Review of Grischuk and Sachin Gravitational Wave Generator via Tokamak Physics

Transcription

1 Review of Grishuk ad Sahi Gravitatioal Wave Geerator via Tokamak Physis ANDRW WALCOTT BCKWITH Physis departmet Chogqig Uiversity College of Physis, Chogqig Uiversity Huxi Campus No. 55 Daxuehe Nalu, Shapigba Distrit, Chogqig whih is i Chiese: 重庆市沙坪坝区大学城南路 55 号重庆大学虎溪校区 People s Republi of Chia Rwill9955b@gmail.om Abstrat: - Usig Grishuk ad Sahi (1975) amplitude for the geeratio due to plasma i a toroid, we 3 4 geeralize this result for Tokamak physis. We obtai evidee for strai values up to h d term i 6 a Tokamak eter, with a miimum value of five meters above the Tokamak eter. These values are a order of magitude suffiiet to allow for possible detetio of gravitatioal waves. The ritial breakthrough is i utilizig a burig plasma drift urret, whih relies upo a thermal otributio to a eletri field. The gravitatioal wave amplitude would be detetable i part also due to io.510 m se, where the is the umerial io desity, usually about io 10 m, i.e. about oe out of a millio of the preset atmospheri pressure, whereas is a ofiemet time value for Tokamak plasma, here at least.5 seods. This value, as give above ad by Wesso (011), is the threshold for plasma fusio burig; the temperature obtaied is the mai driver for how oe ould oeivably detet of 5 amplitude as low as h d term 10 five meters above the Tokamak eter TTemp 100KeV 5metersaboveTokamak Key-Words: - Tokamak physis, ofiemet time (of Plasma), amplitude, Drift urret 1 Itrodutio Russia physiists Grishhuk ad Sahi [1] obtaied the amplitude of a Gravitatioal wave () i a plasma as G (1) A(amplitude ) h 4 We a diagram the situatio out as follows Fig. 1 We outlie the diretio of Gravitatioal wave flux. If the arrow i the middle of the Tokamak rig perpediular to the diretio of the urret represets the z axis, we represet where to put the detetio devie as 5 meters above the Tokamak rig alog the z axis. This diagram was iitially from Wesso [] Note that a simple model of how to provide a urret i the Toroid is provided by a trasformer ore. This diagram is a example of how to idue the urret I, used i the simple Ohms law derivatio referred to i the first part of the text Io ore I I Primary widig ISBN:

2 Fig. Flux hage provided by a trasformer ore, i the simple urret model first referred to i this paper. This figure is from Wesso [] Here, is the eletri field whereas is the gravitatioal wavelegth for geerated by the Tokamak i our model. Note, if 6 10 Hz 300 meters, so we will be assumig a baselie of the order of 9 10 Hz.3 meters, as a start for detetio above the Tokamak. We will examie the would-be eletri field, i ways differet from the iitial Ohms law.a geeralized Ohm s law ties i well with Figures 1 ad above J () I order to obtai a suitable eletri field, to be deteted via 3DSR tehology [3, 4] (Li et al, 009), we will use a geeralized Ohm s law as give by Wesso []( page 146), where ad B are eletri ad mageti fields, ad v is veloity. We should uderstad that this uderuts the use of Figure above. 1 J v B (3) We will be lookig for a appliatio for radial free eletri fields beig applied e.g., Wesso[] ( page 10) dp e r v B (4) dr Here, = io desity, th speies, e = io harge, th speies, r = radial eletri field, v = perpediular veloity, of th speies, B = mageti field, ad P = pressure, th speies. The results of q. (3) ad q. (4) are Cost b J 4 4 v 4 R G G G R e = (1 st ) + ( d ) (5) Here, the 1 st term is due to 0, ad the d dp term is due to 1 v B with the 1 st dx e term geeratig 10 i terms of amplitude strai 5 meters above the Tokamak, whereas the d 6 term has a i terms of amplitude above the Tokamak. The artile has otributios from amplitude from the 1 st ad d terms separately. The seod part will be tabulated separately from the first otributio assumig a miimum temperature of T Temp 10KeV as from Wesso []. h strai values whe the first term of q.(5) is used for differet Tokamaks We ow look at what we a expet with the simple Ohm s law alulatio for strai values. As it is, the effort lead to o usable amplitude values of up to 10 for wave amplitudes 5 meters above a Tokamak, ad i the eter of a Tokamak. I.e. this would be usig Ohm s law ad these are sample values of the Tokamak geerated amplitude, usig the first term of q. (5) ad obtaiig the followig value h G G J First term 4 4 (6) We summarize the results of suh i our first table as 9 give for whe 10 Hz.3 meters ad with odutivity ( tokamak plasma ) 10m se ad with the followig provisios as to iitial values. What we observe are a rage of Tokamak values whih are, eve i the ase of ITR (ot yet built) beyod the reah of ay tehologial detetio devies whih are oeivable i the omig deade. This table ad its results, assumig fixed odutivity values ( tokamak plasma ) 10m se as well as.3 meters is why the author, after due osideratio ompleted his derivatio of results as to the d term of q. (5) whih lead to eve for whe osiderig the results for the Chiese Tokamak i Hefei to have[5] G G Jb Seod term 4 4 R h v e (7) ISBN:

3 or values 10,000 larger tha the results i ITR due to q.(6). We summarize the results of suh i our first table as give for whe 9 10 Hz.3 meters ad with See appedix A below whih has useful data Table 1: Values of strai at eter of Tokamak, ad 5 meters above Tokamak: Note that we are settig.3 meters, ( tokamak plasma ) 10 m se, usig q.6 above for Amplitude of. What makes it madatory to go the d term of q. (5) is that eve i the ase of ITR, 5 meters above the Tokamak rig, the amplitude is 1/10,000 the size of ay reasoable detetio devie, ad this iludig the ew 3DSR tehology (Li et al, 009) [3,4]. Hee, we eed to ome up with a better estimate, whih is what the d term of q.(5) is about whih is derived i the ext setio 3.haig strai Amplitude via utilizig a burig Plasma drift urret: q.(4) The way forward is to go to Wesso, [] (011, page 10) ad to look at the ormal to surfae idued eletri field otributio dp 1 v B dx e (8) If oe has for vr as the radial veloity of ios i the Tokamak from Tokamak eter to its radial distae, R, from eter, ad B as the diretio of a mageti field i the fae of a Toroid otaiig the Plasma, i the agular diretio from a miimal toroid radius of R a, with 0, to R a r with, oe has v for radial drift veloity of ios i the R Tokamak, ad B havig a et approximate value of: vb v R B (9) Also, as a first order approximatio: From Wesso [] ( page 167) the spatial hage i pressure deoted dp dx B (10) b Here (ibid), the drift urret, usig ar, ad drift urret b for Plasma harges, i.e. b 1/ ddrift TTemp (11) B dr Figure 3 below itrodues the role of the drift urret, i terms of Tokamaks b P r/a Fig. 3 Typial bootstrap urrets with a shift due to r/a where r is the radial diretio of the Tokamak, ad a is the ier radius of the Toroid This figure is reprodued from Wesso [] The oe has b B e 1 d drift drift B e B dr 1 d drift e drift dr (1) Now, the behavior of the umerial desity of ios, a be give as follows, amely growig i the radial diretio, the ISBN:

4 exp r (13) drift drift iitial This expoetial behavior the will lead to the d term i q.(5) havig i the eter of the Tokamak, for a igitio temperature of T 10KeV a value of h d term G B 4 e b G TTemp 10 e 4 5 Temp (14) As show i Fig. 4 (opied from Wesso 011), [] there is a ritial igitio temperature at its lowest poit of the urve i the havig T 30KeV as Temp a optimum value of the Tokamak igitio 0 3 temperature for io 10 m, with a still permissible temperature value of T 100KeV with a value of Temp safe upper boud 0 3 io 10 m, due to from page 11, [] the relatioship of q.(15), where is a Tokamak ofiemet of plasma time of about 1-3 seods, at least due to m 3 se io (15) Also, as show i Fig. 4, T 100KeV, the oe ould Temp safe upper boud have at the Tokamak eter, i.e. eve the Hefei based PRC Tokamak h G TTemp d term TTemp 100KeV 4 e 10 (16) 3 This would lead to, for a readig 5 meters above the Tokamak, the lead to for the the Hefei PRC Tokamak[5] h d term TTemp 100KeV 4 5metersaboveTokamak G TTemp 10 e 5 (17) Note that the support for up to 100 KeV for temperature a yield more stability i terms of thermal Plasma ofiemet as give i Fig. 5 below, amely from [] we have Power L-mode Igitio -partile power H-mode Codutio loss quilibrium Temperature (m -3 s) T (kev) Fig. 4 The value of required to obtai igitio, as a futio of temperature. Figure reprodued from Wesso [] Fig 5 Illustratig how irease i temperature a lead to the H mode regio, i Tokamak physis where the desigated equilibrium poit, i Fig. 5 is a kow way to balae odutio loss with alpha partile power, whih is a kow way to irease i.e. Tokamak ofiemet of plasma time[] 4. Details of the model i terms of terms of addig impurities to the Plasma to get a loger ofiemet time (possibly to improve the haes of detetio). ISBN:

5 We add this detail i, due to a questio raised by Dr. Li who wished for loger ofiemet times for the Plasma i order to allegedly improve the haes of detetio for a detetor 5 meters above the Tokamak i Hefei. Wesso [] (011) stated that the ofiemet time may be made proportioal to the umerial desity of argo/ eo seeded to the plasma [](page 180). This depeds upo the ature of the Tokamak, but it is a kow tehique, ad is suitable for aalysis, depedig upo the speifis of the Tokamak. I.e. this is a detail Dr. Li a raise with his o workers i Hefei, PRC i 014 [5]. 5. Colusio. geeratio due to the Thermal output of Fusio i a Tokamak, ad ot due to ad B field urrets. Further elaboratio of this matter lies i the viability of the expressio derived, amely q. (18) repeated below h d term TTemp 100KeV 4 5metersaboveTokamak G TTemp 10 e 5 (18) The importae of the formulatio is i the expliit importae of temperature. i.e. a temperature rage of at least 10KeV T 100KeV. I makig this rage Temp for q.(15), are must also be take to obtai a suffiietly log ofiemet time for the fusio plasma i the Tokamak of at least 1 seod or loger, ad this is a matter of applied egieerig depedet upo the istrumetatio of the Tokamak i Hefei, PRC. The author hopes that i 014, there will be the begiig of ofirmatio of this proess so that some studies may ommee. If so, the the ext questio will be fidig if the istrumetatio of Li ad olleagues (009) a be utilized ad developed. This is expeted to be extremely diffiult, but the Tokamak fusio proess may allow for falsifiable testig ad evetual verifiatio. Akowledgemets The author thaks. Dr. Yag Xi whom imbued the author with the bakgroud i the U of Housto to obtai a dotorate i physis Also, my reetly deeased father is thaked whom disussed deades ago with me as to the worth of five dimesioal geometry, i osmology. Also, the Chogqig Uiversity physis departmet is thaked for the affiliatio whih has lead to this artile beig formed i the first plae for review, ad that also Dr. Fagyu Li, who eouraged me to explore suh issues. This work is supported i part by Natioal Nature Siee Foudatio of Chia grat No Referees: 1. L.P. Grishhuk, M.V. Sazhi xitatio ad Detetio of Stadig Gravitatioal Waves, Zh. ksp. Theor. Fiz 68, pp (1975) Mosow. J. Wesso; Tokamaks, 4 th editio, 011 Oxford Siee Publiatios, Iteratioal Series of Moographs o Physis, Volume F.Y. Li et al., Phys. Rev. D 80, (009), arxiv re-q/ (009) 4. [R.C. Woods et al, Joural of Moder physis, umber 6, startig at page 498, (011) 5. J. Li,et al, A Log Pulse high Cofiemet Plasma regime i the experimetal Advaed Super odutig Tokamak, Nature Physis (013), doi / phys 795, Published November 17, 013 ISBN:

6 Appedix A Table 1: Values of strai at eter of Tokamak, ad 5 meters above Tokamak:.3 meters, ( tokamak plasma ) 10 m se, usig q.6 above for Amplitude of. xperimet Site/ loatio Plasma urret, i (Mega-Amps) MA Strai, h, i eter of the Tokamak Strai, h, 5 meters above the eter of the Tokamak JT Culham, Oxfordshire (UK) 8 = 3. MA (irular plasma) MA (Dshape plasma) ASDX Garhig (GR) DIII-D Sa Diego (USA) HL-A Chegdu (PRC) HT-7U Hefei (PRC) ITR(plaed) Sait Paul Les- Durae (FR) ISBN: