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THRUST MEASUREMENTS OF MICROWAVE-, SUPERCONDUCTING-AND LASER-TYPE EMDRIVES

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Propellantless propulsion concepts based on electromagnetic waves like the EMDrive are claimed to be far superior with respect to the state of spacecraft propulsion systems. Such devices consist of enclosed cavities with different geometric shapes that are injected with electromagnetic waves, producing unidirectional thrust without expelling propellant. Additional concepts emerged from theories like quantised inertia and involve laser-type EMDrives with optical cavity resonators and fiberoptic loops in the infrared spectrum. Claimed forces of these devices in the micronewton range are confronted with growing scepticism when basic conservation laws are applied. With cutting-edge measurement devices, we were able to characterize these concepts in a space-like environment with nanonewton resolution for thruster masses of up to 10 kg. Additionally, we enhanced our inverted double pendulum thrust balance with the ability to perform thrust measurements at cryogenic temperatures (65 K) to operate also a superconducting EMDrive that was claimed have orders of magnitude higher thrust compared to classical resonators. In this paper, we present changes to each setup, based on criticism to our latest results, as well as thrust measurements of each device. Neither the EMDrive cavities nor the infrared laser resonators created a net-thrust above our balance noise. With the exception of the superconducting EMDrive, our data limits anomalous thrust below the threshold of classical propulsion with photon pressure for equivalent power-levels. Despite the enhancements made to each device, we did not detect any evidence in favour of the proposed theories.
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IAC-21,C4,10-C3.5,1,x63502
THRUST MEASUREMENTS OF MICROWAVE-, SUPERCONDUCTING- AND
LASER-TYPE EMDRIVES
Oliver Neunziga, Marcel Weikertb, Martin Tajmarc
a Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307 Dresden,
Germany, oliver.neunzig@tu-dresden.de
b Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307 Dresden,
Germany, marcel.weikert@tu-dresden.de
c Institute of Aerospace Engineering, Technische Universität Dresden, Marschnerstrasse 32, 01307 Dresden,
Germany, martin.tajmar@tu-dresden.de
Abstract
Propellantless propulsion concepts based on electromagnetic waves like the EMDrive are claimed to be far superior
with respect to the state of spacecraft propulsion systems. Such devices consist of enclosed cavities with different
geometric shapes that are injected with electromagnetic waves, producing unidirectional thrust without expelling
propellant. Additional concepts emerged from theories like quantised inertia and involve laser-type EMDrives with
optical cavity resonators and fiberoptic loops in the infrared spectrum. Claimed forces of these devices in the
micronewton range are confronted with growing scepticism when basic conservation laws are applied. With cutting-
edge measurement devices, we were able to characterize these concepts in a space-like environment with nanonewton
resolution for thruster masses of up to 10 kg. Additionally, we enhanced our inverted double pendulum thrust balance
with the ability to perform thrust measurements at cryogenic temperatures (65 K) to operate also a superconducting
EMDrive that was claimed have orders of magnitude higher thrust compared to classical resonators. In this paper, we
present changes to each setup, based on criticism to our latest results, as well as thrust measurements of each device.
Neither the EMDrive cavities nor the infrared laser resonators created a net-thrust above our balance noise. With the
exception of the superconducting EMDrive, our data limits anomalous thrust below the threshold of classical
propulsion with photon pressure for equivalent power-levels. Despite the enhancements made to each device, we did
not detect any evidence in favour of the proposed theories.
Keywords: Propellantless propulsion, EMDrive, laser resonator, superconductor, thrust balance
Acronyms/Abbreviations
COM – Center of mass
SC – Superconductor
EM – Electromagnetic
YBCO – Yttrium-Barium-Copper-Oxide
QI – Quantised Inertia
1. Introduction
The reliance of modern propulsion systems on
propellant puts strong limits on their ability to perform
large-scale space exploration. So far, the ultimate
propellantless propulsion concept is pure photon
pressure, e.g. produced by a laser. Solutions to break
through this limit may hide in yet unknown interactions
of fundamental properties like mass and inertia. The
emergence of novel theories and concepts that allow
experimental research of propulsion candidates is an
important aspect to reach this goal.
Some of these theories predict forces in the µN range
and also well above for attainable power-levels in a
laboratory environment. Our goal is to develop advanced
testing facilities, manufacture promising thruster
candidates and characterized them in order to find out if
they work as promised.
We recently reported results of a thorough test
campaign to characterise both the so-called EMDrive [1],
which uses microwaves inside a copper resonator, as well
as Laser-EMDrive [2], which uses optical resonators in
various different configurations. During our tests we
could reproduce forces on our balance that were similar
to the ones reported by others or claimed by some of the
proposed theories, however, our measurements also
revealed that their origin was not real but linked to a
number of setup-related issues like thermal-induced
mechanical stress on the balance. Once all thrusters were
properly mounted, all false-positives disappeared and all
measurements were below the equivalent photon thrust
limit considering the power levels used.
After receiving criticism from the advocators of both
concepts [3, 4], in this paper we will implement all the
requested changes and even expand the capabilities of
our thrust balance:
Instead of using an EMDrive cavity with flat end caps
and a dielectric disc inside like the one published by
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NASA [5], we removed the dielectric and used spherical
end caps.
Next, we implemented the capability to cool thrusters
to cryogenic temperatures on the balance while retaining
µN thrust resolution. This enabled us to test an EMDrive
with superconducting end caps that should greatly
enhance its thrust.
Lastly, we implemented several setup changes to the
laser cavities to test various suggestions of why we
obtained a null result.
2. Testing environment
Thrust measurements in the sub-µN regime require
the detection of environmentally induced effects that may
lead to false-positive thrust signals. These false-positives
are often indistinguishable from real thrust and therefore
difficult to detect in the first place. We observed and
decreased the most influential errors induced by
electromagnetic interactions with external magnetic
fields in close vicinity, thermal interactions with the
thrust balance and especially atmospheric convection.
Each individual test series presented in the following
chapters was exposed to the same environmental
conditions for comparability. Tests took place inside our
cylindrical vacuum chamber with an inner diameter of
0.9 m, a length of 1.5 m and a minimum operating
pressure in the region of 10e-7 mbar with a Pfeiffer
Turbopump supported by an Edwards scroll pump. The
vacuum chamber features its own concrete basis that is
separated from the lab building to decrease seismic noise
to the thrust balance. Continuous enhancements in
decreasing environmental influences enabled us to reach
the desired thrust noise benchmark of photon pressure.
This means, that we are able to compare each thrust
concept with its operating power level to the equivalent
thrust if we converted the same power directly into a
beam of photons. Devices under test must exceed this
threshold to be of significant interest for space propulsion
applications.
Fig. 1: CAD-rendering of the inverted counterbalanced
double-pendulum thrust balance developed at TU
Dresden.
An important part of the high thrust resolution was
the development of a thrust balance based on an inverted
counterbalanced double pendulum (fig. 1). The
measurement principle includes a deflecting frame onto
which thrusters apply a force that linearly deflects a
spring-mounted parallelogram (fig. 2). The deflection is
measured with an attocube IDS3010 Interferometer and
converted into thrust values by previously characterizing
the correlation between spring deflection and applied
forces. The balance is able to detect the continuous force
of a 0.5 W steady-state laser, which translates to 1.67 nN
with a thrust-to-noise ratio of 10 and can support thruster
masses of up to 10 kg.
Fig. 2: Measurement principle of the inverted double-
pendulum thrust balance.
Setups with laser-resonators operated in a vacuum
level of 10e-6 mbar due to the low laser power levels and
therefore high-resolution requirements. This vacuum
level also reduces false thrust signatures from outgassing
components that may occur due to heat generation from
the impacting laser beam.
The EMDrive with a spherical endcap operated in the
same vacuum chamber at a higher pressure of 10e-2 mbar
as it was sufficient for the desired thrust noise. The
superconducting version of the EMDrive on the other
hand required the usage of liquid and solid nitrogen as a
coolant. The measurement process and environmental
pressure with a nitrogen gas generator will be discussed
in a later section of this paper.
Prior to each set of measurements the thrust balance
is calibrated to ensure unaltered operating conditions. By
applying consecutive forces of different magnitudes with
a voicecoil, we characterize the correlation between
applied force and resulting balance deflection with
statistical significance. Each data point is transferred into
a linear fit of commaned force against measured
displacement to verify linear deflective behaviour of the
torsional springs. The so-called calibration factor, usually
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in the range of 1 µN/µm, is used to convert displacements
into corresponding thrust values.
Thermal drifts due to heat generation on the balance
are always present and superimposed on the thrust signal.
As long as the drift is within a tolerable magnitude, we
use software tools with LabView to automatically
remove them. Every thrust measurement presented in the
following subsections is an average of consecutive
measurements with the same operating parameters to
further decrease the balance resolution and highlight the
existence of force plateaus.
A summary of every measured thrust value, discussed
in the following chapters, is presented in appendix B.
3. Microwave EMDrive
The EMDrive is a tapered resonant cavity operated
with electromagnetic waves in the microwave spectrum.
Microwaves resonating back and forth inside the tapered
resonator are proposed to exceed a significant net-force
due to a difference in radiation pressure between both
end-plates.
In a recent publication [1] we presented our approach
to manufacture and operate the EMDrive similar to the
cavity tested at the NASA Eagleworks laboratory, as it is
the first peer-reviewed measurement of an EMDrive with
a positive thrust result. We identified and eliminated
several measurement influences that result in false-
positive thrust effects with the same signature as seen by
White et al [2]. The predominant influence included
thermally induced center of mass (COM) shifts that
create convincing thrust signatures. These signatures are
often misinterpreted as real thrust in torsion balance
measurements, like the ones used by NASA. After
eliminating the influences, we attained a thrust resolution
that was below the equivalent photon-pressure threshold
and our latest thrust measurements [1] did not reveal any
thrust above balance noise originating from the NASA-
like cavity. For the cavity presented in this paper, we
made several setup changes to gain the desired operating
conditions, as suggested by Shawyer [6].
3.1 EMDrive - Experimental Setup
The device used the same cavity geometry utilized in
previous tests [1], but we replaced the flat end plate on
the larger side with a spherical end-cap and removed the
dielectric (HDPE) within the cavity entirely to reduce the
phase deviation described by Shawyer [6]. The small
endcap remained flat and has a tight fit within the
cylindrical flange of the cavity that allows fine-tuning.
Geometric dimensions of the cavity are shown in
figure 3. Furthermore, we increased the quality factor of
the cavity at important resonant frequencies to further
increase predicted force values.
Fig. 3: Geometrical dimensions of the copper cavity with
a spherical end-cap at the large diameter.
For the electrical setup, we operated the EMDrive in
the same manner as before with an on-board battery-pack
with six Lithium-Ion cells and balancing electronics for
recharging to supply the microwave amplifier without the
need for electrical feedthroughs on the balance. We
utilized the liquid metal feedthroughs solely for data
acquisition as they would interfere with thrust
measurements otherwise. Additionally the electrical
setup on the balance, as seen in appendix A, figure 21,
contained the following components:
-Mini Circuits ZX95-2041-S + voltage-controlled
frequency generator
-Mini Circuits ZX73-2500-S + voltage-controlled
attenuator to control the output power of the amplifier
-EMPower SKU 1164 RF solid-state amplifier with a
maximum output power of 50 W and an amplification
of 47 dB
-MECA CN-1.950 circulator to prevent damage to the
amplifier from reflected power
-Mini Circuits BW-N30W20 + fixed attenuator
-Mini Circuits XZ47-40LN-S + power meter
-Maury Microwave 1878B three-stub tuner for
impedance matching directly coupled to the feed
antenna
A major difference to our previous tests is the
attachment of a sensing antenna to the cavity with an N-
Type connector. The antenna is located near the small
end cap and positioned 90° relative to the feed antenna
position. It serves as an indicator for microwave power
being present inside the cavity. However, the absolute
power value cannot be determined with the sense
antenna, because the power at the antenna position is
mode-dependent. The electrical setup consumed up to
100 W of power during operation on the balance, which
is a considerable amount of heat generation on the
balance that may interfere with measurements.
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For tuning purposes, we used an Anritsu MS46121A
single-port Vector Network Analyzer. The additional
sensing antenna allowed a more precise tuning process
with a two-port analyser. In this way, the important
power transmission S21 through the cavity could be
determined.
Our thrust measurements involved four resonance
frequencies ranging between 1918 MHz and 2054 MHz
with loaded Q values of up to 1027.
3.2 EMDrive – Results & Discussion
Our previous measurement campaigns with the
NASA-like cavity revealed numerous influences that
created convincing thrust signatures. We identified the
mounting position of the cavity on the balance as the
most influential source of these false positive thrust
effects. For comparability, the cavity presented in this
paper was mounted and operated in the same manner as
the tests with the NASE-like cavity. The EMDrive was
mounted to the upper balance platform in a hanging
position using two bearings with bolts that allowed for
deflections in the horizontal direction (fig. 4). The
hanging setup contained the cavity and every electrical
component that is required to operate it. This way, heat
generation and therefore COM switches from thermally
expanding components occur isolated on the hanging
setup. Most micronewton thrust measurement principles
are sensitive to COM switches to a certain degree. By
isolating these kind of deflections from the measurement
axis, our tests gained a large enhancement in sensitivity
even though we generated high thermal stress on the
device under test.
Fig. 4: Measurement setup of the EMDrive mounted to
the thrust balance with a bearing suspension hanging
from the upper platform.
We identified four resonance frequencies in the
bandwidth between 1900 MHz and 2100 MHz (appendix
A, fig 23). Power measurements of the sense antenna are
presented in figure 22 as well, but as mentioned before,
this is not an absolute value for the power in the cavity as
it is mode dependent.
Thrust measurements were performed for each of the
four resonance frequencies at 1918 MHz, 1946 MHz,
2030 MHz and 2054 MHz with corresponding loaded-Q
values and modes summarized in table 1. By using worst-
case assumptions and the simplified equations without
geometric adjustments, the predicted force values
reached up to 22.5 µN for the power levels used, but each
thrust measurement at either of the resonance frequencies
resulted in balance noise only. Furthermore, the balance
resolution during measurements reached values that
excluded thrust generation of the EMDrive above its
equivalent photon pressure for the given amount of
power (Q=1) despite Q-values of several hundreds.
Table 1: Detected resonance frequencies of the EMDrive
cavity with corresponding loaded Q-values and their
modes.
Resonance Frequency Q
Loaded,S11
Mode
1918
MHz
113
Hybrid
1945
MHz
486
210
2030 MHz
2054
MHz
677
1027
TE 113
TE 020
Another claim by the inventor is the necessity of a
constant force that counteracts the EMDrive motion, the
so-called preload [6]. Although this violates the classical
conservation of momentum, this preload is supposed to
withhold the cavity motion to store up potential energy
within the device and release it as kinetic energy after
reaching a certain threshold. An important aspect is the
absolute value of this preload, because it must be below
the predicted force values. We realised the preload in our
setup by commanding forces with the voicecoil, used for
calibrations, while the EMDrive was operating. This way
the EMDrive experiences a counteracting force with a
defined magnitude in either direction. If the preload
works as intended, the measured thrust should exceed the
commanded thrust by a not-clearly defined amount. With
predicted thrust values of several tens of micronewton,
we decided to command a preload of ±10 µN and
compare it to a balance calibration of ±10µN while the
EMDrive was not operating. We tested the preload for
each of the four resonant frequencies in both directions.
The results are presented in appendix A, figure 25. None
of the resonant frequencies responded to the preload and
there was no difference in measured thrust while the
EMDrive operated. Although we counteracted the cavity
motion, it did not release any stored up kinetic energy.
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In summary, the cavity with a spherical endcap and
no dielectric did not produce any thrust above our
balance noise.
Fig. 5: Thrust measurement of the EMDrive with a
spherical end-cap at 1918 MHz resonance frequency.
The operating condition is indicated by the amplifier
current.
Fig. 6: Thrust measurement of the EMDrive with a
spherical end-cap at 2030 MHz resonance frequency.
The operating device is indicated by the amplifier current
4. Superconducting EMDrive
The quality factor of a microwave cavity strongly
depends on the electrical conductivity of the cavity end-
plates. The higher the conductivity, the lower the power
loss with each reflection of the electromagnetic wave.
According to Shawyer the highest performance of an
EMDrive involved superconducting end-caps, enabling
quality factors that are orders of magnitude above pure
copper end caps [6, 7]. A superconductor is a material
with no electrical resistivity when cooled below its so-
called critical temperature Tc. This leads to advantageous
properties in reflecting electromagnetic waves and boosts
the predicted force values of an EMDrive. Shawyer
claims extraordinary thrust performance with his so-
called 3rd generation EMDrive utilizing YBCO high-
temperature superconductors instead of copper [6].
4.1 Superconducting EMDrive - Experimental Setup
We manufactured our own version of a
superconducting cavity by using a copper cylinder with a
diameter of 160 mm and a length of 210 mm. Copper
end-plates are tightly fit into the flanges on each side of
the cylinder (fig 7). Two sapphire substrates with a thin
film of YBCO coating were mounted on each end plate.
A HDPE disc with a thickness of 40 mm was pressed
against one of the YBCO substrates to access the desired
resonant modes. The assembled cavity was then mounted
inside a milled Polystyrene (XPS) box that served as a
reservoir for liquid nitrogen while cooling the whole
cavity below the critical temperature. Remaining gaps
between the XPS and the cavity were sealed using
STYCAST FT2850 cryogenic epoxy with the 24LV
catalyst. For better thermal conductivity between the
copper caps and the superconducting waver, we used
Apiezon N cryogenic vacuum grease and a 3D printed
PEEK structure to press the waver against the copper
surface.
Fig. 7: Geometrical dimensions of the copper cavity with
superconductors on each end with a dielectric (HDPE) in-
between.
The usage of liquid nitrogen as a coolant introduces
various difficulties with the operating electronics, as
most of the components are not suitable for cryogenic
temperatures. We therefore decided to change the setup
in a way that none of the HF-components are exposed to
the cryogenic cavity. This was possible by separating the
feed antenna physically from the cavity. The Antenna
was mounted next to the thrust balance on a rigid
structure and submerged into the superconducting cavity
that was placed on the moving platform of the thrust
balance. There was no mechanical contact between the
cavity and the feed antenna. For cavity tuning purposes,
we mounted the antenna to a micrometer-linear stage for
precise alignments. The miniscule movements during
thrust measurements between antenna and cavity in the
sub-µm range did not interfere with the cavity tuning.
This allowed us to feed the cavity with power from the
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outside of the vacuum chamber contrary to the EMDrive
setup with the spherical endcap. The electrical setup, as
shown in appendix A, fig. 22, involved a Rigol
DSG2011Z frequency generator, amplified with the
EMPower SKU 1164 RF solid-state amplifier.
Another challenge of this superconducting cavity is
an increased complexity when it comes to thrust
measurements. YBCO has a critical temperature of 92 K,
which means, that the end caps must stay at cryogenic
temperatures with liquid nitrogen (77 K) while mounted
to a temperature-sensitive test-bed. We fed the XPS
reservoir with liquid nitrogen from a dewar outside of the
vacuum chamber. To prevent air-humidity from
condensing and forming ice on the thrust balance, we
lowered the pressure to 10e-1 mbar inside the chamber.
Afterwards, we utilized a LN
2
condenser to fill the
vacuum chamber with nitrogen gas until it reaches its
triple point at a pressure of 125 mbar. Below this pressure
value, nitrogen exists in the form of solid ice that prevents
the liquid from entering the reservoir. We then filled the
reservoir to create a nitrogen bath around the copper
cavity and cool the superconducting end-plates below its
critical temperature. Five K-thermocouples indicate the
filling level and monitor the temperature of the
superconductors. After reaching the superconducting
state, we reduced the chamber pressure again to 10e-
1 mbar to exploit the solid aggregate state of nitrogen for
thrust measurements. Liquid nitrogen or liquids with low
viscosity in general on a thrust balance add undesired
oscillations through boiling and fluid motion, hence
increasing the noise. By lowering the pressure around the
XPS reservoir, the liquid bath solidifies and interrupts the
fluid motion. As a side effect, the transition from liquid
to solid further decreases the temperature by 15 K, which
supports the superconducting state. Thrust measurements
took place in this environment although solid nitrogen is
still able to transition into the gas phase when heated,
which creates undesired cold gas thrust in undefined
directions.
4.2 Superconducting EMDrive – Results & Discussion
Thrust measurements for the superconducting cavity
were performed below and above the critical temperature
T
c
of the SC to directly compare the influence of
superconducting end-caps. The XPS-box, containing the
cavity, was mounted on the upper platform of the thrust
balance (fig. 8). The advantage of an adjustable
measurement range and resolution with our thrust
balance was a slight disadvantage for this specific setup.
The balance reacts on mass changes on the measurement
platform by increasing the calibration factor, which is
linked to the sensitivity. This leads to a slight degrade in
thrust resolution while the nitrogen-ice evaporates during
heat generation. We therefore performed short
calibrations in-between each measurement to account for
this effect. Furthermore, the stored amount of nitrogen
ice within the reservoir limited the available
measurement time to around 30 minutes per filling.
Although we prevented liquid motion by creating
nitrogen-ice, evaporation still interfered with
measurements and increased the thrust noise.
Fig. 8: The superconducting EMDrive within the XPS-
reservoir mounted to the thrust balance inside our
vacuum chamber.
Within a bandwidth between 1800 MHz and
2000 MHz, we tuned the cavity for at least one resonance
frequency at room temperature and scanned an even
larger bandwidth for additional frequencies that should
emerge after cooling the cavity below T
c
. First tests
involved the cavity with the dielectric positioned in close
vicinity to one of the SC-substrates. Unfortunately, the
scanned bandwidth did not reveal additional resonance
frequencies after the T
c
transition, as shown in the
comparison in appendix A, fig. 25. While the tuned
resonance frequency at 1843 MHz was still present, no
additional peaks arised from the SC. Subsequent cavity
tuning efforts did not improve the situation.
Nonetheless, we performed thrust measurements,
including the dielectric, at different temperatures. The
results are presented in figure 9 with a comparison
between measured thrust below and above T
c
at the
resonance frequency of 1843 MHz. Because the cavity
was mounted in a way that showed false positive thrust
signatures in previous tests with high calibration-factors
[1], similar signatures appeared. Hanging the cavity from
a single suspension point like the non-SC cavity was not
possible for this setup.
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Fig. 9: Thrust comparison of the superconducting cavity
with HDPE below and above the critical temperature.
Figure 10: Thrust measurement of the superconducting
cavity with HDPE reoriented by 180°.
Inconvenient nitrogen evaporation may be another
source that was responsible for the signature. However,
the direct comparison between both measurements
revealed no effects upon reaching the critical
temperature. The superconductors had no influence.
To verify the thrust signal we reoriented the device by
180° and repeated the thrust measurement with same
operating conditions below the critical temperature. As
seen in fig. 10 the resulting thrust had a similar value and
did not change direction. Considering both cases, the
thrust signature with HDPE is most likely a measurement
artefact.
We suspected that the dielectric was responsible for
the absent resonance frequencies below Tc and therefore
removed it and retested the cavity in addition with a
lower calibration factor of the balance. As seen in
appendix A, figure 26, additional resonance frequencies
occurred at 1819 MHz and 1959 MHz that were only
present below Tc without the HDPE disk. These narrow
SC-peaks were characterized by loaded Q-values of 2600
at 1819 MHz and 2063 at 1959 MHz. Corresponding
thrust measurements at both resonance frequencies below
Tc are presented in figure 11 and 12. For 20 W of
commanded power, we detected no thrust effects above
the balance noise at both SC resonance frequencies.
Fig. 11: Thrust measurement of the superconducting
cavity without HDPE at 1819 MHz SC-resonance
frequency at -202°C with 20 W of commanded power.
Fig. 12: Thrust measurement of the superconducting
cavity without HDPE at 1959 MHz SC-resonance
frequency at -196°C with 20 W of commanded power.
5. Laser-Type EMDrive
A more compact form of an EMDrive, as suggested
by Taylor, involves electromagnetic waves in the infrared
spectrum and optical resonators with lasers rather than
microwaves [8]. Taylor bases his ideas on the theory of
quantised inertia by McCulloch [9, 10, 11]. In a recent
paper [2] we presented our results of an experimental
investigation on QI-Theory with optical resonators. QI-
Theory claims to describe the origin of inertia with a
Modified inertia Hubble-scale Casimir effect (MiHsC).
In this model, inertia of an object emerges from damping
of Unruh radiation while it experiences acceleration. To
explain the origin of inertia McCulloch assumes the
formation of a relativistic Rindler horizon appearing in
the opposite direction to its acceleration that damps
certain wavelengths of the Unruh waves thus creating an
inhomogeneous distribution of radiation pressure. This
process results in the effect we perceive as inertia with a
modified inertial mass mi, including the standard inertial
mass m, the speed of light c, the diameter of the
observable universe Θ and the magnitude of acceleration
of the object compared to the surrounding matter ||and
is given by
= 1 − 
||) (1)
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In a laboratory environment, acceleration of regular
masses are so low that this effect only appears cosmic
scales. QI’s key assumption, however, involve photons at
the speed of light instead of regular masses resonating
back and forth between reflective surfaces of a laser
cavity. Photons supposedly perceive acceleration with
each reflection and therefore creating Unruh radiation
that can be damped by placing an electrically conductive
metal-plate in close vicinity of the reflective surface.
Photons themselves carry momentum that can
exchange with surfaces and produce a force F
Photon
according to equation (2) for full photon absorption
where P is the power of a laser beam and c the speed of
light. The most important part of the prediction according
quantized inertia is an additional factor S that leads to the
simplified equation (3) without geometric properties
included.

=
(2)

=

(3)
The factor S represents the number of reflections
inside the optical resonator, the so-called force
amplification factor. From this equation, it appears that
the produced thrust is given by the classical radiation
pressure multiplied by the number of reflection inside
each resonator. In the classical interpretation of this
experiment, a laser beam resonating back and forth inside
an enclosed containment should only produce heat and
miniscule mechanical oscillations of the cavity rather
than amplified thrust in one direction as it contradicts
Newton’s action-reaction principle.
The goal of the past test series was thrust
measurements with high S-values to compare the data to
a beam trap that absorbs the photons on the balance rather
than resonate the beam prior to absorption. Recent
criticism by McCulloch on our reported negative thrust
results and resonator setups lead us to change specific
setups according to his suggestions [8].
5.1 Silver Cavity Resonators – Experimental Setup
We previously tested a variety of metal cavity
resonators with different geometries and reflectivities
made from copper and silver, but no abnormal thrust
above the photon pressure was found [2]. The resonators
were initially milled from copper and polished to gain a
measured reflectivity of approximately 89%, which
translates to a force amplification factor of 9 for the used
808nm laser wavelength. To compare each of the three
resonators with a different amplification factor, we
electroplated the exact same resonators with a thin layer
of pure silver, leading to an enhanced reflectivity of
97.5%, thus an amplification factor of 39. The three
geometries were named CC/CX (concave/convex),
CC/CC (concave/concave) and CIRCLE according to
their respective geometry.
The laser source was a modular diode-pumped solid-
state laser-kit by Leybold. The laser emits a fixed
wavelength of 808 nm with adjustable power-levels
between 0.01 W and 0.65 W. It is supported by Peltier
elements for temperature-controlled wavelength
stabilization even in vacuum.
For accurate force predictions and comparability
between each setup, we used a Coherent LaserCheck
power-meter to measure the laser power prior to entering
each resonator. The powermeter offers a maximum
detectable power of 1 W for wavelengths between
400 nm and 1064 nm with a resolution of 0.01 µW.
The thrust measurements took place by positioning
each resonators on the balance that is targeted by a laser
source next to the balance on a rigid structure. This way
we would expect pure photon thrust at least because the
photons are absorbed on the balance and transferring all
their momentum to the mounted cavity.
According to McCulloch the resonators should have
never been able to generate thrust due to an aluminium
plate being present that supposedly prevents Unruh
radiation to interact as intended [4]. In our setup, the plate
served as a protection against low-power side coils of the
laser beam that may affect the temperature sensitive
balance components and create false-positive thrust
signals. We removed the aluminium case from the cavity
and retested each of the three resonators with otherwise
equal operating conditions.
5.2 Silver Cavity Resonators – Results & Discussion
Prior to each measurement we made sure that the laser
enters the cavities by using an infrared sensitive camera
and a Coherent LaserCheck powermeter. As an example,
the illuminated cavity CC/CX is shown in figure 13.
After the laser alignment, the cavities were closed with a
polished silver lid to prevent scattered laser power from
escaping the cavity. The only setup change of removing
the aluminium plate did not have any effect on measured
thrust whatsoever.
Fig. 13: The illuminated cavity CC/CX on the thrust
balance.
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Thrust measurements of every cavity for an input
power of 467 mW resulted in pure photon thrust (S=1).
No anomalous thrust was found nor suppressed by the
aluminium plate used in previous tests, as seen in the
exemplary thrust measurement in figure 14 and the
summarized thrust values in appendix B, table 1.
Fig. 14: Exemplary thrust measurement of the CC/CX
resonator for a measured laser power of 467 mW.
5.3 Taylor Resonator – Experimental Setup
Additional tests involved high-finesse optical
resonators, following the ideas of Taylor [8], to increase
the number of reflections by several orders of magnitude
compared to the silver cavities. These resonators utilized
an asymmetric beam trajectory between two mirrors,
originating from Nd:YAG crystals in between that
convert the initial laser wavelength of 808 nm to
1064 nm while widening the beam (appendix A, fig. 28).
For this setup, we used the same Leybold solid-state
laser-kit, extended with highly reflective mirrors from
Laser Components as well as the Coherent powermeter
to measure the laser power before entering the resonator.
The resonators reached up to 1000 internal reflections
(S-value) and increased force predictions by many orders
of magnitude according to eq. (3). No anomalous thrust
was detected in any configuration [2].
Fig. 15: The Taylor setup enhanced by a tapered metal
cavity and a metal end-plate surrounding the laser beam
trajectory.
However, according to recent criticism by McCulloch
these setups should have never produced thrust because
the beam requires an asymmetric metal cavity
surrounding the laser beam [4]. Therefore, we
manufactured an aluminium cone and encapsulated the
beam trajectory of the Taylor-light setup completely with
an additional aluminium endcap at the resonator exit
(fig. 15).
5.4 Taylor Resonator – Results & Discussion
The addition of an electrically conductive metal cone
around the laser beam trajectory in combination with a
metal end plate made the confirmation of a stable
resonator more difficult. An active resonator is indicated
by the conversion of the initial 808 nm wavelength into
1064 nm due to the half-mirrored Nd:YAG crystal. The
opposed mirror is permeable for the very low power
fraction of the 1064 nm wavelength that manages to
penetrate the highly reflective mirrors. This fractional
laser power escapes the resonator and hits an infrared
sensitive detection card to verify the active resonator.
After this procedure, the aluminium end plated is
mounted to the backside of the mirror to completely
encapsulate the beam trajectory.
Thrust measurements at two power levels of 289 mW
and 493 mW resulted in pure photon thrust (S=1) despite
predicted thrust values that were magnitudes above the
balance noise. No anomalous thrust was detected in
presence of a tapered aluminium cone around the laser
beam, as seen in an exemplary thrust measurement in fig
16 and the summarized thrust data in appendix B.
Fig. 16: Thrust measurement of the Taylor-Setup for a
measured laser power of 493 mW with an added tapered
metal-cone surrounding the laser beam.
5.5 Fiberoptic Loop – Experimental Setup
The third type of photon based resonators, that was
subject to tests, is a fiber-optic loop. By feeding a laser
into several windings of fiber-optic wire, the travelling
photons perceive a change in acceleration relative to the
surrounding matter while changing direction, according
to QI-Theory. In contrast to the metal cavity resonators,
the fiber-optic loop possesses an accurately defined value
for the force amplification factor S of up to 3300, that is
determined by the number of windings. This advantage
enables very accurate force predictions according to eq.
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(3). The emerging Rindler horizon of the accelerated
photons were substituted with an artificial horizon in the
shape of an aluminium plate positioned close to loop
windings. This artificial horizon should dampen the
emerging Unruh radiation asymmetrically, leading to a
unidirectional force (fig 17). The asymmetric loop
retested in this measurement series utilized 2.2 km of
multimode fiber wound around a 3D-printed
Polyetheretherketone (PEEK) mount with a radius of
70 mm on the big end and 40 mm on the small end. The
centre points of each radii are 150 mm apart from each
other.
Fig. 17: Proposed thrust generation principle of photons
inside an asymmetric fiberoptic loop in presence of an
Unruh-shield.
Additional claims McCulloch after our recently
reported negative thrust results [4], suggested that the
vacuum chamber itself was responsible for the non-
existent thrust. Due to its electrically conductive walls
surrounding the fiberoptic loop, Unruh radiation is
cancelled before interacting with the photons. We
therefore decided to retest the device and completely
neglect measurement influences by placing the thrust
balance on a marble table outside of the vacuum chamber
in our lab (fig. 18). We carefully picked a location with
the least amount of electrically conductive materials in
close proximity of the thrust balance. Especially in front
of and behind the fiber-optic coil there were no metallic
objects in at least 80 m distance. This way, Unruh waves
were not cancelled by anything besides the respective
Unruh-shield position close to the loop.
The fiber-optic cable was fed by a semiconducting
laser that was directly attached to it. It was supplied by
LUMILOOP and features a wavelength of 830 nm with
up to 1 W of power. It is supplied by a battery-pack and
a miniature power supply on the balance. Contrary to
previous setups with the Leybold laser-kit, the photons
on this setup are created and terminated on the balance
itself. This means, that there are no photon momentum
exchange with the thrust balance, unlike tests with the
silver cavities for example.
Fig. 18: The asymmetric loop mounted to the thrust
balance on a marble table outside of the vacuum chamber
with an Unruh-shield close to the bigger radius.
5.5 Fiberoptic Loop – Results & Discussion
With an expected decrease in balance resolution due
to atmospheric pressure and convection, we performed
three sets of measurements with varying Unruh-shield
positions and compared the results.
For force predictions we used the average power
between fiber input power and measured power at the end
of the 2.2 km fiber to account for losses inside the coil.
Two power levels were tested for each of the three Unruh
shield positions. At first, the Unruh shield was positioned
as close as possible to the big end of the coil. Afterwards
the shield was repositioned to the small side of the coil
and removed entirely in the third and last test. At average
power-levels between laser output- and fiber output-
levels of 31 mW and 203 mW with a force amplification
factor of 3300, measurements resulted in balance noise
only. Even without the protective vacuum environment,
we managed to gain a thrust resolution that is below the
predicted thrust values with worst-case assumptions by a
factor of 14.
Fig. 19: Thrust measurement of the fiberoptic loop with
an Unruh shield close to the small radius and outside of
the vacuum chamber with an average power of 203 mW.
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No anomalous thrust was detected, as seen in
exemplary measurements for the Unruh shield close to
the small loop radius in fig 19 and close to the big loop
radius in fig. 20. The vacuum chamber did not hide the
proposed QI effects.
Figure 20: Thrust measurement of the fiberoptic loop
with an Unruh shield close to the big radius and outside
of the vacuum chamber with an average power of
203 mW.
6. Conclusions
We engaged the recent criticism by the inventors of
our devices under test and performed an extended
investigation on their proposed concepts.
First, we presented new results on the EMDrive with
a refined cavity-geometry utilizing a spherical end-cap
rather than flat and removed the dielectric. Four
resonance frequencies could be identified in the observed
bandwith between 1800 MHz and 2100 MHz with
loaded Q-values of up to 1027. Otherwise similar
operating conditions, compared to our previous tests with
a NASA-like cavity, revealed no anomalous thrust after
eliminating the most influential false-positive thrust
effects. Also an additional investigation into the
inventor’s pre-load condition did not change anything.
A second cavity was manufactured involving YBCO
high-temperature superconductors to boost predicted
thrust values. Initial measurements with a dielectric
prevented the formation of superconducting resonance
frequencies. Only by removing the dielectric, stable
resonances occurred below the critical temperature of
92 K with loaded Q-values of up to 2600. By comparing
thrust measurements above and below the critical
temperature at selected frequencies, we did not detect any
thrust above the balance noise.
Nonetheless, we managed to enhance our thrust
balance to operate devices at cryogenic temperatures
using solid nitrogen. This allows us to investigate
concepts and effects at very low temperatures down to
65 K with sub-micronewton thrust resolution.
Additional thrust measurements of laser-type
EMDrives with infrared resonators involved several
setup enhancements. The devices underwent hardware
changes that supposedly suppressed interactions with
emerging Unruh-radiation in our recent null-results.
None of the enhancements in any laser resonator
setup revealed anomalous thrust. All measurements
stayed within the thrust limit of classical forces due to
radiation pressure (Q=1) for the given amount of power.
In summary, we did not encounter unsolvable false-
positive thrust signatures in any of our tested devices.
Neither the microwave- and superconducting cavities nor
the infrared laser resonators passed our requirements for
a breakthrough in space propulsion.
Acknowledgements
This work has received support from the German
National Space Agency DLR (Deutsches Zentrum für
Luft- und Raumfahrttechnik) by funding from the
Federal Ministry of Economic Affairs and Energy
(BMWi) by approval from German Parliament
(50RS1704), as well as from DARPA DSO under award
number HR001118C0125.
In addition, we thank M. Kößling for support during
the superconducting test campaigns.
References
[1] Tajmar, M., Neunzig, O. & Weikert, M. High-
accuracy thrust measurements of the EMDrive and
elimination of false-positive effects. CEAS Space J
(2021). https://doi.org/10.1007/s12567-021-00385-1
[2] Neunzig, O., Weikert, M. & Tajmar, M. Thrust
measurements and evaluation of asymmetric infrared
laser resonators for space propulsion. CEAS Space J
(2021). https://doi.org/10.1007/s12567-021-00366-4
[3] Shawyer, R. (2021): Notes on the recent Dresden TU
paper. http://emdrive.com/. Accessed 19 Sep 2021.
[4] M. McCulloch (2021) Response to Tajmar’s New
Cavity Results. .
http://physicsfromtheedge.blogspot.com/2021/04/res
ponse-to-tajmars-new-cavity-results.html. Accessed
20 Sep 2021.
[5] White, H., March, P., Lawrence, J., Vera, J.,
Sylvester, A., Brady, D. and Bailey, P.: Measurement
of impulsive thrust from a closed radio-frequency
cavity in vacuum. J. Propuls. Power 33(4), 830–841
(2017)
[6] Shawyer, R.: EmDrive Thrust/Load Characteristics.
Theory, Experimental Results and a Moon Mission.
IAC-19-C4.10.14. 70th International Astronautical
Congress, Washington, D.C., 2019
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Copyright ©2021 by the International Astronautical Federation (IAF). All rights reserved .
IAC-21-C4.,10-C3.5,1,x63502 Page 12 of 15
[7] Shawyer, R.: Second generation EmDrive propulsion
applied to SSTO launcher and interstellar probe. Acta
Astronaut. 116, 166–174 (2015)
[8] Taylor, T.S.: Propulsive forces using High-Q
asymmetric high energy laser resonators. J. Br.
Interplanet. Soc. 70(7), 238–243 (2017)
[9] McCulloch, M.E.: Inertia from an asymmetric
Casimir effect. EPL 101(5), 2013 (2013)
[10] Mcculloch, M.E.: Can the emdrive be explained by
quantised inertia? Prog. Phys. 11(1), 78–80 (2015)
[11] McCulloch, M.E.: Testing quantised inertia on
emdrives with dielectrics. Europhys. Lett. 118(3),
34003 (2017)
Appendix A
Fig. 21: Electrical Setup of the EMDrive with a spherical end-cap and on-board electronics.
Fig. 22: Electrical setup of the EMDrive with superconducting end-caps with the HF-components outside of the
vacuum chamber
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Fig. 23: Spherical EMDrive circulator-power and sense-antenna power measurement between the bandwidth of
1900 MHz-2060 MHz with four resonance frequencies of A) 1918 MHz, B) 1945 MHz, C) 2030 MHz and D)
2054 MHz.
Fig. 24: Simulation of eigenfrequency modes corresponding to frequency peaks in Fig. 22. (A: Hybrid mode, B:
TM210, C: TE 113, D: TE020
Fig. 25
: Thrust measurements of the spherical EMDrive under ± 10µN preload compared to commanded forces
of ± 10µN without an operating EMDrive for: A) 1918
MHz, B) 1945
MHz, C) 2030
MHz, D) 2054
MHz.
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Fig. 28: Illustration of the enhanced Taylor-setup configuration with a tapered metal cavity enclosing the asymmetric
laser beam trajectory.
Fig. 27: Comparison of the measured circulator power below and above the critical tempera
ture. No
additional resonance frequencies occurred with an active superconductor including the dielectric.
Fig. 26: Comparison of the
measured circulator power below and above the critical temperature.
Additional SC resonant frequencies occurred only without a dielectric.
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Appendix B (Thrust measurement summary)
Table 1. Thrust measurements of Ag-plated laser resonators.
Setup Measured Power (P) QI Force Prediction
(F=PS/c)
Classical Photon
Thrust (S=1)
Measured
Thrust
Beam Trap
mW
-
0.93
nN
(0.91 ± 0.31)
nN
mW
-
1.56
nN
(1.51 ± 0.15)
nN
Concave/Convex
(CC/CX)
467 mW 60 nN 1.56 nN (1.52 ± 0.41) nN
Concave/Concave
(CC/CC)
279 mW 36 nN 0.93 nN (1.04 ± 0.12) nN
mW
60
nN
1.56
nN
(1.65 ± 0.14)
nN
Circle
mW
36
nN
0.93
nN
(0.89 ± 0.14)
nN
mW
60
nN
1.56
nN
(1.50 ± 0.17)
nN
Table 2. Thrust measurements of the high-finesse Taylor resonator with a tapered metal cavity surrounding the photon
trajectory.
Setup Measured Power (P) QI Force Prediction
(F=PS/c)
Classical Photon
Thrust (S=1)
Measured
Thrust
Taylor-Light
(+Tapered Cavity)
mW
nN
0.96
nN
(1.01 ± 0.30)
nN
493 mW 822 nN 1.64 nN (1.62 ± 0.26) nN
Table 3. Thrust measurements of the asymmetric fiberoptic coil at atmospheric pressure outside of the vacuum chamber.
Setup Average Fiber Power
(PAverage=Pin-Pout)
QI Force Prediction
(F=PS/c)
Measured Thrust
Fiberoptic coil
(No Unruh-shield)
31
mW
0.34
µN
(0.02 ± 0.26)
µN
mW
2.23
µN
(0.05 ± 0.30)
µN
Fiberoptic coil
(Small radius shielded)
31 mW >0.34 µN (0.01 ± 0.19) µN
203 mW >2.23 µN (0.09 ± 0.18) µN
Fiberoptic coil
(Big radius shielded)
31 mW >0.34 µN (0.02 ± 0.15) µN
mW
>2.23
µN
(0.06 ± 0.16)
µN
Table 4. Thrust measurements of the EMDrive with a spherical endcap.
Resonance
Frequency
Qloaded,S11 Measured
Power in
Cavity (P)
Classical Photon
Thrust (Q=1)
Force Prediction
(F=PQ/c)
Measured Thrust
1918
MHz
113
6 W
20
nN
2261
nN
(13 ±
31)
nN
1945 MHz 486 4.2 W 14 nN 6808 nN (-7 ± 18) nN
2030 MHz 677 10 W 33 nN 22582 nN (-4 ± 38) nN
2054 MHz 1027 5.5 W 18 nN 18841 nN (-11 ± 25) nN
Table 5. Thrust measurements of the superconducting EMDrive.
Resonance
Frequency
Qloaded,S11 Superconducting Measured Power
in Cavity (P)
Force Prediction
(F=PQ/c)
Measured Thrust
1819 MHz
2599
Yes
19
W
µN
(0.14 ± 0.23)
µN
-
No
-
-
(0.05 ± 0.24)
µN
1959 MHz 2063 Yes 18 W 156 µN (-0.33 ± 0.54) µN
- No - - (0.07 ± 0.08) µN
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Response to Tajmar's New Cavity Results
  • M Mcculloch
M. McCulloch (2021) Response to Tajmar's New Cavity Results. .
EmDrive Thrust/Load Characteristics. Theory, Experimental Results and a Moon Mission
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Shawyer, R.: EmDrive Thrust/Load Characteristics. Theory, Experimental Results and a Moon Mission. IAC-19-C4.10.14. 70 th International Astronautical Congress, Washington, D.C., 2019