https://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23Permittivity is typically associated with dielectric materials, however metals are described as having an effective permittivity, with real relative permittivity equal to one.[22] In the low-frequency region, which extends from radio frequencies to the far infrared and terahertz region, the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the complex index n of a metal is practically a purely imaginary number, expressed in terms of effective relative permittivity it has a low imaginary value (loss) and a negative real-value (high conductivity).[23]A model for the dielectric function of metals is the Lindhard or random phase dielectric constant.http://adsabs.harvard.edu/abs/2006ApPhL..89u3106W (Drude-Lindhard)http://link.springer.com/article/10.1007%2FBF0111573031 refs listed toohttp://www.wave-scattering.com/drudefit.html

Quote from: aero on 06/19/2015 01:02 AMQuote from: Rodal on 06/19/2015 12:21 AMQuote from: deltaMass on 06/18/2015 11:32 PMPerhaps an ASIC accelerator card exists for MEEP?There is not much one can find on that for MEEP because it has such a small user's community (big companies can afford commercial codes). However, Time-Domain Finite-Element methods have been accelerated using the Graphics Processing Unit, see for example this: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4168264&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4168264, and the acceleration of a finite difference method like MEEP would be simpler than the one for a Finite Element method. However, the authors only claim an improvement of <<a factor of close to two yet, relative to an Intel CPU of similar technology generation.>> so it doesn't come even close to the factors that @aero is talking about.I think that the best approach is to use a similar finite difference mesh as @aero is using now (just modeling the interior of the cavity and modeling the boundary with boundary conditions) and perform a time-marching finite-difference for the Time-Domain instead of solving the eigenvalue problem.This would enable us to answer what is the nature of the evanescent waves, and the other questions we have posed. (just modeling the interior of the cavity and modeling the boundary with boundary conditions)In that regard, I really really need the complex permittivity of copper at ~2 - 3 GHz. We want to look for evanescent waves which are likely created at the boundaries. But perfect metal may not provide the right "stimulus."Why not just start by seeing whether geometrical attenuation is enough to produce them?Suggestion: take the NASA truncated cone (or any other cone used by the researchers) and using exactly the same cone angle, continue the cone up to the point where the small diameter is 50% of the small diameter used by the researcher (at that point the length of the truncated cone would be extended by approximately the same proportion). Excite this longer cone at the same frequency as used by the researchers. Compare the above geometry (in the Time-Domain) with the interior behavior of the truncated cone used by the researchers.It will be interesting to see

Quote from: Rodal on 06/19/2015 12:21 AMQuote from: deltaMass on 06/18/2015 11:32 PMPerhaps an ASIC accelerator card exists for MEEP?There is not much one can find on that for MEEP because it has such a small user's community (big companies can afford commercial codes). However, Time-Domain Finite-Element methods have been accelerated using the Graphics Processing Unit, see for example this: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4168264&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4168264, and the acceleration of a finite difference method like MEEP would be simpler than the one for a Finite Element method. However, the authors only claim an improvement of <<a factor of close to two yet, relative to an Intel CPU of similar technology generation.>> so it doesn't come even close to the factors that @aero is talking about.I think that the best approach is to use a similar finite difference mesh as @aero is using now (just modeling the interior of the cavity and modeling the boundary with boundary conditions) and perform a time-marching finite-difference for the Time-Domain instead of solving the eigenvalue problem.This would enable us to answer what is the nature of the evanescent waves, and the other questions we have posed. (just modeling the interior of the cavity and modeling the boundary with boundary conditions)In that regard, I really really need the complex permittivity of copper at ~2 - 3 GHz. We want to look for evanescent waves which are likely created at the boundaries. But perfect metal may not provide the right "stimulus."

Quote from: deltaMass on 06/18/2015 11:32 PMPerhaps an ASIC accelerator card exists for MEEP?There is not much one can find on that for MEEP because it has such a small user's community (big companies can afford commercial codes). However, Time-Domain Finite-Element methods have been accelerated using the Graphics Processing Unit, see for example this: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4168264&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D4168264, and the acceleration of a finite difference method like MEEP would be simpler than the one for a Finite Element method. However, the authors only claim an improvement of <<a factor of close to two yet, relative to an Intel CPU of similar technology generation.>> so it doesn't come even close to the factors that @aero is talking about.I think that the best approach is to use a similar finite difference mesh as @aero is using now (just modeling the interior of the cavity and modeling the boundary with boundary conditions) and perform a time-marching finite-difference for the Time-Domain instead of solving the eigenvalue problem.This would enable us to answer what is the nature of the evanescent waves, and the other questions we have posed.

Perhaps an ASIC accelerator card exists for MEEP?

Quote from: deltaMass on 06/19/2015 01:57 AMhttps://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23Permittivity is typically associated with dielectric materials, however metals are described as having an effective permittivity, with real relative permittivity equal to one.[22] In the low-frequency region, which extends from radio frequencies to the far infrared and terahertz region, the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the complex index n of a metal is practically a purely imaginary number, expressed in terms of effective relative permittivity it has a low imaginary value (loss) and a negative real-value (high conductivity).[23]A model for the dielectric function of metals is the Lindhard or random phase dielectric constant.http://adsabs.harvard.edu/abs/2006ApPhL..89u3106W (Drude-Lindhard)http://link.springer.com/article/10.1007%2FBF0111573031 refs listed toohttp://www.wave-scattering.com/drudefit.htmlThanks for trying. Unfortunately those data are in the wrong frequency regime, eg. "between the near visible and soft x-ray regions" I'll keep looking on occation, in the mean time I'll see what we find by relying on geometry as Dr. Rodal suggests.

FYI only. So I search around for competing theories on dark matter and dark energy and stumble across a belief system called the Electronic Universe. Seemed like a reasonable theory and maybe emdrives were interacting with it somehow...but wait...there's more...the EU movement is fringe, very fringe imho. Not gonna go any deeper. Too many easy answers and too little hard data. Slick videos, however.

I need to tweak that value for the permittivity of copper. I had not used the effective mass of the electron. For copper, this turns out to be 1.38*m_{e}, and so the permittivity is correspondingly reduced.So fromEpsilon = i / (Rho (m_{eff}/m_{e}) w)we get at 2.4 GHzEpsilon = i0.00288

(make medium (epsilon 3.4) (D-conductivity (/ (* 2 pi 0.42 0.101) 3.4))

Quote from: deltaMass on 06/19/2015 04:59 AMI need to tweak that value for the permittivity of copper. I had not used the effective mass of the electron. For copper, this turns out to be 1.38*m_{e}, and so the permittivity is correspondingly reduced.So fromEpsilon = i / (Rho (m_{eff}/m_{e}) w)we get at 2.4 GHzEpsilon = i0.00288Thanks so much for all your work, but since now I don't have a real part of permittivity, how will I impliment this model?http://ab-initio.mit.edu/wiki/index.php/Material_dispersion_in_Meep#Conductivity_and_complex_.CE.B5Sorry to send you down a link, but that provides a much better explaination of the model than I could. But just in case you miss it, the example model is given in italics in Scheme code as: (make medium (epsilon 3.4) (D-conductivity (/ (* 2 pi 0.42 0.101) 3.4))

Quote from: aero on 06/19/2015 06:07 AMQuote from: deltaMass on 06/19/2015 04:59 AMI need to tweak that value for the permittivity of copper. I had not used the effective mass of the electron. For copper, this turns out to be 1.38*m_{e}, and so the permittivity is correspondingly reduced.So fromEpsilon = i / (Rho (m_{eff}/m_{e}) w)we get at 2.4 GHzEpsilon = i0.00288Thanks so much for all your work, but since now I don't have a real part of permittivity, how will I impliment this model?http://ab-initio.mit.edu/wiki/index.php/Material_dispersion_in_Meep#Conductivity_and_complex_.CE.B5Sorry to send you down a link, but that provides a much better explaination of the model than I could. But just in case you miss it, the example model is given in italics in Scheme code as: (make medium (epsilon 3.4) (D-conductivity (/ (* 2 pi 0.42 0.101) 3.4))If you are concerned with expressing the relative permittivity only, then useEpsilon_{r} = 1 + i0.00288/Epsilon_{0}from which you can see how much bigger is the imaginary part - about a billion times larger than the real part, since Epsilon_{0} = 8.85*10^{-12}. The real part of the relative permittivity is almost exactly = 1 at these frequencies, for copper.From that you can verify the expression for absolute permittivity that I've been using:Epsilon = Epsilon_{0} * Epsilon_{r} ~= 10^{-11} + i0.00288

Quote from: aero on 06/19/2015 03:16 AMQuote from: deltaMass on 06/19/2015 01:57 AMhttps://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23Permittivity is typically associated with dielectric materials, however metals are described as having an effective permittivity, with real relative permittivity equal to one.[22] In the low-frequency region, which extends from radio frequencies to the far infrared and terahertz region, the plasma frequency of the electron gas is much greater than the electromagnetic propagation frequency, so the complex index n of a metal is practically a purely imaginary number, expressed in terms of effective relative permittivity it has a low imaginary value (loss) and a negative real-value (high conductivity).[23]A model for the dielectric function of metals is the Lindhard or random phase dielectric constant.http://adsabs.harvard.edu/abs/2006ApPhL..89u3106W (Drude-Lindhard)http://link.springer.com/article/10.1007%2FBF0111573031 refs listed toohttp://www.wave-scattering.com/drudefit.htmlThanks for trying. Unfortunately those data are in the wrong frequency regime, eg. "between the near visible and soft x-ray regions" I'll keep looking on occation, in the mean time I'll see what we find by relying on geometry as Dr. Rodal suggests.A Meep Drude-Lorentz model of copper is available in section 1.1.6 of "Notes on metals in Meep", Aaron Webster: http://www.fzu.cz/~dominecf/meep/data/meep-metals.pdf

Quote from: deltaMass on 06/19/2015 08:23 AMQuote from: aero on 06/19/2015 06:07 AMQuote from: deltaMass on 06/19/2015 04:59 AMI need to tweak that value for the permittivity of copper. I had not used the effective mass of the electron. For copper, this turns out to be 1.38*m_{e}, and so the permittivity is correspondingly reduced.So fromEpsilon = i / (Rho (m_{eff}/m_{e}) w)we get at 2.4 GHzEpsilon = i0.00288Thanks so much for all your work, but since now I don't have a real part of permittivity, how will I impliment this model?http://ab-initio.mit.edu/wiki/index.php/Material_dispersion_in_Meep#Conductivity_and_complex_.CE.B5Sorry to send you down a link, but that provides a much better explaination of the model than I could. But just in case you miss it, the example model is given in italics in Scheme code as: (make medium (epsilon 3.4) (D-conductivity (/ (* 2 pi 0.42 0.101) 3.4))If you are concerned with expressing the relative permittivity only, then useEpsilon_{r} = 1 + i0.00288/Epsilon_{0}from which you can see how much bigger is the imaginary part - about a billion times larger than the real part, since Epsilon_{0} = 8.85*10^{-12}. The real part of the relative permittivity is almost exactly = 1 at these frequencies, for copper.From that you can verify the expression for absolute permittivity that I've been using:Epsilon = Epsilon_{0} * Epsilon_{r} ~= 10^{-11} + i0.00288This result is essentially correct, the known result for a conductive metal like copper that:The Real part of the relative permittivity is oneThe Imaginary part of the relative permittivity approaches + Infinity (+3.25*10^8)