Author Topic: EM Drive Developments - related to space flight applications - Thread 3  (Read 1877760 times)

Offline deltaMass

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https://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23

Permittivity 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%2FBF01115730
31 refs listed too

http://www.wave-scattering.com/drudefit.html
« Last Edit: 06/19/2015 02:23 AM by deltaMass »

Offline aero

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https://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23

Permittivity 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%2FBF01115730
31 refs listed too

http://www.wave-scattering.com/drudefit.html

Thanks 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.
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Offline aero

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Perhaps 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

I thought I would start with the Yaun model because it did give the highest thrust/power and my model does resonate very close to 2.45 GHz. The down-side is that my model calculates Q ~12-18 million.
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Offline deltaMass

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After more research & analysis, I get the permittivity of copper at 2.4 GHz to be i0.0032 F/m .

I used the Drude model. Here, we can get a good approximation because at microwave frequencies we are well below the plasma frequency of copper fp = 2.61*1015 Hz
Here the imaginary part swamps the real part by many orders, so the permittivity is almost pure imaginary.

I found the damping time Tau to be 2*10-14 sec (but note only to 1 digit of accuracy).
This is the average time between collisions of the electron gas.
Maybe you can find a more accurate value at the links I provided.

The Drude-derived formula is
Epsilon(w) ~= i Epsilon0 wp2  Tau  (1/w)

and you can use my given values to check my answer.
Remember w = 2 Pi f

NOTE THIS HAS BEEN UPDATED

« Last Edit: 06/19/2015 03:55 AM by deltaMass »

Offline Mulletron

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In search of other effects, found this. Page 12 is interesting too.

On Newton's third law and its symmetry-breaking effects
Mario J Pinheiro
http://iopscience.iop.org/1402-4896/84/5/055004
http://arxiv.org/pdf/1104.5011.pdf

Also pulled from references:
http://www.sciencedirect.com/science/article/pii/S0375960102001883
http://arxiv.org/pdf/nlin/0007034v1.pdf

Some useful info in here:
http://arxiv.org/ftp/arxiv/papers/1308/1308.2755.pdf
« Last Edit: 06/19/2015 03:42 AM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline deltaMass

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https://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23

Permittivity 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%2FBF01115730
31 refs listed too

http://www.wave-scattering.com/drudefit.html

Thanks 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.
Please check my updated post
I get i0.0032

Offline deltaMass

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It turns out that (details available on request :) ) expressions used for the plasma frequency and for the relaxation time Tau can be combined and largely cancelled. These expressions use fundamental constants of the electron and the electron gas. We are left with an extremely simple expression for the permittivity:

Epsilon = i / (Rho * w)

Now Rho, the resistivity of copper at 20oC, is 1.678*10-8 Ohm.m
and w at 2.4 GHz is 1.508*1010 rad/s
so this yields

Epsilon = i0.00397  F/m

This is much more accurate.
« Last Edit: 06/19/2015 04:26 AM by deltaMass »

Offline rfmwguy

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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. ;)

Offline deltaMass

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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. ;)
My advice - stay away. cf. Brain Damage by Pink Floyd. "Got to keep the loonies on the path"

Offline Mulletron

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@dustinthewind has linked to this paper many times but it didn't get discussed much. It has lots of good pertinent info in there including some surprising info for you near field fans:

http://arxiv.org/pdf/1502.06288v1.pdf (note that ref 6 is our favorite anomalous thrust production...paper)

Also pulled out reference 15 as it is of interest:
http://www.asps.it/article2.pdf

Edit:
I was thinking, instead of spending thousands of man hours reading, researching, building stuff and generating hundreds of pages of thread content....how bout we just ask Watson?
http://www.ibm.com/smarterplanet/us/en/ibmwatson/what-is-watson.html

He better not say 42.
« Last Edit: 06/19/2015 05:05 AM by Mulletron »
Challenge your preconceptions, or they will challenge you. - Velik

Offline deltaMass

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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*me, and so the permittivity is correspondingly reduced.
So from
Epsilon = i / (Rho (meff/me) w)
we get at 2.4 GHz

Epsilon = i0.00288
« Last Edit: 06/19/2015 05:02 AM by deltaMass »

Offline aero

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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*me, and so the permittivity is correspondingly reduced.
So from
Epsilon = i / (Rho (meff/me) w)
we get at 2.4 GHz

Epsilon = i0.00288

Thanks 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.B5

Sorry 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))
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Offline WarpTech

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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*me, and so the permittivity is correspondingly reduced.
So from
Epsilon = i / (Rho (meff/me) w)
we get at 2.4 GHz

Epsilon = i0.00288

Thanks 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.B5

Sorry 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))


The real part is practically zero, so use a really small number. :)
Todd

Offline deltaMass

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What he said!

If you need to use another frequency, just ratio it off the value I gave for 2.4 GHz.

e.g. at 3 GHz, use i0.00288 * (2.4/3) = i0.00230
« Last Edit: 06/19/2015 08:06 AM by deltaMass »

Offline deltaMass

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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*me, and so the permittivity is correspondingly reduced.
So from
Epsilon = i / (Rho (meff/me) w)
we get at 2.4 GHz

Epsilon = i0.00288

Thanks 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.B5

Sorry 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 use

Epsilonr = 1 + i0.00288/Epsilon0

from which you can see how much bigger is the imaginary part - about a billion times larger than the real part, since Epsilon0 = 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 = Epsilon0 * Epsilonr ~= 10-11 + i0.00288
« Last Edit: 06/19/2015 08:28 AM by deltaMass »

Offline Rodal

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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*me, and so the permittivity is correspondingly reduced.
So from
Epsilon = i / (Rho (meff/me) w)
we get at 2.4 GHz

Epsilon = i0.00288

Thanks 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.B5

Sorry 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 use

Epsilonr = 1 + i0.00288/Epsilon0

from which you can see how much bigger is the imaginary part - about a billion times larger than the real part, since Epsilon0 = 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 = Epsilon0 * Epsilonr ~= 10-11 + i0.00288
This result is essentially correct, the known result for a conductive metal like copper that:

The Real part of the relative permittivity is one

The Imaginary part of the relative permittivity approaches + Infinity
                                                                                                (+3.25*10^8)


« Last Edit: 06/19/2015 12:30 PM by Rodal »

Offline deuteragenie

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https://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23

Permittivity 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%2FBF01115730
31 refs listed too

http://www.wave-scattering.com/drudefit.html

Thanks 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


Offline Rodal

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https://en.wikipedia.org/wiki/Relative_permittivity#cite_ref-23

Permittivity 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%2FBF01115730
31 refs listed too

http://www.wave-scattering.com/drudefit.html

Thanks 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

Excellent reference for optical range (which constitutes the lion share of MEEP users)

Please notice that:

Maximum wavelength for copper ( in section 1.1.6 of "Notes on metals in Meep", Aaron Webster: 
http://www.fzu.cz/~dominecf/meep/data/meep-metals.pdf)

is only 2 micrometers

Maximum wavelength in their reference (see their Fig. 3): 

Optical properties of metallic films for vertical-cavity optoelectronic devices
Aleksandar D. Rakicī , Aleksandra B. Djurisˇ icī , Jovan M. Elazar, and Marian L. Majewski
http://faculty.kfupm.edu.sa/ee/msunaidi/EE635%20stuff/Rakic%20paper%20on%20metal%20models%201998.pdf

http://www.academia.edu/3606049/Optical_properties_of_metallic_films_for_vertical-cavity_optoelectronic_devices

https://www.osapublishing.org/ao/viewmedia.cfm?uri=ao-37-22-5271&seq=0

is only 10 micrometers

In other words, their data is for the Optical range, much higher frequency than Microwave frequency.

One GHz corresponds to 30 cm wavelength (and to 4 μeV photon energy).
« Last Edit: 06/19/2015 02:07 PM by Rodal »

Offline deuteragenie

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[quote
In other words, their data is for the Optical range, much higher frequency than Microwave frequency.
[/quote]

Ok.  Do we have experimental results for copper at microwave frequency range ?
We could try to build a multi-coefficient model from the experimental data.
See here: https://www.lumerical.com/support/whitepaper/fdtd_multicoefficient_material_modeling.html
I do not know if this is supported by Meep though.
 

Offline Rodal

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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*me, and so the permittivity is correspondingly reduced.
So from
Epsilon = i / (Rho (meff/me) w)
we get at 2.4 GHz

Epsilon = i0.00288

Thanks 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.B5

Sorry 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 use

Epsilonr = 1 + i0.00288/Epsilon0

from which you can see how much bigger is the imaginary part - about a billion times larger than the real part, since Epsilon0 = 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 = Epsilon0 * Epsilonr ~= 10-11 + i0.00288
This result is essentially correct, the known result for a conductive metal like copper that:

The Real part of the relative permittivity is one

The Imaginary part of the relative permittivity approaches + Infinity
                                                                                                (+3.25*10^8)

p. 29 and 30 of:
http://www.phys.ufl.edu/~tanner/notes.pdf

One GHz corresponds to 0.033 1/cm frequency, or 30 cm wavelength (and to 4 μeV photon energy), which is way off to the left outside the range of the image below (observe how the Imaginary part of permittivity goes to +Infinity for low frequencies, and what a huge difference in the value of the imaginary permittivity frequency makes ), since the Imaginary part of permittivity goes to Infinity as 1/ω ,  this behavior makes the Imaginary permittivity of a metal a not a very useful function for conducting materials at microwave frequencies, also notice that the (much smaller) real part is negative:


(*IMHO The Drude model is NOT a useful model to model Copper in the GHz range*)
« Last Edit: 06/19/2015 02:59 PM by Rodal »

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