### Author Topic: EM Drive Developments - related to space flight applications - Thread 5  (Read 965870 times)

#### SeeShells

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2500 on: 12/10/2015 12:55 PM »
I like it, I'll be happy to support it.

Shell

A draft data store is available for critique, review, testing.

http://www.rfdriven.com

Currently, there's no content, just a draft structure.  The database has two views:
1.  A web directory view (so archive.org can grab the content) which is read only
2.  A user DB view (where folks can add content or search for content

Nothing is frozen so now would be a good time to suggest changes, variations, etc.

Ultimately I'll migrate the user DB view to something a bit more robust, but for archive.org, we have to use a directory structure of some kind, else it won't be found.

If anyone wants to start adding content, PM me, and I'll set up an account for you.  Please be specific where you want write permissions.  Write includes delete so don't ask for everything.     Ultimately delete will mean "archive" but not today.

The default DB view login is Guest and the password is Guest
Looking good Glenn, let me know via PM when you're ready to get my data, I'll try and input it. Or, if you prefer, ask me the questions and I'll give you everything I know...which varies from day to day...64K of memory should do the trick.

Well, I'm not sure if this is an idea that people are going to support.

I've got exactly one contributor request, although 26 folks have taken a look, without comment.

Interesting spread of interest (map below).

Thoughts?

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2501 on: 12/10/2015 01:48 PM »
By 235, he probably thinks that I am heavy, very heavy, that I weigh 235 lbs

~~~~~~~~~~~~~

Dr. Rodal,

I'm still missing something in the terminology.
I want to model SeeShells Quartz rod in her CE3 cavity but it is fruitless if I don't get it right.

I have from Shell, here http://www.technicalglass.com/technical_properties.html

that disapation factor < 1E-4, which equals tan delta, and the constant = 3.75 so I calculate the imaginary part of relative permittivity as 3.75E-4 . Now I get shakey. I think I have
epsilon = 3.25 +i3.25E-4 and now the terminology changes and I get more confused.

You wrote CONDUCTIVITY = omega * epsilon"

and the meep units wiki gives meep electrical conductivity = sigma_d = e_r *e_o * c/a . I know e_o, c and a, but if e_r is the real part = the constant, where is epsilon"?

It seems self evident to me that epsilon" must factor into sigma_d somehow.

Or is it so simple as sigma_d = transformation factor * epsilon"  and I misinterpreted above?

If you define the following values for the constitutive properties of fused quartz:

(real value of) relative electric permittivity = εr
= 3.75

tan δ (electric) = 0.0001

then, it follows that:

relative complex permittivity = εr*(1 - i* tan δe)
= εr*(1 - i* 0.0001)

relative complex permittivity =  3.75(1 - i* 0.0001)
= 3.75 - i * 0.0001*3.75
= 3.75 - i * 0.000375

1) I don't understand why you wrote 3.25 instead of 3.75 in your expression (epsilon = 3.25 +i3.25E-4)

2) The sign of the imaginary part should be negative, because a negative imaginary part results in power loss.  A positive sign (as in your expression) would result in power production, which violates the 2nd law of thermodynamics (dielectric materials entail power loss, not power production). (As pointed out in http://forum.nasaspaceflight.com/index.php?topic=38577.msg1453316#msg1453316)

3) I don't understand your discussion of electric conductivity in this context or the questions that follow.  Quartz is a dielectric material, not a metal conductor.  Please try to re-word your question on conductivity to explain the intended context or purpose (are you talking about the conductivity of copper ? )

First, 3.25 was a nervous slip. You make me nervous

Second, in the meep code,
(material (make medium (epsilon epsilon_r) (D-conductivity CU-D-conduct)))
the parameter : CU-D-conduct should be less than zero, that is, negative..

Third, I think that I was still confused, but the light dawned. Is this the correct expression?

sigma-d = epsilon" * e_r *e_o * c/a .
so that conductivity = Omega * sigma_d.

I'll code that up (using the negative sign), print it out and re-post here for validation.

No, it is not true that conductivity = Omega * sigma_d

Here it is step by step (I'm using a positive conductivity, you can add the negative sign):

We know that the conductivity in SI units is σ=ω ε“

σ=ω ε“
=2 π f ε“
= 2 π f (ε“/ε') ε'
= 2 π f tan δe ε'
= 2 π f tan δe (ε'/ εo) εo
= 2 π f tan δe εr εo

Then (from , the conversion between the (dimensionless) Meep conductivity]http://ab-initio.mit.edu/wiki/index.php/Conductivity_in_Meep#Conductivity_and_complex_.CE.B5 ), the conversion between the (dimensionless) Meep conductivity σD and the conductivity σ (in SI units) is:

σD = (a/c) σ /( εr εo)
= 2 π f (a/c)  tan δe

where

a= length scale (I think that aero chose a = 0.3 meters)
c = speed of light in vacuum (299792458 meters / second)
f = frequency (in Hertz = 1 / second)

where you can interpret

σD is the dimensionless Meep conductivity

f (a/c) is the dimensionless frequency (notice that a/c has units of time)

tan δe is the dimensionless expression corresponding to the dimensional imaginary permittivity ε“

I think I've got it now, but I'm having a hard time reconciling this reference:
http://meepunits.wikia.com/wiki/Meep_unit_transformation_Wiki
with this reference:
http://ab-initio.mit.edu/wiki/index.php/Conductivity_in_Meep#Conductivity_and_complex_.CE.B5 ), the conversion between the (dimensionless) Meep conductivity
They seem to be the inverse of one another.
I chose to follow your example and calculated sigma_d =  Q_D_conduct = -1.670715037160664e-12

I did read the previous reference on Fused Quartz more closely and noticed that the data was at 1 MHz, so found another reference which gave data at 100MHz and 3GHz. This reference gave
tan δe     0.0002 @ 100 MHz, 0.00006 @ 3 GHz so I've coded 0.00006 as the loss tangent at 3 GHz.

1) the two references for conversion of Meep conductivity pointed above agree with each other, if one overlooks the subscript "D" (the meaning of the subscript is different in the two references).  Rather than looking at the subscript, start from the concept that the Meep conductivity is dimensionless.

2) you don't point out the reference you found for fused quartz data so it is impossible to comment on its veracity, but on principle I don't agree with choosing properties based on which Internet reference you find based solely on frequency (unless your reference is from a peer-reviewed reference showing the actual measurement vs frequency).

There are different qualities of materials, dependent not only on their material make up but also on their manufacturing method.  Shell may have selected her source for properties based on the supplier of her quartz.  It would be a mistake to ignore that if the data is from her supplier.

RF Cafe data is notoriously unreliable (as previously discussed in these threads).  Microwaves 101 (http://www.microwaves101.com/encyclopedias/quartz) has data that is pretty close to the one given by Shell.

Let's check some numbers, (always a good hygienic thing to do prior to implementing any model), in SI units:

σ= 2 π f tan δe εr εo

for

tan δe = 0.0001 (fused quartz as per Shell's supplier reference)
εr = 3.75 (fused quartz as per Shell's supplier reference)
f = 2.4 E+09 (the same frequency, in Hertz, you used previously)
εo = 8.854187817 E-12  (permittivity of free space vacuum)

hence

σ=  2 π 2.4 E+09  0.0001 3.75  8.854187817 E-12
= 5.006925 E-05

Which is a small number (about the conductivity of drinking water [at very low frequencies, not at microwave frequencies]), as one would require for a dielectric

However, this number (5.006925 E-05) is much larger than the published value for conductivity of fused quartz [at very low frequencies](see for example https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity)

σ=1.30 E−18

which is actually 13 orders of magnitude smaller.

The reason suggested (in http://ab-initio.mit.edu/wiki/index.php/Conductivity_in_Meep#Conductivity_and_complex_.CE.B5 )  for using a fictitious conductivity σ=ω ε“  instead of the imaginary part of the dielectric permittivity ε“ to model the dielectric in Meep is in order to save computer time and for numerical stability since the analysis in terms of complex numbers is much more time consuming and much less numerically stable (a big problem for a Finite Difference formulation ! ).

Quote
Often, you only care about the absorption loss in a narrow bandwidth, where you just want to set the imaginary part of ε (or μ) to some known experimental value, in the same way that you often just care about setting a dispersionless real ε that is the correct value in your bandwidth of interest.
One approach to this problem would be allowing you to specify a constant (frequency-independent) imaginary part of ε, but this has the disadvantage of requiring the simulation to employ complex fields (doubling the memory and time requirements), and also tends to be numerically unstable. Instead, the approach in Meep is for you to set the conductivity σD (or σB for an imaginary part of μ), chosen so that \mathrm{Im}\, \varepsilon = \varepsilon_\infty \sigma_D / \omega is the correct value at your frequency ω of interest. (Note that, in Meep, you specify f = ω / 2π instead of ω for the frequency, however, so you need to include the factor of 2π when computing the corresponding imaginary part of ε!) Conductivities can be implemented with purely real fields, so they are not nearly as expensive as implementing a frequency-independent complex ε or μ.

If working on this, I would check both formulations (the analysis in terms of the fictitious conductivity and the analysis in terms of complex numbers, using the imaginary permittivity) for a small problem with known solution, that can be readily solved by Meep with the complex formulation to double check that the analysis in terms of fictitious conductivity is indeed a good model for the dielectric.

What does your Meep-expert friend (Dr. Dominic if I recall his name correctly) have to say on this matter ?

You can never take these numerical codes on faith.  The reference points to an important bug for calculations using the complex field formulation, in one of the Meep versions, for example.

Quote
The behavior for complex fields was changed for Meep 0.10. Also, in Meep 0.9 there was a bug: when you specified χ(3) in the interface, you were actually specifying \chi^{(3)}/\varepsilon_\infty^4. This was fixed in Meep 0.10.

« Last Edit: 12/10/2015 03:39 PM by Rodal »

#### rfmwguy

• EmDrive Builder (retired)
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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2502 on: 12/10/2015 03:51 PM »
From horn antenna on wikipedia:

"The horn shape that gives minimum reflected power is an exponential taper. Exponential horns are used in special applications that require minimum signal loss, such as satellite antennas and radio telescopes. However conical and pyramidal horns are most widely used, because they have straight sides and are easier to design and fabricate."

While they call it exponential, I've always heard logrithmic. So, I'm all stoked up about the baritone  when it arrives. Note: my wife is already wondering about me, the arrival of the baritone will convince her to summon the white coats

https://en.m.wikipedia.org/wiki/Horn_antenna

It depends on what variables you chose to define the problem.  Suppose that you have only two variables, x and y, related by:

x = y^2

this square function formula (which is well-behaved: there is only one value of x for a given value of y) can also be written in terms of its mathematical inverse:

y = Sqrt[ x]

but the formulation in terms of the inverse, the square root, introduces a number of complexities (there are two possible values of y for a given value of x, and for negative values of x, y becomes imaginary).  It is better to solve the problem in terms of x = y^2.

Similarly the problem can be posed in terms of the exponential or its inverse, the logarithmic function.  The preferred formulation is in terms of the exponential which has nicer properties, including the beautiful fact that the derivative of the exponential function is the same function: the exponential.  Ditto for its integral.
Aha! Believe it or not, I follow you Doc and it makes sense.

Now, if Meep could calculate an exponential frustum with resonance of 2.45 GHz given only one fixed value: large diameter 11 inches (279.4 mm). Length and small diameter would be defined by ideal Return Loss resonance of +30dB or so at 2.45 GHz

My apologies in advance if Meepers just put their fists through their monitors

#### SteveD

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2503 on: 12/10/2015 04:57 PM »
A draft data store is available for critique, review, testing.

http://www.rfdriven.com

Currently, there's no content, just a draft structure.  The database has two views:
1.  A web directory view (so archive.org can grab the content) which is read only
2.  A user DB view (where folks can add content or search for content

Nothing is frozen so now would be a good time to suggest changes, variations, etc.

Ultimately I'll migrate the user DB view to something a bit more robust, but for archive.org, we have to use a directory structure of some kind, else it won't be found.

If anyone wants to start adding content, PM me, and I'll set up an account for you.  Please be specific where you want write permissions.  Write includes delete so don't ask for everything.     Ultimately delete will mean "archive" but not today.

The default DB view login is Guest and the password is Guest
Looking good Glenn, let me know via PM when you're ready to get my data, I'll try and input it. Or, if you prefer, ask me the questions and I'll give you everything I know...which varies from day to day...64K of memory should do the trick.

Well, I'm not sure if this is an idea that people are going to support.

I've got exactly one contributor request, although 26 folks have taken a look, without comment.

Interesting spread of interest (map below).

Thoughts?

You need to login to get to the library.  The site is still in a very basic state.  Directory view needs to become a side menu on the main page.  Suggest more graphics and layout to increase accessibility.

#### oliverio

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2504 on: 12/10/2015 05:07 PM »

Acoustic  ==> speed of sound
Electromagnetic ==> speed of light

Acoustic fundamental natural frequencies are millions of times less than the fundamental natural frequencies in electromagnetic cavities.  Wavelengths are correspondingly vastly different.  Mode shapes are different too

While all of this is true, if the thing looks like a horn, I'd think at least a cursory check of the acoustical literature might be in order to see if it points to mathematical function describing the shape that rfmwguy experimentally arrived at.  The questions, as I see it, are 1. why does the proposed optimal frustum shape look like this, 2. what formula produces the shape and 3. does that formula suggest further optimization.  At the very least, a search of acoustical literature might turn up some elegant math to describe the shape.

Ok, if it's so simply prove it.  What is the function for the optimal shape (highest Q) of an asymmetrical resonance cavity?"

Don't be silly, there is no such function, this question cannot be answered in principle. Any cavity with perfect reflection has the highest Q, the modes of resonance will affect Q, all of which are in principle "correct," and moreover, a cavity like a trombone is not meant to maximize a quantity like Q, it is meant to maximize the harmonic over/undertones of acoustic vibration given a certain frequency. It has nothing to do with Energy efficiency, although power in vs power out is of some relevancy to a trombone's ability to hold a note correctly.  Note though that there is no solution to "the optimal trombone shape;" it's a question that requires more information.

To answer your question I think you would have to specify a mode, frequency, and the properties of your reflector-- change any of these variables and the "highest Q" configuration may change, and for any given set of those variables, there is probably an infinite number of "optimal shapes," many of which would be simpler than others.

#### SteveD

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2505 on: 12/10/2015 05:08 PM »

1. You have thrust but it is small for your test bench to measure. How did you make the aluminum frustum? I mean it is hard to solder aluminum... so how is it held together? One possibility is that your frustum has a very low Q and hence a very low thrust level...

You can see the seam of the cone in this pic.  It's pretty tight, but it hasn't been soldered yet.  (There's a few inches of overlap where those clips at the back are).  I've done some brazing on this (the maggie mount plate) already.  Yes, it's not the easiest, but if you can get it clamped properly, it's not too bad.

I was still debating on when to make it permanent - whether I was going to just run simulations, or bite the bullet and get the miniVNA to tune it.

Don't know where your budget is but two options on the VNA.
http://www.ebay.com/itm/138M-4-4G-SMA-signal-source-generator-simple-spectrum-analyzer-Tracking-source-/111493176997?hash=item19f582dea5
I have this one, ~$70-100 bucks, the software I have is buggy (I think it was corrupted) and I had a very hard time getting them to responding to my emails for new software. The reports are basically favorable, but mention the software issue and make sure you get it with your order. The second one is around$600 miniVNA tiny http://miniradiosolutions.com/54-2/
Software is clean and the device works well. rfmwguy, TheTraveler and I have bought this model.

Shell

PS: Nice work and a thought on coupling the parts together.

This software might be of interest to anyone going the solid state / software defined radio route:

#### SteveD

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2506 on: 12/10/2015 05:39 PM »

Acoustic  ==> speed of sound
Electromagnetic ==> speed of light

Acoustic fundamental natural frequencies are millions of times less than the fundamental natural frequencies in electromagnetic cavities.  Wavelengths are correspondingly vastly different.  Mode shapes are different too

While all of this is true, if the thing looks like a horn, I'd think at least a cursory check of the acoustical literature might be in order to see if it points to mathematical function describing the shape that rfmwguy experimentally arrived at.  The questions, as I see it, are 1. why does the proposed optimal frustum shape look like this, 2. what formula produces the shape and 3. does that formula suggest further optimization.  At the very least, a search of acoustical literature might turn up some elegant math to describe the shape.

Ok, if it's so simply prove it.  What is the function for the optimal shape (highest Q) of an asymmetrical resonance cavity?"

Don't be silly, there is no such function, this question cannot be answered in principle. Any cavity with perfect reflection has the highest Q, the modes of resonance will affect Q, all of which are in principle "correct," and moreover, a cavity like a trombone is not meant to maximize a quantity like Q, it is meant to maximize the harmonic over/undertones of acoustic vibration given a certain frequency. It has nothing to do with Energy efficiency, although power in vs power out is of some relevancy to a trombone's ability to hold a note correctly.  Note though that there is no solution to "the optimal trombone shape;" it's a question that requires more information.

To answer your question I think you would have to specify a mode, frequency, and the properties of your reflector-- change any of these variables and the "highest Q" configuration may change, and for any given set of those variables, there is probably an infinite number of "optimal shapes," many of which would be simpler than others.

So um, doesn't that described the banned ones spreadsheet?  I think we've just argued our way to the answer to an important question: why a frustum.  That answer would seem to be that it is a horn antenna delivering power between the two endplates with minimal loss.  That would suggest that the maths related to this type of antenna could be tied into TTs spreadsheet to produce an optimized shape for a particular mode or set of modes.

Assuming this thing actually does anything besides generate complex measurement errors, we can now say that some of this seems to reflect known physics.  Those known physics suggest that the unknown involves the endplates.  Assuming the reports of curved endplates working are correct, we also know that the unknown does not require flat endplates.  That's a much smaller unkknown than we started with.

#### lmbfan

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2507 on: 12/10/2015 06:01 PM »
From horn antenna on wikipedia:

"The horn shape that gives minimum reflected power is an exponential taper. Exponential horns are used in special applications that require minimum signal loss, such as satellite antennas and radio telescopes. However conical and pyramidal horns are most widely used, because they have straight sides and are easier to design and fabricate."

While they call it exponential, I've always heard logrithmic. So, I'm all stoked up about the baritone  when it arrives. Note: my wife is already wondering about me, the arrival of the baritone will convince her to summon the white coats

https://en.m.wikipedia.org/wiki/Horn_antenna

It depends on what variables you chose to define the problem.  Suppose that you have only two variables, x and y, related by:

x = y^2

this square function formula (which is well-behaved: there is only one value of x for a given value of y) can also be written in terms of its mathematical inverse:

y = Sqrt[ x]

but the formulation in terms of the inverse, the square root, introduces a number of complexities (there are two possible values of y for a given value of x, and for negative values of x, y becomes imaginary).  It is better to solve the problem in terms of x = y^2.

Similarly the problem can be posed in terms of the exponential or its inverse, the logarithmic function.  The preferred formulation is in terms of the exponential which has nicer properties, including the beautiful fact that the derivative of the exponential function is the same function: the exponential.  Ditto for its integral.
Aha! Believe it or not, I follow you Doc and it makes sense.

Now, if Meep could calculate an exponential frustum with resonance of 2.45 GHz given only one fixed value: large diameter 11 inches (279.4 mm). Length and small diameter would be defined by ideal Return Loss resonance of +30dB or so at 2.45 GHz

My apologies in advance if Meepers just put their fists through their monitors

I suggest a series of cylinders with a height at most one half the pixel size/resolution of the simulation (perhaps one tenth? analysis could be done to determine the optimum divisions).  The radius would be determined by an exponential/logarithmic function based on the minimum/maximum diameter and the desired length.  For instance, in pseudo code (z is along the axis of symmetry):

small_rad = 1big_rad = 5.5length = 5step = .1constant = 10^(log10(big_rad/small_rad)/length)z = 0while z <= length :    current_radius = (constant^z)*small_rad    make_cylinder(radius = current_radius, height = step, center = (0,0,z))    z = z + step

This will make cylinders patterned on the logarithmic shape posted by Dr. Rodal above.  Doing a "make_cylinder(radius = current_radius + thickness, ..." first, then subtracting the above will make a frustum shape.  A "make_cylinder(radius = small_rad, height = thickness, center=0,0,0)" will put in a small end cap, something similar would put in the large end cap.  Offset in the "z" direction can be accomplished by changing the "z=0" line to something like "z=height/2" for centering on (0,0,0).  Somewhat obviously, swapping "z" out for "x" or "y" and (0,0,z) with (x,0,0) etc. will change the axis of the frustum, I forget which convention Aero uses.

Implementing the above in meep should be straightforward.  The shape will be inexact, but then, so is meep.  Setting a finer resolution for the cylinders than for meep should result in a nicely anti-aliased boundary.

#### ThereIWas3

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2508 on: 12/10/2015 06:10 PM »
Now, if Meep could calculate an exponential frustum...

The easy way to define shapes in meep is to build it out of the primitives sphere, cylinder, cone, block, and ellipsoid.  Anything other than that will require manual construction of the shape.  Unless it proves really necessary,  lmbfan's suggestion to approximate it with a series of primitives should work, though I think using the 'cone' primitive would give a better approximation of the horn shape.

Given the equation for the shape, we can have it calculate the indiviual cones.  Meep is controlled through a general purpose programming language (Scheme) so many things are possible.  What the documentation calls the "ctl file" is actually a Scheme source file.
"If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea" - Antoine de Saint-Exupéry

#### RFPlumber

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2509 on: 12/10/2015 06:31 PM »

Don't know where your budget is but two options on the VNA.
http://www.ebay.com/itm/138M-4-4G-SMA-signal-source-generator-simple-spectrum-analyzer-Tracking-source-/111493176997?hash=item19f582dea5
I have this one, ~$70-100 bucks, the software I have is buggy (I think it was corrupted) and I had a very hard time getting them to responding to my emails for new software. The reports are basically favorable, but mention the software issue and make sure you get it with your order. The second one is around$600 miniVNA tiny http://miniradiosolutions.com/54-2/
Software is clean and the device works well. rfmwguy, TheTraveler and I have bought this model.

Just a minor correction: the $70 device above is not a VNA, it is not even a scalar NA, it is actually a spectrum analyzer (I own this device, this is what I call a NWT-70-like spectrum analyzer). There is apparently a way to use it as poor-man's scalar NA by utilizing a source of flat wide-band noise (they sell the module), but IMHO this is a really perverted way. The corresponding scalar NA is nwt-4000 http://www.ebay.com/itm/NWT4000-138M-4-4G-sweep-simple-spectrum-analyzer-generator-Case-/181745836241?hash=item2a50e560d1:g:MmoAAOSwstxVVV0t, and it will already set you back$245. I own this one too. The reason I say "corresponding" is that these are all clones of the original projects by a German guy BG7TBL http://www.dl4jal.eu (The page is in German, but the credit is still due). He also wrote the software ("WinNWT") which is what will be enclosed with those ebay shipments from China. The software is half-English and half-German, and it has been written to support all kinds of devices by BG7TBL, so a large part of it is not even applicable to the particular functionality provided by each of these 2 devices. At the end of the day it does work though, so the $245 price tag is likely the lowest one can get a scalar NA for. If I knew about miniVNA back then I would likely order one instead of these, but, also, not everyone needs a vector NA. A scalar one is just fine for finding resonance frequencies. I wish I could advise you on what mode to tune the cavity for, but as I keep repeating, my understanding is that nobody really knows the answer. #### lmbfan • Member • Posts: 55 • Phoenix • Liked: 42 • Likes Given: 42 ##### Re: EM Drive Developments - related to space flight applications - Thread 5 « Reply #2510 on: 12/10/2015 06:55 PM » Now, if Meep could calculate an exponential frustum... The easy way to define shapes in meep is to build it out of the primitives sphere, cylinder, cone, block, and ellipsoid. Anything other than that will require manual construction of the shape. Unless it proves really necessary, lmbfan's suggestion to approximate it with a series of primitives should work, though I think using the 'cone' primitive would give a better approximation of the horn shape. Given the equation for the shape, we can have it calculate the indiviual cones. Meep is controlled through a general purpose programming language (Scheme) so many things are possible. What the documentation calls the "ctl file" is actually a Scheme source file. Great idea! The loop would look like: ...last_radius = small_radiuswhile z <= length : current_radius = (constant^z)*small_rad make_truncated_cone(radius1 = last_radius, radius2 = current_radius, height = step, center = (0,0,z)) last_radius = current_radius z = z + step The values of "radius1" and "radius2" may have to be swapped, depending on how meep builds the cylinder. This would replace step-wise with linear interpolation between the shapes, which will fit the small end of the cavity well, but as the curvature increases, will become increasingly poorly fitted. But it's still much better than step-wise. #### SeeShells • Senior Member • Posts: 2367 • Every action there's a reaction we try to grasp. • United States • Liked: 3101 • Likes Given: 2668 ##### Re: EM Drive Developments - related to space flight applications - Thread 5 « Reply #2511 on: 12/10/2015 06:58 PM » Don't know where your budget is but two options on the VNA. http://www.ebay.com/itm/138M-4-4G-SMA-signal-source-generator-simple-spectrum-analyzer-Tracking-source-/111493176997?hash=item19f582dea5 I have this one, ~$70-100 bucks, the software I have is buggy (I think it was corrupted) and I had a very hard time getting them to responding to my emails for new software. The reports are basically favorable, but mention the software issue and make sure you get it  with your order.

The second one is around $600 miniVNA tiny http://miniradiosolutions.com/54-2/ Software is clean and the device works well. rfmwguy, TheTraveler and I have bought this model. Just a minor correction: the$70 device above is not a VNA, it is not even a scalar NA, it is actually a spectrum analyzer (I own this device, this is what I call a NWT-70-like spectrum analyzer). There is apparently a way to use it as poor-man's scalar NA by utilizing a source of flat wide-band noise (they sell the module), but IMHO this is a really perverted way. The corresponding scalar NA is nwt-4000 http://www.ebay.com/itm/NWT4000-138M-4-4G-sweep-simple-spectrum-analyzer-generator-Case-/181745836241?hash=item2a50e560d1:g:MmoAAOSwstxVVV0t, and it will already set you back $245. I own this one too. The reason I say "corresponding" is that these are all clones of the original projects by a German guy BG7TBL http://www.dl4jal.eu (The page is in German, but the credit is still due). He also wrote the software ("WinNWT") which is what will be enclosed with those ebay shipments from China. The software is half-English and half-German, and it has been written to support all kinds of devices by BG7TBL, so a large part of it is not even applicable to the particular functionality provided by each of these 2 devices. At the end of the day it does work though, so the$245 price tag is likely the lowest one can get a scalar NA for.

If I knew about miniVNA back then I would likely order one instead of these, but, also, not everyone needs a vector NA. A scalar one is just fine for finding resonance frequencies.

I wish I could advise you on what mode to tune the cavity for, but as I keep repeating, my understanding is that nobody really knows the answer.
RFPlumer, Thanks!!!

I'll pull this software down to see if I can get it running as a second check. I knew it wasn't the best when I bought it but I got it before I had any funding and was using personal funds.

Shell

#### X_RaY

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2512 on: 12/10/2015 07:23 PM »
Some Time ago i had a short general discussion with Dr. Rodal about consequences using different materials for the frequency tuning of a cavity resonator. However, I like to share the EMPro results.
I focused on TE011 and TM010 only in this analysis, nevertheless the result is surprising.
I found very interesting differences for these modes using both dielectric and conductive tuning elements.
For TM010 and TE011 the frequency shifts down with a dielectric tuning element what's in agreement with well known theory.
The reaction of the resonant frequency of these modes is very different using a conductive tuning rod instead of a dielectric.
The TE011 shifts slightly to a higher frequency while the TM010 frequency travel rapidly to a much lower value! Interesting fact so far.

Results are in the  .ods file below.

Description:
The used model is cylindrically, 30mm long and 40mm in diameter. The tuning rod is 4mm in diameter. I shifted the length from 0...15mm in 5mm increments. The rod is placed at one of the end plates along the central z-axis.
The material of the tuning element was defined as Copper and
Polyether-ether-ketone (PEEK) with epsilon=3.5
« Last Edit: 12/10/2015 07:47 PM by X_RaY »

#### Rodal

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2513 on: 12/10/2015 07:24 PM »
By 235, he probably thinks that I am heavy, very heavy, that I weigh 235 lbs

~~~~~~~~~~~~~

Dr. Rodal,

I'm still missing something in the terminology.
I want to model SeeShells Quartz rod in her CE3 cavity but it is fruitless if I don't get it right.

I have from Shell, here http://www.technicalglass.com/technical_properties.html

that disapation factor < 1E-4, which equals tan delta, and the constant = 3.75 so I calculate the imaginary part of relative permittivity as 3.75E-4 . Now I get shakey. I think I have
epsilon = 3.25 +i3.25E-4 and now the terminology changes and I get more confused.

You wrote CONDUCTIVITY = omega * epsilon"

and the meep units wiki gives meep electrical conductivity = sigma_d = e_r *e_o * c/a . I know e_o, c and a, but if e_r is the real part = the constant, where is epsilon"?

It seems self evident to me that epsilon" must factor into sigma_d somehow.

Or is it so simple as sigma_d = transformation factor * epsilon"  and I misinterpreted above?

If you define the following values for the constitutive properties of fused quartz:

(real value of) relative electric permittivity = εr
= 3.75

tan δ (electric) = 0.0001

then, it follows that:

relative complex permittivity = εr*(1 - i* tan δe)
= εr*(1 - i* 0.0001)

relative complex permittivity =  3.75(1 - i* 0.0001)
= 3.75 - i * 0.0001*3.75
= 3.75 - i * 0.000375

1) I don't understand why you wrote 3.25 instead of 3.75 in your expression (epsilon = 3.25 +i3.25E-4)

2) The sign of the imaginary part should be negative, because a negative imaginary part results in power loss.  A positive sign (as in your expression) would result in power production, which violates the 2nd law of thermodynamics (dielectric materials entail power loss, not power production). (As pointed out in http://forum.nasaspaceflight.com/index.php?topic=38577.msg1453316#msg1453316)

3) I don't understand your discussion of electric conductivity in this context or the questions that follow.  Quartz is a dielectric material, not a metal conductor.  Please try to re-word your question on conductivity to explain the intended context or purpose (are you talking about the conductivity of copper ? )

First, 3.25 was a nervous slip. You make me nervous

Second, in the meep code,
(material (make medium (epsilon epsilon_r) (D-conductivity CU-D-conduct)))
the parameter : CU-D-conduct should be less than zero, that is, negative..

Third, I think that I was still confused, but the light dawned. Is this the correct expression?

sigma-d = epsilon" * e_r *e_o * c/a .
so that conductivity = Omega * sigma_d.

I'll code that up (using the negative sign), print it out and re-post here for validation.

No, it is not true that conductivity = Omega * sigma_d

Here it is step by step (I'm using a positive conductivity, you can add the negative sign):

We know that the conductivity in SI units is σ=ω ε“

σ=ω ε“
=2 π f ε“
= 2 π f (ε“/ε') ε'
= 2 π f tan δe ε'
= 2 π f tan δe (ε'/ εo) εo
= 2 π f tan δe εr εo

Then (from , the conversion between the (dimensionless) Meep conductivity]http://ab-initio.mit.edu/wiki/index.php/Conductivity_in_Meep#Conductivity_and_complex_.CE.B5 ), the conversion between the (dimensionless) Meep conductivity σD and the conductivity σ (in SI units) is:

σD = (a/c) σ /( εr εo)
= 2 π f (a/c)  tan δe

where

a= length scale (I think that aero chose a = 0.3 meters)
c = speed of light in vacuum (299792458 meters / second)
f = frequency (in Hertz = 1 / second)

where you can interpret

σD is the dimensionless Meep conductivity

f (a/c) is the dimensionless frequency (notice that a/c has units of time)

tan δe is the dimensionless expression corresponding to the dimensional imaginary permittivity ε“

I think I've got it now, but I'm having a hard time reconciling this reference:
http://meepunits.wikia.com/wiki/Meep_unit_transformation_Wiki
with this reference:
http://ab-initio.mit.edu/wiki/index.php/Conductivity_in_Meep#Conductivity_and_complex_.CE.B5 ), the conversion between the (dimensionless) Meep conductivity
They seem to be the inverse of one another.
I chose to follow your example and calculated sigma_d =  Q_D_conduct = -1.670715037160664e-12

I did read the previous reference on Fused Quartz more closely and noticed that the data was at 1 MHz, so found another reference which gave data at 100MHz and 3GHz. This reference gave
tan δe     0.0002 @ 100 MHz, 0.00006 @ 3 GHz so I've coded 0.00006 as the loss tangent at 3 GHz.

1) the two references for conversion of Meep conductivity pointed above agree with each other, if one overlooks the subscript "D" (the meaning of the subscript is different in the two references).  Rather than looking at the subscript, start from the concept that the Meep conductivity is dimensionless.

2) you don't point out the reference you found for fused quartz data so it is impossible to comment on its veracity, but on principle I don't agree with choosing properties based on which Internet reference you find based solely on frequency (unless your reference is from a peer-reviewed reference showing the actual measurement vs frequency).

There are different qualities of materials, dependent not only on their material make up but also on their manufacturing method.  Shell may have selected her source for properties based on the supplier of her quartz.  It would be a mistake to ignore that if the data is from her supplier.

RF Cafe data is notoriously unreliable (as previously discussed in these threads).  Microwaves 101 (http://www.microwaves101.com/encyclopedias/quartz) has data that is pretty close to the one given by Shell.

Let's check some numbers, (always a good hygienic thing to do prior to implementing any model), in SI units:

σ= 2 π f tan δe εr εo

for

tan δe = 0.0001 (fused quartz as per Shell's supplier reference)
εr = 3.75 (fused quartz as per Shell's supplier reference)
f = 2.4 E+09 (the same frequency, in Hertz, you used previously)
εo = 8.854187817 E-12  (permittivity of free space vacuum)

hence

σ=  2 π 2.4 E+09  0.0001 3.75  8.854187817 E-12
= 5.006925 E-05

Which is a small number (about the conductivity of drinking water [at very low frequencies, not at microwave frequencies]), as one would require for a dielectric

However, this number (5.006925 E-05) is much larger than the published value for conductivity of fused quartz [at very low frequencies](see for example https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity)

σ=1.30 E−18

which is actually 13 orders of magnitude smaller.

The reason suggested (in http://ab-initio.mit.edu/wiki/index.php/Conductivity_in_Meep#Conductivity_and_complex_.CE.B5 )  for using a fictitious conductivity σ=ω ε“  instead of the imaginary part of the dielectric permittivity ε“ to model the dielectric in Meep is in order to save computer time and for numerical stability since the analysis in terms of complex numbers is much more time consuming and much less numerically stable (a big problem for a Finite Difference formulation ! ).

Quote
Often, you only care about the absorption loss in a narrow bandwidth, where you just want to set the imaginary part of ε (or μ) to some known experimental value, in the same way that you often just care about setting a dispersionless real ε that is the correct value in your bandwidth of interest.
One approach to this problem would be allowing you to specify a constant (frequency-independent) imaginary part of ε, but this has the disadvantage of requiring the simulation to employ complex fields (doubling the memory and time requirements), and also tends to be numerically unstable. Instead, the approach in Meep is for you to set the conductivity σD (or σB for an imaginary part of μ), chosen so that \mathrm{Im}\, \varepsilon = \varepsilon_\infty \sigma_D / \omega is the correct value at your frequency ω of interest. (Note that, in Meep, you specify f = ω / 2π instead of ω for the frequency, however, so you need to include the factor of 2π when computing the corresponding imaginary part of ε!) Conductivities can be implemented with purely real fields, so they are not nearly as expensive as implementing a frequency-independent complex ε or μ.

If working on this, I would check both formulations (the analysis in terms of the fictitious conductivity and the analysis in terms of complex numbers, using the imaginary permittivity) for a small problem with known solution, that can be readily solved by Meep with the complex formulation to double check that the analysis in terms of fictitious conductivity is indeed a good model for the dielectric.

What does your Meep-expert friend (Dr. Dominic if I recall his name correctly) have to say on this matter ?

You can never take these numerical codes on faith.  The reference points to an important bug for calculations using the complex field formulation, in one of the Meep versions, for example.

Quote
The behavior for complex fields was changed for Meep 0.10. Also, in Meep 0.9 there was a bug: when you specified χ(3) in the interface, you were actually specifying \chi^{(3)}/\varepsilon_\infty^4. This was fixed in Meep 0.10.

Here is another explanation of what we are doing.  The Maxwell equation attached below shows the relationship between the field H and the field E (this is the usual formulation, Meep uses the field instead to define the conductivity )

where, in the equation attached below,

σs = static conductivity

In conductors, this first term (inside the parenthesis in the equation below): σs/(ωε'), dominates the last term ε′′/ε′ .  In metals, the real part of the permittivity is usually equal to the permittivity of free space (in other words, for metals, the relative permittivity is practically one), and the imaginary part is close to zero. (That's how DeltaMass modeled copper, remember ? ).  For metals,the conductivity is due almost entirely to  σs, which is due to the collisions of electrons, while the polarization dependent term  ε′′/ε′ is negligible.

The ε′′/ε′ term describes how much power supplied by an external electric field is dissipated as motion and heat (https://en.wikipedia.org/wiki/Dielectric_heating). In dielectrics,  the conductivity is due almost entirely to polarization loss (dipole motion): in a dielectric this term ε′′/ε′ usually dominates the first term  σs/(ωε').

In order to avoid the trouble of having to use a numerical solution involving complex terms (which is very computer time consuming and fraught with numerical instabilities, a big problem for a finite difference solution) it is suggested that instead of using the tiny, correct static conductivity for the dielectric (in this case fused quartz), that a fictitious, much higher conductivity is input into the program such that

σfictitious/(ωε') =  ε′′/ε′

or

σfictitious = (ωε') (ε′′/ε′)
= ω  ε′′

For fused quartz, we previously showed:

σstatic=1.30 E−18

while

σfictitious = 5.006925 E-05

The fictitious conductivity σfictitious is 13 orders of magnitude higher than the static conductivity σstaticSo indeed we verify that for the dielectric (fused quartz) conductivity is due almost entirely to polarization loss (dipole motion), as expressed by the last  ε′′/ε′ term which completely dominates the first term  σs/(ωε') due to static conductivity.

It is simply a neat way to get to input into Meep the dielectric power loss due to the ε′′/ε′ term in Maxwell's equation, as if it would be due to an inherent static conductivity.  Mathematically, it should be completely equivalent to inputting the complex permittivity, but numerically is much better behaved, and therefore much more preferable.
« Last Edit: 12/10/2015 09:43 PM by Rodal »

#### demofsky

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2514 on: 12/10/2015 08:29 PM »
I'm not going to take sides on this and I am not going to send an email to Chris.   Everyone should just settle down and get back on track before Chris gets so annoyed at the whole lot of us that he shuts down the thread for good.   Let's see some experimental results and focus on what we know and what we can do to get to the bottom of this em-drive phenomena.  Enough with the distractions.

I have been on this EM Drive thread since thread number one.  Some people presently contributing to these threads were not present at that time and may be unfamiliar with its history, and how these threads are such a headache for the NSF moderators and for NSF administration.

Thread number had to be closed, completely shut down by NSF administration for several days because of exchanges that also resulted in banning of individuals.  At that time it was unknown whether the EM Drive would continue to exist.

This kind of stuff happens on the EM Drive thread much more often than in the conventional threads about NASA and Space X.

Multiple people have been banned and are sorely missed.

If the audience wants these threads to continue it is a question of self moderation and not arguing with moderators on their established guidelines, in order to make the moderator and NSF administration's job easier - or at least more similar to their regular monitoring of other threads-.

Self moderation or self censorship?  How do you avoid groupthink?

This is not an area of settled science.  There were literal fistfights when quantum mechanics were first introduced so I am not surprised there are conflicts.

What I like is that there are many folks trying mightily to build and improve experimental rigs so we can resolve whether there is an actual signal or not.

#### RFPlumber

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2515 on: 12/10/2015 08:34 PM »
Just a minor correction: the \$70 device above is not a VNA, it is not even a scalar NA, it is actually a spectrum analyzer...
RFPlumer, Thanks!!!
I'll pull this software down to see if I can get it running as a second check. I knew it wasn't the best when I bought it but I got it before I had any funding and was using personal funds.
Shell

You're welcome Take this device, connect its freq output to its input directly, and then in WinNWT software go to "sweepmode" tab and run any freq scan. You will get a flat line at like -70 dBm, which is not what one woud expect from a scalar NA in such a configuration. However, if one attaches an external rf source to its input then the same freq scan will show a nice spectrum plot The same device can also be used as an RF generator (using the VFO tab). It cannot be used as RF power meter (so forget about the wattmeter tab). Note that apparently this is device is not the same as the original spectrum analyzer "adaptor" or an "add-on" by BG7TBL, and hence all references to "spectrum analyzer" ("SA") in the WinNWT software are not applicable to this device.

The other one mentioned (NWT-4000) will come with the exact same software, but the sweepmode will work as expected for a scalar NA, and the wattmeter tab will be working as well (though it requires calibration with a good known power meter if it is to be used for absolute power measurements).

Figuring all this out was a royal pain...

#### oliverio

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2516 on: 12/10/2015 08:49 PM »
On the subject of achieving a resonance lock, I don't think this is possible with an analog-type setup.

I think what needs to be done here is coupling a miniVNA Tiny with a source of software-defined radio, determining the resonant frequency of your frustrum given a mode you wish to elicit, and then running a constant loop between the VNA and the SDR such that any variation in the resonance conditions is equilibriated by a shift in the output from the SDR source (by modulating power on the fly).

This is the most simple, guaranteed way to achieve a constant resonance.  The resonant properties of an object are so complicated that for everything excepting an ideal material you are going to see fluctuations vs. time-- and if I am correct about this (I may not be), small perturbations to a resonant state in a cavity like this will cause a series of wildly spiraling effects.  Those who are familiar with tuning a string instrument will no doubt have noticed that if you play two very dissonant strings at once, it sounds stable.  If you play a note that is slightly out of resonance instead (but very close to the same frequency or a harmonic interval of it) you will observe a phenomenon sometimes called "unraveling;" the two notes will start to oscillate and form other subtones with a frequency and intensity that varies.

If I am correct you will see the same thing happening if, for example, you whack an operant EMdrive with a hammer.  If you want to achieve a semistable mode generation, you're almost certainly going to have to couple software monitoring (at the least) with a variable power source.

If you have an EMdrive and the hardware, and you can show me how data is sent from the relevant hardware, I will write you a program in C that does this.  Should be simple enough as long as you can identify the output from the VNA you wish to achieve-- at that point it's just vary-and-check.
« Last Edit: 12/10/2015 08:52 PM by oliverio »

#### aero

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2517 on: 12/10/2015 09:58 PM »
@ Dr. Rodal,

I need to thank you for your efforts to teach me a little, and your results. "Thank You!"

I do not have a background in E&M and as such should probably never taken up meep. It is not a cookbook program even for these simple problems. You found the error that has been hounding us for months when you asked me why I wrote e = e' + je''.  I didn't know any better and you educated me. After changing the sign to minus and making runs, it seems as though the Q values in the millions are gone, and likely hundreds of thousands are gone, too.

I have not yet any final numbers on any cavity quality factor so this is preliminary, almost premature, but I also want to inform all meepers that the models which I wrote, and some have been distributed, all contain this very serious error. Let me call it a bug, The sign change can easily be made in the line next after the term CU-D-conduct is defined and calculated. Just use:
(set! CU-D-conduct (- 0 CU-D-conduct))
The actual numeric value that is calculated is about 113 times to large. Dr. Rodal has gone to great lengths explaining the correct way to calculate the value, I suggest you look through the preceding several pages and follow along. Or, wait until there is a new version provided, which may take some time.

Dr. Rodal - Unfortunately the reference I found for permittivity of fused Quartz was RFcafe. I have looked for other sources but they are rare. I did find this one reference that seems to confirm Shells' original reference values.

http://rsnz.natlib.govt.nz/volume/rsnz_77/rsnz_77_05_008500.pdf

So at this time, I am wondering which value to use. The national Lab data above should be reliable.

One thing I did notice though while searching is that the dielectric constant of fused Quartz is sensitive to temperature, doubling in value at 200 degrees C. Though I don't know that the temperature in the cavity will change dramatically, it may change in the Quartz enough to have an effect.

For now, I think I am going to remove the Quartz rod model and focus on nailing some results with the corrected copper model.

Retired, working interesting problems

#### ThereIWas3

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2518 on: 12/10/2015 10:03 PM »
I have a meep resonance run going as we speak, using SeeShell's project dimensions and the corrected permittivity number for Copper.   It should be complete later this evening.
"If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea" - Antoine de Saint-Exupéry

#### ThereIWas3

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##### Re: EM Drive Developments - related to space flight applications - Thread 5
« Reply #2519 on: 12/10/2015 11:32 PM »
And the results are in: resonance at 2.4959 GHz with a Q of 8155.   It works!

Deriving the mode shape will take a bit more work.

Edit:  oops I misread the results.  The Q came out -8937, which can't be right.  The 8155 figure was from the NSF1701 model.
« Last Edit: 12/11/2015 02:53 AM by ThereIWas3 »
"If you want to build a ship, don’t drum up people to collect wood and don’t assign them tasks and work, but rather teach them to long for the endless immensity of the sea" - Antoine de Saint-Exupéry

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