With the establishment of vanishing net electrostatic fields in a toroidally symmetric tokamak at equilibrium [R. W. Johnson, to appear in Phys. Rev. D], one is left needing an explanation for the measurement of an apparent radial electric field in e
xperiments. Two scenarios are proposed, depending on the type of measurement being considered. Indirect measurement via the radial equation of motion for an impurity species possibly measures that species net radial viscous force, and direct measurement via the motional Stark effect might reveal electric fields generated by the shifting of the toroidal magnetic flux density.
The calculation presented in A neoclassical calculation of rotation profiles and comparison with DIII-D measurements by Stacey, Johnson, and Mandrekas, [Physics of Plasmas, 13, (2006)], contains several errors, including the neglect of the toroidal e
lectric field, an unphysical expression for the electrostatic potential, and an unevaluated relation among its parameters. An alternative formulation is discussed.
From a common expression for the poloidal electrostatic field of a tokamak, in the limit of large aspect ratio and concentric circular flux surfaces, one may determine the associated potential. This potential satisfies Poissons equation, which reduce
s to Laplaces equation when the medium has vanishing charge density, in axial geometry but not toroidal geometry. A simple transformation takes the potential over to the correct harmonic form for tokamak coordinates, and the resulting electrostatic field is calculated. From the radial field one may estimate the supporting charge density on the boundary, and from the poloidal field one may determine a prediction for the radial dependence of the electron temperature, which does not compare well with a rough estimate of the profile often seen in a tokamak.
The calculation presented in Rotation Velocities and Radial Electric Field in the Plasma Edge by W. M. Stacey [Contrib. Plasma Phys. 46, (2006)] contains an inconsistent treatment of the electrostatic potential. Comparing the expressions for the pote
ntial associated with the radial electrostatic field with that associated with the poloidal electrostatic field reveals the inconsistency. A field-theoretic perspective implies that the electrostatic field must vanish in a model based upon the physics of a neutral, conducting fluid.
The neoclassical prescription to use an equation of motion to determine the electrostatic field within a tokamak plasma is fraught with difficulties. Herein we examine two popular expressions for the equilibrium electrostatic field so determined and
show that one fails to withstand a formal scrutiny thereof while the other fails to respect the vector nature of the diamagnetic current. Reconsideration of the justification for the presence of the equilibrium electrostatic field indicates that no field is needed for a neutral plasma when considering the net bound current defined as the curl of the magnetization. With any shift in the toroidal magnetic flux distribution, a dynamic electric field is generated with both radial and poloidal components, providing an alternate explanation for any measurements thereof.
The continuous wavelet transform may be enhanced by deconvolution with the wavelet response function. After correcting for the cone-of-influence, the power spectral density of the solar magnetic record as given by the derectified yearly sunspot numbe
r is calculated, revealing a spectrum of odd harmonics of the fundamental Hale cycle, and the integrated instant power is compared to a reconstruction of global temperature in a normalized scatter plot displaying a positive correlation after the turn of the twentieth century. Comparison of the spectrum with that obtained from the Central England Temperature record suggests that some features are shared while others are not, and the scatter plot again indicates a possible correlation.
The resistive magnetohydrodynamic (MHD) equations as usually defined in the quasineutral approximation refer to a system of 14 scalar equations in 14 scalar variables, hence are determined to be complete and soluble. These equations are a combination
of Navier-Stokes and a subset of Maxwells. However, one of the vector equations is actually an identity when viewed from the potential formulation of electrodynamics, hence does not determine any degrees of freedom. Only by reinstating Gausss law does the system of equations become closed, allowing for the determination of both the current and mass flow velocity from the equations of motion. Results of a typical analysis of the proposed electromagnetic hydrodynamic model including the magnetization force are presented.
