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Of those gauge theories of gravity known to be equivalent to general relativity, only the biconformal gauging introduces new structures — the quotient of the conformal group of any pseudo-Euclidean space by its Weyl subgroup always has natural symplectic and metric structures. Using this metric and symplectic form, we show that there exist canonically conjugate, orthogonal, metric submanifolds if and only if the original gauged space is Euclidean or signature 0. In the Euclidean cases, the resultant configuration space must be Lorentzian. Therefore, in this context, time may be viewed as a derived property of general relativity.

Hot plasma dielectric response models, which are now used in most linear full wave codes, are formulated in Fourier space assuming that particle's Larmor radius is much smaller than the scale of spatial nonuniformity of magnetic field. Such approximation assumes that the spatial scale of plasma dielectric response to the RF field is limited to a few Larmor radii, which is accurate for a limited range of wave frequencies ω. The scale of plasma dielectric response along the magnetic field line could be comparable to the scale of the magnetic field nonuniformity when ω is close to the particle's cyclotron frequency ωc or when ω is much smaller than ωc, which requires the use of a more accurate model. In the present approach, the hot plasma dielectric response is formulated in configuration space without limiting approximations by numerically calculating the plasma conductivity kernel based on the solution of the linearized Vlasov equation in nonuniform magnetic field. Results of the conductivity kernel calculation in hot collisionless plasma are presented for 1-D mirror and 2-D tokamak magnetic field configurations for ω∼ωc. Self-consistent simulation of RF fields using the calculated conductivity kernel of 1-D mirror magnetic field is made. A new parallel full wave RF code, based on the presented approach of accurate self-consistent modeling of plasma dielectric response in configuration space, is under development.

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