jX8 SQr2` *H+mHiBQMb

6B`bi- r2 +QMbB/2` i?2 M2i TQr2` Q7 `7 }2H/ #v BMi2;`iBM; SQvMiBM; p2+iQ` Qp2`

+`Qbb b2+iBQMH `2X

lbBM; UjXReV@UjXRe2V- r2 Q#iBM

1 × "^∗· ˆ2^z = ErB_θ^∗− E^θB_r^∗

am#biBimi2 UjX88V BMiQ UjX89V M/ ;2i

lM/2` bbmKTiBQMb i?i i?2 bi`m+im`2 Bb r2FHv MQM@mMB7Q`K- 7`2[m2M+v Bb #Qp2 +miQz 7`2[m2M+v- M/ `7 }2H/ /Q2bMǶi ;`Qri? iQQ 7bi- r2 +M BM72` i?i*

tX hF2 z M/ t /2`BpiBp2b iQ UjX8NV

fmn,z ≃ ikzr

aQHp2 fmn+ M/ fmn−

am#biBimi2 UjXeR#V M/ UjXejV BMiQ

UjX8dV-P_net^mn ≃ −x²_mnKmn

w_f^mn= w^mn_E + w^mn_B = x²_mnKmn TQr2` T2` mMBi H2M;i?

dP_net^mn

dz =−x²_mn

8 Kmn_2#

f_mn,tz^∗ fmn,z+ f_mn,t^∗ fmn,zz

$. UjXe3V

lbBM; i?2 rp2 2[miBQM UjXkNV- b2+QM/ i2`K Q7 UjXe3V +M #2 2tT`2bb2/ b x²_mnKmn am#biBimi2 UjXeNV BMiQ

UjXe3V-dP_net^mn

TQr2` /2TQbBi2/ #v #2K

= 0 UjXdkV

*QKT`2 iQ 2[miBQM Q7 +QMiBMmBiv-dW

dt ++

P = 0, UjXdjV

r?2`2 W M/ P `2 2M2`;v M/ Qmir`/ TQr2` ~mt `2bT2+iBp2HvX p^mn_Ohm Bb P?KB+

TQr2` HQbb T2` mMBi H2M;i?

p^mn_Ohm=−x²_mnKmn

8 k_mn² ∆_2#

(1 + i)f_mn,t^∗ fmn

$. UjXd9V

jXe h?2 aBM;H2 KQ/2 bbmKTiBQM Q7 hBK2@BM/2T2M/2Mi bBKmHiBQMb

Hi?Qm;? i?2 KmHiB@KQ/2 iBK2@/2T2M/2Mi SA* +Q/2 Bb TQr2`7mH iQ BMp2biB;i2 KQbi Q7 T`Q#H2Kb +QM+2`MBM; i?2 ;v`Qi`QMb- Bi Bb p2`v iBK2@+QMbmKKBM; iQ ;2i

`2bmHiX h?2`27Q`2- #27Q`2 iBK2@/2T2M/2Mi bBKmHiBQM- iBK2@BM/2T2M/2Mi bBKmHiBQMb

`2 2+QMQKB+H iQ Q#iBM bQK2 BM7Q`KiBQMb bm+? b i?2 bi`i@Qb+BHHiBQM i?`2b?QH/ Ist -i2KTQ`H ;`Qri? `i2 ωiM/ bim`i2/ 2{+B2M+v ηout M/ +Q``2bTQM/BM; T`K2i2`bX h?2 QMHv i?BM; r2 ?p2 iQ /Q QM i?2 T?vbB+b Bb iQ KF2 ?`KQMB+ iBK2@

/2T2M/2M+2 bbmKTiBQMX >2M+2 i?2 }2H/ 7mM+iBQM #2+QK2b

f (z, t) = F (z)e^−iωt. UjXd8V

lM/2` i?Bb bbmKTiBQM- Bi Bb KQ`2 +QMp2MB2Mi iQ BM+Hm/2 i?2 }2H/ T?b2 BMiQ i?2 2z2+iBp2 T?b2 BM i?2 2[miBQMb Q7 T`iB+H2 KQiBQMbX

e^{−i ˜}^As = e^−iAse^−iωt UjXdeV

h?2 2z2+iBp2 T?b2 #2+QK2b ˜As = ωt− sφ + (s − m)ψ + (m − s/2)πX h?2 `i }2H/b

`2 2pHmi2/ BM mMB7Q`K z ;`B/b- r?2`2b i?2 T`iB+H2b `2 2pHmi2/ BM mMB7Q`K iBK2 bi2TX b `2bmHi- i?2 TQbBiBQMb Q7 T`iB+H2b `2 MQi Dmbi Ki+?BM; i?2 mMB7Q`K z ;`B/bX AMbi2/BM; Q7 SA* K2i?Q/ r2 /QTi2/ #27Q`2- 7Q` [mbB@biiB+ bii2 M/

iBK2@BM/2T2M/2Mi bBKmHiBQM- Bi Bb 2bB2` iQ 2pHmi2 i`D2+iQ`B2b Q7 T`iB+H2b QM i?2 mMB7Q`K z bi2TX "2+mb2 tBH p2HQ+Biv Q7 i?2 2H2+i`QM vz Bb Hrvb Km+? H`;2` i?M x2`Q Ui?2 Q`/2` Q7 K;MBim/2 Q7 2H2+i`QM p2HQ+Biv Bb #Qmi bT22/ Q7 HB;?i

cV-dX dz = dt

dz dX

dt = 1 vz

dt , UjXddV

r?2`2 X Bb QM2 Q7 i?2 2H2+i`QM TQbBiBQMb Q` KQK2MimKbX L2ti- `2r`Bi2 UjXkNV

h?2`27Q`2- e^iAs BM bQm`+2 i2`K #2+QK2b e^{i ˜}^As b r2HHX 6Q` iBK2@BM/2T2M/M2i +Q/2 rBi? ?`KQMB+ iBK2@/2T2M/2M+2- i?2 +H+mHiBQM Q7 iBK2 2pHmiBQMb Bb mMM2+2bb`vX q2 bQHp2 Bi b #QmM/`v +QM/BiBQM T`Q#H2KX i i?2 2H2+i`QM #2K 2Mi`M+2- M BMBiBH ;m2bb Q7 }2H/ KTHBim/2 %F (z = 0)% M/ 7`2[m2M+v `2 BMTmi2/ M/ +H+mHi2

M/ BMi2`;i2 7QHHQrBM; rp2 2[miBQMb

bi2T MmK#2`X E22T bQHpBM; i?2 }2H/b HQM; z mMiBH MQi?2` #QmM`v- r?2`2 }2H/b biBb7v Qmi;QBM; #QmM/`v +QM/BiBQM b r2HHX

F^′(z = L) =

AM T`+iB+2- 7Q` ;m2bb 7`2[m2M+v ω- r2 2tT`2bb #Qp2 2[miBQMb b 7QHHQrb

D(ω) =

⎧⎪

⎪⎪

⎨

⎪⎪

⎪⎩

F^′(z = L)− ikzF (z = L), B7 ω > ωc

F^′(z = L) + κzF (z = L), B7 ω < ωc.

h?2 Qmi;QBM; #QmM/`v +QM/BiBQM Bb biBb}2/ rBi? bm{+B2Mi bKHH D(ω)- r?B+? +QmH/

#2 ++QKTHBb?2/ rBi? bQK2 `QQi@}M/BM; H;Q`Bi?KbX

AM bmKK`v- iQ T2`7Q`K bBM;H2 KQ/2 iBK2@BM/2T2M/2Mi bBKmHiBQM- i?2 }2H/b

`2 KQ/B}2/ b

f (z, t) → F (z) UjX3yV

∂

∂zf (z, t) → d

dzF (z) UjX3y#V

∂

∂tf (z, t) → − iωF (z), UjX3y+V

i?2 2z2+iBp2 T?b2 Bb

As→ ωt + As = ωt − sφ + (s − m)ψ + (m − s

2)π, UjX3RV

BMi2;`i2 #Qi? }2H/b M/ T`iB+H2b BM mMB7`QK z bi2T M/ bQHp2 7`2[m2M+v ω rBi?

`QQi@}M/BM; H;Q`Bi?KX

**jXd ++2H2`iBM; *H+mHiBQMb 7`QK i?2 H;Q`Bi?@**

**KB+ *QM+2Ti**

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+mHiBQM rBi? ;`2i MmK#2` Q7 7mM+iBQM +HHbX q2 +M T`2T`2 i#H2 UM ``v BM T`+iB+2V }HH2/ rBi? T`2+QKTmi2/ pHm2b Q7 7mM+iBQMb r?B+? `2 +HH2/ 7`2[m2MiHv /m`BM; bBKmHiBQMX 7i2` T`2T`iBQM- i?2 +Q/2 `mMb b mbmH mMH2bb 7mM+iBQM +HHbX

AMbi2/ Q7 +HHBM; 7mM+iBQM- r2 HQQF mT 7mM+iBQM pHm2b BM i?2 T`2+QKTmiBM; i#H2 iQ bp2 +QKTmiiBQM iBK2X Ai Bb +QMp2MB2Mi M/ MQ /B{+mHiv iQ KQ/B7v +Q/2 rBi?

i#H2 HQQF@mT H;Q`Bi?KX h?Bb K2i?Q/ +M #2 `2+Q;MBx2/ b `2TH+BM; +Tm `mMiBK2 +H+mHiBQM rBi? K2KQ`v ++2bbX qBi? bm{+B2Mi K2KQ`B2b- i?2 Hii2` Bb Km+? 7bi2`

i?M 7Q`K2`X

AM Qm` KQ/2H- Bi bT2M/b KQbi Q7 +QKTmiiBQM iBK2 QM +H+mHiBM; T`iB+H2 i`D2+@

iQ`B2b- r?2`2 Bb 7Q+mb2/ iQ ++2H2`i2 bT22/ Q7 +H+mHiBQMX q2 M22/ 2B;?i pHm2b Q7

"2bb2H 7mM+iBQMb iQ +H+mHiBM; /BbTH+2K2Mib Q7 T`iB+H2 BM `2H M/ KQK2MimK

bT+2b 7Q` bBM;H2 KQ/2 7i2` QM2 iBK2 bi2T- r?B+? `2 Js, Js+1, Js−1, J_s^′, Js−m, Js+1−m, Js−1−m

M/ J_s^′_−mX 6Q` ivTB+H +H+mHiBQM Q7 ;v`Q@KQMQi`QM BM h>x `2;BK2 rBi? /m`iBQM Q7 R-yyy Mb- Qp2` Ry⁴ T`iB+H2b `2 +QMbB/2`2/ rBi? Qp2` Ry⁷ iBK2 bi2TbX

h?2`27Q`2-"2bb2H 7mM+iBQMb `2 +HH2/ Qp2` Ry¹¹ iBK2b 7Q` bBM;H2 KQ/2 +H+mHiBQM5

L2ti- r2 i`v iQ `2/m+2 i?2 mb;2 Q7 K2KQ`vX h?2 7Q`KmH Q7 "2bb2H 7mM+iBQM 7Q`

}`bi /2`BpiBp2 Bb

J_p^′(x) = 1 2

Jp−1(x)− Jp+1(x)&

, UjX3kV

r?2`2 p Bb s Q` s − mX >2M+2- i#H2 rBi? Js(kmnrL)- Js−1(kmnrL)- Js+1(kmnrL )-Js−m(kmnrC)- Js−1−m(kmnrC) M/ Js+1−m(kmnrC) Bb 2MQm;? iQ ;2i HH 2B;?i pHm2b Q7 #Qp2@K2MiBQM2/ "2bb2H 7mM+iBQMbX

LmK#2` Q7 ;`B/ TQBMib Bb +?Qb2M #v Ryyy iBK2b `/BH KQ/2 BM/2t nX 6B;X jXj /BbTHvb pHm2b Q7 "2bb2H 7mM+iBQMb M/ i?2B` 2``Q`b pb x 7Q` m = 3 M/ n = 18 rBi?BM 0− xmn- r?B+? BM/B+i2b i?i 2``Q` Bb #2HQr Ry⁻⁶ rBi? R3-yyy ;`B/ TQBMibX

h?2 `M;2 Q7 `;mK2Mi Q7 "2bb2H 7mM+iBQM Bb #2ir22M y M/ kmnrw = xmnX ++Q`/@

BM; iQ i?2 bHQr@p`BiBQM T`QT2`iv Q7 ;mB/BM; +2Mi2` `/Bmb rC- r2 /Q MQi M22/ H`;2

`M;2 Q7 kmnrCX i i?2 bK2 iBK2- G`KQ` `/Bmb rL p`B2b /`biB+HHv +QKT`BM;

0 10 20 30 40 50 pHm2b Q7 "2bb2H 7mM+iBQMb i R3-yyy BMi2;2` ;`B/bX h?2M +H+mHi2 pHm2 i ?H7@BMi2;2`

;`B/b #v HBM2` BMi2`TQHiBQM- M/ +QKT`2 i?2K rBi? ++m`i2 pHm2bX 1``Q` Bb Q#iBM2/

7`QK #bQHmi2 pHm2 Q7 /Bz2`2M+2 #2ir22M BMi2`TQHiBQM pHm2 M/ ++m`i2 pHm2X

iQ rCX >Qr2p2`- kmnrL +M #2 2tT`2bb2/ b i?2 rp2 T`QT;iBQM +QM/BiBQM M/ i?2 +QMbi`BMi Q7 bT2+BH `2HiBpBivX Gbi i2`K Bb #Qmi s #2+mb2 Q7 #2K@rp2 bvM+?`QMBx2/ +QM/BiBQMX h?2`27Q`2- r2 HKQbi /2i2`KBM2 i?i mTT2` #QmM/ Q7 kmnrL Bb s- r?B+? Bb Km+? bKHH2` i?M xmn U≃ 83X3 7Q` m = 3 M/ n = 18V 7Q` i?2 ?B;? Q`/2` KQ/2X

**jX3 ++2H2`iBM; *H+mHiBQMb 7`QK i?2 S?vbB+H**

*QM+2Ti

h?2 QT2M@2M/ +pBiv- r?B+? Bb +QKKQMHv miBHBx2/ b i?2 ;v`Q@KQMQi`QM- Bb +QK@

TQb2/ Q7 irQ `2~2+iBp2 #QmM/`B2bX PM i?2 bB/2 Q7 i?2 2H2+i`QM #2K 2Mi`M+2- i?2`2 Bb mbmHHv +miQz b2+iBQM iQ ;2i Ryy W `2~2+iBQMX 6B;X jX9 b?Qrb i?i `7 }2H/b

#2ir22M z = 0.0 − 0.3 +K Bb HKQbi x2`Q- bQ Bb i?2 #2K bbQ+Bi2/ T2`im`#iBQMX h?Bb bm;;2bib B;MQ`BM; i?2 #2K@rp2 BMi2`+iBQM ?2`2 M/ b?B7i i?2 2H2+i`QM #2K 2Mi`M+2 iQ z = 0.3 +KX 6QHHQrBM; i?Bb i`B+F- +QKTmiBM; iBK2 Q7 bBKmHiBM; T`iB+H2b

#2+QK2b RXN +KfkXk +K ≃ 3eXj WX Ai Bb rQ`i? MQiBM; i?i- rBi? iT2`2/

"@}2H/-tBH M/ i`Mbp2`b2 p2HQ+BiB2b Q7 M 2H2+i`QM #2K +?M;2 HQM; TQbBiBQM z 2p2M i?Qm;? i?2`2 Bb MQ `7 }2H/bX h?2`27Q`2- BMBiBH #2K T`K2i2`b b?QmH/ #2 +Q``2+i2/

b r2HHX

**jXN amKK`v Q7 :v`Qi`QM@`2Hi2/ *Q/2b**

lT iQ MQr- i?2`2 `2 MmK2`Qmb bim/B2b QM i?2 ;v`Qi`QM BM T`Q72bbQ` ErQ@_v

*?mǶb ;`QmTX h#H2 jXR b?Qrb i?i HH ;v`Qi`QM@`2Hi2/ +Q/2b BM Qm` ;`QmTX 6`QK 2`HB2` bim/B2b QM i?2 HBM2` bi;2 Q7 ;v`Q@KQMQi`QMb #v oHbQp 2[miBQM- iFBM; i?2

+imH bi`m+im`2b BMiQ +QMbB/2`iBQM- mT;`/2BM; T`iB+H2 i`D2+iQ`B2b iQ i?2 MQMHBM2`

bi;2 M/ ;2i iBK2@/2T2M/2Mi BMp2biB;iBQM- +T#BHBiB2b Q7 bBKmHiBQM Bb 2M?M+2/

#mi +QMbmKBM; iBK2 /`;b HQiX 6Q` ++QKTHBb?BM; Qm` ;QH BM M 2+QMQKB+H iBK2-Bi Bb #2ii2` iQ mM/2`biM/ bbmKTiBQMb M/ mb;2b Q7 2+? +Q/2 M/ iQ /QTi i?2

`B;?i QM2X

h#H2jXR,"`B27BMi`Q/m+iBQMbQ7HH;v`Qi`QM@`2Hi2/+Q/2bBMi?2Qb+BHHiQ`ivT27`QKT`Q72bbQ`ErQ@_v*?mǶb;`QmTXLQi2i?i+Q/2bH#2H2/ rBi?∗`2MK2/#vK2#2+mb2Q7H+FBM;mMB}2/MK2bX }H2MK2i`2iK2MiQ7T`iB+H2bKQ/2bbmKTiBQM/QKBMivT2iBK2@/2T2M/2M+2#QmM/`v+QM/BiBQMbQHp2/[mMiBiB2bBM`QQi@}M/BM; +pBivMQbBM;H2KQ/2i2KTQ`HiBK2@BM/2T2M/2MiQmi;QBM;rp2ωU+QKTH2tV `7bkMQbBM;H2KQ/27`2[m2M+viBK2@BM/2T2M/2MiQmi;QBM;rp2Γ(z=0)U+QKTH2tV [Tpb#-[TpbpHBM2``2HiBpBbiB+oHbQp2[MXbBM;H2KQ/27`2[m2M+viBK2@BM/2T2M/2MiB/2H+pBivMQ ;v`QKQMQi`QM∗ `2HiBpBbiB+/vMKB+bbBM;H2KQ/27`2[m2M+viBK2@BM/2T2M/2MiB/2H+pBivMQ HBM2`Bbi∗ HBM2``2HiBpBbiB+oHbQp2[MXbBM;H2KQ/27`2[m2M+viBK2@BM/2T2M/2MiQmi;QBM;rp2ωU`2HV-Ist HBM2`rB∗ HBM2``2HiBpBbiB+oHbQp2[MXbBM;H2KQ/2i2KTQ`HiBK2@BM/2T2M/2MiQmi;QBM;rp2ωU+QKTH2tV ;QbBK`2HiBpBbiB+/vMKB+bbBM;H2KQ/27`2[m2M+viBK2@BM/2T2M/2MiQmi;QBM;rp2ωU`2HV-|F(z=0)| TB+bBK`2HiBpBbiB+/vMKB+bKmHiB@KQ/2i2KTQ`HiBK2@/2T2M/2Mi"*Qmi;QBM;rp2MQ 9y

0.0 0.5 1.0 1.5 2.0 0.1

0.2 0.3 0.4

rw(cm)&|f|

0.0 0.5 1.0 1.5 2.0

0.1 0.2 0.3 0.4

rw(cm)&|f|

0.0 0.5 1.0 1.5 2.0

z (cm) 0.1

0.2 0.3 0.4

rw(cm)&|f|

TE⁽³⁾_3,18,1

TE⁽²⁾_2,12,5

TE⁽¹⁾_1,6,8

6B;m`2 jX9, h?2 rHH `/Bmb `rM/ }2H/ T`Q}H2 pb TQbBiBQM z Q7 h1⁽³⁾_3,18,1- h1⁽²⁾_2,12,5- h1⁽¹⁾_1,6,8 KQ/2b i i?2B` Qb+BHHiBQM i?`2b?QH/bX h?2 bBM;H2 KQ/2 iBK2@BM/T2M/2Mi bBKmHiBQM Bb 2KTHQv2/X h?2 Tm`TH2 p2`iBH /b? HBM2 /2MQi2 i?2 TQbBiBQM Q7 z = 0.3 +KX

*?Ti2` 9

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 40-52)

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*?Ti2` 9