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The author, Dr. Andrew Beckwith, authorizes Myron D. Stokes, Publisher, eMOTION! REPORTS.com, a legacy automotive/aerospace research and analysis site and Managing Director, Global HeavyLift Holdings, Inc., a Defense Logistics Agency listed Federal Contractor, as to the dissemination of the following Tokamak applied physics notes for Gravitational wave generation, as his acting manager of public release of the aforementioned document. The information within will be peer reviewed , but the basic technology is intended for humankind as far as fundamental physics advancement world wide.

The notes, within, were created by Dr. Beckwith, in the Keyuan Hotel in room 1205, in Chongqing, PRC, as part of a joint USA-PRC endeavor as to GW physics; the notes are correctly identified by Gary Stephenson , as a civilian employee of the US air force, as pertinent to " Higher drift current during fusion burning" as an enabler of high GW amplitudes, of the order of h ~ 10^-25 to 10^-26 which are candidates for testing of GW direct identification technology incurrent development in both PRC and in America. The notes were also written up as of November 4 to November 12, in an eight day period, in room 1205 of the Keyuan hotel as of Chongqing University under the auspices of Chongqing University department of physics, in work which was enabled by the hospitality of Chongqing University which took unusually comprehensive steps as to the proper circumstances for the creation of this work so cited by the Author.

The following individuals should be thanked as far as their discussions and input as to formation of the "Higher drift current during fusion burning" which is crucial to the development of this material.

a. Dr. Fangyu Li, whose interest in Tokamak physics never flagged, as to its utilization. He informed the author during a stay from November 2 to November 13 of his partnership with a Tokamak fusion laboratory as of Hefei, PRC, which would serve as a test bed of GW amplitudes. His physics questions were timelyand very important during the 12 days of stay in Chongqing University.

b. Dr. Fan, Chief scientific administrator of Chongqing University wrote in administrative authorization of Dr. Beckwith's visit to Chongqing University and also as part of a 40 year friendship with Dr. Li, accompanied Dr. Li to the Tokamak fusion laboratory as of Hefei, PRC, which the author saw in photographs as to the facility, and the chief engineering officer who runs the Hefei Tokamak facility

The above written statement should be part of a slide share release of this basic information as set up by Myron D. Stokes, of Global Heavylift Holdings corporation without further delay.

Andrew Beckwith, PhD, written in Setauket, New York, as of 6 PM, November 16 ( November 17, PRC time, Chongqing), 2013

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- 1. `Review of the Grischuk and Sachin Gravitational Wave Generator Via via Tokamak Physics A. Beckwith1 1) abeckwith@uh.edu, Chongqing University department of physics; Chongqing, PRC, 400044; Abstract Using the Grischuk and Sachin (1975) amplitude for the GW generation due to plasma in a toroid, we generalize this result for Tokamak physics. We obtain evidence for strain values of up to h2 nd −term ~ 10−23 − 10−24 in the center of a Tokamak center, with a minimnum value of h ~ 10−26 five meters above the center of the Tokamak center. These values are an order of magnitude sufficient to allow for possible detection of gravitational waves, in the coming decade, according to Chinese researchers who are trying to do such in Hefei, PRC. The critical breakthrough is in utilizing a burning plasma drift current, which relies upon a thermal contribution to an electric field. The gravitational wave amplitude would be 20 −3 τ sec detectable in part also due to nion × E > .5 ×10 ×m × , where the nion is the numerical ion density , usually about 1020 ×m −3 , i.e. about one out of a million of the present atmospheric pressure, whereas τ E is a confinement time value for the Tokamak plasma, here at least .5 seconds. This value, as given above is one given and by Wesson in his Tokamak classic reference(2011),. This is the threshold for plasma fusion burning; and the temperature so obtained is the main driver for how one could conceivably detect GW of amplitude as low as h ~ 10−25 five meters above the the center 2 nd −term TTemp ≥100 KeV 5− meters −above −Tokamak of the Tokamak center. Key words: Tokamak physics, confinement time (of Plasma),space-time GW amplitude, Drift current PACS: 52.25.-b, 52.27.-h, 52.25.Xz 1. Introduction In 1975, in [1], Russian physicists Grishchuk and Sachin (1975) obtained the following amplitude of a Gravitational wave (GW) in a plasma which is given as A(amplitude− GW) = h ~ G 2 2 ×E ×λGW c4 (1) 1
- 2. Fig. 1 ( see Figure 1.63 (a) of Wesson, page 14) Text: We outline the direction of Gravitational wave “flux”. If the arrow in the middle of the Tokamak ring perpendicular to the direction of the current represents the z axis, we represent where to put the GW detection device as 5 meters above the Tokamak ring along the z axis. Note that a simple model of how to provide a current in the Toroid is provided by a transformer core. This diagram is an example of how to induce the current I, used in the simple Ohms law derivation referred to in the first part of the text Fig. 2 ( see Figure 1.63 (b) of Wesson, page 14) Text: Flux change provided by a transformer core, in the simple current model first referred to in this paper. Here, E is the electric field whereas λGw is the Gravitational gravitational wavelength for GW generated by the 6 Tokamak, in our model. Note, if ωGW ~ 10 Hz ⇒ λGw ~ 300 meters , so we will be assuming a baseline of the order of 2
- 3. ωGW ~ 109 Hz ⇒ λGw ~ .3 meters , of about a foot, as a start for GW detection above the Tokamak. What we will be doing is to examine the would- be electric field, and this in ways different from the initial Ohms law .A generalized Ohm’s law ties in well with Figures 1 and 2 above. J = σ ×E (2) In order to obtain a suitable electric field, which is to be detected via 3DSR technology [2](Li et al, 2009), we will use a generalized Ohm’s law as given by Wesson [3] (2011, as seen in page 146), where E and B are for electric and magnetic fields, and v is for velocity. We should understand that this undercuts the use of Figure 2 above. E = σ −1 J − v × B (3) What we will be looking for is an application for radial free electric fields being applied, namelye.g., [3] Wesson, (2011, page 120) n j e j × Er + v⊥ j B ) = − ( dPj (4) dr n j = ion density, jth species, e j = ion charge, jth species, Er = radial electric field, v⊥ j = perpendicular veolocity, of jth species, B = magnetic field, and Pj = pressure, jth species. The results of Eq. (3) and Eq. (4) Here, are 2 2 G 2 2 G Const G Jb 2 2 st nd ×E × GW ~ 4 × λ 4 ×λGW + c 4 × n × + v R ×λGW = (1 ) + (2 ) c c R e (5) Here, the 1st term is due to ∇ × E = 0 , and the 2nd term is due to En = dPj 1 × − ( v × B ) n with the 1st term dxn n j ×e j h ~ 10−38 − 10−30 in terms of GW amplitude strain 5 meters above the Tokamak , whereas the 2 nd term has an h ~ 10 −26 in terms of GW amplitude above the Tokamak. The article has contributions from generating amplitude from the 1st and 2nd terms separately. The second part will be tabulated separately from the first contribution assuming a minimum temperature of T = Temp ~ 10 KeV as from Wesson [3](2011) 2. GW h strain values when the first term of Eq.(5) is used for different Tokamaks We now look at what we can expect with the simple Ohm’s law calculation for strain values. This is work which the Author with Gary Stevenson and Amara Angelica did in late 2012. As it is, the effort lead to non usable GW amplitude values of up to h ~ 10 −38 − 10 −30 for GW wave amplitudes 5 meters above a Tokamak, and h ~ 10 −36 − 10−28 in the center of a Tokamak. I.e. this would be using Ohm’s law and these are sample values of the Tokamak generated GW amplitude, using the first term of Eq. (5) and obtaining the following value 2 G G J 2 2 hFirst −term ~ 4 ×E 2 ×λGW ~ 4 × ×λGW c c σ (5a) 3
- 4. 9 We summarize the results of such in our first table as given for when ωGW ~ 10 Hz ⇒ λGw ~ .3 meters and with conductivity σ (tokamak − plasma ) ~ 10 ×m 2 sec and with the following denountment. What we observe are a range of Tokamak values which are, even in the case of ITER (not yet built) beyond the reach of any technological detection devices which are conceivable in the coming decade. This table and its results, assuming fixed conductivity values σ (tokamak − plasma) ~ 10 ×m 2 sec as well as λGw ~ .3 meters is why the author, after due consideration completed his derivation of results as to the 2 nd term of Eq. (5) which lead to even for when considering the results for the Chinese Tokamak in Hefei to have 2 hSecond −term ~ G 2 2 G J 2 ×E ×λGW ~ 4 × b + v R ×λGW values 10,000 larger than the results in ITER due to Eq.(5a). c4 c n ×e Table 1: Values of strain at center of Tokamak, and 5 meters above Tokamak: λGw ~ .3 meters , σ (tokamak − plasma ) ~ 10 ×m 2 sec , using Eq.5a6 above for Amplitude of GW. Experiment Site/ location Plasma Strain, h, in Strain, h, 5 current, in center of the meters above (mili-Amps) Tokamak the center of MA the Tokamak JET Culan (UK) 5-7 h ~ 10 −31 h ~ 10−33 ASDEX Garching (GER) 2 h ~ 10−32 h ~ 10−34 DIII-D San (USA) h ~ 10−32 h ~ 10−34 HL-2A Chengdu (PRC) .45 h ~ 10−34 h ~ 10−36 HT-7U Hefei (PRC) .25 h ~ 10−36 h ~ 10−38 15 h ~ 10−28 − 10−29 h ~ 10−30 − 10 −31 Diego 1.5-3 ITER(planned) Saint Paul Les-Durance (FR) What makes it mandatory going to go the 2nd term of Eq. (5) is that even in the case of ITER, 5 meters above the Tokamak ring, that the GW amplitude is 1/10,000 the size of any reasonable GW detection device, and this including the new 3DSR technology [2](Li et al, 2009). Hence, we need to come up with a better estimate, which is what the 2nd term of Eq.(5) is about which is derived in the next section 3 . Enhancing GW strain Amplitude via utilizing a burning Plasma drift current: Eq.(4) 4
- 5. The way forward is to go to Wesson, [3](2011, page 120) and to look at the normal to the surface induced electric field contribution En = dPj 1 × − ( v × B) n dxn n j × j e (6) vR as the radial velocity of ions in the Tokamak from the center of a Tokamak center, to its radial distance, R, from the center, and Bθ being as the direction of a magnetic field in the ‘face’ of a Toroid containing the Plasma, in the angular θ direction from a minimal toroid radius of R = a , with θ = 0 , to R = a + r with θ = π , one has vR for radial drift velocity of ions in the Tokamak, and Bθ having a net If one has for approximate value of: ( v × B ) n ~ vR ×Bθ (7) Also, as a first order approximation: From reference Wesson [3] (2011, page 167) the spatial change in pressure denoted dPj dxn = − Bθ ×jb (8) Here (ibid), from Wesson[3], on page 167 the drift current, using charges, i.e. jb ξ ~− ξ = a R , and drift current jb for Plasma 1/2 dndrift × Temp × T Bθ dr (9) Figure 3 below introduces the role of the drift current, in terms of Tokamaks 5
- 6. Fig. 3: ( see page 167 of Wesson, Figure 4.91) Text: Typical bootstrap currents with a shift due to r/a where r is the radial direction of the Tokamak, and a is the inner radius of the Toroid Then one has Bθ × jb n j ×e j ) ( 2 B2 ξ ~ θ2 × 2 e j Bθ 1/ 4 2 1 dndrift ξ × × ~ 2 ej ndrift dr 2 1/4 1 dndrift × × ndrift dr 2 (10) Now, the behavior of the numerical density of ions, can be given as follows, namely growing in the radial direction, then ndrift = ndrift initial % ×exp [ α ×r ] (11) , beloive as (b) of Wesson, page NOT A : This exponential behavior then will lead to the 2 nd term in Eq.(5) having in the center of the Tokamak, for an ignition temperature of TTemp ≥ 10 KeV a value of 6
- 7. %2 2 2 G G ξ α TTemp 2 2 2 h2 nd −term ~ 4 ×Bθ ×( jb n j ×e j ) ×λGW ~ 4 × ×λGW ~ 10−25 2 c c ej (12) 1/4 As shown in Fig. 4 (from Note that by page 11 of reference [3], Wesson [3]2011), that there is a critical ignition temperature at its lowest point of the curve in the figure on page 11 having optimum value of the Tokamak ignition temperature for value of TTemp safe −upper −bound relationship of Eq.(13), where to TTemp ≥ 30 KeV as an nion ~ 1020 m −3 , with a still permissible temperature ≈ 100 KeV with a value of nion ~ 10 20 m −3 , due to from page 11, [3] the τ E is a Tokamak confinement of plasma time of about 1-3 seconds, at least due nion × E > .5 ×1020 ×m −3 × τ sec (13) Fig. 4 : The value of n τ E required to obtain ignition, as a function of temperature Also, as shown in Fig. 4if one is using the curve on page 11 of [3] , that TTemp safe −upper −bound one could have at the center of a Tokamak center, i.e. even the Hefei based PRC Tokamak %2 2 G ξ α TTemp 2 ~ 4× ×λGW ~ 10−23 c ej2 1/4 h2 nd −term T Temp ≥100 KeV (14) 7 ≈ 100 KeV , then
- 8. This would lead to, for a GW reading 5 meters above the Tokamak, then lead to for then the Hefei PRC Tokamak %2 2 G ξ α TTemp 2 ~ 4× ×λGW ~ 10−25 2 c ej 1/4 h 2 nd −term TTemp ≥100 KeV 5− meters − above −Tokamak (15) Note that the support for up to 100 KeV for temperature can yield more stability in terms of thermal Plasma confinement as give in Fig. 5 below, namely from [3] we have Fig 5 ( Fig. 1.5.2. of Wesson, page 13) Text: Illustrating how increase in temperature can lead to the H mode region, in Tokamak physics where the designated equilibrium point, in Fig. 5 is a known way to balance conduction loss with alpha particle power, which is a known way to increase τ E i.e. Tokamak confinement of plasma time 4. Details of the model in terms of terms of adding impurities to the Plasma to get a longer confinement time (possibly to improve the chances of GW detection). We add this detail in, due to a question raised by Dr. Li who wished for longer confinement times for the Plasma in order to allegedly improve the chances of GW detection for a detector 5 meters above the Tokamak in Hefei. What Wesson (2011) stated is that the confinement time may be made proportional to the numerical density of argon/ neon seeded to the plasma. (See page 180). of [3]. This depends upon the nature of the Tokamak, but it is a known technique, and is suitable for analysis, depending upon the specifics of the Tokamak. I.e. this is a detail Dr. Li can raise with his co workers in Hefei, PRC in 2014. 5. Conclusion. GW generation due to the Thermal output of Fusion in a Tokamak, and not due to E and B field currents. Further elaboration of this matter lies in the viability of the expression derived , namely Eq. (15) repeated 8
- 9. %2 2 G ξ α TTemp 2 h ~ × ×λGW 2 nd −term TTemp ≥100 KeV 5− meters − above −Tokamak c 4 ej2 (15) 1/4 The importance of the formulation is in the explicit importance of temperature. i.e. a temperature range of at least 10 KeV ≤ TTemp ≤ 100 KeV . In making this range for Eq.(15), care must also be taken to obtain a sufficiently long confinement time for the fusion plasma in the Tokamak of at least 1 second or longer, and this is a matter of applied engineering dependent upon the instrumentation of the Tokamak in Hefei, PRC. The author hopes that in 2014, there will be the beginning of confirmation of this process so that some studies may commence. If so, then the next question will be finding if the instrumentation of [2]Li and colleagues (2009) can be utilized and developed. This is expected to be extremely difficult, but the Tokamak fusion process may allow for falsifiable testing and eventual verification. Bibliography [1] L.P. Grishchuk, M.V. Sazchin “ Excitation and Detection of Standing Gravitational Waves, Zh. Eksp. Theor. Fiz 68, pp 1569-1582 (1975) Moscow [2] F.Y. Li et al., Phys. Rev. D 80, 064013 (2009), arxiv re-qc/0909.4118 (2009) and R.C. Woods et al, Journal of Modern physics 2, number 6, starting at page 498, (2011) [3] J. Wesson; “Tokamaks”, 4th edition, 2011 Oxford Science Publications, International Series of Monographs on Physics, Volume 149 9
- 10. %2 2 G ξ α TTemp 2 h ~ × ×λGW 2 nd −term TTemp ≥100 KeV 5− meters − above −Tokamak c 4 ej2 (15) 1/4 The importance of the formulation is in the explicit importance of temperature. i.e. a temperature range of at least 10 KeV ≤ TTemp ≤ 100 KeV . In making this range for Eq.(15), care must also be taken to obtain a sufficiently long confinement time for the fusion plasma in the Tokamak of at least 1 second or longer, and this is a matter of applied engineering dependent upon the instrumentation of the Tokamak in Hefei, PRC. The author hopes that in 2014, there will be the beginning of confirmation of this process so that some studies may commence. If so, then the next question will be finding if the instrumentation of [2]Li and colleagues (2009) can be utilized and developed. This is expected to be extremely difficult, but the Tokamak fusion process may allow for falsifiable testing and eventual verification. Bibliography [1] L.P. Grishchuk, M.V. Sazchin “ Excitation and Detection of Standing Gravitational Waves, Zh. Eksp. Theor. Fiz 68, pp 1569-1582 (1975) Moscow [2] F.Y. Li et al., Phys. Rev. D 80, 064013 (2009), arxiv re-qc/0909.4118 (2009) and R.C. Woods et al, Journal of Modern physics 2, number 6, starting at page 498, (2011) [3] J. Wesson; “Tokamaks”, 4th edition, 2011 Oxford Science Publications, International Series of Monographs on Physics, Volume 149 9

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