The following paper could give DIYer some ideas to build their cavity:
http://arxiv.org/abs/1603.07423
Emphasis on the following statement in this reference:
<<Three-dimensional (3D) superconducting microwave cavities
with large mode volumes typically
have high quality factors>>
As I prove here:
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474347#msg1474347the larger the volume, the higher the Q for low order mode shapes. (Lower mode shapes are usually higher amplitude).
Puzzling that Shawyer's proposed superconducting EM Drive is small volume:
as the Q would be larger, with larger volume.
Why does Shawyer propose to use 8 such EM Drives instead of a larger one?
Second generation EmDrive propulsion applied to SSTO launcher and interstellar probe
RogerShawyer
Acta Astronautica 116 (2015) 166–174
A single larger one would be more efficient. Make it two if you seek reliability/robustness.
The following paper could give DIYer some ideas to build their cavity:
http://arxiv.org/abs/1603.07423
Emphasis on the following statement in this reference:
<<Three-dimensional (3D) superconducting microwave cavities with large mode volumes typically
have high quality factors>>
As I prove here:
https://forum.nasaspaceflight.com/index.php?topic=39214.msg1474347#msg1474347
the larger the volume, the higher the Q for low order mode shapes. (Lower mode shapes are usually higher amplitude).
Puzzling that Shawyer's proposed superconducting EM Drive is small volume:
as the Q would be larger, with larger volume.
Why does Shawyer propose to use 8 such EM Drives instead of a larger one?
Second generation EmDrive propulsion applied to SSTO launcher and interstellar probe
RogerShawyer
Acta Astronautica 116 (2015) 166–174
A single larger one would be more efficient. Make it two if you seek reliability/robustness.
A single larger one would be more efficient. Make it two if you seek reliability/robustness.
Heat Dr. Rodal, heat is the killer of a high Q system. This way you could pulse them for a specific duty cycle and let the thermal issues with a high power run at a very high Q settle down.
Shell
A single larger one would be more efficient. Make it two if you seek reliability/robustness.
Heat Dr. Rodal, heat is the killer of a high Q system. This way you could pulse them for a specific duty cycle and let the thermal issues with a high power run at a very high Q settle down.
Shell
But that's the point of using a larger cavity: the dissipated heat is smaller using a larger cavity than by using several smaller cavities.
This is even more important in superconducting cavities: to minimize the internal surface area per unit volume.
But that's the point of using a larger cavity
At a certain point we need to draw the line. Otherwise why not build an emdrive that operates at 1Mhz and is 300+ meters? Stacking is the best way to increase thrust once a standard size is established.
But that's the point of using a larger cavity
At a certain point we need to draw the line. Otherwise why not build an emdrive that operates at 1Mhz and is 300+ meters? Stacking is the best way to increase thrust once a standard size is established.
Yes, but this is a compromise between the drive efficiency (the bigger the better) and manufacturing costs and abilities.
For similar powerplants, for example for a turbofan for a commercial airliner, the choice is well known: both Boeing and Airbus have gone to just 2 larger turbofan jet engines.
To maximize energy efficiency and power, that's clearly the way to go (using 8 jet engines looks like something ancient and energy-wasting from the 1950's).
I have the impression that Shawyer's choice was based on his manufacturing/testing ability: it was easier to make a small EM Drive for R&D purposes.
Concerning cavities, Nobel Prize winner Luis Alvarez designed and built a famous 40 ft long huge cavity in the 1940's for one of the first particle accelerators, and had it built by an Airplane company, as bigger is better for a cavity resonator was true even then.
I think that this artist did not take into account that "bigger is better than many smaller" when drawing this futuristic design with many (10 or more?) EM Drive engines:
I think that this artist did not take into account that "bigger is better than many smaller" when drawing this futuristic design with many (10 or more?) EM Drive engines:
More like this then?
Ha!
I don't recall seeing that one before. I had to look it up
Star Trek Expanded Universe
USS Pegasus (NCC-612)
STARSHIP
Saladin Class
Name: USS Pegasus
Registry: NCC-612
Class: HermesType: ScoutAffiliation: Federation Starfleet
USS Pegasus (NCC-612) was a Hermes-class scout — of the Monoceros subclass — on active duty in Starfleet during the 23rd century. (Star Fleet Technical Manual)
Keith Wyndham was the commanding officer of Pegasus in 2257. Leonard McCoy was a junior medical officer on the ship. (Orion Press: "The Difference")
Here are two more Hermes-class:
Monomorphic could you so kind to got a look to the magnetic field vectors of the so called "TE013" mode in your small tapered please ? Is it equal to my pic below?
I also have the strong assumption that the mode notation is still wrong since the mode numbers based on cartesian coordinates and not longer cylindrical.
I guess the correct notation wold somewhat like TE203 or TE023.
Monomorphic could you so kind to got a look to the magnetic field vectors of the so called "TE013" mode in your small tapered please ? Is it equal to my pic below?
Looks equal to me. So you think this is TE203?
Of course it's pure convention. The problem is, the system was made for rectangular waveguides and cavities not for a tapered one (and in contrast the cylindrical shapes, based in cylinder coordinates).
Since the base of this model is quadratic one can choose a- and b- side (or x,y), the result is a difference in the notation of the mode you like to describe. We had similar problems with the conical mode notation some threads ago.
It's hard to find a precise description for conditions like that based on the international standards for cylindrical or rectangular mode shapes.
For example in the past we saw mode shapes in the top of a truncated conical cavity equal to a specific TXmn mode but at the bottom end the shape was complete different. Therefore Monomorphic´s current design is easier to describe but it still depends on conventions we have to define (like what is the a- and b- side).
Of course it's pure convention. The problem is, the system was made for rectangular waveguides and cavities not for a tapered one (and in contrast the cylindrical shapes, based in cylinder coordinates).
Since the base of this model is quadratic one can choose a- and b- side (or x,y), the result is a difference in the notation of the mode you like to describe. We had similar problems with the conical mode notation some threads ago.
It's hard to find a precise description for conditions like that based on the international standards for cylindrical or rectangular mode shapes.
For example in the past we saw mode shapes in the top of a truncated conical cavity equal to a specific TXmn mode but at the bottom end the shape was complete different. Therefore Monomorphic´s current design is easier to describe but it still depends on conventions we have to define (like what is the a- and b- side).
Well said.
Just when I thought I got the mode down pat
On the other hand it could make for some interesting modes of action between the two plates.
Monomorphic, will you be running superconducting sweep sims the trapezoidal prism and "wedge" shape of the same? Thanks FL
Dear all
solving the gravitational wave propagation integral 
(and thus the Einstein field equations in weak field limit because the integral is then an equivalent formulation of them) in the weak field limit and in the case of a cylindrically symmetric hollow resonator with an oscillating internal energy density I have found out that even in the original
einstein theory (without hoyle-narlikar modifications) there is a difference in the radiated gravitational field between the two + and - z directions if in addition to the 00-component of the energy-momentum tensor (mass energy density) and the 0a / a0 energy current density terms there are non-zero stress components in radial or axial direction.
For what follows I described the cavity in local cylindrical coordinates with it's symmetry axis
aligned along the z axis. I modelled the cavity using mass density distributions of lorentzian shape which allows for an analytic solution of the integral in a constant retardation phase approximation. This also allows to derive an analytic expression for the 0z component of T from the 00 component via the continuity equation. After solving the integral for the h field I determined the scalar 
at two different locations "above" and "below" the resonator. I assumed a length for the resonator of 1 m and a diameter of 20 cm. The thickness of the walls is determined by the coefficients of the lorentzian shape functions more less to be of the order of mm to cm. The total power fluctuating inside the cavity was assumed to be P = 1 MW. The maximum stress amplitude in axial direction (diagonal tensor component Tzz) was assumed to be 10^4 N/m˛. The frequency of energy fluctuation was chosen as 150 MHz. That said the 00 (tt) component of the energy momentum tensor was split in a time dependent and independent part.
with
and
The energy current density component Ttz can be derived from this expression
but although straight forward it is so unduly complicated and long, that I don't write it here.
While I chose the stress components Trr,Tphiphi,Tzz
to be oscillating with the same frequency but with a possible different phase delta relative to the oscillating energymass flow.
in which there is 
The Result of the calculations is that, as can be seen in the first attached picture, when there are zero stress components Trr,Tphiphi,Tzz and only non-zero energy mass density and energy flow density components Ttt,Ttz, there is no difference (green line) between the amplitudes of the radiated gravitational wave field above (blue line) and below (red line) the resonator.
But: In the case of a non zero stress component Tzz, however, depending on the relative phase delta (blue line 0, red line pi/2, green line pi) there are amplitude differences between the wave fields above and below the resonator
Interestingly the difference is smallest for a phase of pi/2. This just corresponds to the case when the stress maximum is reached when the fluctuating energymass density has its maximum in the center of the resonator. Coincidence? This somehow reminds one of the predicted Woodward effect relative phase behaviour doesn't it?
To be clear: The amplitude difference is tiny. It is no artefact, but up to now it cannot explain the total thrust Eagleworks measured but the findings are interesting and it might well be that there are unknown facets of a more accurate modified theory (Hoyle Narlikar) that will give a larger amplitude difference.
I will admit that this takes me way beyond my pay grade and I'm just now slowly getting a grasp of what you did.
The one question I'd have for you and maybe anyone here is to clear up why the stress seems to be increasing as the equation progresses in time? We are looking at a relative short time in cycles (<5) and I see a growth. The question begs to be answered, what happens if it's extended a few thousand cycles?
Shell
Dear all
...
I will admit that this takes me way beyond my pay grade and I'm just now slowly getting a grasp of what you did.
The one question I'd have for you and maybe anyone here is to clear up why the stress seems to be increasing as the equation progresses in time? We are looking at a relative short time in cycles (<5) and I see a growth. The question begs to be answered, what happens if it's extended a few thousand cycles?
Shell
The stress is not growing with time.
The cyclic average cannot grow with time, according to the equations presented, which are functions of the cosine of time (a cyclic function with time that cannot grow with time over many cycles). There is no function of time outside the cosine function in any of the equations presented.
Looking at the equations, all you have are cosine variations with time and phase.
(Essentially, Cos
2 [ω t'] variation for the time-time component (density of relativistic mass) and Cos[2 ω t' + δ] for the normal stress components):
in which there is
a) T
tt (this time–time component is the
density of relativistic mass = mass/Volume, i.e. since E = m c
2, m/V= (E/V)/c
2,
the energy density divided by the speed of light squared),
and
b) The normal, diagonal, stress components T
zz, T
rr, T
φφ .
Ttt (the density of relativistic mass = mass/Volume) is a function of the inverse of Cos2 [ω t'] (a cosine does not grow with time, but it varies cyclically with time) plus a constant (*).
The normal stress components, for example Tzz are functions of Cos[2 ω t' + δ] (again, a cosine does not grow with time, but it varies cyclically with time).Therefore, all you can have, as remarked by the author is:
depending on the relative phase delta (blue line 0, red line pi/2, green line pi) there are amplitude differences between the wave fields above and below the resonator
The question begs to be answered, what happens if it's extended a few thousand cycles?
Shell
ANSWER: It will continue oscillating for infinite time. According to the equations presented the cyclic average will not grow with time, not in a thousand cycles, nor in a billion cycles, nor in an infinite number of cycles_________________
(*) t' = t - t
retThe term Cos2 [ω t'] is summed to a constant and squared, and it appears in the denominator. None of that changes its cyclic character. Its cyclic average cannot grow with time.
I ran a more detailed sweep of the wedge geometry and was able to identify a number of TE modes. The modes are listed in the order they appeared during the sweep (2Ghz - 3Ghz).
There were a number of what appeared to be TM modes, but those are not included in this image.
Monomorphic, of these two forms in which is it easiest to develop a strong (and therefore better) resonant state? thnx, FL
BTW the second shape is a truncated pyramidal rectangle that is concave bottom, convex top. Image below posted previously. The only EM "horn" not yet to the best of my knowledge explored (second attached ...w/or w/out concave/convex.
...
The question begs to be answered, what happens if it's extended a few thousand cycles?
Shell
ANSWER: It will continue oscillating for infinite time. According to the equations presented the cyclic average will not grow with time, not in a thousand cycles, nor in a billion cycles, nor in an infinite number of cycles...
It is a great benefit that DaCunha has provided the simple analytical equations, because they enable one to make that strong assessment, even for infinite time. This is the great benefit of closed-form solutions: they enable one to rapidly understand the behavior and to extrapolate it, if required to infinite time, something that would not be possible with numerical methods like finite difference, finite element, boundary element etc., which besides suffering in that respect with respect to closed-form solutions, are also subject to convergence, numerical and stability errors. This is not possible with pictures either, only equations give us the power to be able to extrapolate into the future behavior, outside of the range shown by a picture.
So why the missing side walls in Roger's SC cryo EmDrive thruster?
Just maybe the top and bottom Rf mirrors (let's call them what they are) direct & beam the microwave photons from end to end without letting them hit the side walls?
If so there should be a BIG effect on reducing eddy current losses (no side walls), boosting Q (desired goal is increased cavity discharge time) to harvest the max momentum transfer (maxed number of Rf mirror reflections) from a short initial Rf excitation pulse.
The Thrust curve that is there after the Rf pulse ends is due to retained cavity energy slowly decaying, yet still capable of generating force. The less the losses in the cavity during the decay time (from no eddy currents induced in the missing side walls), the longer the cavity energy will remain active and generate force.
I consider these two images as being major breadcrumbs from Roger to DIY EmDrive researchers/builders. Would suggest the missing side walls will also work with non SC cryo frustums. However the end plates need to be very good Rf mirrors that can very accurately direct and beam the microwave photons back and forth between the 2 Rf mirrors without touching the side walls.
Given the sensitivity of Emmett Browns rig (and looking at the tangle of wires in the pictures) might not Lorentz forces be an issue?
I don't think so. It looks to me like he is powering it with AC.
At 1:03 of the 2 mN video the AC cord is disconnected. I doubt the same sensitivity would be achieved with the cord plugged in. The plastic of the thick cord is very thermally responsive too. Still though not a bad rig. As said in other posts, a battery and inverter would be better.
On the other hand it could make for some interesting modes of action between the two plates.