Analysis of magnetic probe signals including effect of cylindrical conducting wall for field-reversed configuration experiment

A confinement field is disturbed by magnetohydrodynamic (MHD) motions of a field-reversed configuration (FRC) plasma in a cylindrical conductor. The effect of the conductor should be included to obtain a spatial structure of the disturbed field with a good precision. For this purpose, a toroidal current in the plasma and an eddy current on a conducting wall are replaced by magnetic dipole and image magnetic dipole moments, respectively. Typical spatial structures of the disturbed field are calculated by using the dipole moments for such MHD motions as radial shift, internal tilt, external tilt, and n=2 mode deformation. Then, analytic formulas for estimating the shift distance, tilt angle, and deformation rate of the MHD motions from magnetic probe signals are derived. It is estimated from the calculations by using the dipole moments that the analytic formulas include an approximately 40% error. Two kinds of experiment are carried out to investigate the reliability of the calculations. First, a magnetic field produced by a circular current is measured in an aluminum pipe to confirm the replacement of the eddy current with the image magnetic dipole moments. The measured fields coincide well with the calculated values including the image magnetic dipole moments. Second, magnetic probe signals measured from the FRC plasma are substituted into the analytic formulas to obtain shift distance and deformation rate. The experimental results are compared to the MHD motions measured by using a radiation from the plasma. If the error included in the analytic formulas and the difference between the magnetic and optical structures in the plasma are considered, the results of the radiation measurement support well those of the magnetic analysis.