68 JAXA-RR r v m Ó e ε 0 E = - Ó/ r f f 0 f 1 f = f 0 + f 1 x k f 1 = f k e ikx Ó = Ó k e ikx Ó k 3
|
|
- れんか やなぎしま
- 5 years ago
- Views:
Transcription
1 67 1 Landau Damping and RF Current Drive Kazuya UEHARA* 1 Abstract The current drive due to the rf travelling wave has been available to sustain the plasma current of tokamaks aiming the stational operation. Simple derivation of Landau damping and radio-frequency current drive is described on the standpoint of particle acceleration and deceleration by the rf potential, whereas the current drive is usually described by the quasi-linear theory. This picture is available to understand the physical picture of Landau damping and the current drive. This report starts from the original explanation of Landau damping and then describes the picture of the Landau damping due to the potential as well as the application to the current drive. Finally the new formation of the current drive theory is tried to given. Keywords: Landau damping, radio-frequency current drive, particle trapping, physical picture On the oscillation of the electron plasma Institute of physical problem J. Phys. USSR ) 3 4) Japan Atomic Energy Agency
2 68 JAXA-RR r v m Ó e ε 0 E = - Ó/ r f f 0 f 1 f = f 0 + f 1 x k f 1 = f k e ikx Ó = Ó k e ikx Ó k 3
3 2007/ g = f k (v, t = 0) ε v, e -i t Im ( ) - >- å g f 0 ε = k-iî k Ó k e -i k t-î k t k Î k kx<<1 p Î k. 4 N = ˇå -å f 0dv p = (e 2 N/e 0 m) 1/2 Dawson Jackson C-S Wu 5 7 f Ecos(kz- t) 5 t = 0 v = v 0 z = z 0 z = v 0 t+z 0 v 1 = (ee/mï[sin (kz 0 + Ït)-sin (kz 0 )] 6 Ï = kv 0 - z = z 0 + v 0 t + z 1 5 kz 1 << 1 cos(kz 1 )~1 sin(kz 1 )~kz 1 mv 2 /2 z 0 7 f t å Ë 8 df (v))/dv < 0 df (v))/dv > 0
4 70 JAXA-RR ) Í = Í 0 cos (kz - t) /k = V z = z-vt dz /dt = v, dz/dt = v v = v-v Í = Í 0 coskz 2 Í = 0 v 0 9 v c = (2 eí/m) 1/2 (mv 2 )/2 = m (v v c 2 )/2 v 0 < v c Í(z ) v -v v Í 0 -(v-v)+v v = -2(v-V) = -2 v T T T = mv v = -2 mvv v v > V T v < V 2 z Í (z ) dt/dt = P N v f v /L -v c v c v 10 L s f V f(v + v ) = f(v) + v f (V) s 1 v 0 s 2 s = v 4 c f (V)/2 L = 2e 2 Í 2 0 f (V)/m 2 L W w W E = <E 2 z >/2ε 0 = ε 0 k 2 Í 2 0 /2 W T W T = p = (e 2 N/ε 0 m) 1/2 W W = W E + W T = ε 0 (kí 0 ) 2 T + W w = 0 dt/dt = -dw w /dt 11 dw w /dt = ÎW w Î V = /k Î = 2 mvns/ε 0 (kí 0 ) 2 = 4 e 2 Nf (V)/ε 0 mlk 3 kl = 8/Û 12
5 2007/ ) JFT 2 10 JT MA 11) TRIAM-1 M 12) Ecos(kz - t) 13 13) F F = m v/ t = -2mv v /L (mv)/ t N f P 14 = E eq = F/-e = 2mv v /el E eq J current = env = ˆE eq ˆ ˆ = e 2 N /m (= 1/v) 15 ˆ 14) 13 F N E 0 = kí 0 P F F = ee eff ˆ/e J current J current P
6 72 JAXA-RR F.F. Chen Introduction to plasma physics 15 energy momentum 1 z 0 17 t å Ë d(mv)/dt z0 = ee eff E eff 3 energy momentum 18 Ú ei mdv/dt = ee eff - mvú ei d/dt = 0 19 j = -eˇå vf(v)dv v -å 20 16, 17 1 D. D. Ryutov, Plasma Phys. Contr. Fusion 41 (1999) A 1 2 L. D. Landau, J. Phys., UUSR, 10 (1946) 25 3 L. D. Landau, Phys Z. Sowjet, 10 (1936) 154
7 2007/ J. Dawson, Phys. Fluids, 4 (1961) J. D. Jackson, Plasma Phys. 1 (1960) 71 7 Ching-Sheng Wu, Phys. Rev. 127 (1962) A. Sakharov, Memoirs (Knopf, New York, 1990) p T. Yamamoto et al., Phys. Rev. Lett. 45 (1980) K. Uehara, JAERI-M H. Zushi et al., Nucl Fusion 39 (1999) T. H. Stix, The Theory of Plasma Waves (McGraw-hill, New York, 1962) p ˆ v 3 ˆ = e 2 N /m - > v 3 /V ) F. F. Chen, Introduction to Plasma Physics (Plenum Press, NewYork and London, 1974) p ) K. Uehara, Phys. Fluids B 3 (1991) ) J. H. Malmberg and C. B. Wharton Phys. Rev. Lett. 17 (1966) 175 & K. Yamagiwa et al., J. Phys. Soc. Jpn. 40 (1976) 1157
2 3 4 mdv/dt = F cos(-)-mg sin- D -T- B cos mv d/dt = F sin(-)-mg cos+ L- B sin I d 2 /dt 2 = Ms + Md+ Mn FMsMd MnBTm DLg 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Hm H h
More information. ev=,604k m 3 Debye ɛ 0 kt e λ D = n e n e Ze 4 ln Λ ν ei = 5.6π / ɛ 0 m/ e kt e /3 ν ei v e H + +e H ev Saha x x = 3/ πme kt g i g e n
003...............................3 Debye................. 3.4................ 3 3 3 3. Larmor Cyclotron... 3 3................ 4 3.3.......... 4 3.3............ 4 3.3...... 4 3.3.3............ 5 3.4.........
More informationThe Plasma Boundary of Magnetic Fusion Devices
ASAKURA Nobuyuki, Japan Atomic Energy Research Institute, Naka, Ibaraki 311-0193, Japan e-mail: asakuran@fusion.naka.jaeri.go.jp The Plasma Boundary of Magnetic Fusion Devices Naka Fusion Research Establishment,
More information128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds
127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
More informationV(x) m e V 0 cos x π x π V(x) = x < π, x > π V 0 (i) x = 0 (V(x) V 0 (1 x 2 /2)) n n d 2 f dξ 2ξ d f 2 dξ + 2n f = 0 H n (ξ) (ii) H
199 1 1 199 1 1. Vx) m e V cos x π x π Vx) = x < π, x > π V i) x = Vx) V 1 x /)) n n d f dξ ξ d f dξ + n f = H n ξ) ii) H n ξ) = 1) n expξ ) dn dξ n exp ξ )) H n ξ)h m ξ) exp ξ )dξ = π n n!δ n,m x = Vx)
More informationeto-vol2.prepri.dvi
( 2) 3.4 5 (b),(c) [ 5 (a)] [ 5 (b)] [ 5 (c)] (extrinsic) skew scattering side jump [] [2, 3] (intrinsic) 2 Sinova 2 heavy-hole light-hole ( [4, 5, 6] ) Sinova Sinova 3. () 3 3 Ṽ = V (r)+ σ [p V (r)] λ
More informationE 1/2 3/ () +3/2 +3/ () +1/2 +1/ / E [1] B (3.2) F E 4.1 y x E = (E x,, ) j y 4.1 E int = (, E y, ) j y = (Hall ef
4 213 5 8 4.1.1 () f A exp( E/k B ) f E = A [ k B exp E ] = f k B k B = f (2 E /3n). 1 k B /2 σ = e 2 τ(e)d(e) 2E 3nf 3m 2 E de = ne2 τ E m (4.1) E E τ E = τe E = / τ(e)e 3/2 f de E 3/2 f de (4.2) f (3.2)
More information1 1 1 1-1 1 1-9 1-3 1-1 13-17 -3 6-4 6 3 3-1 35 3-37 3-3 38 4 4-1 39 4- Fe C TEM 41 4-3 C TEM 44 4-4 Fe TEM 46 4-5 5 4-6 5 5 51 6 5 1 1-1 1991 1,1 multiwall nanotube 1993 singlewall nanotube ( 1,) sp 7.4eV
More information1 2 LDA Local Density Approximation 2 LDA 1 LDA LDA N N N H = N [ 2 j + V ion (r j ) ] + 1 e 2 2 r j r k j j k (3) V ion V ion (r) = I Z I e 2 r
11 March 2005 1 [ { } ] 3 1/3 2 + V ion (r) + V H (r) 3α 4π ρ σ(r) ϕ iσ (r) = ε iσ ϕ iσ (r) (1) KS Kohn-Sham [ 2 + V ion (r) + V H (r) + V σ xc(r) ] ϕ iσ (r) = ε iσ ϕ iσ (r) (2) 1 2 1 2 2 1 1 2 LDA Local
More information1 filename=mathformula tex 1 ax 2 + bx + c = 0, x = b ± b 2 4ac, (1.1) 2a x 1 + x 2 = b a, x 1x 2 = c a, (1.2) ax 2 + 2b x + c = 0, x = b ± b 2
filename=mathformula58.tex ax + bx + c =, x = b ± b 4ac, (.) a x + x = b a, x x = c a, (.) ax + b x + c =, x = b ± b ac. a (.3). sin(a ± B) = sin A cos B ± cos A sin B, (.) cos(a ± B) = cos A cos B sin
More information02-量子力学の復習
4/17 No. 1 4/17 No. 2 4/17 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = 2 2m 2 ψ(r,t)+v(r)ψ(r,t) ψ(r,t) Wave function ψ(r,t) = ϕ(r)e iωt steady state 2 2m 2 ϕ(r)+v(r)ϕ(r) = εϕ(r)
More informationJ表紙.dpt
250 16 IEC 60730 AA IEC 60065 1985 1989 1989 IEC 60085 1984 IEC 60127 1974 IEC 60161 1965 IEC60227-5 1997 450/750V IEC60245-4 1994 450/750V IEC 60317-0-1 1990 IEC60384-14 1993 14 IEC 60730 IEC61000-2-2
More information5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1
4 1 1.1 ( ) 5 1.2, 2, d a V a = M (1.2.1), M, a,,,,, Ω, V a V, V a = V + Ω r. (1.2.2), r i 1, i 2, i 3, i 1, i 2, i 3, A 2, A = 3 A n i n = n=1 da = 3 = n=1 3 n=1 da n i n da n i n + 3 A ni n n=1 3 n=1
More information2012専門分科会_new_4.pptx
d dt L L = 0 q i q i d dt L L = 0 r i i r i r r + Δr Δr δl = 0 dl dt = d dt i L L q i q i + q i i q i = q d L L i + q i i dt q i i q i = i L L q i L = 0, H = q q i L = E i q i i d dt L q q i i L = L(q
More information006 11 8 0 3 1 5 1.1..................... 5 1......................... 6 1.3.................... 6 1.4.................. 8 1.5................... 8 1.6................... 10 1.6.1......................
More informationš ( š ) (6) 11,310, (3) 34,146, (2) 3,284, (1) 1,583, (1) 6,924, (1) 1,549, (3) 15,2
š ( š ) ( ) J lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ¾ 13 14. 3.29 23,586,164,307 6,369,173,468 17,216,990,839 17,557,554,780 (352,062) 1,095,615,450 11,297,761,775 8,547,169,269
More information,., 5., ,. 2.2,., x z. y,.,,,. du dt + α p x = 0 dw dt + α p z + g = 0 α dp dt + pγ dα dt = 0 α V dα dt = 0 (2.2.1), γ = c p /c
29 2 1 2.1 2.1.1.,., 5.,. 2.1.1,. 2.2,., x z. y,.,,,. du dt + α p x = 0 dw dt + α p z + g = 0 α dp dt + pγ dα dt = 0 α V dα dt = 0 (2.2.1), γ = c p /c v., V = (u, w), = ( / x, / z). 30 2.1.1: 31., U p(z),
More informationuntitled
24 2016 2015 8 26,,,,,,,,,,,, D.,,, L.,,, E.,,,,,, 1 1,,,,, 2,,, 7 1 2, 3 4 5 6 7 Contribution No.: CB 15-1 20 40,,,,,,,, 3,,,,, 10,,,,,,, 2, 3 5, 7 ,,, 2,, 3,, 4,,,,,,,,,,,,, 4,,,,,,,,, 1, 50, 1, 50 50,
More information1) K. J. Laidler, "Reaction Kinetics", Vol. II, Pergamon Press, New York (1963) Chap. 1 ; P. G. Ashmore, "Catalysis and Inhibition of Chemical Reactio
1) K. J. Laidler, "Reaction Kinetics", Vol. II, Pergamon Press, New York (1963) Chap. 1 ; P. G. Ashmore, "Catalysis and Inhibition of Chemical Reactions", Butterworths, London (1963) Chap. 7, p. 185. 2)
More information1. ( ) 1.1 t + t [m]{ü(t + t)} + [c]{ u(t + t)} + [k]{u(t + t)} = {f(t + t)} (1) m ü f c u k u 1.2 Newmark β (1) (2) ( [m] + t ) 2 [c] + β( t)2
212 1 6 1. (212.8.14) 1 1.1............................................. 1 1.2 Newmark β....................... 1 1.3.................................... 2 1.4 (212.8.19)..................................
More information…_…C…L…fi…J…o†[fiü“ePDF/−mflF™ƒ
80 80 80 3 3 5 8 10 12 14 14 17 22 24 27 33 35 35 37 38 41 43 46 47 50 50 52 54 56 56 59 62 65 67 71 74 74 76 80 83 83 84 87 91 91 92 95 96 98 98 101 104 107 107 109 110 111 111 113 115
More information59 1 2 3 6 7 8 10 12 13 14 15 16 17 18 19 20 21 23 24 25 26 46 49 30 33 36 38 39 40 42 44 41 45 56 43 52 2 3 4 5 6 7 8 9 q w e r t y u i o!0!1!2!3!4!5!6!7!8!9 @0 @1 @2 @3 @4 10 @5 J @6 @7 @8 @9 #0 #1 #2
More information4/15 No.
4/15 No. 1 4/15 No. 4/15 No. 3 Particle of mass m moving in a potential V(r) V(r) m i ψ t = m ψ(r,t)+v(r)ψ(r,t) ψ(r,t) = ϕ(r)e iωt ψ(r,t) Wave function steady state m ϕ(r)+v(r)ϕ(r) = εϕ(r) Eigenvalue problem
More informationuntitled
SPring-8 RFgun JASRI/SPring-8 6..7 Contents.. 3.. 5. 6. 7. 8. . 3 cavity γ E A = er 3 πε γ vb r B = v E c r c A B A ( ) F = e E + v B A A A A B dp e( v B+ E) = = m d dt dt ( γ v) dv e ( ) dt v B E v E
More informationJIS Z803: (substitution method) 3 LCR LCR GPIB
LCR NMIJ 003 Agilent 8A 500 ppm JIS Z803:000 50 (substitution method) 3 LCR LCR GPIB Taylor 5 LCR LCR meter (Agilent 8A: Basic accuracy 500 ppm) V D z o I V DUT Z 3 V 3 I A Z V = I V = 0 3 6 V, A LCR meter
More informationohpr.dvi
2003/12/04 TASK PAF A. Fukuyama et al., Comp. Phys. Rep. 4(1986) 137 A. Fukuyama et al., Nucl. Fusion 26(1986) 151 TASK/WM MHD ψ θ ϕ ψ θ e 1 = ψ, e 2 = θ, e 3 = ϕ ϕ E = E 1 e 1 + E 2 e 2 + E 3 e 3 J :
More informationï ñ ö ò ô ó õ ú ù n n ú ù ö ò ô ñ ó õ ï
ï ñ ö ò ô ó õ ú ù n n ú ù ö ò ô ñ ó õ ï B A C Z E ^ N U M G F Q T H L Y D V R I J [ R _ T Z S Y ^ X ] [ V \ W U D E F G H I J K O _ K W ] \ L M N X P S O P Q @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ r r @ @
More information<4D F736F F D2092B28DB882C982C282A282C42E646F63>
Íû Ñ ÐÑw x ÌÆÇÇ ÇÊÊ ÉÈÉÃÑ ÐÑwà v Ê ÉÇÂdvÊwÎxÇiÊ vèéìêéèâ Ñ ÐÑwÊËÊÊÎwÈÂÈËÉÊÊÆÇ ÍËÊfuÊ~ÎËÊÍÇÊÈÍÇÉÂvw ÊÉÌÊyÎÍÇÉÎÉÈÉÆÌÈ ÇÊwÊÂÇÊÎÿÉfÊÈÍvwÉÈÉ vwêêêuvwîuèâéêvèíéwéâéê ÎyÉÈ ÍÂÇÉÿÊvwÉÈ ÎÂsÌÊÂÆÍÆÊgyÉÈÉÇÈÉÆÉÉÇÍÊ
More informationm dv = mg + kv2 dt m dv dt = mg k v v m dv dt = mg + kv2 α = mg k v = α 1 e rt 1 + e rt m dv dt = mg + kv2 dv mg + kv 2 = dt m dv α 2 + v 2 = k m dt d
m v = mg + kv m v = mg k v v m v = mg + kv α = mg k v = α e rt + e rt m v = mg + kv v mg + kv = m v α + v = k m v (v α (v + α = k m ˆ ( v α ˆ αk v = m v + α ln v α v + α = αk m t + C v α v + α = e αk m
More information( ) s n (n = 0, 1,...) n n = δ nn n n = I n=0 ψ = n C n n (1) C n = n ψ α = e 1 2 α 2 n=0 α, β α n n! n (2) β α = e 1 2 α 2 1
(3.5 3.8) 03032s 2006.7.0 n (n = 0,,...) n n = δ nn n n = I n=0 ψ = n C n n () C n = n ψ α = e 2 α 2 n=0 α, β α n n (2) β α = e 2 α 2 2 β 2 n=0 =0 = e 2 α 2 β n α 2 β 2 n=0 = e 2 α 2 2 β 2 +β α β n α!
More informationK E N Z U 2012 7 16 HP M. 1 1 4 1.1 3.......................... 4 1.2................................... 4 1.2.1..................................... 4 1.2.2.................................... 5................................
More informationI ( ) 1 de Broglie 1 (de Broglie) p λ k h Planck ( Js) p = h λ = k (1) h 2π : Dirac k B Boltzmann ( J/K) T U = 3 2 k BT
I (008 4 0 de Broglie (de Broglie p λ k h Planck ( 6.63 0 34 Js p = h λ = k ( h π : Dirac k B Boltzmann (.38 0 3 J/K T U = 3 k BT ( = λ m k B T h m = 0.067m 0 m 0 = 9. 0 3 kg GaAs( a T = 300 K 3 fg 07345
More information30
3 ............................................2 2...........................................2....................................2.2...................................2.3..............................
More information( ) ) ) ) 5) 1 J = σe 2 6) ) 9) 1955 Statistical-Mechanical Theory of Irreversible Processes )
( 3 7 4 ) 2 2 ) 8 2 954 2) 955 3) 5) J = σe 2 6) 955 7) 9) 955 Statistical-Mechanical Theory of Irreversible Processes 957 ) 3 4 2 A B H (t) = Ae iωt B(t) = B(ω)e iωt B(ω) = [ Φ R (ω) Φ R () ] iω Φ R (t)
More informationuntitled
24 591324 25 0101 0002 0101 0005 0101 0009 0101 0012 0101 0013 0101 0015 0101 0029 0101 0031 0101 0036 0101 0040 0101 0041 0101 0053 0101 0055 0101 0061 0101 0062 0101 0004 0101 0006 0101 0008 0101 0012
More information( š ) œ 525, , , , ,000 85, , ,810 70,294 4,542,050 18,804,052 () 178,710 1,385, , ,792 72,547 80,366
( š ) 557,319,095 2,606,960 31,296,746,858 7,615,089,278 2,093,641,212 6,544,698,759 936,080 3,164,967,811 20. 3.28 178,639,037 48,288,439 170,045,571 123,059,601 46,985,970 55,580,709 56,883,178 19. 4.20
More information.w..01 (1-14)
ISSN 0386-7617 Annual Research Reports No.33, 2009 THE FOUNDATION FOR GROWTH SCIENCE ön é
More information1 a b cc b * 1 Helioseismology * * r/r r/r a 1.3 FTD 9 11 Ω B ϕ α B p FTD 2 b Ω * 1 r, θ, ϕ ϕ * 2 *
448 8542 1 e-mail: ymasada@auecc.aichi-edu.ac.jp 1. 400 400 1.1 10 1 1 5 1 11 2 3 4 656 2015 10 1 a b cc b 22 5 1.2 * 1 Helioseismology * 2 6 8 * 3 1 0.7 r/r 1.0 2 r/r 0.7 3 4 2a 1.3 FTD 9 11 Ω B ϕ α B
More informationτ p ω πτ p ω π τ p (t) = 2 2 t 2 exp(i t)exp 8 2 S(,t) = s( ) (t )d d 2 E x dz 2 = 2 E x z E x = E 0 e z, = + j = 1 2 0 tan = 0, v = c r 10 11 Horn Circulator Net Work Analyzer t H = E t E = H E t B =
More information2 (March 13, 2010) N Λ a = i,j=1 x i ( d (a) i,j x j ), Λ h = N i,j=1 x i ( d (h) i,j x j ) B a B h B a = N i,j=1 ν i d (a) i,j, B h = x j N i,j=1 ν i
1. A. M. Turing [18] 60 Turing A. Gierer H. Meinhardt [1] : (GM) ) a t = D a a xx µa + ρ (c a2 h + ρ 0 (0 < x < l, t > 0) h t = D h h xx νh + c ρ a 2 (0 < x < l, t > 0) a x = h x = 0 (x = 0, l) a = a(x,
More information磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp May 14, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 262 Today s Lecture: Mode-mode Coupling Theory 100 / 262 Part I Effects of Non-linear Mode-Mode Coupling Effects of Non-linear
More informationUndulator.dvi
X X 1 1 2 Free Electron Laser: FEL 2.1 2 2 3 SACLA 4 SACLA [1]-[6] [7] 1: S N λ [9] XFEL OHO 13 X [8] 2 2.1 2(a) (c) z y y (a) S N 90 λ u 4 [10, 11] Halbach (b) 2: (a) (b) (c) (c) 1 2 [11] B y = n=1 B
More information1 1.1 [ 1] velocity [/s] 8 4 (1) MKS? (2) MKS? 1.2 [ 2] (1) (42.195k) k 2 (2) (3) k/hr [ 3] t = 0
: 2016 4 1 1 2 1.1......................................... 2 1.2................................... 2 2 2 2.1........................................ 2 2.2......................................... 3 2.3.........................................
More information<4D F736F F D F8DE98BCA8CA797A78FAC8E9988E397C3835A E815B82CC8A E646F63>
ˆ Ñ Ñ vìéê d Ê ÍÉÂÊÊÊ ÆÂ Æ Ç ÇÂÊ ~ÌÈÉ ÇÉÂÿ Â ss ÊÌ Ë sê~ Ê ÆÂ ~ÌÊÎÌÈÊÈÌÂ ÊÂ Ê ~ÊÉÆÉÊÂ ÇÉÉ ÇÈÂ Â Â Â xâîööð ÊÇÈÍÉÊÉÉÂÇÊÉÌÂÉÌÊÉÌÊÂ Ê Ê u Ç ÌÉÉÇÉÂ Ã ÃÊ ÈÂ ÊÆÇÍÃw ÃÎ v Êv ÊÑ Ñ vêî Í}ÌÂ Ã ÃÇÍÂ Ê vê u Ç ÇÆÉÊÎ
More informationA 99% MS-Free Presentation
A 99% MS-Free Presentation 2 Galactic Dynamics (Binney & Tremaine 1987, 2008) Dynamics of Galaxies (Bertin 2000) Dynamical Evolution of Globular Clusters (Spitzer 1987) The Gravitational Million-Body Problem
More information( ) g 900,000 2,000,000 5,000,000 2,200,000 1,000,000 1,500, ,000 2,500,000 1,000, , , , , , ,000 2,000,000
( ) 73 10,905,238 3,853,235 295,309 1,415,972 5,340,722 2,390,603 890,603 1,500,000 1,000,000 300,000 1,500,000 49 19. 3. 1 17,172,842 3,917,488 13,255,354 10,760,078 (550) 555,000 600,000 600,000 12,100,000
More information24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x
24 I 1.1.. ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x 1 (t), x 2 (t),, x n (t)) ( ) ( ), γ : (i) x 1 (t),
More informationC:/KENAR/0p1.dvi
2{3. 53 2{3 [ ] 4 2 1 2 10,15 m 10,10 m 2 2 54 2 III 1{I U 2.4 U r (2.16 F U F =, du dt du dr > 0 du dr < 0 O r 0 r 2.4: 1 m =1:00 10 kg 1:20 10 kgf 8:0 kgf g =9:8 m=s 2 (a) x N mg 2.5: N 2{3. 55 (b) x
More informationfm
ÁÔÖÐÖÕ Ð +1 f ª ª ª ª ««««ªªª f ª ªª ª ªª ª ªª ª f ªªª ªª ª ªªª f ªª ª f f ªª ª ª ª ~ &'(556#46 &'(5#761 &'(5/#0 &'(5/#0 &'(5%;%.' &'(5/+)+ &'(5*++ &'(12+0 &'(1*#0&&90 &'(1*#0&/#' &'(12+072 &'(1#+4
More information1 Fourier Fourier Fourier Fourier Fourier Fourier Fourier Fourier Fourier analog digital Fourier Fourier Fourier Fourier Fourier Fourier Green Fourier
Fourier Fourier Fourier etc * 1 Fourier Fourier Fourier (DFT Fourier (FFT Heat Equation, Fourier Series, Fourier Transform, Discrete Fourier Transform, etc Yoshifumi TAKEDA 1 Abstract Suppose that u is
More information1: Sheldon L. Glashow (Ouroboros) [1] 1 v(r) u(r, r ) ( e 2 / r r ) H 2 [2] H = ( dr ψ σ + (r) 1 2 ) σ 2m r 2 + v(r) µ ψ σ (r) + 1 dr dr ψ σ + (r)ψ +
1 1.1 21 11 22 10 33 cm 10 29 cm 60 6 8 10 12 cm 1cm 1 1.2 2 1 1 1: Sheldon L. Glashow (Ouroboros) [1] 1 v(r) u(r, r ) ( e 2 / r r ) H 2 [2] H = ( dr ψ σ + (r) 1 2 ) σ 2m r 2 + v(r) µ ψ σ (r) + 1 dr dr
More information²ÄÀÑʬΥ»¶ÈóÀþ·¿¥·¥å¥ì¡¼¥Ç¥£¥ó¥¬¡¼ÊýÄø¼°¤ÎÁ²¶á²òÀÏ Asymptotic analysis for the integrable discrete nonlinear Schrödinger equation
Asymptotic analysis for the integrable discrete nonlinear Schrödinger equation ( ) ( ) 2016 12 17 1. Schrödinger focusing NLS iu t + u xx +2 u 2 u = 0 u(x, t) =2ηe 2iξx 4i(ξ2 η 2 )t+i(ψ 0 +π/2) sech(2ηx
More information1: (Emmy Noether; ) (Feynman) [3] [4] {C i } A {C i } (A A )C i = 0 [5] 2
2003 1 1 (Emmy Noether 1) [1] [2] [ (Paul Gordan Clebsch-Gordan ] 1915 habilitation habilitation außerordentlicher Professor Außerordentlich(=extraordinary) 1 1: (Emmy Noether; 1882-1935) (Feynman) [3]
More informationa L = Ψ éiγ c pa qaa mc ù êë ( - )- úû Ψ 1 Ψ 4 γ a a 0, 1,, 3 {γ a, γ b } η ab æi O ö æo ö β, σ = ço I α = è - ø çèσ O ø γ 0 x iβ γ i x iβα i
解説 4 matsuo.mamoru jaea.go.jp 4 eizi imr.tohoku.ac.jp 4 maekawa.sadamichi jaea.go.jp i ii iii i Gd Tb Dy g khz Pt ii iii Keywords vierbein 3 dreibein 4 vielbein torsion JST-ERATO 1 017 1. 1..1 a L = Ψ
More informationchap1_MDpotentials.ppt
simplest Morse : simplest (1 Well-chosen functional form is more useful than elaborate fitting strategies!! Phys. Rev. 34, 57 (1929 ( 2 E ij = D e 1" exp("#(r ij " r e 2 r ij = r i " r j r ij =r e E ij
More information, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. main.tex 2011/08/13( )
81 4 2 4.1, 1.,,,.,., (Lin, 1955).,.,.,.,. f, 2,. 82 4.2. ζ t + V (ζ + βy) = 0 (4.2.1), V = 0 (4.2.2). (4.2.1), (3.3.66) R 1 Φ / Z, Γ., F 1 ( 3.2 ). 7,., ( )., (4.2.1) 500 hpa., 500 hpa (4.2.1) 1949,.,
More informationプラズマ核融合学会誌11月【81‐11】/小特集5
Japan Atomic Energy Agency, Ibaraki 311-0193, Japan 1) Kyoto University, Uji 611-0011, Japan 2) National Institute of Advanced Industrial Science and Technology, Tsukuba 305-8569, Japan 3) Central Research
More informationuntitled
Unit 4. n 1 = n 1 ex[i(k x ωt + δ n )] n 1 : k: k = π/λ δ n : k = kxˆ, δ n = n 1 = n 1 os(k x x ωt) v = ω k k k Re(ω) > Im(ω) > Im(ω) < Im(k) E 1 = E 1 ex[i( k x - ωt)] E 1 : + v g ω ω ω ω = = xˆ + yˆ
More informationn ξ n,i, i = 1,, n S n ξ n,i n 0 R 1,.. σ 1 σ i .10.14.15 0 1 0 1 1 3.14 3.18 3.19 3.14 3.14,. ii 1 1 1.1..................................... 1 1............................... 3 1.3.........................
More informationchap03.dvi
99 3 (Coriolis) cm m (free surface wave) 3.1 Φ 2.5 (2.25) Φ 100 3 r =(x, y, z) x y z F (x, y, z, t) =0 ( DF ) Dt = t + Φ F =0 onf =0. (3.1) n = F/ F (3.1) F n Φ = Φ n = 1 F F t Vn on F = 0 (3.2) Φ (3.1)
More informationq π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ
H k r,t= η 5 Stokes X k, k, ε, ε σ π X Stokes 5.1 5.1.1 Maxwell H = A A *10 A = 1 c A t 5.1 A kη r,t=ε η e ik r ωt 5. k ω ε η k η = σ, π ε σ, ε π σ π A k r,t= q η A kη r,t+qηa kηr,t 5.3 η q η E = 1 c A
More information数学Ⅱ演習(足助・09夏)
II I 9/4/4 9/4/2 z C z z z z, z 2 z, w C zw z w 3 z, w C z + w z + w 4 t R t C t t t t t z z z 2 z C re z z + z z z, im z 2 2 3 z C e z + z + 2 z2 + 3! z3 + z!, I 4 x R e x cos x + sin x 2 z, w C e z+w
More informationロシア語便覧 1
- -È - - -ÚÂÎ Û Ë±ÚÂÎ, ÔËÒ ±ÚÂÎ - apple ÒÂÍappleÂÚ ±apple, Ë ÎËÓÚÂ±Í apple flì ±apple, Ù apple ±Î ÒÚÓ±Î, ÒÚÓÎ ± αÒ, ÎÂ±Ò ; ÎÂÒ ±, ÎÂÒÓ± ÁÛ±, ÁÛ± ; ÁÛ±, ÁÛ Ó± -, -Ë ÒÚÓÎ ±, ÊÛappleÌ ±Î, ÏÛÁ±Ë, ÒÎÓ appleë±
More informationスケーリング理論とはなにか? - --尺度を変えて見えること--
? URL: http://maildbs.c.u-tokyo.ac.jp/ fukushima mailto:hukusima@phys.c.u-tokyo.ac.jp DEX-SMI @ 2006 12 17 ( ) What is scaling theory? DEX-SMI 1 / 40 Outline Outline 1 2 3 4 ( ) What is scaling theory?
More information官報(号外第196号)
( ) ( ) š J lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ¾ 12 13. 3.30 23,850,358,060 7,943,090,274 15,907,267,786 17,481,184,592 (354,006) 1,120,988,000 4,350,000 100,000 930,000 3,320,000
More information18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
More information量子情報科学−情報科学の物理限界への挑戦- 2018
1 http://qi.mp.es.osaka-u.ac.jp/main 2 0 5000 10000 15000 20000 25000 30000 35000 40000 1945 1947 1949 1951 1953 1955 1957 1959 1961 1963 1965 1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989
More informationsec13.dvi
13 13.1 O r F R = m d 2 r dt 2 m r m = F = m r M M d2 R dt 2 = m d 2 r dt 2 = F = F (13.1) F O L = r p = m r ṙ dl dt = m ṙ ṙ + m r r = r (m r ) = r F N. (13.2) N N = R F 13.2 O ˆn ω L O r u u = ω r 1 1:
More information( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e
( ) Note 3 19 12 13 8 8.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R, µ R, τ R (1a) L ( ) ) * 3) W Z 1/2 ( - )
More informationII No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
II No.1 [n/] [1]H n x) H n x) = 1) r n! r!n r)! x)n r r= []H n x) n,, H n x) = 1) n H n x) [3] H n x) = 1) n dn x e dx n e x [4] H n+1 x) = xh n x) nh n 1 x) ) d dx x H n x) = H n+1 x) d dx H nx) = nh
More informationMott散乱によるParity対称性の破れを検証
Mott Parity P2 Mott target Mott Parity Parity Γ = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 t P P ),,, ( 3 2 1 0 1 γ γ γ γ γ γ ν ν µ µ = = Γ 1 : : : Γ P P P P x x P ν ν µ µ vector axial vector ν ν µ µ γ γ Γ ν γ
More informationAharonov-Bohm(AB) S 0 1/ 2 1/ 2 S t = 1/ 2 1/2 1/2 1/, (12.1) 2 1/2 1/2 *1 AB ( ) 0 e iθ AB S AB = e iθ, AB 0 θ 2π ϕ = e ϕ (ϕ ) ϕ
1 13 6 8 3.6.3 - Aharonov-BohmAB) S 1/ 1/ S t = 1/ 1/ 1/ 1/, 1.1) 1/ 1/ *1 AB ) e iθ AB S AB = e iθ, AB θ π ϕ = e ϕ ϕ ) ϕ 1.) S S ) e iθ S w = e iθ 1.3) θ θ AB??) S t = 4 sin θ 1 + e iθ AB e iθ AB + e
More information1
5-3 Photonic Antennas and its Application to Radio-over-Fiber Wireless Communication Systems LI Keren, MATSUI Toshiaki, and IZUTSU Masayuki In this paper, we presented our recent works on development of
More informationII Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R
II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =
More informationB 1 B.1.......................... 1 B.1.1................. 1 B.1.2................. 2 B.2........................... 5 B.2.1.......................... 5 B.2.2.................. 6 B.2.3..................
More information1 [ 1] (1) MKS? (2) MKS? [ 2] (1) (42.195k) k 2 (2) (3) k/hr [ 3] t = 0 10 ( 1 velocity [/s] 8 4 O
: 2014 4 10 1 2 2 3 2.1...................................... 3 2.2....................................... 4 2.3....................................... 4 2.4................................ 5 2.5 Free-Body
More information215 11 13 1 2 1.1....................... 2 1.2.................... 2 1.3..................... 2 1.4...................... 3 1.5............... 3 1.6........................... 4 1.7.................. 4
More informationeto-vol1.dvi
( 1) 1 ( [1] ) [] ( ) (AC) [3] [4, 5, 6] 3 (i) AC (ii) (iii) 3 AC [3, 7] [4, 5, 6] 1.1 ( e; e>0) Ze r v [ 1(a)] v [ 1(a )] B = μ 0 4π Zer v r 3 = μ 0 4π 1 Ze l m r 3, μ 0 l = mr v ( l s ) s μ s = μ B s
More informationš š o š» p š î å ³å š š n š š š» š» š ½Ò š ˆ l ˆ š p î å ³å š î å» ³ ì š š î å š o š š ½ ñ š å š š n n å š» š m ³ n š
š š o š» p š î å ³å š š n š š š» š» š ½Ò š ˆ l ˆ š p î å ³å š î å» ³ ì š š î å š o š š ½ ñ š å š š n n å š» š m ³ n š n š p š š Ž p í š p š š» n É» š å p š n n š û o å Ì å š ˆ š š ú š p š m å ìå ½ m î
More information4 2 Rutherford 89 Rydberg λ = R ( n 2 ) n 2 n = n +,n +2, n = Lyman n =2 Balmer n =3 Paschen R Rydberg R = cm 896 Zeeman Zeeman Zeeman Lorentz
2 Rutherford 2. Rutherford N. Bohr Rutherford 859 Kirchhoff Bunsen 86 Maxwell Maxwell 885 Balmer λ Balmer λ = 364.56 n 2 n 2 4 Lyman, Paschen 3 nm, n =3, 4, 5, 4 2 Rutherford 89 Rydberg λ = R ( n 2 ) n
More information2 Chapter 4 (f4a). 2. (f4cone) ( θ) () g M. 2. (f4b) T M L P a θ (f4eki) ρ H A a g. v ( ) 2. H(t) ( )
http://astr-www.kj.yamagata-u.ac.jp/~shibata f4a f4b 2 f4cone f4eki f4end 4 f5meanfp f6coin () f6a f7a f7b f7d f8a f8b f9a f9b f9c f9kep f0a f0bt version feqmo fvec4 fvec fvec6 fvec2 fvec3 f3a (-D) f3b
More information4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
More informationEuler Appendix cos, sin 2π t = 0 kx = 0, 2π x = 0 (wavelength)λ kλ = 2π, k = 2π/λ k (wavenumber) x = 0 ωt = 0, 2π t = 0 (period)t T = 2π/ω ω = 2πν (fr
This manuscript is modified on March 26, 2012 3 : 53 pm [1] 1 ( ) Figure 1: (longitudinal wave) (transverse wave). P 7km S 4km P S P S x t x u(x, t) t = t 0 = 0 f(x) f(x) = u(x, 0) v +x (Fig.2) ( ) δt
More information