N a b d Z i e Z a f bphys-el.univ.kiev.ua/resources/PlasmaPhys.pdf · G e M ' «» G G 'M M M §·...
229
Ʉ Ʉ ɢʀɜɫɶɤɢɣ ɧɚɰɿɨɧɚɥɶɧɢɣ ɭɧɿɜɟɪɫɢɬɟɬ ɿɦɟɧɿ Ɍɚɪɚɫɚ ɒɟɜɱɟɧɤɚ Ɏɚɤɭɥɶɬɟɬ ɪɚɞɿɨɮɿɡɢɤɢ ɟɥɟɤɬɪɨɧɿɤɢ ɬɚ ɤɨɦɩɸɬɟɪɧɢɯ ɫɢɫɬɟɦ Ʉɚɮɟɞɪɚ ɮɿɡɢɱɧɨʀ ɟɥɟɤɬɪɨɧɿɤɢ ȱɈȺɧɿɫɿɦɨɜ Ɏɿɡɢɤɚ ɩɥɚɡɦɢ Ʉɨɧɫɩɟɤɬ ɥɟɤɰɿɣ Ʉɢʀɜ 18
Transcript of N a b d Z i e Z a f bphys-el.univ.kiev.ua/resources/PlasmaPhys.pdf · G e M ' «» G G 'M M M §·...
18
7
9
99
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29
2
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22 2
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7
9
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79
99
3
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7
77 2
8
5
6
–
–
–
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.
Boyd T. J.J.
-
8
9
1.1.
– –
1 2
–
– –
2 1030 ) – 7 108 3 103 3
)
1
2
–
10
108
10 3 – – –
107 –
—
108
00
7
10 10
–
– 10 10
11
10
–
– 10
–
1013
12
– 300
–
n 327 702
108 108 108 Tp 7 10 10 10 Te 10 10 10
Te p
–
– 1 103 3
10 –
–
–
13
1 –
10 10 8 10 ² 10
103
D E F
2 103 3
D
3
3 3 –
–
F 130
14
0 10 3
D E F
0
– –
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7
– )
–
15
16
–
20 –
–
17
–
–
3
–
107
10
– 10 7
10
2 – 10 1 102 – 103
–
18
1
2
– 10 3
– – 101018 3
10 1011 3
2 103
1.2 –
19
1.11
1.12
1.1
11 3
12 13
1 3) 10
10
3 Frans Michel Penning – –
20
Q quiescent plasma –
Q 1
–
10 1013 3 – –
–
21
18
8
1
20 3
2 –
11
– –
–
–
22
Q
23
2
2
« » «
l
x ( x l 2
2
–
5 2 Irving Langmuir –
24
en x4 4E n e x
2
22 4d xm eE e n x
dt
2
22 pe
d x xdt
24p
n em
2
–2
2p
pf
–
–
– 2 pT
p
25
q
(
2
4
4 e n n 4
5
expB
e rn r n
k T 5
r
(Charles Augustin de Coulomb –
4 (Petrus Josephus Wilhelmus Debije Peter Josseph Wilhelm Debye –
5 (Ludwig Eduard Boltzmann –
— 2
26
r
5 4
B
ek T
24
B B
e r n een rk T k T
2Dr
2
24B
Dk Trn e
22
d drr dr dr
q r
r f r r
2d df fdr r dr r
2 2
22 2
d d d df d f df df d fr r f r rdr dr dr dr dr dr dr dr
2D
ffr
2
exp expD D
r rf C Cr r
r 2C
expD
C rrr r
4
(Siméon Denis Poisson –
–
(Pierre –
27
Dr rC q
Drr
rqr exp 5
2 Dr
TeB
DP P
vk Trm
Te Bv k T m
BTe
k Tvm
D
Tr
n
–
D
–
4
28
E
DU Er
D BeEr k T 2
22
4 4p Te p DTeBD B
D D
m v m rmvk TE n er n k Ter er e e
2
4 4 D
E En ne er
22
22
2maxE
pf n
q q e q e
q e q e
29
2
2
Bk T
e n ( n –
Be n k T 2
Dn r
D DN nV 24
D DV r –
BD D
k TN nV
e n25
–
25
2.2.2.
–
30
22
– –
Te
B Teh mv n
– f W dn dW dZ dW
w W W f W w W dZ dW
F
B
w WW W
k T
FW –
4 2mdZ WdW h
h –
4 2
F
B
m Wf Wh W W
k T
(Louis Victor Pierre –
mv k mv
(James Clerk Maxwell –
Enrico Fermi –
–
31
x y z F
B
d nf pdp dp dp h W p W
k T
2 2 22
2 2x y zp p ppW p
m m
–
PV const
2 2 2F FW k m2
Fk n –
F BW k T w W
w W –
B Te Dmv r
p B ek T–
2.4 – – – –
– – – –
– – – – –
32
– 2 4
2.2.3
expe i e i iB
a a B
n n g g Wmk Tn g h k T
( en in an – kg – kh – iW –
2Bk T mc
ce eB mc ( B –
–
(Meghnad Saha –
e a
a (Max Karl Ernst Ludwig Planck –
5 5
33
2.2.4.
2 4T K T eB
2 ne -3 na -3 Te Ti lf
2 4 2 5
5 2 4 2
2
2 2
4
4
5 4 4 5
5 5 5 4 4 5 5 4 4 4
2
eT eB
34
Q
2.3
2.3.1.
N
F r v t r r t v v t
t
F r v t
E B
–
N N
N N ND D X X X t
i i iX r v N
Josiah Willard Gibbs –
(Joseph Liouville –
35
N N ND X X X t dX dX dX 4
kdX k k k xk yk zkdx dy dz dv dv dv
N
N N ND X X X dX dX dX
NdX dX dX
NX X X S S N
!!S S N N S S N
Nf X X X t D X X X t dX dX dXN S
S N ! ! SN N S N
Sf Sf
S N
S
N N Nf X t N D X X X t dX dX dX
f X t dX N
S
S S ii
f X X X t f X t
f r v t f X t
f r v t drdv dr dxdydz r
x y zdv dv dv dv v
trnvdtvrf
n r t dr N
vf r v t dv J r t
–
r v t f r v t dv r tn r t
36
– r v t
f
4
2.3.3
dttvrdf 42
42 i i
vi ii i
x vdf f f f f f df dfv f v f v vdt t x t v t t t dr dv
df dr df dv f
v v v
f d dvf vft dr dv
Fmdt
vd 44
F –df f df F dfvdt t dr m dv
45
Sir Isaac Newton –
37
F –
F m e E c v B
2.3.4
45
– I f
f df F dfv I ft dr m dv
4
2 v
2v v 2v 5
v
2.5
2222 vmvmvm 2 22
2 2
2 2 2m v m vm v
v v v
22m 2 2 2
2
22 2 2m v m m vv m v v
m
2
22m m v m v v
m
2m v vm v
2 2m
38
m m 2
22 2 22 2
v v v vv v v v v v vv v
2
– u
–
2.3.5
q J dN
sind d d dN Jq d 5
dv v
2v
J uf r v t dv 54 u v v –
d dN Jq d uq f r v t dv d 55
v v dv
2 2 2v v dv
2 2 2dn f r v t dv 5 dv
dN dv uq f r v t f r v t dv d
dv
dN dv uq f r v t f r v t dv d
dv dv dv dv
dN dNI f uq f f f f d dvdv
f v
39
f f r v t f f r v t v 2v –
v 2v –
q
u
2v
v 2v v
2v v v – v
–
f df F dfv uq f r v t f r v t f r v t f r v t d dvt dr m dv
2.3.6
F f v
I f
f f f f
ln ln ln lnf f f f
m v m v m v m v
2 22 2
2 2 2 2m v m vm v m v
2
ln2
m vf A A m v A
A A A –A A A – n
T v
40
2
exp2 2B B
m v vmf v nk T k T
2.3.7.
f f F fv uq f f f f d dvt r m v
f r v t–
f r v t v
I f
f r v t f v f r v t | |f f
f
I f uq f f f f f f f f d dv 4
I f
u Tvq q
q q d f
2 2T Tf fI f qv f r v t f dv nqv f r v t
Tnqv
–
df f fdt
f t f f t t
41
–
Ivf
mF
rfv
tf
f – i e I –
( I F –
F e E v Bc
2.3.9
E B
E E E B B B 2
E B – E B –
d Drdn
T
Te pe
Tn v
d n
E B
d
E B
42
f f e fv E v Bt r m c v
E B 22
tB
cErot ; j
ctE
cBrot 4 ;
4Ediv ; Bdiv
ar t e f r v t dv ;
j r t e vf r v t dv
– –
( 24
fl – free
f Tel v k
Tekv t t
22
D E B H
– E B –
24 –
43
t t
2.4
–
25 –
2.4.1.
H – h
drodynamic H
a
25
44
n fl
HL f Hn l a L
H fL l
2.4.2.
i i i
i i i i i edv en mnMn p en E v B v vdt c
e e ee e e e e i
dv en mnmn p en E v B v vdt c
i e i e B i ep n k T – M m
–
–
i e i e i e i e i e i ek
k i e i ek kk k
dv r t v v v v vx v v vdt t x t t x t
e i
e i e i
ndiv n v
t
i i e ee Erot B n v n v
c c t; Brot E
c t;
4 i ediv E e n n ; div B
(Hendrik Antoon Lorentz –
–
45
eT iT
5
2.4.3.
e in n n
i ej en v v j
e iT T T
2e i Bp p p nk T M m ( M – m –
nM iv v
e e i een mnp enE v B v vc
dvMn p j Bdt c
i ej en v v
i ej en v v 2ep p
2 een enp enE v B jc
2e nm
4
(André – – –
46
2en enjp enE v B j Bc c
5
v iv
B p const 5E j
– 5
j E
n nvt
4B jc
; BEc t
; B E
T const~T n
2.4.4
(Georg Simon Ohm – – –
– –
–
(Hannes Olof Gösta Alfvén; –
(
47
2 lnBe e e
k Tj jE v B p v B nc en c e
j
2
4
4
B j c cc E c v B v B Bt c
cv B B
ev v
B B B B
2
4B cv B Bt
L
22
2 2 2 22
2
4 4~
44
pM
vBv B Lv ne LvL Lv R
c B c c m cc BL
MR R Lv
2 2 24 pc c
– (George Gabriel Stokes
— ( (
(Osborne Reynolds – –
48
MR
B v Bt
MR
H
2 2H pc Lv
–
~H L v
pL c
2 4c Lv *E E c v B
E v Bc
2.4.6
L
S B
L
t
S S
B dS BdS
t t S LS S
49
S S S S
S S S S
B B dS B dS B B dS BdS
~S t B B O t B B 2 t
2.7
2
S S S
B BB t t B t dS t dS t dSt t
5
S dS v t dl
dl – L a b c c b a
2S L L S
B dS B v t dl t v B dl t v B dS
S
Bt v B dSt
vconst
2.4.7
2
4B c Bt
(George Green –
50
– 2 4mD c
2D mL D L – –
D
2 2 24H D mL D L c H L v
mR 5
2 2
51
3
–
–
–
– 1
3
2
expBe i e i i
a a B
mk Tn n g g Wn g k T
(
e , i , a g – iW – 2
iW
1
2 (Erwin Rudolf Josef Alexander Schrödinger; 1961 –
(1921
(194 (1956 (1
52
4
3.1
–
3.1
3.2
– –
3.2 -
ff
rfv
tf (
2
exp2 2B B
m v umf nk T k T
(
– 2 62n T u
n n r T T r u u r
f
f
f f f f f (
4 (Llewellyn Hilleth Thomas; 1992 – – 1946
–
53
L ~f f L
( f f f t
f fvr
(
f v f (
3.2 u
– 5 – Bq k T (
–
2
2mvq v f dv (
BB
ff v k Tk T
2 2
5 2 2 exp2 2 2 22B
B BB B
m m mv mvv k T nk T k Tk T k T
2
2 2BB B
mvv k T fk T k T
(
2 2 4 2 2 2
2 2 2 2 2 2x x
B x BB B B B
mv mv m d mv v v vq v v k T f dv e k T f dvk T k T k T dx k T
6 46 4
6 2 2 6 2 2B BB B B B
m mv v mn mk T f dv v v k Tk T k T k T k T
(
x 2 2xv v
6 4
6 2 2B B
mn m v vk T k T
(
5 (Jean Baptiste Joseph Fourier; – ( 1822
(1826 (
–
54
4v
42
4 4 2exp 42 2B B
v f v dvm mvv v v dvk T k T
f v dv
2261 15exp
2 22B
B B
k Tm mvv dvk T k T m
(
6
2Bk Tvm
(
n2 2
1 2
2 1 !!expn
n
nx ax dx
a n n n (
52
Bnk Tm
(
5 1
P f Tc nl v (
5 2pc – 6 p const T Bv k T m –
f Tl v –
3
3.2 x
x xu u z
xz z
zux
xz (
– 2 2 2
2 2 x x y zB B
m mf r v n v u v vk T k T
(
6
55
xz
x
f uf vv z
(
2 1 xmv z
xz x zmv v f dv (
( 2 2 2x x x
xz x z y z z x x zx x
f u u f um v v dv m dv dv v v dv m v f dvv z z v z
(
xv 2zm v f dv (
1B f Tnk T nl mv (
2
3.2
J D n (
D –
f f v nn
(
J v fdv (
2
21 1 ff T
lD l v (
f Tl v –
3.2
– –
56
3.2
3.3
3.3
i en n
a a e Couln vq n vq
aq Coulq – q
q q d sind d d – q –
d
a a e Couln q n q
a a e Couln q n q
a Coulq q
e Couln vq
2
57
– Coulq
trq q d
–
– b
2 Db r Db r
2
2trq q d q d ( 8
2 42 2sin 2
eqW
(
min
2 22 28 cos 2 8 22 4 lnsin 2Coul
e eq dW W
8 Ernest Rutherford – ( 1898
– ( – –
(
58
min
Dr 2 2
minD
e eb W r W
( 9
W BW k T
min2 4 4
D B B B
e e ne e nr W k T k T k T
22
~ lnCoulB
eqk T
ln ln ln 92
BD
k T Ne n
DN – 5 ln
224 ln
9CoulB
eqk T
ne -3 Te
2 6 9 16
14 1 5 4 8 19 24
1 25
11 12 1 12
2 5 8 12 1 8 9
15 1 4 1 1 2
1 2 4
5 18 5 15
4 4 5 14 4 18
14
22 lnCoulq
T eB
59
2 2 eT K n
( 1 4
~ln
3.3.2
1
Tnqv
~Te B ev k T m ~Ti B iv k T M
e iT T q
(
(2 1 2
4 41~ ~
ln ln lnB e B e D
eee B e p
k T m k T Nmn k T e ne
(
–
2
ee
m M –
1 2 1 21 2
4~ ~ln ln
B i i iDii ee
p e e
M k T T TN M Mne m T m T
(
– ii
m M e iT TM m
1 2 4~ ~ ~ln ln
B e Dei ee
p
M k T NM Mm m e n m
(
ei –
60
e iT T
~ii eeMm
~ei iiMm
1Mm
( 5
ei ii ee
ee
ii – ei
2
4~ ~ ~ln ln
B e Df e Te ee D
k T Nl v rne
( 6
22
4~ ~ln
B i if i Ti ii f e
e
k T Tl v lne T
6
3.3.3
Vl Vl
ee
ee
lnD
p VlN
lnp
VlDN
3.3.4
61
1 2
4~ln
B iii H
M k Tne
1 2
4~lnB e
ee H
m k Tne
~H phL v – L –
phv –
lnD
p HN
1 2
lniD
p He
TN Mm T
DN – ( 1DN ( i eT T
– H
~ ~ph H f Te eeL v l v
lnTe D
p Hph
v Nv
–
1 2 4~ln
B iei H
M k Tm ne
lnD
p HN M
m
H M m
62
Q
3.4.1
2 2
5 2
1 2 4~ ~ln
B ee p e Te f
k Tc n v l
m e ( 9
m eT M iT
5 2
1 2 4~ln
B ii
k TM e
9
e iT T M m e i –
Bk T
( 5 2 1 2
4~ln
B ee
k T me
5 2 1 2
4~ln
B ii
k T Me
(
~e iT T i e
1Ti
Te
Mv Mmv m
3.4.2
9
e e ej en v ( 41
9
63
e
ee
mveE ( 42
– ee
eee e
ev E Em
42
ln lnB eee D
e
k Te Nm m ne mn
4
– 1 2
lnB iii i
i ee
k Te TmM M ne M T
4
4
2
ee e eee e e
e E e nj en E Em m
41
e 2
1 2 2~ln
B ee eee
k Te nm m e
( 44
eT en~ 1ee en
44
1 2 2~ln
B ii
k TM e
4
3.4.3 -
1 2
4~lnB e
ee
m k Tne
e eemv ev
e Tev v
B ek T 2 2emv ev
64
ev e eemv2
ev ev (
3.3fr e eeF mv
. 1E
1v
thrv
2E
2 thr
ee thr
mveEv
5
4 4
21 2 2
ln ln~ thrthrthr
ne neeE mvmvm mv
ln~thr
nevmE
6
thr Tev v
thr Tev v 2E – 6
lnthr
B e
neE Ek T
5 –
3.4.4.
5 6
65
5 j E v
–
e 1mR
ln1
D p
v cc N L
8
9
3.4
–
2
3.5.
–
3.5.1.
66
5 22
1 2 41 1 1 B e
e f Te Te ee
k TD l v v
m e n ( 49
5 25 2 1 2
1 2 41 B i i
i ee
k T TmD DM e n M T
( 49
49
2
~ f Tee Te B e
e ee
l vD mv k Te m e e
49 i B i
i
D k Te
3. –
49
4
e iJ
x e
e e e enJ En Dx
ii i i i
nJ En Dx
E – 11 i eE x e n n
e i
i en n n
i eJ J J
(Albert Einstein; 1955 – XX ( (
(1914 ( ( 1916
1916
— 11 (Johann Carl Friedrich Gauß; 1855 –
–
67
1 1 e i
e i e i
D D nJx
anJ Dx
(
aJ D n (
i e e ia
i e
D DD ( 54
– e i
ia i e
e
D D D ( 54
e iT T T 2a iD D ( 54
e a iD D D
1 2e i e e ee e e a e i e e e
e
n n n nmEn D D D D D D Dx x x M x
45 1~ ~e e B
e e
D n k TEn x eL
1e eL n n x –
68
ii i i
nEn Dx
2 2~ ~ Bi e
k TEn neL e L
L
–
3.5.3.
3.5.4
5
69
3.5
e
e edv enmn p enE v Bdt c
E
e e ev v v 6
56 55ev
ee
dv enmn v Bdt c
; 55
e eenp enE v Bc
55
55 ce eB mc 55 –
ev 55 B
2e e e
en enp B en E B v B B en E B v Bc c
( 5 2enB c
e E Dv v v ( 5
2E
E Bv c
B( 58
70
–
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D
p Bv c
enB( 59
–
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3.6
6
2
71
fl12 LR
2 2 2
2 2 2~ ~ ~Le Te B ee
ce
R v mc k TDe B
~ 1 L fR l ce
2 2
e Le
e f ce
D RD l
ce
–
12 (Sir Joseph Larmor 1942 – –
72
2 9 (Te iT T
B e e enenk T n enE v B mnvc
( 61
61
61 en
61
61 B 56
2B e en e
enk T n B en E B B v mn v Bc
( 62
( 61ev B
e e e Ec Dcnv D E v v
n(
21B en
ece en
k T mD 64
–
21en
ece en
e m 65
–
22 1Ec
en ce
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B( 66
– 58– collisions –
22 1Dc
en ce
c p Bv
enB( 6
73
– 59
–
641ce en
ce en
~ 1ce en f Ll R1ce en
( 6
1ci in 64 ( 65
2
2in
iMc
eB ( 64
2
2 2B in
iMc k TD
e B ( 65
~en in en in n Te Tiq n v ( 68
nn – ~en inq q
~ ~in en Ti Tev v m M ~ ~ ~i e i e Ti TeD D Mv mv M m (
( 41 ( 41 49 ( 49 –
1Li Ti ce
Le ci Te
R v m M MR v M m m
3.5.7
14 (B LehnertF Hoh 5
– –
Lehnert – –
14 F –
74
zE
zE zE 8
z zE B E
BB
3.8 - – – 2 –
– –
15 16
15 1928 1998 – (1991 – 1956
16 –
75
3.5.8
–
5
28 1p B
4 5
5 –
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1p j Bc
; ( 69
1 jE v Bc
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eee n m –
B 1 1E B v B B j Bc
(
B B ) 69
2v cE B B p
c (
E Dv v v 2E
E Bv c
B
2
2Dc pv
B (
–
76
22
2 2B e i
D
nc k T Tnc pJ nv nB B
( 4
4
2
2B e inc k T T
DB
( 5
5( 42
2 22 2 2
2 2 2 22 21 1 Te LeB B
ee ee ee ee
mcv Rmc k T k T m cDe B m e B eB
( 5
Le TeR mcv eB –
5 ( 5
5
D 2B
nn 5
2 2
22 ln
Te
ne cDB v
( 5
D 2D An
2 2 22n nA n A n A nt
( 6
61 2n r t n r n t
6 2212
2 1 2
1 1dn A nn dt n n
(
2
2
nn t
t ( 8
– 1 t
77
3.5.9
1 B 21 B 5
( 8 5
18 19
16B
Bck TD D
eB ( 9
– 4 4
3.5.10
4
(David Joseph Bohm; 1992 –
–
– –
18 Eric Henry Stoneley Burhop –
19 (Sir Harrie Stewart Wilson Massey; –
(
78
3.9.
3.10 – –
5
3.5
D~RL2
79
3.5
80
4
–
4.1
4.1.1
F –
F
–
4
81
2drcv F B
eB
FF qE
2Ecv E B
B
-
2
2dr
B grad Bmv cve B
z const z
I z
/ /v
2/ / 2c
RF mvR
R – –
82
2/ /
2 2drmv cv R BeB R
z z
z
2LR B const )
)
~ 1LR B
-
L cR v c qB mc 2
cv const ~v v B 6)
83
2 2
zv v const 7) v zv
0zv
r z
6 22 vv
B B
sinv v sinv v v –
2sin sin B B 8) sin 1
maxsin B B 9)
maxsin B B 0)
84
4.2.
1
2 Bp nk T
1dvMn p j B
dt c
1p j Bc
11)
j
1
1921 1989) – –
) –
1971) –
–
1926 2011) –
85
0div j 12) j
cj B 0B 1 )
11) 1 ) 2 7
0B 0
0 0
1 0B p 0j p
p const
( p p p
p p const
86
2
11) 1
1 1
21 1 1 1 1j B B B B B B B B B Bc
)
11 2 1Bp B B )
b B B u b b u u
u b b u – u 2B
2 2 2B B b b B 16)
b b
2 2 2B B B B B B B 16 )
B B B b
0b B B 17)
16 16–
2 1 1Bp B B b b B B B B 18)
18) b B )
B B B B
1 2nB R n – R –
9
2 B B n R
87
2 2B Bp n
R
2 8mp B 2B R –
2 2T u x2 2 1u x R
2B
28mp p p B
4.9 – –
– –
–
–
9
–
88
. z -
z
z r z z
1
z zB r z const
z B r
1 – p zB B
0j 0zB–
rBdrd
rcjz 20)
1
–
7 –
z z
zz const r r
n re 1 re
2 2B Bdp ddr dr r
21)
to pinch – 1 1r zdiv B r rB r r B B z
1 0rr rB r 0rB
89
0Bdp d rBdr r dr
21
11 2r dr 2 2
0 0
1 Bdp dr dr rB r drdr r dr
22)
2 2 2
00 0 0
2B
k Tr dp r p prdr k T nrdr N 2
N – 2 Bp nk T
0p 2 2 8rB
2rB I c I – 2
2 2Bc k TN I 2
2 z 6
–
–
z –
z -
6 Willard Harrison Bennett 1987) –
90
4. - 0zj 0B
j– z
2
8zBp const 2
1
1
1
z
1) –
2 2
–
91
4.11 -
– –
1 – – – –
1
–
1 8
7 1977) – )
–
92
4.1 –
–
– – –
z
4.
z
4.
93
– 1010 – 10
4.3.
–
–
8 9
8 1919) –
190
9 1886 –
94
10
6 6
7
10 –
95
–
4.4.1
–
–
1 –
xz
– –
kg k –
4.14 – –
- –
- AF – gF –
11 – 12
11 Martin David Kruskal 2006) –
96
–
–
z
dr icMgveB
dr ecmgveB
dr i dr ev v
z
–
–
4.4. .
12 1997) –
) ) )
97
28mp p p B
~ 1 16
4.1
1 –
16
Tia v
Ti B iv k T M – a –
4.4. – z –
–
z 17
98
4.1
z
8 1 18
– Aa v Av B nM –
a –
4.18
4.4
99
4.4
12
8
4.5
2 7
–
4. .1 -
19 19
4.19
100
1 2 surfn H H j c )
19
– tear –
0x z 0x 0x
0x 0x y 20 z
20
exp i t ikz
16
226mBkc 6)
–
4. -
–
101
4. . 1
1 –
n x 0dn dx
z zB e B x
yz
1 ~ exp y zn i t ik y ik z
x 21 x z
yx 1n
x
4.
E yz B z x
2g s 27)
102
2
zs ci ce ee
y
kk
1
0
0
1 dnLn dx
2 0
0
1g
dngL n dx
L – ee
21 2 TevpgR R
28)
p – – R –
4.
2
–
–
y
0 0n n y – z 22 e iT T
~ exp x zn i t ik x ik z
e B e ep k T n
e iT T
103
22
z x zk k k
0ep en 29)
ep
0e
B e
n enk T
)
x x z zE i k e k e
y x
yE cv cB B x
y
0ii
n n vt
i en n
t t
0
0
1 1 dnL n dy
2)
yn y
0 0i i y y
dn nn v n v vy dy L
0e
yn nvt L
1) yv
en
0e B e en ck T nt eBL x
B e
xck T keBL
)
–
x
ci
104
Te Tez
mv vM k
xk
9
– 6 8
4.
4.
10 – 100
105
4.6
4.
2H H H H He n MeB H H H p MeB ) H H He n MeB
7 108
4.
2
4
– n –
n
rt PPP P – tP –
rP –
106
rtrt PPPPP0
0P –
rt PPP 10
2
0P AW n v 1 2A A W –
– v –
212CnPr
C 10 6 1/2 – nkPt
2 22 1 2 21AW v n k T n CT n
2 1 2
1
k Tn f TAW v CT
n )
107
n >10 T ~109 n 10 T ~2 108
4. –
– z
6
4. –
–
–
– –
–
2008) –
108
–
iT =12 n =10
7
4. torus –
16
–
– -
–
7
16 1997) — )
1966
109
– 7 e –
– 8
– ~10 12
Wendelstein 7
–
–
– – –
4.
110
17 18 10 10 9
1012 6 8 26
11
10 – 100
–
– –
7 108 p
p
– p –
p
–
9: 1 – –
- – -
p
17 1922 2001) –
1989)
18 – 2000)
111
– –
.
)
–
–
4.
112
4.
113
5
–
5.
–
–
5.1.1.
mE r t E i t i kr mE k
dvmn enE pdt
(
Tnkp B n – v –
0n div nvt
(
(
0 0 1Bvmn en E k T nt
( 1
114
10 0n n v
t (
1n – 01 nn
1n v E( ( 1mn mv :
0 0 1m m B mi mn v en E ik Tkn 1 0 0m mn n kv (
k
1m
mTe
ie kEkv
m k v (
mTkv BTe (
m Tem m
Te
k kE viev Em k v
(
m Tem m m
Te
k kE vie nj env Em k v
(
1
4 1 EH jc c t
(
ˆ4 i ij E E
c c c ( 7
EkEkk 7
/ /4
Te
ine ii E E Ec cmc k v
(
1 ˆj E ˆ
i ne m
ne m i 0
115
/ /41 1 p
TeTe
nek vm k v
(
/ / – mnep 4 –
0Ek7
4 ine ii E E Emc c c
(
41 1 1p
c
ne nm n
(
– 4 emnc –
–
4 41 1 pe pine nem M
/ / 1 pe pi
Te Tik v k v
04pi n e M –
/ /
0 0ˆ 0 0
0 0 (
z k ˆ k
– 0Tev
41 nem
(
Tekv Te phv k v
1
4 ne m p cn n
116
5. p
p
( ˆ EBc t
1 BEc t
( 14
1 H B
B E i t ikr
14
0ˆi k B i k E 0i k E ik B 0k c (
k :
0 0ˆk k E k kE k E k k B k E ( 16
14 0n k k
ˆ 0n n E n E E
E nEEE ||
||n E nE ||n n E n E 16
|| || / / || 0n E n E E E E
/ / || 0n E E ( 17
17 ||E E
/ / || 0E 0n E ( 1818
|| 0E / / 0
117
0En ( n
ck p ( 19
1
:
1ph
p
ck
; 1
1g pk c
k (
1
5. – –
p n
cn n
p
5.
–
5.
118
( / / ( ( 0pi
1p
Tek v
1p Te p Dk v k r (
5. / / (
Tekv k
lnD
p HN M
m
~ 1H p
lnD
p VlN
~ 1Vl p
(
/ /i j i j
ij ij
k k k kk k
k k (
/ / (
Te ik v
119
/ /p pTe
Te Te
k vk ik v k v
( 3
/ /
( 3
1 3 Tep
k v ( 4
Tekv
p
3 1 3p Te p Dk v k r ( 4
i
3l i
/ / / / / /li i i (
/ /
/ /
/ /
( 6
p D Te pr v
/ /p
p
p p Te
p
k v
/ /
/ /
18
p
D Dkr k r ( 6
4 6
3ph Te Dv v kr
00vk
0v
3 k –
120
3 3
5. –
– ph Tev v
p
Tev
Tev
Te ik v
5.
– –
Q
121
4
5. – –
– 10 3n f 2 – 8 34 10n 170f 3 – 7 31 10n f
– p Tea v
a –
122
4
4 p ka k – a –
p Tea v
1ka 1ka
5.
Tev ~e iT T
e iT T
0iT 4
0E
E
dv edt M
( 7
v –
0ii
n div n vt
( 8
4 i ee n n (
4 –
123
0eB e
en nk T
( 30
z
z zeT const 7 ( 30
en in 0
z v et M z
; 0 0in vnt z
; 4 i ee n nz
; 0eB e
en nk T
v in : v et M z
; 0in n et M z
in en
1 0piDz r t z
04pi n e M –
04D B er k T n e – i t ikz
:
1s
D
k ck r
(
s B ec k T M
–
/ / || 0E
/ /
0Te Ti pe pi Te Ti pi Te pe Tik v v k k v v v v
1 4Te Ti pe pi Te Ti pe pi Te Ti pi Te pe Tik v v k v v k k v v v v
0pi 0Tiv 1
pi
k s D pic r –
124
1Dkr phv k
5.
~ ~ 1i e Dn n k r (
sc 1Dkr
0 0sc p 0p 0 – –
0 B ep n k T 1 0~p n
0 0Mn
5.
Q
pi
5.1
125
5. – –
–
–
5.1
8 3
6
126
5.
c 0k v
ck v n n
5
( ˆ 1 4E E jc t c t c
Te phv v –
B z
mE t E i t
0dv em eE v Bdt c
( 34
34
0Dr
127
0x x yei mv eE v Bc
;
0y y xei mv eE v Bc
; ( 3
z zi mv eE 3 z
zz
ieEvm
( 36
x c y
xc
e i E Ev
m; c x y
yc
e E i Ev
m ( 37
c eB mc –
xv yv – xE yE
xE –
yE y x –
Evenj 0 ( 38
ˆ – 37 ( 38
0
0
0
0 0
c
c c
c
c c
i
e n im
i
( 39
38 7 4 E i E i Ec c c
( 40
4 ij
ij ij i ( 41
40
//
00
0 0
ii (
1 p
c
; // 1 p ; c p
c
( 43
128
4p ne m –
/ / 13
43 0B 0c 0
ij ij
B c 0 1
//
1 0 00 1 00 0
( 44
5.
1 :
n n E n E E
0n k k 0k c z y n
x16
//
x y
x z y y z z
y z y y z
n E i E
i E n E n n E
n n E n E
( 4
y zn n n
// // //sin cos 1 cos sin sin 0n n
( 46 k B
sinyn n coszn n n
n –
phv kk
( 47
////
gv e ek kk
( 48
129
/ /e e k
0c 0
46 n ( 49
5. ( 0
0( ||||
4| nn (
0 ( 0
(1n ( 1 1
4 0yn zn n
x
y
E i iE n
0zE (
( 1
1 1 1c P P cP P
c c c c
n (
P
c
kc
k 70n –
1 – c 0n :
1 4 P c c
p 0c
c
130
3 n c 1n
5. .
– c p – c p
2 ' – –
c
n n
n phv c n
1n
5.
y 46
// // 0n n (
// 0n n (
131
1 //n ; n (
4 yn n 0zn 0x yE E 0zE (
B B
0zE x
y
E i iE
(
( 43 n
1 p p
p c
n
1 1p p
UH UH
kc c
(
k 1 4 P c c
UH p c ( 60
UH UH p 0c
5. .
. –
132
60 1 UH
8 0c
p
5.2.5.
// // //sin cos 1 cos sin sin 0n n
p p c p c p c c p
p c p c
c k
1 1
1 4 cosp c p c p c
( k
sinyn n coszn n n
/ /
0;
0;
0
x y
x z y y z z
y z y y z
n E i E
i E n E n n E
n n E n E
0;
cos cos sin 0;x
y z
y z
E n
E n E n
E n E n
0xE y
z
Etg
E
0c p –
0 p
–
133
p 1 4 P c c
5. . – c p – c p . 1
2 –
0c
0c
ci ce pe
cosp
c
c k
134
cosc
p
k c
/ / cos
n
:
cosx
y
E iE
0zE
5.2
5.2
k
c UH
5.
135
5.
14
vMn p B Bt
(
83 n nvt
– ( 86 B v Bt
– (
p n const 1 –
0n n 0p p 0 zB B e 0v ( (
n p B v ( :
0 01
4vMn p B Bt
; 0 0n n vt
;
0B v Bt
; 0 0
p np n
( 64
v t v 64
:
0n n div ; 0B rot B ( 64 64
a b b a a b a b b a
0B const
0 0 0 0B B B B Bz
(
B – 64 –
136
0B
0B Bz
0zB B (
x y –
11 z
11 0B z
5.11
63
0
0 0
00 0 0
x z
x y z
y y yx xz z z
B BBe e e z xB B BB BB B BB B B
y z z x x y z yB
0 0 zBB B Bz
( 66
63 p 63 66
0 0 00
0 4 4 zp B BBMn n B
t n z ( 67
B 67 ( n – 64
0 00 0 4 4
B BMn pt z
( 68
0 0
0 0S
p pcMn
( 69
– 330 0
0 04 4AB Bcn M
( 70
– 68
137
s A Ac c ct z
( 68
– –
68 0B
//div divz
/ / / /
S Sc ct z z
; ( 71
S A Ac c ct z
(
71 ( //
5.
z 71 ( // //
Sct z
; ( 71
Act z
(
71 6
1Dkr
4B 4
0x y 0
z x 1
138
5.12
xz – 0k
– / / 0k
– x
5.3.3
( 1
0
0
4 1S
A
c pc B
( 73
sc 1 (
/ / 073
Act z
(
A Ac ct z
( 74
0
0B
1
xz x 1 1 0k
139
1 0z
Ac ( 0 sc
0p 8B
/ / 08B – p n const
– – 13
5.13
– – –
1 (
i t ikr
// // //S Sk c c k k ;
// // //A S A Sk c k c k c c k (
// sk c
k
// //A S Sk c k c k c k k ( 76 76
140
// 0S A S Ak c c c c k k ( 77 77
4 sinA S A S A Sk c c c c c c sin k
k ( 78
( –
–
1 4 sinph A S A S A Sv c c c c c c ( 79
( 0
////
gv e ek kk
0 //Ac k //Sc k ( 78
A sc c 71 (
k k 78
A Sc c k 0 ( 78 (
14 0sc
4 A S Ac c c
5.14.
141
5.3
5.3.
5.4
–
–
5.4
0zk v 0zk v zk –
0v zk k
0v k
142
0 phv v
1 0 phv v 1
1 t
0 0 0
sin ph phv t vv t v kv
( 80
5.15. –
0v–
– 0 0v –
0v k – 0v k
0 coskv ( 81
0 0k v 81
0 phv v 0
ph phv v
0phv v
3p k v (
143
31
phvv (
01 3p
Tev v ( 83
–
0 0zk v
c
5.4
q
v c
rad
R R v tqE r tc R
rad
v t RqB r tc R
( 84
0r r t
0r t q r r t – 0j r t qv r r t
0R r r t t t R c 0r t – tr R c – 6
0dv dt q m v B6
0R R cos sinL x c y cR e t e t
0c qB mc 0LR mv c qB
cd Rv t t tdt c
00 0 0 0 0
0c
RR R R R R R R t
R
sin
rad rad
qv t tE r t B r t
c R t ( 84
t – R
144
–
v t
( 84 v t sin t R t
: n n
c
1m v c
1c c
*cn
–
17 ( arccos v c –
5.1
5.4
145
*
/ /1 cosc
n
ph
nvv
n 8
*c // v c
v – –
phv –
( 88 */ / cosn n c
ph
v nv
( 88
n phv k *
// cos ckv n
*// 0ck v n ( 89
/ /v –
0n ( 81 // 0v
/ / 1k v // cos phv v
v
n ( 89
/ / 1k v // cos phv v
vn 89
/ /v
0n 89
ck v n ( 89 89
– n
146
5.4
5.4 e iT T
– 109 3
9
147
6
–
–
6.
6.
vvtv
tx
xv
tv
dtttrvd
i
i
i
R3
1
j env
–
148
04 expiB e
ee n nk T
6.
1
3
3 0sv v vc vt z z
v – sc –
1-2-3-4.
6.2 –
; –
–
1
149
3 3v z 31
0u uut z
2
2
3 3v z
–
– –
s
z Vt V –
2 2
2 02
d v vVvd
3
2 3
2 6v vv V 4
v –
– –
-
dv edt M
;
150
0ii
n div n vt
;
04 expiB e
ee n nk T
zz ut u –
dv v v z v vvdt t z t t z
v dv dvz d z d
v dv dvut d t d
0dv dv e du vd d M d
; 0ii
dn du n vd d
;
2
02 4 expiB e
d ee n nd k T
5
2
12v euv C
M; 2in v u C 6
C –
1 0C 2 0C n u
in
02 2
in un
u e M
5
2
02 2
14 exp1 2 B e
d eend k Te Mu
8
0 2
14 exp1 2 B e
ef enk Te Mu
2 204 2 1 2 expB
B e
ef d n Mu e Mu k Tk T
9
– u
–
– 2
151
2B ee k T Mu
3. -
u const
212B e B e B e
e e ek T k T k T
2
2 22
1 321 2
e eMu Mue Mu
22
0 2 22 2 2
1 1 3 142B e B e
ed en ed Mu k T k TMu
2BMu k T
6.1.4
2 2
2u u uut z z
11
2–
2 2u z
2
152
z
1-2-3-4-5
6.5
153
– –
M –
– 0M 2M
0 1M
0 1M
–
0 1M
6.7
–
154
–
6.1.6
– –
3 2
3 2u u u uut z z z
123
12
2 2
2 02
d u du uVud d
13
z Vt – V – 3 4 5
8
6.8 –
- - –
3
155
4
6.9.
–
u 12
–
–
4 24
156
ISEE5
6.1
6.1
6.
6.
2P E 2 2mP E
expmE E i t
0Rem m mj E en v 1 5
vEme
dtvd 1
–
5 No
157
2 2mm
m
i eEeEvm i m
1
220
2
mne
2 2 2
02 22 2
m mE e n EPm
1
0 032 B e eP n k T T 1
eT 0eT – – 03 2 B e ek T T –
0n –
P P 2
200 02 2
0
1 3 12 2
em B e
e
e n TE k T nTm
1
2
20
1m e
P e
E TE T
19
2 2
022
3 B eP
k T mE
e2
–19 m pE E 02e eT T
m pE E 2
158
6.
mE r t E r t
B c Et
mE r t E r t 0r t –trrtr 0
mE r rr
00m m m r r
E r E r r E
01 1
m m mdv e eE r t v B E r r t E t v E tdt m c m
2 v d r dt
2
021
m m md r e d rE r r t E t E tdt m dt
21
mE r 21
159
1 2r r r
12
02 md r e E r t
dt m 22
1 0
2meE r
r tm
1 2r r – 1r 2r
22
2 2 2m m
m meE eEd r e t E t t E t
dt m m m2
2 22 2 m m m me t E E t E E
m 23
–
22 2 2
2 2 2 22 m m m md r d r e E E E Edt dt m
24
21
2m m m m mE E E E E
2 2
22 2 24 m
d r e Edt m
25
2 2
22 24S m
d r eF m E rdt m
26
SF e 2
24meE r
rm
2 2 2
160
2
0 0 20
exp exp m
B e S
e r En r n nk T E
28
2 202
2
4 B eS
mk TE
e29
– . m SE E
29
6.
6
2
2 imv W 30
iW – 30
2 22
2
4 ii
mWE
e 31
2 2m iE E
eT19 B e ik T W 2 2
1m iE E 2 2 2 2
21 02 2
3 3 ii i B e
m mWE W k T
e e32
0B e ik T W 2 21i iE E
– m M
6.
43
2
2
S
P
EE
20
21
p B e
i i
E k TE W
12
21 0
4 13
S i
i B e
E WE k T
4 3~ ~ 10 10m M 2 2P SE E
0B e ik T W 2 21p iE E
B ek T – –
2 21S iE E– –
2 2 21P i SE E E
161
0B e ik T W
6.2
6.2
1
0 0r t a 0 0dr dt t b
6.
6.
2
241m
ne
n
162
6.11.
6 1 – 2 – 3 – 4 – 5 –
6 – – 8 – - –
11 – 12 – 13 – 14 – -
15 –
6.12
7 40=L 50=0P
=f 1110=n 3
6. v x t
2 2
2 22 2 0Te pv vv v
t x B e
Tek Tvm
2 2 2 2
p Tek v
2 2 2p Tek v
6 74 13
163
2 20
0
1p pn
n
0pv x t u x t i t
u t 0p
2 2
020 0
02
Tep
p
vu u ni ut x n
n m sE E
2
0 2m
s
En nE
2 2 20p Tek v
0p
m
m uE i
e
2
20 4 Te
unn v
2 2
0 22 2
0
02 4
pTe
p Te
vu ui u ut x v
u 2u
22
2 | | 0i qt z
36
– –
–
164
6.13
–1 2
1
exp 22 2
b ic z c tx t
qch b z c t 2
1 1 22 0b c c c
1c 2c – .
6.3
6.
8
6.4.1. l-s
l s – 1l 2l
s
1 2l l s 1 2l l sk k k
14
8
165
6.14 l s 1 –
– -
2l
1l
1l 2l
2l 1l s
m s
Te l
eEmv
mE 1 – s –
6.
20 –
12 1 2I X r X r dr
1X 2X
6.4
6.4
6.
166
6. 5
-
–
-
6.
–
X –
167
5
6.
–
6.5
168
7
– – –
–
–
7
4 –
0x0x – 7 1
z kx z
p
xE zE yH s yE xH zH
1 1 1mE r t E i t ikz x 0x ;
2 2 2mE r t E i t ikz x 0x ; 0;m mx mzE E E
2 0E k E
0k c 1 1 2 –
2 2 21 0k k 2 2 2
2 0k k
169
0E
mx mzkE i E
1 20 0z zE x E x 1 20 0x xE x E x
1 2mz mzE E
1 2
1
k
0 1
7 1 - – –
–
7 7 7
2 2 22 2
2 22p
p
k c 7 8
2 2 2
2
4 4 4 2 2 2
2
4 2p
p p
c k
c k c k 7 8
7 8 7 1 7 1– 7 1
0
170
–
–
1 7 8
1
7.2
7 2
z
E r t E r i tyz
11 dnLn dz
DL r
14 20 0E k z E 0k
c
20 0E E k z E
xyz
171
2 2202 2 0x x
xE E k z Ey z
;
2 2202 2
2 2202 2
0;y y y zy
yz z zz
E E E E k z Ey z y y z
EE E E k z Ey z z y z
xE s
yE zE p 1 s
x x yE r E z ik y 2
22 0x
z xd E k z Edz
2 2 20z yk z z k k
zk z const
x zE z A ik z
1zk L L
A zk
z xE z A z i z
2
LA
dzdA ~
dzd
Ldzd 1~2
2
z LA d dz z
zdA k Adz
2
2 zd dkdz dz
xE
0I
xdE dA di iA idz dz dz
;
1 p s
2 – –
172
022 2 2
2 2 2
II II
zd E d A dA d d di i i iA i A idz dz dz dz dz dz
1 zk L
2
2 0zdA k z Adz
0
z
zz
k z dz
02 2
2
dzdiA
dzd
dzdA
2 0zz
dkdA k Adz dz
A 0
z
AA zk z
0 0
1 21 z z
x z z yz zz
E z A i k z dz A i k z dz i t ik yk z
– 1A 2A –
– 0z
2 0zk
0 0
1 21 z z
x z z yz zz
E z B z dz B z dz i t ik yz
2 2z zz k z
1 0A
2 0A z
2~z zg mv E 0m zE A k z z
173
1 11 1 2 22 2 20 2 2
0
1 22
pz zzg y y
z z
k kv k z k k ck c k c k
constk
zkczk
Az z
zz
0
20~
0zk2
y zz k k
0yk k – z2z
yk
s
A
xdE dz
1 1 2 21 2
1 12 2
x z zz z
z zz z
dE dA A dk dA A dki k A i i k A idz dz k dz dz k dzk k
xE – 1A 2A
1 1 2 21 12 2
z z
z zz z
dA A dk dA A dki idz k dz dz k dzk k
7 24 2
1 1 2 21 22 2 2
x z zz z z z
z z
d E dA iA dk dA iA dki k k A i i k k A idz dz dz dz dzk k
1
1 1 2 2
2 2z z
z zz z
dA iA dk dA iA dki k i i k idz dz dz dzk k
6dA dz
2z
z
dA A dk idz k dz
1A 2A
174
2A 1A
– –
- s
z 0z 0z
s–
– – –
syz s
x
2 2 0B
z
175
2A
1A 1B Im 0
1 2A A
–
z
n
z
p
p
xE zE
xB
0j
0B ik z E
0k c
0B ik E
7
E E E ;
B B B B
0E ik B
20
1B k B B
176
2
01 0B B k B
z x 28
0
1 xz
BEik z y
0
1 xy
BEik z z
28
y t x yB r t e B z i t ik y
0
y
rot B dB dzik B
zdedz
0 00
x y z
x
y
e e ed dBrot B d dz edz dz
dB dz ik B
2
2 202
1 0yd B d dB k k Bdz dz dz
0B z const
28
0
yz
k BE
k z
0
resz
p resz
p–
–
L ( 0k L )
177
p z
z
LkE
zE mz
00 2
0k L
mE – – L –
p
0
2 0
–
p s
105
p
10
178
7.3
–
–
–
–
–
l s
–
20 0E E r k E
179
p
2
20 1 1P
2 20 0E E k E k r E
r
0 1E E E ~ nnE
0 0 2 0
0 0E E k E ; 1 1 2 1 2 0
0 0E E k E k E 0E
00mE E ik r 0 0mk E
1E
11E r E k ikr dk
r
r K iKr dK
0
0 0m mr E E K iKr ik r dK E K k iK r dK
0K K k
2 2 21 1 0 1 0 0mE k k kE k E ikr dk k E K k iK r dK
0
2011
220 kkEkEkkEkk m
K k k
0201
2220 kkEkkEkkkk m
01 kkEkEk m
180
20 0 1 02
1 02 2 2 20 0
mm m
k E k k k kE k kE k k E k kE
k k k k
021 0 2 2
0m m
k kE r k E k kE ikr dk
k k
–
mE
0k – 0k
r
– k
0k k
0K k k
0K k – 0k k d 2d K 02 k –
p
0 1
i1 4i 41
181
8
e
2 24 20e r 2 2
0r e mc –
V V n V enV
sc eP Bn B –
B
–
7.4.
–
182
T const
0n z 0 0n n z
2
0
Tev ei v n En m
4E en
;
04B j ik Ec
0E ik B
0j en v2
2 0Te
n ei j ev n Em
0
2 2
0Teev e nj i n Em
0
1
4n E
e 1
0 2 2
0
4Teiv e nj E i E
m 0
0 2 2
04Tev e n EB i E i Ec m c c
T Tev c 2 201 4 n z e m
2
00
TiB E ik z E
k
2 2
01 0TE E k z E
183
yE r E z ik y yz 2
2 202 0y x x
d k E k z Edz
;
22 2 2
02
222 2 2
02 2
1 0;zy y T y y y y
y zy z T y z
dEd k E k k E i k z Edz dz
dE d Ed k E ik k z Edz dz dz
– xE s –
yE zE p–
0k z 0y yn k k7
22 2 2
2
22 2 2
2
1 0;y zT y y y T
yzT y z y T
d E dEn E ind d
dEd E n E ind d
yE
zE 2
2 2 2 2 2 21 2 1
2 2
1 1 1 0yz z z zT T z z T z z
z z
nd E d E d E dEd dn n n Ed n d d d n d d
59
2
1z yn n 2 22z T yn n
– z0d dz
2 22 21 22 2 0z z z
d dn n Ed d
2
1 1 2 1 2 1 2 2 21
1 1z z
z
E A i A i n B i B in
0
zn d 1
1 p A 1 B
2
184
1zn k L
L –
2yn 2 2
T yn0 zE
1 zn
1) –
1 –
11 zn 3' –
2zn
A B
A B
3
2 2 21
1 1
1 z z zz z
z z
n n ndE nxd da b y ia ibd d dn n
1 1 2 1a A i A i 1 2 2 2b B i B i
1 21 1
dA dAx i id d
1 22 2
dB dBy i id d
zE
eT Tev 6 107T 2 10–
~ 10–
0 100L
185
321 zz z ndE nia ib
d
2 2
1 1
1z z
z z
n nx d dy a bd dn n
52 321
2zz z nd E na b
d
73 521
3zz z nd E nia ib
d
3 32 21 1z zz zn nn nd dx y a b
d d
5 53 32 21 1z zz zn nn nd dx y a b
d d
146 7 7 94 5 5 72 2 21 1 1
4z z zz z z zn n nd E n n nd dia ib ix iy a b
d d d
4 275 5 5
21 1 1 12 2 2 2
2 2
4 27 7 32 2 2
2 2 2 22 2
1
1 .
T yzz z z z
T z T z
T yz z z
T z T z
nnn n n nd d dx y ad n d n d
nn n nd d dbd n d n d
x yx y
zn 2
1 221
134
yz z
z
na dx b n nn d
; 2
22
134
y
z
n dy bn d
;
2 232
2 21 1 2
13 14
y yz
z z z
n nna dx bn n n d
; 2
13 22 2
134
yz
z z
nn b dy an n d
2 1T
1,2 1exp2
dA ix x
d 1,2 2exp
2dB i
y yd
1,2 1
2,1 121
exp 1 1 exp2 2 z
dA i d A id d n
186
3 31 2 1 22 2
1 2 2 25 51 1
1 1exp exp2 2
z z z zz z
z z
n n n nn nB i B in n
;
2 111 1 2 1 2,1 23 2 2
2 2
exp 1 1 1exp exp exp2 2
z
z T z
i ndB d A i A i B id d n n
p
0yn
z
0d d
21 0zn
2yn
22 0zn
2 2T yn
0
p
~ 1 0k L
0 zE yE
1 2i i
1 2i i
187
k p 0k
0yn ;
7 4
7.5 -
5–
l s
–
–
0zf v
–
188
-
10vv 1Bnn
-
0v
00 pB nn
000 Bpi nnn –
– Bn pn Bv pv
2
0
p Tep p
p
v ve n vt m n
5
–
0B
Bv ev vt m
6
189
0p
p p
nn v
t7
0 0B
B B Bn n v v nt
8
4 B Pe n n 9
rkititrf ~
00 vev z zx kkk 0 5
2
0
Tepz z p z
p
v ei v k n kn m
;
2
0
Tepx x p x
p
v ei v k n kn m
;
0z Bz zek v v km
;
0x Bx xek v v km
;
0
0z pz x px pp
k v k v nn
;
00
Bx Bx z Bz z
B
nk v k v k vn
;
2p Be n n k
22 2 2
20
1 1 0pTe B
z
k vi k v i
1
220
2 4 men pp22
02 4 menBB
1
0B 0
2 2 2 2
p Tek v 0p 0Tev
2 20z Bk v
z Bk v
1 24
4
190
–
k 0
0xk 5 1
2 2 2 2 2 2 2 2
2 20 0 0
1 1 1 1p Te p Te B pB Bk v k v
kv kv kv
0B
6
– 0vvTe
0B
6
– –
7
14
– 2
k 2 –
p 0vk p
5 k 0p v
0Tev v
xk 6 7 k
191
(0Tev v B p )
(0Tev v B p
–
Tev 2B –
2 2 2 2
2 20
1 0p Te Bk v
kv 4
0vkz
k 40kv 0kv 7
0kv
2
2 2 220 00 0 0
1 1 1 1 21 1kv kvkv kv kv
4 2 20
00
2 0B
kv5
192
2000 1 kv 2222
0 Tep vk
0 5 5 2 2
0B
0
Bi 6
6 2
0
B 6
0~ Bn 5
0 6
00
0 0
B
kv7
0Bj en v
2
4 0jt z
221 p
ikzti 04
Bev nk
0 eW
193
0
5 7
00
0 0
B
kv 0
00222
0 Tep kvkv2B
5
2
020
12
B kv 1
00kv 2
0
2B
11 1 1
2i
2
00~
2 2B
Bn 2
0Bn –
pkv0
0 5
02 22
0 ybxyxxf
0
x 0
0
kvy 0
Bb
xf 01x 02 yx0df dx
194
021 ybxf 20
2 yby
xf
xf xf
02xf
20 yby 5
b y 50 0
00 2
0 0
Bby kv
2000 1 kv
0 00
Bkv 6
0 phk v phv –
0
0 02B B
ph
vv
7
0
0 02B
p p
nvv n
7
0 phv v
0Tev 0
2 2 2
2 2p p p
p p pi iiv
8
1 2
2
20
Bp kv
9
k
195
0
1 B
p
kv
0
0 – 0p
– p
21k –
–
-
9 9
9
2
2d xm edt x
m kx
2
2mked x kx
dt m
1kx 2 0mex k x
m
mek
m
0
pkv
196
9 –
- –
10
-
-
Bv
kv ph Bph vv
197
kvB
~ 1Bk vN
zvf zvf
8
11 - ( 210 ttt )
– – 1t 2t
SS
- -
–
8
198
9 6
– 109
–
– bv
22
2 21 0pib
bkv
2 24pi ne M –
bkv
199
bkv 2
2221
b
pi bkv 105
2 0 22pi bkv
pi
0 Tev v
–
– k k
9
0 Tev v
0 Tev v
9
200
- 1 – –
– 4 –
–
0 Tev v
LU 0I 0 1Tev v I
– 1R
201
–
1
di tLEN dt
L – N – i t
1 Walter Rogowski 1947 –
202
RC
i t
–
dB dt– RC
203
–
–
1 – –
–
e M 2
2
204
e M
1 – –
1 2 – 2 – –
–
2 2 3H H He n MeB 2 3 4H H He n MeB
–
40
–
205
3 10
233 235 239Pu
8.1.5.
–
2
24crmn
e
n R
8.4
5–
–
206
8.5 –
dI
dx
0
ic s e
vdI n Idx
v
c i s – 0v – v – en –
L 0 1
0
lne
c i
I In
L v v
207
0I 1I – L
3
W W z const
R –
1 – – – –
V x x V W
0
12
V W dWx V
M V W
x R r – V x
22 2
2
2ciE B
M x R xV x V x V x qU x
R x
ci – W
V x – –
3
208
.1
–
8.2.1.
– –
fV floating –
–
–
0iu 0n
209
V x iu x
0iu
20
2i i
eV xu x u
M7
M –
V
en in
0 00
20
21
ii
i
i
u nn x nu x eV x
Mu
e iT TV x
0 expeB e
eV xn x n
k T 9
2
02 20
14 4 exp1 2
i eB e
d V eVe n n endx k TeV Mu
10
B eeV k T 204x n e k T x r
2
2 2
1 exp1 2
dd
10
0i B eu k T M –
s B e 10 0d d 0
2
22
1 21 1 exp 12
dd
11
2 0
210
2 2 22
2 4 21
2 2 2 12
1 –
1
11
211d
d 13
0 21exp 1 14
21exp 1f
xV x Vr
14
0x 0xfV ( 0fV –
1
14 9fV V 0x
14 0
20
02
1i
f
i
nneV
Mu
00 exp fe
B e
eVn n
k T 15
1f B eeV k T 15
0 20
0 1 fi
i
e Vn n
Mu 00 1 f
eB e
e Vn n
k T 15
20
f f
B e
e V e VMu k T
1
15
211
Bf
k TVe
7
1f B eeV k T 713
8.2 9
– –
–
–
0e in n n
sV space –
sV
p sV V V pV – probe –
e ii i i
8.9 –
–
8.10
212
Te Tiv v
sV V ei i
sV V
pV
pV
sV
fV V
fV V
pV
– 0i B eu k T M
maxB e
i sk TM
sn – p B eeV k T
2
0iu B ek T M2s B ek T e
sn
00 0
ss
B e
e nn n nk T
max 0B e
i Bk TM
0 exp4
pTeB
B e
eVen vk T
20
B e
Tek Tv
m–
213
ln i V eT
sV V
014sat Te 21
Tev eT sati
0n 1 l r –
2 3
02 22
td i edV m
22
2 p
t
e Vv
m 23
8.2
11
8.11
– V 11 E V x x –
214
2
2 10 3 5
2i eT T
fV sV BI satI
–
2 4 3 3 2 204 exp
3iH ff
i ebr B eB e
W Z gdW hn nd k Tk T
215
100 h mc – iHW –
Z – ffg –
Z
–
Z
1 – – – –
2 B e
hck T
4
eT
1Z
216
n 2 4
3 3 2 40
5
4 exp3
iH n fb ni e
rec B eB e
W Z g W hdW n nd k Tn k T
n nW h – n Z n – n fbg –
n
2
5 expn fbrec n
ff B ebr
dW d Z g WdW d n g k T
1Z 22n n
Z 2Z– 4Z
B ek T h
lg lgB e
dW hconst ed k T
e dW d
1 – –
217
i en n
4
im in i
i ii m n i iI A N
i im nA – iN –
i –
1 1 2
2
expB e
n W Wn k T
1 1
2 2
11 1 2
2 2
expm n
m n B e
AI W WI A k T
mnA
mnf
mnA
2mn
mnfA const
4
218
1 23 3
1 1 1 2 2 2lnB eW Wk T
I f I f
g
i i ii m m n i iI g A N
1 2 B eW W k T
im
0 i i ie m e e m m j
jn N T v N A
im eT – im 0N imN –
im jj
A
im imN
1 1 0i
i
i
m e ei m n e i m e e
m jj
T vI A N n const T v
A
11 1
2 2
1
2 2
m e em ne
m n m e e
T vAI C TI A T v
1
2
m e ee
m e e
T vT
T v1 1
2 2
m n
m n
AC
A
5 2P1/2
3P1/2 3/2
219
im eT
1 1m nA eC T
1 2I I5
8.3.3.
f vf c
2
00 2 2
0
expI I
0 – 0I – –
0
2 ln 2
vc
220
iT
0
22 ln 2 B ik Tc M
40
2
0
1i
B
McTk
0M M – 0M –
212
0iT K
B
2 2ce eBW
mc
2ceW g
g –
410B 3 50
510(30
221
8.3.4.
E
W E M
M –
–
– 1 3
ea Tev n M m 1 3
ia Tiv n
M
2 3
0E en
2 3
0W E n –
2 4 30W E n
Tet v
222
– – Tev –
opt Te optnv
opt
1 Tet v 2E e
0opt
Te
N r Nmv a
N r N – 2 20a me
–2
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