卒 業 論 文 - art.aees.kyushu-u.ac.jp

1 18 2 .. 1 1. 2 4. 4. 4. 4. ECR 5. 3 8. 8. 8. 8. 8. 8. 9. PIC 10. 10. 11. 11. 11. 12. 13. 13. Null-collision 16. 19. FDTD 19. 19. 19. 21. 21. PEC(Perfect Electric Conductor ) 21. Mur 21. 22. PIC FDTD 25. 4 27. 27. 27. 29. 29. 31. 34. 38. ECR 2nd Harmonic ECR ( ) 38. ECR 2nd Harmonic ECR ( ) 41. 46. 5 51. 52. 54. 1 . 1955 4 . 8 .. MUSES-C .. (1).. Electron Cyclotron Resonance : ECR .. MUSES-C .. (2) .. 1.. ECR .. 2nd Harmonic ECR . (3) . PIC (Particle In Cell Method) FDTD Finite Difference Time Domain Method . PIC+FDTD .. ECR . FDTD . PIC . FDTD+PIC .. 2.. 3. 2 .. 3 .. 3 . 1. (Ionization). 2. (Acceleration). 3. (Neutralization).. 1 .. (Electron Cyclotron Resonance : ECR) .. ECR .. 4. dv m = ev B ( ). dt m v e B . rL . mv . rL = ( ). eB. v B .. eB. ce = ( ). m .. ECR . ECR rf .. ce .. ce = rf ( ). ECR . ECR Bres ( ) ( ) .. m rf Bres = ( ). q ECR .. ECR . 5.. 6. E. B.. B E.. B. E. B. E. ECR . ECR . 7.

2 3 .. PIC(particle-in-cell) FDTD. finite-difference-time-domain . FDTD .. (4).. = q(E + v B ). dv ( ). m dt dx =v ( ). dt m v x t q . E B 1 cm3 1010 . 1014 .. 10 .. leap-frog . 8. x n +1 x n = v n +1 2 ( ). t n .. v n +1 2 v n-1 2 q n 1 n +1 2. t = E + v m . ( ) . + v n-1 2 B n ( ). 2 . n- 1 2 n t 2 n + 1 2 . n t 2 . v n +1 2 .. v n +1 2 x n + 1 .. Av n +1 2 = S ( ).. q t n = Bx ( ). 2m q t n = By ( ). 2m q t n = Bz ( ). 2m = 1+ 2 + 2 + 2 ( ). E B . A S . 1 .. A= 1 . 1 ( ).. v xm + cE xn + v ym v zm .. S = v ym + cE yn + v zm v xm ( ). v m + cE n + v m v m . z z x y . c = q t m m = n 1 2 .. v n +1 2 = A 1 S ( ). 1+ 2 + . 1 . A 1 = 1 + 2 + .. 1 + 2 . ( ). + . 9. (5). Te kb ne .. De . 0 k bTe De =. ne e 2 ( ).. De ( ). pe . ne e 2. pe =. me 0 ( ).. t pe 1. ( ).. t pe 1. ( ).. c eB. c = ( ). me . 1. t << c ( ).. PIC (6).. PIC Particle In Cell method . (i , j , k ) . dx1, dx 2, dy1, dy 2, dz1, dz 2 V1 V8.

3 (x , y , z ) E ( x , y , z ) V . V1 V8 . 10.. Vn An = (n = 1 8) ( ). V.. E ( x , y , z ) = A1 E (i , j , k ) + A2 E (i + 1, j , k ) + A3 E (i + 1, j , k + 1) + A4 E (i , j , k + 1). + A5 E (i , j + 1, k ) + A6 E (i + 1, j + 1, k ) + A7 E (i + 1, j + 1, k + 1) + A8 E (i , j + 1, k + 1). ( ).. N (i, j , k ) .. V1. (i , j , k ) = qN ( ). V2.. j = qnv ( ).. V1. j (i , j , k ) = qNv ( ). V2. PIC ( ) . ( ) . ( ) . PIC . De ~ 10 4 m .. - - - . (7) . 0,1 .. l N E . 11.. dn = nN dl ( ).. n = n0 exp( N l ) ( ). n0 l = 0 l ,l + dl .. Pinitial (l )dl = exp( N l )N dl ( ). l . P(l ) = Pinitial (l )dl l 0 ( ). = 1 exp( N l ). P(l ) .. = lP(l )dl 0. 1 ( ). =. N .. l r . r = P(l ). l . = 1 exp ( ).. l = ln(1 r ). ( ). r 1 r r . l = ln(r ) ( ). v .. v =. ( ). = Nv .. = (E ) ( ). 12.. total m Pcollision,m .. total = ngas total v m Pcollision,m = 1 exp( ngas total v m t ). ( ). ( ). = 1 exp( total t ). ngas v m m total.

4 R1 0 < r1 < 1 Pcollision,m > r1 m t .. r2 . elastic excitation . ionization . elastic 0 r2 . total elastic + excitation r2 elastic . total total elastic + excitation + excitation + ionization r2 elastic . total total total = elastic + excitation + ionization .. (8) (9) (10) .. (v1 ,v 2 ) (v1 ,v 2 ).. v1 =. 1. (v1 + v 2 u ) ( ). 2. 13. v 2 =. 1. (v1 + v 2 + u ) ( ). 2. u = v 2 v1 . v e v n . v e v n . v n . u = v n v e v e m M . (11) . m + M cos M sin . v e = ve + h ( ). m+M m+M. h . hx = v er cos ( ). vex vey cos v e vez sin . hy = ( ). ver vex vez cos ve vey sin . hz = ( ). ver . ver = vey2 + v ez2 ( ). ve = v ex2 + v ey2 + v ez2 ( ). ( ) . Eincident,e . Escattered,e .. Escattered,e = Eincident,e ( ). Eincident,e . g ( ) (12) Eincident,e . eV . Eincident ,e sin . g ( ) = (0 ) ( ).. 2 1 + Eincident ,e sin 2 ln 1 + Eincident ,e . 2 .. cos = 1 +. {. 2 1 (1 + Eincident, e ) 3. r }. Eincident, e ( ). 14.

5 ( ) . = 2 r4 ( ).. E excitation Eincident,e Escattered,e . v~ . Escattered,e = Eincident,e E excitation ( ).. E. v~ = v e 1 excitation ( ). Eincident,e . ( ) v~ ( ) v v~ e v e ( ) ( ) . Eincident,e ( ) Escattered,e E excitation . eV .. Eincident,e Escattered,e . Ecreated,e E ionization . Escattered,e + E created,e = Eincident,e Eionization ( ).. (13) . Eincident,e Eionization . Escattered,e = B tan r5 tan -1 . ( ). 2B. B eV . E . E = Eincident,e Escattered,e ( ). ( ) . E. v~ = v e 1 ( ). Eincident,e ( ) v e . v~ v ( ) ( ) . e Eincident,e ( ) Escattered,e E ionization . 15. eV .. E created,e = E Eionization ( ). v e . ve 2 E created,e v created,e = ( ). ve m v created,e v e ( ) . E created,e . ( ) . Null-collision (14) (15). Null-collision fake . E . fake < total ( ).. total = elastic + excitation + ionization + fake ( ).. collision ( ). total v = = constant n gas fake collision Pcollision,m . Pcollision,m.

6 3. 2. 3. 3 . total = elastic + excitation + ionization + fake . elastic + excitation + ionization r2 1 Null-Collision Process total Null-Collision Process .. Null-Collision collision ngas 2 10-12. m3/sec . 16. PIC . 17. Xe . Xe Xe . 18. (16) (17). FDTD .. FDTD Finite Difference Time Domain method . FDTD .. H. E = 0 ( ). t E. H = 0 +J ( ). t E H 0 0 J .. FDTD .. Yee (18) E . H . ( ) ( ) . ( )~( ) x , y , z t (i, j , k ) . n . t 1 1. n+ n . Hx 2. (i , j + 1 2 , k + 1 2) = H x (i , j + 1 2 , k + 1 2) +. 2. 0 (i , j + 1 2 , k + 1 2). E yn (i , j + 1 2 , k + 1) E yn (i , j + 1 2 , k ) E zn (i , j , k + 1 2) E zn (i , j + 1, k + 1 2) . + . z y . ( ). t 1 1. n+ n . H 2. (i + 1 2 , j , k + 1 2) = H 2. (i + 1 2 , j , k + 1 2) +. 0 (i + 1 2 , j , k + 1 2). y y E zn (i + 1, j , k + 1 2) E zn (i , j , k + 1 2 ) E xn (i + 1 2 , j , k ) E xn (i + 1 2 , j , k + 1) . + . x z . ( ). 19. t 1 1. n+ n . Hz 2. (i + 1 2 , j + 1 2 , k ) = H z (i + 1 2 , j + 1 2 , k ) +.

7 2. 0 (i + 1 2 , j + 1 2 , k ). E xn (i + 1 2 , j + 1, k ) E xn (i + 1 2 , j , k ) E yn (i , j + 1 2 , k ) E yn (i + 1, j + 1 2 , k ) . + . y x . ( ). t E xn +1 (i + 1 2 , j , k ) = E xn (i + 1 2 , j , k ) +. 0 (i + 1 2 , j , k ). n + 12 n+. 1. H z (i + 1 2 , j + 1 2 , k ) H z 2 (i + 1 2 , j 1 2 , k ).. y . n+. 1. n+. 1.. Hy 2. (i + 1 2 , j , k 1 2) H y 2 (i + 1 2 , j , k + 1 2) . + J x (i + 1 2 , j , k ) . z .. ( ). t E yn +1 (i , j + 1 2 , k ) = E yn (i , j + 1 2 , k ) +. 0 (i , j + 1 2 , k ). n + 12 n+. 1. x H (i , j + 1 2 , k + 1 2 ) H 2. (i , j + 1 2 , k 1 2).. x z . n+. 1. n+. 1.. Hz 2. (i 1 2 , j + 1 2 , k ) H z 2 (i + 1 2 , j + 1 2 , k ) . + J y (i , j + 1 2 , k ) . x .. ( ). t E zn +1 (i , j , k + 1 2) = E zn (i , j , k + 1 2 ) +. 0 (i , j , k + 1 2). n + 12 n+. 1. y H (i + 1 2 , j , k + 1 2 ) H y 2. (i 1 2 , j , k + 1 2).. x . n+. 1. n+. 1.. +. Hx 2. (i , j 1 2 , k + 1 2) H x (i , j + 1 2 , k + 1 2) J (i , j , k + 1 2).

8 2.. y z .. ( ). 1. n+. ( )~( ) n + 1 2 H 2.. 1. n . E n H 2. n + 1 . 20. 1. n+. E n +1 H 2. E n . 1. n+. H 2. E n E n .. x , y , z . 10 . t Courant . 1. t ( ). 1 1 1. v + +. ( x ) ( y ) ( z )2. 2 2.. PEC(Perfect Electric Conductor ) . 0 PEC .. Mur (19).. Mur .. x = 0 x E z . v x . E z = E z ( x + vt ) ( ).. E z 1 E z ( ). =0. x v t x = 0 ( ) . ( ) FDTD .. 21. E z E zn E zn 1. =. t t n . 1 ( ). E z 2. =v x x x = 0, x . x = x 2 ( ) . 1 1. n n . E zn (1 2) E zn 1 (1 2) E 2. (1) E z 2 (0). =v z ( ). t x ( ) E zn (1 2), E zn 1 (1 2) FDTD . E z . v t x n E zn (0, j , k + 1 2 ) = E zn 1 (1, j , k + 1 2 ) +. v t + x {. E z (1, j , k + 1 2) E zn 1 (0 , j , k + 1 2) }. ( ). Mur .. Mur . PEC . x E x y E y . V. Ex = ( ). x . rln . a . V. Ey = ( ). y . rln . a . V r a .. Z . 1 R ( ). Z= ln 2 r R r P .. 22. V2 ( ). P=. 2Z. ( ) ( ) V ( ) ( ) . E x r = x 2 E y r = y 2 . E x (IFED , JFED , KFED ) = E x (IFED 1, JFED , KFED ).

9 V (n t ) ( ). = . x x . ln . 2 a . E y (IFED , JFED , KFED ) = E y (IFED , JFED 1, KFED ). V (n t ) ( ). = . y y . ln . 2 a . (IFED , JFED , KFED ) . 23. FDTD .. 24. PIC FDTD . PIC FDTD. (20) (21) . FDTD . PIC . FDTD . PIC FDTD .. PIC ( ) FDTD ( ) .. PIC FDTD 2~40. PIC 1 3 . X Y - Z 3 .. E e . PIC .. E e . PIC E e .. E e (m ) = E ei Ai A i ( ). i i Eei i Ai ( ) . m . E e . 25.. 26. 4 .. +Z 1eV .. 1, 2( 8 8 6 mesh) .. 27.. 28.. V . V 20 eV .. ---------------------------------------- ---------------------------------------- ------------------------- GHz 5 10 13 sec 2 10 11 sec 1 eV. sccm Xe 2 W. mm T. 21480 . ---------------------------------------- ---------------------------------------- ------------------------- . (a)~(c) . (a)~(c) .. 29. (a) 5 10 11 s . (b) 1 10 10 s . (c) 10 10 s .. (a) 5 10 11 s , (b) 1 10 10 s , (c) 10 10 s . 30.. 1~3 YZ . 1 XY . +Z .. ECR .. +Z .. Z .. 1~3 .. 1 mm .. 31. 1~3 YZ.

10 1 XY . 32. 1~3 . 33.. (100 ) 1,2 .. 1 2 . 2 . eV .. mm .. 34. 15 nsec .. 35. (a)XY . (b)YZ .. (a) XY , (b) YZ . 36.. 37.. ECR 2nd Harmonic ECR ( ). (a) ECR (b) 2nd Harmonic ECR . (a), (b) ECR . 2nd Harmonic ECR 2nd Harmonic ECR 180 .. (a),(b) 2nd Harmonic ECR ECR . ECR .. ECR . 38. (a) ECR. (b) 2nd Harmonic ECR.. (a) ECR, (b) 2nd Harmonic ECR. 39. (a) ECR. (b) 2nd Harmonic ECR.. (a) ECR, (b) 2nd Harmonic ECR. 40. ECR 2nd Harmonic ECR ( ). (a),(b) (a),(b) . (a),(b) (a),(b) .. (a) (b) ECR .. (a),(b) 1, 2 ECR . 2nd Harmonic ECR 1 .. (a),(b) ECR . ECR . ECR.. (a),(b) 2nd Harmonic ECR 2nd Harmonic ECR ( ) 2 .. ECR,2nd Harmonic ECR . 2nd Harmonic ECR . ECR . ECR . 41. (a) ECR. (b) 2nd Harmonic ECR. 15 nsec . (a) ECR, (b) 2nd Harmonic ECR. 42. (a) ECR. (b) 2nd Harmonic ECR. 15 nsec . (a) ECR, (b) 2nd Harmonic ECR. 43. (a) ECR. (b) 2nd Harmonic ECR.. (a) ECR, (b) 2nd Harmonic ECR.. ECR 19770 . 2ndECR 12087.