Frequency spectrum analysis on the force contribution in a micronewton electromagnetic thruster Dimitri Charrier (Author Not Attending) APS March Meeting 2016 Monday – Friday, March 14 – 18, 2016; Baltimore, Maryland Session B46: Instrumentation I: Detectors, Sensors, Signal Processing & Analysis 11:15 AM – 2:03 PM, Monday, March 14, 2016 Room: 311 Sponsoring Unit: GIMS Chair: James Matey, NIST
Principle Thought experiment initially reported by David P. Goodwin Electromagnetic energy emitted by an ideal coil: Receiver disc E E E EMCoil EMSide 1 EMSide 2 Emitting coil EM waves on Side 1 go to vacuum mainly. EM waves on Side 2 go to disc and might be lost in vacuum : Side 1 Side 2 E E E EMSide 2 EMDisc EMSide 2 lost Energy balance can be written on disc: E W E E EMDisc Disc Heat EMWave EM waves create Lorentz force on metallic disc EM waves create eddy currents on metallic disc Emitted field Eddy currents create Joule heating (black body radiation) Thermal radiation Eddy currents might reemit EM waves Reemitted field Force A RESULTANT FORCE IS EXERTED IN THE COIL-DISC DEVICE D.P. Goodwin, A possible propellantless propulsion system, AIP Conf. Proc. 552 (2001) 976 – 978. doi:10.1063/1.1358037.
Goals of this work Demonstrate experimentally that electromagnetic waves emitted by a coil submitted to a square voltage signal can produce a force on a coaxial metallic disc rigidly attached to the coil. For this observation, a bench for measuring micrometer displacements was used with a coil-disc device hung on a translation pendulum. Develop analytical models predicting the resultant force using different equivalent impedance circuits: R, RL and RLC. For that it is important to consider the so-called square voltage signal in time domain is decomposed in the sum of signal in frequency domain.
Experimental bench for measuring micrometers Non-contact sensor Calibrated curve C. Coupeau, J.C. Girard, J. Grilhé, Plasticity study of deformed materials by in situ atomic force microscopy, J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 16 (1998) 1964. doi:10.1116/1.590234.
Experimental bench for measuring micrometers Optical-voltage converter Voltage output to LabView 2 optical fibers PC of acquisition connected to a PC Wood box laid on a stable table O 1 d 1 Displacement mirror 1 disc Coil-Disc device z μr hang in a wood box F steel plates z 0 coil mirror 2 http://dscharrier.free.fr Displacement O 2 d 2
Results Measurement of displacements with 100 s On/Off Averaged displacements at 15 MHz generator voltage sequences (20 V – 15 MHz) On 1 0.5 Off Displacement ( m) First model / mirror 1 R circuit 0.4 0 d=(d 1 +d 2 )/2 0.3 d ( m) -1 1 On 0.2 Displacement ( m) Off / mirror 2 0 0.1 0.0 -1 0 100 200 300 400 500 600 700 0 5 10 15 20 Time (s) U (V) A damping of pendulum is visible after an On or Off sequence. Drift lower than 0,2 m over 700 s was observed on the whole setup. D.S.H. Charrier, Micronewton electromagnetic thruster, Appl. Phys. Lett. 101 (2012) 034104. doi:10.1063/1.4737940. D.S.H. Charrier, Erratum: “ Micronewton electromagnetic thruster ”, Appl. Phys. Lett. 105 (2014) 149902. doi:10.1063/1.4897969.
Force calculations Different configurations of impedance circuits were used to calculate the current 𝑠 2 2𝜌𝑠𝐶 𝜍1 1 𝐶 𝑨1 𝑒 in the force equation 𝐺 𝑒𝑗𝑡𝑑 = 𝑇 2 𝑀 2 𝑒𝑠 𝑢 0 𝑗 𝑆𝑑𝑝𝑗𝑚 𝑢 = 𝑉 𝑢 First model 𝑆 𝑑𝑝𝑗𝑚 R circuit R coil 𝑉 1 − 𝑓𝑦𝑞 − 𝑢 L coil 𝑗 𝑆𝑀𝑑𝑝𝑗𝑚 𝑢 = 𝑆 𝑑𝑝𝑗𝑚 𝜐 RL circuit R coil Improved models L coil 2 2 2 2 𝑎 𝑆𝑀𝐷𝑑𝑝𝑗𝑚 = 𝑆 𝑑𝑝𝑗𝑚 + 𝑀 𝑑𝑝𝑗𝑚 𝜕² 𝑆 𝑑𝑝𝑗𝑚 − 𝑘𝜕 𝐷 𝑡𝑢𝑠𝑏𝑧 𝑆 𝑑𝑝𝑗𝑚 + 𝐷 𝑡𝑢𝑠𝑏𝑧 𝑀 𝑑𝑝𝑗𝑚 𝜕² − 𝑀 𝑑𝑝𝑗𝑚 Stray Stray coil C coil 𝜕 2 − 𝑀 𝑑𝑝𝑗𝑚 ² 2 2 2 capacitance 𝑆 𝑑𝑝𝑗𝑚 + 𝜕² 𝐷 𝑡𝑢𝑠𝑏𝑧 𝑆 𝑑𝑝𝑗𝑚 + 𝐷 𝑡𝑢𝑠𝑏𝑧 𝑀 𝑑𝑝𝑗𝑚 R coil
Onset frequency Calculated displacements with different impedance models -1 0 1 2 3 4 5 6 7 8 10 10 10 10 10 10 10 10 10 10 8 8 10 10 7 7 10 10 6 6 10 10 5 5 10 10 -6 m) 4 4 10 10 Displacement (10 3 3 10 10 2 2 10 10 Onset frequency at circa 170 kHz 1 1 10 10 in case of RL equivalent circuit 0 0 10 10 -1 -1 10 10 Experimental data (wo core) (10-6 m) Mono-frequency / RL (10-6 m) -2 -2 10 10 Mono-frequency / RLC / C=1nF (10-6 m) Mono-frequency / RLC / C=1pF (10-6 m) -3 -3 10 10 Mono-frequency / RLC / C=1fF (10-6 m) -4 -4 10 10 Angstrom -1 0 1 2 3 4 5 6 7 8 10 10 10 10 10 10 10 10 10 10 Frequency of the square wave generator containing a spectrum of mono-frequency (Hz)
Conclusions Energy emitted by the coil is partially converted into a force in the coil-disc device: proof- of-concept is shown. First analytical model was proposed with a simple R circuit but showed discrepancies between calculations and experimental data until one order of magnitude. Improved RL impedance equivalent circuit has been built and has shown a onset frequency at 170 kHz. Therefore further investigations need to take into account the different EM frequencies involved in the device. If existing, stray capacitance C from the coil should be much below 1 nF. A complete model should take into account the Joule heating (black body emission) coming from eddy currents in the disc. Possibly, finite element analysis is required for a better description.
Acknowledgements ‘ Flying Circus of Physics ’ book by Jearl Walker for having inspiring this work. Think out of the box! French CPER and Région Poitou-Charentes for post-doc funding. APS committee for having accepted the abstract for a talk.
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