How the Thrust of Shawyer s Thruster can be Strongly Increased

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1 How the Thrust of Shawyer s Thruster an be Strongly Inreased Fran De Aquino Professor Emeritus of Physis, Maranhao State Uniersity, UEMA. Titular Researher (R) of National Institute for Spae Researh, INPE Copyright 014 by Fran De Aquino. All Rights Resered. Here, we reiew the deriation of the equation of thrust of Shawyer s thruster, by obtaining a new expression, whih inludes the indexes of refration of the two parallel plates in the tapered waeguide. This new expression shows that, by strongly inreasing the index of refration of the plate with the largest area, the alue of the thrust an be strongly inreased. Key words: Satellite Propulsion, Quantum Thrusters, Shawyer s Thruster, Radiation Pressure, Mirowae Energy. 1. Introdution Reently a NASA researh team has suessfully reprodued an experiment [1] originally arried out by the sientist Roger Shawyer [], whih point to a new form of eletromagneti propulsion, using mirowae. The Shawyer deie is a thruster that works with radiation pressure. It proides diretly onersion from mirowae energy to thrust. In the Shawyer thruster the mirowae radiation is fed from a magnetron, ia a tuned feed to a losed tapered waeguide, whose oerall eletrial length gies resonane at the operating frequeny of the magnetron. The inidene of the mirowae radiation upon the opposite plates R1 and R, in the tapered waeguide, produe fore Fg1 and F g, respetiely (See Fig.1). The area of R1 is muh greater than the area of R, therefore the power inident on R1 is muh greater than the power inident on R. Consequently, the fore F g1 exerted by the mirowae radiation upon the plate R1 is muh greater than the fore F g exerted upon the plate R. In the deriation of the expressions of Fg1 and F g, Shawyer assumes total refletion of the radiation inident upon both plates. Thus, the expression of the thrust T obtained by him is P0 1 1 g g T = Fg Fg = () 1 where g1 and g are the group eloities of the inident radiation on the plates R1 and R, respetiely; P 0 is the radiation power and is the speed of light in free-spae. Here, we reiew the deriation of Eq. (1), obtaining a new expression for T, whih inludes the indexes of refration n r1 and nr of the plates R1 and R, respetiely. This new expression shows that, by inreasing the index of refration of R1, the alue of T an be strongly inreased. R1 R F g1 F g Magnetron Fig. 1 Shemati diagram of Shawyer s thruster.. Theory Consider a beam of photons inident upon a flat plate, perpendiular to the beam. The beam exerts a pressure, dp, upon an area da = dxdy of a olume d V = dxdydz of the plate, whih is equal to the energy du absorbed by the plate per unit olume du dv.i.e., ( )

2 du du du dp = = = ( ) d V dxdydz dadz Substitution of dz = dt ( is the speed of radiation through the plate; = n r, where nr is the index of refration of the plate) into the equation aboe gies ( du dt) dpda = () 3 Sine dpda = df we an write: du dt dp df = = ( 4) By integrating, we get the expression of the fore F ating on the total surfae A of the plate, i.e., P P P P F = = = = n r () 5 where P is the power absorbed by the plate. Thus, the fores Fg1 and F g, ating on the plates R1 and R of the Shawyer deie are expressed by P F g1 = nr1 and Fg = nr ( 6) where and P are respetiely the powers absorbed by the plates R1 and R; nr1 and n r are respetiely the indexes of refration of the plates R1 and R. Therefore, the expression of the thrust T = F g 1 Fg, is gien by P T = n r1 n r ( 7) If n r1 = nr, then the equation aboe an be rewritten as follows n 1 P 1 T = r () 8 P 1 If A 1 >> A (partiular ase of Shawyer s thruster) the power inident on A1 is muh greater than the power P inident on A. Then, P << 1. In this ase, Eq. (8) redues to n 1P T r 1 () 9 From Eletrodynamis we know that when an eletromagneti wae with frequeny f and eloity inides on a flat plate with relatie permittiity ε r, relatie magneti permeability μ and eletrial ondutiity r σ, its eloity is redued to = nr where n r is the index of refration of the material, whih is gien by [ 3] ε μ 1 ( ) n = = r r r + σ ωε + 1 ( 10) If σ >> ωε, ω = πf, Eq. (10) redues to nr = μrσ 4πε 0 f ( 11) Thus, if the plate R1 is made of Copper ( μ r = 1, σ = S/m [ 4]), then for f =. 54GHz, Eq. (11) gies n r 1 ( 1) By substitution of this alue into Eq. (9), we get T P 1 ( 13) In the Shawyer experiment the total power produed by the magnetron is P0 = 850W. Part of this power is absorbed by the waeguide, and by the plate R (plate with lower area). Assuming that the remaining power is about 40%-50% of P 0, then the power radiation absorbed by the plate R1 is 400W. By substitution of this alue into Eq. (13), we obtain a theoretial thrust out put of T 18mN, whih is in lose agreement with the thrust measured in the Shawyer experiment. Now, if the plate R1 is made of a magneti material with ultrahigh magneti permeability, for example Metglas 714A Magneti Alloy, whih has μ r =1,000, 000 [5], 7 then Eq. (11) tells us that n r If n r1 >> nr and P 1 >> P then Eq. (7) gies n 1P T r N ( 13) This result shows an inreasing of about 1,000 times in the thrust of Shawyer s thruster. It is known that Pulse-modulated Radar Systems an radiate high power of mirowaes during short time interals (pulses), eah pulse being followed by a relatiely long resting period

3 during whih the transmitter is swithed off. Usually the pulses are of 1μs and the pulse repetition time of 1,50 μs. These systems an radiate about 10 6 watts (or more) at eah pulse. Howeer, the aerage power of the radar, due to the time interal of 1,50 μs, is only some hundreds of watts. Pulse-modulated Radar Systems operating in the range of GHz are urrently in use. This means that it is possible to proide the Shawyer s Thruster with a mirowae soure similar to those existing in these systems in order to produe radiation pulses with power of about 1 megawatt and frequeny of.54 GHz. Thus, by using this mirowae soure and Metglas 714A, the thrust, aording to Eq. (13), would be of the order of 10,000 N. If the mirowae soure radiates pulses with 10 megawatts power then the thrust an reah up to 100kN. In order to understand the Shawyer s Thruster it is neessary to aept the existene of the Quantum Vauum, predited by the Quantum Eletrodynamis (QED). The free spae is not empty, but filled with irtual partiles. This is alled the Quantum Vauum. When a radiation propagates through it the radiation exerts on the Quantum Vauum a fore (due to the momentum arried out by radiation), in the opposite diretion to the diretion of propagation of the radiation. Based on this fat, we show in Fig. (), how Shawyer s Thruster works, and why its thrust an be strongly inreased by strongly inreasing the index of refration of the plate with the largest area. Now, we will onsider an apparent disrepany between the expression of the momentum deried by Minkowski [6] and the expression deried by Abraham [7]. While Minkowski s momentum is diretly proportional to the refratie index of the medium, Abraham s momentum possesses inerse proportionality. From Eletrodynamis we know that the expression of the momentum, q, is gien by [ 8] E E E 1 q = = = n r ( 14) where E is the total energy of the partile. Note that the expression of the momentum gien by Eq. (14) is inersely proportional to the refratie index of the medium ( n r ). Howeer, starting from Eq. (5), we obtain, the following expression for the momentum: U U q = = n r 3 ( 15 ) whih is diretly proportional to the refratie index of the medium ( n r ). Howeer, U is different of E ; U is the absorbed energy, whih transformed into kineti energy. Thus, the orrelation between E and U is gien by E = E 0 +U, where E 0 = m0 is the rest inertial energy of the partile, and E = m 0 1 = E0 1. Then, we an write that U = E 1 1 ( 16 ) For << we hae 1 1. Thus, Eq. (16) an be rewritten in the following form U = E 17 whene we obtain U Note that the term ( ) ( ) = E ( 18 ) E is exatly the expression of the momentum q (See Eq. (14)). Thus, we an write that U q = and therefore, U q = ( total refletion ( total absorption ) ) ( 19 ) ( 0 ) This equation, as we hae already seen, leads to Eq. (15). Thus, the orrelation between E and U (Eq. 16), larifies the expression of the momentum, i.e., the momentum as a funtion of the absorbed energy, whih is transformed into kineti energy, U, is diretly proportional to the refratie index of the medium, n r, while the momentum as a funtion of the total energy of the partile, E, is inersely proportional to the refratie index of the medium, n r.

4 4 A A 1 F 0 P 0 Quantum Vauum n r =1 S (a) A 1 A R = F 0 + F n T P 0 n r = 1 n r >1 S (b) Fig. Quantum Thruster. Figure (a) shows that, when a radiation with power P 0, emitted from the System S, propagates through it, from A to A 1, with eloity, the radiation exerts on the Quantum Vauum a fore F 0 = P 0 / (due to the momentum arried out by radiation), in the opposite diretion to the diretion of propagation of the radiation. Figure (b) shows that, if inside the system S there is a region with index of refration great than 1, then, when the radiation passes through this region it eloity is redued to = /n r, where n r is the index of refration of the region. Consequently, the radiation exerts on the Quantum Vauum a fore F n = P 0 /, whih is greater than F 0. Thus, in this ase, the total fore exerted on the Quantum Vauum in the diretion from A 1 to A is R = F 0 + F n. On the other hand, aording to the ation reation priniple, the system S is propelled with a fore T (equal and opposite to R). Thus, if n r >> 1 then F n >> F 0. Consequently, T = R F n.

5 5 Referenes [1] Brady, D., et al., (014) Anomalous Thrust Prodution from an RF Test Deie Measured on a Low-Thrust Torsion Pendulum, NASA Johnson Spae Center, Houston, TX, United States, ID , JSC-CN [] Shawyer, R., (006 ) A Theory of Mirowae Propulsion for Spaeraft, Theory paper V 9.3, Satellite Propulsion Researh Ltd. [3] Queedo, C. P. (1977) Eletromagnetismo, MGraw- Hill, p. 70. [4] Hayt, W. H. (1974) Engineering Eletromagnetis, MGraw-Hill, Portuguese ersion (1978) Eletromagnetismo, p. 51. [5] [6] Minkowski H. (1910) Math Ann ;68:47. [7] Abraham M. (1910) Rend Pal ;30:33. [8] Landau, L. And Lifhitz, L. ( 1969)Theorie du Champ, Ed. MIR, Mosow, Portuguese ersion (1974), Ed. Hemus, S.Paulo, p.38.