LmK2`B+H bbmKTiBQM- JQ/2H

M/ H;Q`Bi?K

jXR 1H2+i`QK;M2iB+ qp2 1[miBQM rBi? aQm`+2b

q2 rBHH BMi`Q/m+2 ?Qr iQ KQ/2H M QT2`iBM; ;v`Qi`QM BM iBK2 /QKBM BM 7QHHQr@

BM; b2+iBQMbX(Rk)(e)(Rj) Jtr2HHǶb 2[miBQMb BM :mbbBM mMBi `2

∇ · 1 = 4πρ UjXRV

∇ · " = 0 UjXR#V

∇ × 1 = − 1 c

∂"

∂t UjXR+V

∇ × " = 4π c C +1

c

∂1

∂t. UjXR/V

PT2`i2 ∇× QM UjXR/V- mb2 UjXR#V- UjXR+V M/ p2+iQ` i`BTH2 T`Q/m+i B/2MiBiv

∇ × (∇ × ") = ∇(∇ · ") − ∇²", UjXkV

M/ i?2M r2 Q#iBM

∇(∇ · ")

=y − ∇²" = 4π

c ∇ × C + 1 c

∂

∂t(∇ × 1)

=−¹_c^∂"_∂t

= 4π

c ∇ × C − 1 c²

∂²

∂t²", UjXjV Rd

Q`- i?2 BM?QKQ;2M2Qmb 2H2+i`QK;M2iB+ rp2 2[miBQM

q2 MHvx2 i?Bb 2[miBQM BM +vHBM/`B+H +QQ`/BMi2 M/ 7Q+mb QM i?2 z +QKTQM2Mi,

%1

h?Bb Bb MQi  2bv T`Q#H2K r?2M +m``2Mi i2`K C Bb T`2b2MiX q2 bbmK2 i?i i?2`2 Bb MQ bQm`+2 iQ ;2i i?2 T`2HBKBM`v FMQrH2/;2 Q7 +QH/ KQ/2 }2H/,

%1

iBQM Q7  +B`+mH` rp2;mB/2 rBi? mMB7Q`K rHH `/Bmb rw M/ rBi?Qmi rHH HQbb Ui.e.

ρ4 yV- Bz Bb 2bv iQ #2 bQHp2/ #v b2T`iBQM Q7 p`B#H2b K2i?Q/X 6Q` h1mn

KQ/2-Bz(r, θ, z, t) = Jm(kmnr)e^imθ(C+e^+ikzz+ C₋e^−ikzz)e^−iωt, UjXdV

r?2`2 C+ M/ C<sub>−</sub> `2 KTHBim/2b Q7 7Q`r`/ M/ #+Fr`/ rp2 `2bT2+iBp2Hv- m Bb BMi2;2`- Jm(x)Bb m@i? Q`/2` "2bb2H 7mM+iBQM M/ kmn= xmn/rw- xmnBb n@i? MQMx2`Q

`QQi Q7 J<sub>m</sub><sup>′</sup> (x) = 0X hQ bBKTHB7v 2tT`2bbBQM Q7 2H2+i`QK;M2iB+ }2H/b- T?vbB+H [mMiBiv UH27i@?M/ bB/2 Q7 UjXdVV Bb Q#iBM2/ 7i2` iFBM; `2H T`i Q7 T?bQ` U`B;?i@?M/ bB/2 Q7 UjXdVVX am#biBimi2 UjXdV BMiQ UjXeV M/ ;2i

% ∂²

h?2 /Bz2`2MiBH 2[miBQM Q7 "2bb2H 7mM+iBQM Bb U`2TH+2 x rBi? kmnrV

x² d²

>2M+2 UjX3V #2+QK2b

%ω²

c² − kmn² − k²z

&

B_z = 0. UjXRyV

_2KQp2 i`BpBH bQHmiBQM Bz = 0 M/ i?2M r2 ;2i i?2 /BbT2`bBQM `2HiBQM

ω² = ω_cmn² + c²k_z², UjXRRV

r?2`2 ωcmn = ckmn Bb +miQz 7`2[m2M+vX "2+mb2 Q7 Jtr2HHǶb 2[miBQM- i`Mbp2`b2 +QKTQM2Mib Q7 7Q`r`/ M/ #+Fr`/ h1mn KQ/2 2H2+i`QK;M2iB+ }2H/b b?QmH/ #2

"_⊥ =± ik_z

k_mn² ∇tBz UjXRkV

1_⊥ =− iω

ck²_mnˆ2z × ∇tBz, UjXRk#V Q`- BM KQ`2

/2iBH-Br =ikz

k_mnJ_m^′ (kmnr)e^imθ(C+e^+ikzz− C−e^−ikzz)e^−iωt UjXRjV B_θ =k_zm

k²_mnrJ_m(k_mnr)e^imθ(C₊e^+ikzz− C−e^−ikzz)e^−iωt UjXRj#V Er =− ωm

ck_mn² rJm(kmnr)e^imθ(C+e^+ikzz+ C₋e^−ikzz)e^−iωt UjXRj+V Eθ =− iω

ckmn

J_m^′ (kmnr)e^imθ(C+e^+ikzz + C₋e^−ikzz)e^−iωt. UjXRj/V

A7 rHH HQbb Bb BM+Hm/2/- Dmbi KQ/B7v k²_mn i2`K BM rp2 2[miBQM

k_mn² → kcmn²

%1− (1 + i) δ

r_w(1 + m² x²_mn− m²

ω² ω²_cmn)&

, UjXR9V

r?2`2 δ Bb bFBM /2Ti?X *QMbB/2`  bi`m+im`2 U+pBiv Q` iT2`2/ rp2;mB/2V rBi? MQM@

mMB7Q`K rHH `/Bmb rw(z)M/ rHH `2bBbiBpBiv ρ(z) HQM; x@tBb- `2H2b2 i?2 +QMbi`BMi QM iBK2 /2T2M/2M+2 e<sup>−iωt</sup>- M/ HHQr KmHiB@KQ/2 T`QT;iBQMbX A7 MQM@mMB7Q`KBiv Bb r2F 2MQm;? bm+? i?i KQ/2 +QMp2`bBQMb `2 M2;HB;B#H2- Dmbi KQ/B7v i?2 z M/ t

RN

/2T2M/2M+2b Q7 2H2+i`QK;M2iB+ }2H/b h?mb- 2H2+i`QK;M2iB+ }2H/b `2

Bz = + q2 i`2i +m``2Mi bQm`+2 i2`K b bbQ+Bi2/ #2K T2`im`#iBQM Ui.e. +QH/ KQ/2 2H2+@

i`QK;M2iB+ }2H/b TT`QtBKiBQMV- M/ bm#biBimi2 UjXReV BMiQ UjX8V M/ ;2i

_2# +

QM #Qi? bB/2b Q7 UjXRdV M/ BMi2;`i2 #v T`ib

r?2`2 r2 mb2/ UjXRe/V- UjXRe2V M/

' rw

TQM2Mi Q7 +m``2Mi /2MbBiv C_⊥ +QMi`B#mi2 iQ ;2M2`i2 Q` #bQ`# 2H2+i`QK;M2iB+ }2H/b Q7 h1 KQ/2bX

*m``2Mi /2MbBiv C(`, t) Bb Q#iBM2/ 7`QK KQiBQMb Q7 2H2+i`QMbX 1H2+i`QM #2K Bb BM@

D2+i2/ BMiQ BMi2`+iBQM `2;BQM 7`QK z = 0X M 2H2+i`QM Bb +?`+i2`Bx2/ #v Bib BMBiBH TQbBiBQM M/ KQK2MimK X0j^′ ≡ (ψ0, Pz0, φ0)j^′(6B;X jXR)X *m``2Mi /2MbBiv +QmH/ #2 /2MbBiv 7`QK  #mM+? Q7 2H2+i`QMb rBi? bBKBH` i`D2+iQ`B2b BM T?b2 bT+2 +M #2

kR

6B;m`2 jXR, h?2 2H2+i`QM Q`#Bi rBi? "@}2H/ BMbB/2  rHH `/Bmb rw +B`+mH` rp2;mB/2X SQbBiBQM M/ KQK2MimK Q7 i?2 2H2+i`QM BM +vHBM/`B+H +QQ`/BMi2 `2 U`-θ-xV M/ UP<sub>⊥</sub>, φ, P<sub>z</sub>VX h?2 2H2+i`QM T2`7Q`Kb +v+HQi`QM KQiBQM `QmM/ ;mB/BM; +2Mi2` HQ+i2/ i UrC, ψ- xV rBi?

G`KQ` `/Bmb rL = v<sub>⊥</sub>/Ωc = P<sub>⊥</sub>/meΩeX Ωc = Ωe/γ M/ Ωe = eBz0/mec `2 `2HiBpBbiB+

M/ `2bi 2H2+i`QM +v+HQi`QM 7`2[m2M+B2b `2bT2+iBp2HvX(e)

/2b+`B#2/ 2z2+iBp2Hv #v  K+`Q

T`iB+H2-Cj =− 1 r?2`2 Nbj Bb MmK#2` Q7 2H2+i`QMb Q7 j@i? K+`Q T`iB+H2X h?2M

' 2π iQ KQ/2H 2H2+i`QM #2K rBi? }MBi2 K+`Q T`iB+H2bX AM }MBi2 /Bz2`2M+2 iBK2 /QKBM

kk

U6.h.V K2i?Q/- iBK2 Tbb2b rBi? bi2T ∆t /Bb+`2i2HvX h?2`27Q`2- Ni`Mbp2`b2 K+`Q T`iB+H2b `2 BMD2+i2/ BMiQ BMi2`+iBQM `2;BQM i ∆t BMi2`pHbX *?`;2 BM+`2K2Mi 7i2`

QM2 BMD2+iBQM Bb

BM UjXk8V biBb}2b MQ`KHBxiBQM +QM/BiBQM

Ni`Mbp2`b2+

jt=1

W_jt = 1. UjXkeV

aQ 7`- r2 /Bb+mbb i?Bb KQ/2H BM Q`/BM`v +vHBM/`B+H +QQ`/BMi2 (r, θ, z, P<sub>⊥</sub>, φ, Pz, γ, t) r?B+? Bb bmBi#H2 iQ bQHp2 }2H/b QM +B`+mH` #QmM/`v +QM/BiBQMX >Qr2p2`-  KQ`2 mb27mH MHvbBb Bb #mBHi QM bHQr@iBK2 b+H2 +QQ`/BMi2 (rC, ψ, z, r_L, φ, P_z, γ, t)(6B;X jXR)X

TTHvBM; i?2 `2+m`bBQM `2HiBQMb M/ bmKKiBQM i?2Q`2K(6B;X jXk) Q7 "2bb2H 7mM+iBQM

J_m^′ (x) + m

6B;m`2 jXk, .B;`K Q7 i`BM;H2 7Q` bmKKiBQM i?2Q`2K Q7 "2bb2H 7mM+iBQMX

ˆ2_⊥ = p_⊥/v_⊥- ˆ2φ = ˆ2z × ˆ2⊥ M/ Asj = −sφ + (s − m)ψ + (m − ^s₂)π `2 mb2/X Ai Bb ?2HT7mH i?i i?2 T?b2 i2`K Q7 UjXk3V Bb 6Qm`B2` 2tTM/2/ BMiQ BM}MBi2 bBMmbQB/H

?`KQMB+b iQ ?M/H2 i?2 `2bQMMi ?`KQMB+X h?2 MQM@`2bQMMi ?`KQMB+b +QmH/ #2 i`2i2/ b MQBb2 i2`Kb Q` ;Bp2M mT BM +H+mHiBQMX .Bb+`2i2 7Q`K Q7 rp2 2[miBQM UjXkyV 7i2` mbBM; UjXk3V Bb

% ∂² r?2`2 i M/ p /2MQi2 i?2 H#2Hb Q7 mMB7Q`K bTiBH M/ i2KTQ`H ;`B/b `2bT2+iBp2HvX AM }MBi2 /Bz2`2M+2 K2i?Q/- r2 +QKTmi2 i?2 }`bi M/ b2+QM/ /2`BpiBp2 Q7 }2H/ #v BM7Q`KiBQM QM i?2 ;`B/bX

d

>2M+2

hQ bBKmHi2  Qb+BHHiQ`- i?2 `7 }2H/ ;`Qrb 7`QK  MQBb2 H2p2H iQ  bB;MB}+Mi

KTHBim/2X "2HQr  }2H/ i?`2b?QH/- }2H/ 7mM+iBQM f(Zi, tp)Bb /Bbim`#2/ #v  `M/QK

KTHBim/2 M/ T?b2 bB;MH 2p2`vr?2`2X h?2 7`2[m2M+v bT2+i`mK Q7  `M/QK bB;MH Bb  mMB7Q`K /Bbi`B#miBQM- r?B+? `2bmHib BM  2[mH TQr2` BMD2+iBQM i 2+? 7`2[m2M+v 7Q` 2+? KQ/2X h?2 #2K bbQ+Bi2/ T2`im`#iBQM Q7 bi`i@Qb+BHHiBQM KQ/2 Bb 7Q`K2/

7i2` /Bbim`#BM; M/ /2HBp2`B2b 2M2`;v iQ Bib }2H/bX

LQi2 i?i M2Bi?2` K+`Q T`iB+H2 MQ` rp2 +M KQp2 KQ`2 i?M QM2 bTiBH bi2T

∆z 7i2` QM2 iBK2 bi2T ∆tX hQ pQB/ MmK2`B+H 2``Q`- r2 b?QmH/ Q#2v *Qm`Mi bi#BHBiv +QM/BiBQM

c∆t

∆z < 1, UjXjjV

r?B+? HBKBib i?2 mTT2` #QmM/ Q7 iBK2 bi2T M/ BM~m2M+2b bBKmHiBQM T`Q+2bb iBK2X

jXk S`iB+H2@i`+BM; Q7 1H2+i`QM JQiBQMb

6`QK L2riQMǶb Hr Q7 KQiBQM d

dtS = −e(1 + p

c × "), UjXj9V

r?2`2 /2`BpiBp2 Q7 KQK2MimK M/ 2H2+i`QK;M2iB+ }2H/b +M #2 2tT`2bb2/ b d

1 = E_⊥ˆ2_⊥+ E_φˆ2φ

7i2` mbBM; UjXkdV@UjXkd+V- 2[miBQMb 7Q` KQK2MimK bT+2 `2 dP_⊥

JmHiBTHv !

(3.39a) + i(3.39b)" #v 2tT(φ − π/2) M/ i?2M r2 ;2i

re^iθ− rCe^iψ=−irLe^iφ, UjX9yV

Q`

rCe^iψ = irLe^iφ+ re^iθ. UjX9RV hF2 iBK2 /2`BpiBp2 iQ H27i@?M/ bB/2 Q7 UjX9RV- KmHiBTHv Bi #v 2tT(−iψ) M/ Q#iBM

drC

dψ/dt 2bBHvX h?2 iBK2 /2`BpiBp2 i2`Kb Q7 `B;?i@?M/ bB/2 Q7 UjX9kV `2 d

7i2` bm#biBimiBM; UjX9jV M/ UjX9j#V BMiQ UjX9kV- mbBM; UjXkdV@UjXkd+V- UjXj3V@

UjXj3+V M/ UjXjNV@UjXjN#V- 2[miBQMb 7Q` `2H bT+2 `2

drC

6`QK 2M2`;v +QMb2`piBQM- r2 ;2i dE/dt = mec²dγ/dt =−e1 · pX lbBM; UjXk3V

jXj S`iB+H2@BM@+2HH J2i?Q/ M/ q2B;?iBM; a+?2K2b

_2r`Bi2 UjXkNV Ai Bb BM+QMp2MB2Mi iQ mb2 UjXkNV #2+mb2 MQM@mMB7Q`K TQbBiBQM Q7  T`iB+H2 zj +M MQi

#2 Dmbi Ki+?BM; i?2 mMB7Q`K ;`B/ ZiX h?2 bBKTH2bi rv iQ Mbr2` i?Bb [m2biBQM Bb i?2 x2`Qi? Q`/2` r2B;?iBM; 7mM+iBQM M2`2bi@;`B/@TQBMi UL:SV

δ(z_j− Zi)→ 1 Bb 7Hb2X h?Bb K2i?Q/ Bb 7bi BM +QKTmiiBQM #mi MQBbv #2+mb2 /Bb+QMiBMmBiB2b Q7 T`iB+H2 /Bbi`B#miBQMX hQ +m`2 MQBb2 T`Q#H2K- }`bi Q`/2` r2B;?iBM; 7mM+iBQM T`iB+H2@

BM@+2HH USA*V Bb bKQQi?2` M/ rBi?Qmi /Bb+QMiBMmBiB2b BM T`iB+H2 /Bbi`B#miBQMX

δ(zj− Zi)→ 1 qB/i? Q7 T`iB+H2 /Bbi`B#miBQM #2+QK2b /Qm#H2- bQ /Q2b +QKTmiBM; iBK2X >Qr2p2`-r2 +M 2KTHQv H2bb K+`Q T`iB+H2b BM i?Bb `i?2` MQBb2H2bb K2i?Q/X  KQ`2 ~2tB#H2 r2B;?iBM; 7mM+iBQM Bb

r?2`2 Lcell Bb +2HH rB/i?X *?QB+2 Q7 Lcell Bb BKTQ`iMi iQ KF2  i`/2@Qz /2+BbBQM

#2ir22M +QKTmiBM; bT22/ M/ ++m`+vX

jX9 h`2iK2Mi Q7 i?2 1z2+i Q7 P?KB+ GQbb2b

_2r`Bi2 UjXkNV ;BM

*QMbB/2`BM; i?2 P?KB+ HQbb- k²_mn BM H27i@?M/ bB/2 Q7 UjXkNV b?QmH/ #2 KQ/B}2/ b 7QHHQrbX

h?2`2 `2 irQ KDQ` 2z2+ib Q7 HQbb 7+iQ` BM rp2 2[miBQMX 6B`bi- HQbb 7+iQ` /2@

+`2b2b `2H T`i Q7 k<sup>2</sup><sub>mn</sub>- bQ `7 }2H/ T`QT;iBM; BM  HQbbv rp2;mB/2 Bb Dmbi HBF2 BM  H`;2` rp2;mB/2 rBi? rHH `/Bmb rw BM+`2b2/ #v  72r bFBM /2Ti? δX a2+QM/- HQbb 7+iQ` T`QpB/2b BK;BM`v T`i 7Q` k_mn² X >2M+2- BM  bQm`+2 7`22 +b2- 2Bi?2` rp2 7`2[m2M+v- rp2 MmK#2`- Q` #Qi? TQbb2bb BK;BM`v T`iX AM Qi?2` rQ`/b- `7 }2H/ Bb

ii2Mmi2/ BM  HQbbv rp2;mB/2X "mi ii2MmiBQM i2`K BM  rp2 2[miBQM b?QmH/

rQ`F b }`bi iBK2 /2`BpiBp2 Q7 }2H/X

% ∂² r?2`2 ω Bb 2tT2+i2/ rp2 7`2[m2M+vX AM+Hm/BM; P?KB+ HQbb 2z2+i M/ mbBM;

∂

∂tf_i^p = f_i^p+1− fi^p−1

2∆t , UjX8kV

kN

/Bb+`2i2 7Q`K Q7 rp2 2[miBQM #2+QK2b

hQ bBKmHi2 M Qb+BHHiQ`- r2 BKTQb2 QT2M #QmM/`v +QM/BiBQMb r?B+? HHQr `7 }2H/b iQ Tbb i?Qm;? i?2 2M/b Q7 BMi2`+iBQM bi`m+im`2 rBi?Qmi `2~2+iBQMX #bQ`#BM;

#QmM/`v +QM/BiBQM U"*V- M 2z2+iBp2 K2i?Q/ iQ `2/m+2 bTiBH K2b?2b- Bb 2bv iQ BKTH2K2Mi #2+mb2 r2 H`2/v BM+Hm/2 P?KB+ HQbb BM Qm` KQ/2HX Cmbi 2ti2M/ i?2 2M/ Q7 BMi2`+iBQM bi`m+im`2 rBi?  mMB7Q`K rp2;mB/2 M/ BM+`2b2 rHH HQbb Q7 Bi bHQrHv iQ T`2p2Mi `2~2+iBQM #27Q`2 2t?mbiBQMX _2~2+iBQM Q7 "* b?QmH/ #2 #2HQr

@8y /" KQM; TQbbB#H2 7`2[m2M+B2bX

在文檔中 繞軸旋轉電子束產生兆赫波電子迴旋脈射機制研究 (頁 27-40)