Todd Desiato (@WarpTech)'s Evanescent Wave Theory
==> NOTE: This is very much out of date. Todd Desiato (@WarpTech on Nasaspaceflight forums) has updated his theory. For the time being please see the EM Drive thread or search posts under member WarpTech on Nasaspaceflight forums. This is a recent version: http://forum.nasaspaceflight.com/index.php?action=dlattach;topic=41732.0;attach=1392848;sess=45576
Todd Desiato (@WarpTech on Nasaspaceflight forums) has put forth a theory that explains the EMDrive's thrust as a result of evanescent waves derived from the asymmetrical attenuation of the cavity. The evanescent waves interfere with the standing wave oscillations such that a pressure gradient is momentarily created inside the frustum that can cause impulses of thrust as the cavity charges and discharges its resonant stored energy. Evanescent waves are exponential functions, they are either increasing or decreasing in amplitude.
An Introduction to the Polarizable Vacuum Model of General Relativity
The idea that the vacuum of space-time could be modeled as a variable refractive index (K) was originally published by R. H. Dicke, in 1957 and was known as the "eps, mu formalism".  Before he had conceived of the General Relativity (GR) theory, Albert Einstein wrote a short paper about the work done by gravity on light propagating in a gravitational field and used a variable speed of light approach.  The Polarizable Vacuum (PV) Model was later developed by Harold Puthoff as an alternative approach to GR, merely a different interpretation of the data regarding gravity we have available to us today. It was shown that metric coefficients derived using Puthoff's Lagrangian density, which differed slightly from Dicke's, were a first order approximation of the Schwarzschild solution of GR and could account for the gravitational red-shift of light, gravitational time dilation and length contraction, the perihelion of the planet Mercury and of course, gravitational lensing. Puthoff also derived an alternative solution to the Reissner-Nordstrom solution of GR.  The PV Model however did not explain black holes. Todd Desiato wrote a paper explaining how the Event Horizon still existed in the PV Model for an inward falling particle that is emitting light.  Based on these works of Puthoff and Desiato, and also some online correspondence, Joe Depp wrote a pair of papers that simply changed the leading constant from c^4/K^2 to (c/K)^4, for consistency within the theory. This minor change corrected the Lagrangian density of Puthoff to yield the exact Schwarzschild and Reissner-Nordstrom solutions, identical to GR. Depp also showed the equations of motion of the refractive index provided the solution for an infinite massive wire, that matched the GR solution as well. [5, 6]
The PV Model is an Engineering tool. It facilitates an understanding of the vacuum medium in a way that is engineering friendly. It permits solutions in the context of a Lagrangian formalism, that can be applied to electromagnetic fields with the aid of QED and gauge potentials. In the model, a gravitational field is interpreted as a variable refractive index that alters space-time and determines the relative scale of rulers and clocks in the altered region, as measured by a distant observer in an unaltered region of space-time. One obvious advantage of working on warp drive and FTL travel from the perspective of a distant observer is that in Relativity, the speed of light remains constant in the local inertial reference frame. Observers in the local frame cannot measure anything moving FTL locally, with local rulers and clocks. Therefore, it is advantageous for engineers to understand what to expect, what to look for and why there is a need to make observations from the perspective of a distant observer in an unaltered reference frame, outside of the effects to be measured.
Application of Theory to the EmDrive
According to @WarpTech, the EMDrive function mimics a variable refractive index but only across the specific wavelengths that correspond to its internal geometry. The equations for waves propagating in a waveguide have a direct correlation to the PV Model, in that the wave velocity inside the waveguide is a function of its dimensions. A tapered waveguide such as the EM Drive as Shawyer describes it, has a variable wave velocity that is different at each end. The waves accelerate as they move from the small end toward the larger end. In such a description, the waveguide mimics the variable refractive index medium of the PV Model within a narrow bandwidth near the cut-off of the waveguide. In other words, it creates an accelerated reference frame across this narrow bandwidth.
This variable speed of light is the result of attenuation, caused by the relative phase-shift between the incoming and outgoing waves α = j(k - β), where k is the phase of the incoming wave and β is the phase of the outgoing wave. Thus, there is constructive and destructive interference between the evanescent wave and the standing wave that results in a variable speed of light, within this bandwidth.
The equation for force as given by Juan Yang is the correct equation, per Maxwell's equations. What is not given are the exact expressions of E and H fields to plug into them. Simple harmonic functions of sin(ωt), cos(ωt) will not result in thrust, as pointed out by Greg Egan. However, multiplying these functions by exponentially increasing or decreasing amplitudes, exp(±t/τ), do not meet the requirement of his argument, that the time average of the fields is zero.
The EM Drive is intentionally designed to have asymmetrical attenuation. As such, energy is reflected from the large end to be stored at the small end as induced currents. Standing waves store energy and as such, store mass. As the EM drive charges and the Q ramps up, energy from the input source is reflected from the large end and stored in the small end on each successive reflection cycle. This energy is stored as induction currents caused by the near-field effects of evanescent waves. Due to the phase shift, the Power Factor is not zero as it is with standing waves. Therefore, work can be done to move the EM Drive. This dynamic action of storing mass-energy toward the front causes the center of mass to walk forward. The increasing pressure on the small end causes the EM Drive to accelerate forward due to the internal pressure gradient, until the pressure is equalized. Then the cycle builds again. This dynamic implies that a high Q value is not required, but rather how quickly can energy be ramped up under extreme attenuation conditions.
On 6/6/15 @WarpTech published the following papers to the NSF forum:
- File:Desiato-EM Drive Mechanism-v2.pdf which proposes an explanation of the underlying mechanism.
There is not yet enough experimental data to validate @WarpTech's theory. Additional data, particularly from superconducting EmDrive experiements, may result in data that is relevant to validating or disproving this theory.
Predictions and Evidence
Notably, it is solely the geometry of the frustum that is relevant to this effect under @WarpTech's theory. A higher power level or higher Q would not result in higher thrust. The Q factor is only relevant as a measure of the stored amount of energy. The frustum itself does not need to resonate, and to this end, @WarpTech has proposed decoupling the resonance chamber from the attenuation chamber. He suggests a design where resonance is induced in a long cylindrical waveguide, then energy is periodically dumped into a frustum to attenuate. So far this design has not been tested. See List of Suggested Experiments
Another interesting consequence of @WarpTech's theory is that the EmDrive must be considered a Warp Drive. However, because the warp effect is limited to a portion of the EM spectrum (with frequency corresponding to the size of the frustum), the effect would not be detectable via the laser warp interferometer employed by NASA EagleWorks, as the distortion would occur at microwave wavelengths. This prediction appears to be in conflict with the report of a positive distortion by the laser interferometer at EagleWorks. However, it remains to be seen if the interferometer test can be reproduced, especially in a vacuum. According to @WarpTech's theory the EmDrive could not theoretically be used for faster than light travel, because in order to do so the effect would need to happen over a much wider bandwidth which covers all of the frequencies and modes of sub-atomic particles and fields. The reason gravity is so difficult to control with EM fields is directly related to the necessary bandwidth and power spectrum over which it interacts. The EM Drive is only mimicking this behavior over a very narrow bandwidth.