This thread has resulted in great synergy between NSF contributors and Paul March at NASA, and I wanted to take this opportunity to name a partial list of accomplishments and thank everybody that has contributed -including a few humble persons who privately asked me not to list their numerous valuable contributions -(please forgive me if I am missing important contributions, tell me what I missed, or if you disagree, what I should correct):Consideration was made of whether the experimental measurements of thrust force were the result of an artifact. Dr. Rodal, one of the contributors, solved the nonlinear, fully coupled system of differential equations (including magnetic damping) of an inverted torque pendulum with Mathematica to examine whether parasitic modes or nonlinear dynamics could be involved. Chaotic motion and strange attractors were also examined. Comparison with the experimental results showed that none of these nonlinear dynamics effects were involved in the experimental measurements at NASA Eagleworks, and therefore a nonlinear dynamics cause was eliminated. Dr. Rodal (in the US) also conducted Power Spectral Density and Autocorrelation analysis of NASA's experimental data and worked with another contributor, @frobnicat, (in France) to examine the dynamics of the experimental response. They concluded that indeed NASA's experimental measurements exhibited the expected response of NASA's torque pendulum as excited by an initial thrust force impulse followed by a thrust force response during the 30 to 40 sec length of the experiments. Dr. Rodal analyzed possible thermal instability (thermal buckling of the flat ends) as a cause for the measured thrust and reported this at NSF and at ResearchGate (
https://www.researchgate.net/publication/268804028_NASA%27S_MICROWAVE_PROPELLANT-LESS_THRUSTER_ANOMALOUS_RESULTS_CONSIDERATION_OF_A_THERMO-MECHANICAL_EFFECT). A thermo-mechanical effect (thermal buckling) is shown that occurs in less than 1 second (for the copper thickness employed for the microwave cavity), with a temperature increase of a degree C or less and that results in forces of the same magnitude as reportedly measured by NASA. Moreover, this thermal instability produces forces in the same direction as measured, and it will occur in a vacuum (since the heating can be due either to induction heating from the axial magnetic field in a TE mode or resistive heating due to the axial electric field in a TM mode). However, this effect can only explain the initial impulsive force and cannot explain the longer 30 to 40 second measured force. Thus the thrust force measured for up to 40 second is not nullified by this explanation either.
Thermal expansion effect as posited by a team from Oak Ridge National Labs for another propellant-less set of experiments was also eliminated as a possible source by the NSF contributors because it would result in forces in the complete opposite direction as the forces measured by NASA.
One of the participants in the NSF forum is Dr. McCulloch (an academic from the UK), who independently developed a tentative theoretical explanation for the EM Drive: assuming that photons have inertial mass, which is caused by Unruh radiation, whose wavelengths must fit inside the EM Drive cone, more Unruh waves fit in at the wide end of the EM Drive, so photons traveling along the axis would always gain mass going towards the wide end and lose it going the other way. This is equivalent to expelling mass towards the wide end, so the EM Drive must move towards its narrow end to conserve momentum. This agrees with the (forward) direction of movement of the EM Drive in reported NASA experiments. Dr. McCulloch derived a simple formula to predict the thrust force and published his theory in the journal Progress in Physics (
http://www.ptep-online.com/index_files/2015/PP-40-15.PDF). In his blog and published paper he acknowledges the help from NSF participants (@aero, and @Fornaro) in estimating the geometrical dimensions of the EM Drives tested in the US, UK, and China.
Another participant in the NSF forum, @Notsosureofit (Ph.D. Physics) developed and posted an analysis of the EM Drive thrust considering an accelerating frame of reference caused by a dispersive cavity resonator and obtained a formula to predict the thrust of the EM Drive that takes into account the electromagnetic mode shape of the EM Drive (unlike the formulas of McCulloch and Shawyer that do not explicitly include mode shape information).
@frobnicat and Dr. Rodal conducted statistical analyses of the experimental data. @frobnicat wrote a computer program that included hundreds of possible combinations of the experimental parameters (such as power input, frequency, Q (quality factor of resonance), geometrical dimensions, etc.) to the first few powers. Interestingly the best fitting formulas were similar to the theoretically derived formula by Notsosureofit and also McCulloch's formula.
Astrophysicist TMEubanks examined whether the EM Drive could be coupling to the (Dark Matter) Axion background. He concluded that this is very unlikely (by up to 20 orders of magnitude) due to the findings of the Axion Dark-Matter experiment, looking for yoctowatts (10^-24) of RF power in the 2 - 20 micro-eV range, precisely the range of the EM Drive, by tuning the cavity's resonant frequency to the axion mass. There is simply no way that the Drive is coupling to the axion background - the ADMX would see a whopping signal.
Dr. Rodal obtained an exact solution for the electromagnetic modes in a cavity with similar geometry as the NASA's EM Drive using Mathematica and the theory of spherical waves developed by the Russian/American scientist Schelnukoff. The resulting equations are very similar to the ones posted by Greg Egan (
http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html) . Dr. Rodal calculated the natural frequency for electromagnetic modes tested in the EM Drive, from this exact solution, to compare with the NASA predictions by Frank Davies NASA/JSC/EP5 using Finite Element Analysis with the computer code COMSOL. The exact solution results calculated by Dr. Rodal at the NSF forum are only 1% different from the NASA calculations using COMSOL. This confirms the validity of NASA's COMSOL analysis, and that the finite element mesh used was fine enough to result in predicted frequencies that are less than 1% from the exact solution, hence confidence can be had on those calculations. The validity of NASA's COMSOL calculations has been simultaneously confirmed by experimental comparison with the IR thermal camera image produced for mode shape TM212.
NSF member @aero is using MIT's Finite Difference computer code MEEP to calculate the force produced by evanescent waves escaping from the EM Drive and interacting with the stainless steel vacuum chamber. This work is in progress.
Despite considerable effort at NSF to dismiss the reported thrust as an artifact the EM Drive results have yet to be falsified. After consistent reports of thrust measurements from EM Drive experiments in the US, UK, and China, at thrust levels several thousand times in excess of a photon rocket, and now under hard vacuum conditions, the question of where the thrust is coming from deserves serious inquiry.