed, and operated to measure the plasma current, from which the pressure profile is deduced through a mathematical process called reconstruction. Both isotropic and anisotropic models are introduced and used to obtain the equilibrium. The need for an anisotropic pressure model is evident since electron cyclotron resonance heating produces highly anisotropic plasmas in LDX. Compared to the isotropic pressure models, the anisotropic model predicts a larger peak beta for a given set of magnetic measurements due to a modification in the current-pressure relationship. We have achieved a peak beta in excess of 26 % using the anisotropic model. One of the important results of this work involves characterizing the properties of reconstructing LDX plasmas. Because the floating coil is superconducting, it must be ensured that the flux linked to it is kept constant while deducing the plasma current. A significant difficulty in reconstructing LDX plasmas is that the magnetic sensors are sensitive mostly to the plasma dipole moment due to their large distances from the plasma. This means that a family of current and pressure profiles with the same dipole moment fits the magnetic measurements equally well. X-ray emissivity data is used as a supplemental measurement to unequivocally determine the pressure profile. Simulation results show that adding internal flux loops close to the plasma can increase their sensitivity to higher order moments. In addition to demonstrating the feasibility of achieving high beta, the magnetic diagnostics have decisively shown that LDX plasmas routinely have supercritical pressure profiles that exceed the MHD limit. The plasmas we have achieved to date have a significant fraction of hot electrons, which are susceptible to a kinetic analog of the MHD interchange mode called the hot electron interchange mode (HEI). Although the MHD gradient limit is slightly increased by incorporating pressure anisotropy, the best fit profile usually gives a pressure gradient that substantially exceeds even the 3 anisotropic limit. Magnetic measurements herefore confirm that the hot electrons are not sub ject to the MHD interchange mode, and the HEI is the relevant instability. The HEI’s have been measured by Mirnov coils, and their occurrences have been correlated to drops in flux measurements. Lastly, a stored energy-plasma current relationship has been derived, and its result has been used to estimate the energy confinement time of LDX plasmas with different heating frequency compositions.