ape 5. Lo Waes Wae e s o compaed ae dep: < < L π Fom ea ae eo o <<π s ; om oe dep z s ; ea a eca om zeo a e oom o a mamm a e sace ma ma >> s s ; amos ozoa moo z p s ; dosac pesse Dep-aeaed coseao o mass dz z s Lez e o eao dz dz
odc dep-aeaed eoces: dz dz e ae [ ] [ ] [ ] [ ] Leaz assm ae sma
Dep-aeaed eqao o moo : z p z z 444 4 3 444 4 z z ssm ozoa eoc ade s cosa oe dep so a ae aso cosa oe dep ad ea oe dep s Lez e dz dz dz z z odc coeco acos β ad β sc a β β dz dz dz e ae
[ ] [ ] [ ] z z β β z z β β β β z z z z ssm o co eqae o Ee eqao ad eaz O a oom e co eqao ecomes Deea espec o
Ss e eazed momem eqao ; ae eqao Ee H E F H H 4 H H
4 H H K K H s Gee s a
o-osca de H cos H cos cos H cos H cos ma H H cos cos ma H cos ma cos ma Fo e ode o ocae a π 3 cos o π L L 3 LL 4 4 Reaed opcs: Locao o aae es ad sce aes o da poe pa
Wae eeco om peoaed-a casso eaaes ae aae coss-secos Te eqaos desc e cae as ae ; F F s e emac oda codos o cae as ad F F e ae ; o ea co eqao oe dep ad cae d ddz z dz z d
s e emac oda codos o e as ad de e coss-secoa aeae eoc ~ d e ae dz z ~ ~ dz z [ ] ~ ~ ~ Leaz assm sma oom sope ad s LKFSB ; o ; Eqao o moo same as eoe Deea e co eqao... s e eqao o moo 5.36 eoo
E 5. J J H cos oe eampe: ssme o sad ae: cos Eq. 5.36 o cosa s Ss e assmed soo
cos m d d m d d m m d d d d m d d d d Besse eqao Te eea soo o e Besse eqao s m Y m J Sce as ms e zeo. Ts Y m J cos s e osoe oda codo H cos m J m J H cos
Sep poem Eaesce modes ae mpoa ea e sep 4 < < 4. osde o e poesse modes H H cos cos ε H cos ε Te mac codos a e sep ae a damc a emac So o e asmsso ad eeco coeces κ κ e case o >> κ : Pe sad ae Reo κ : Te ae o e same e as e sad ae s
asmed o Reo >> κ : No asmsso κ : F eeco pase s
Sec Sec s a oscao a as a s aa eqec sead o o da eqec H cos cos ; o L L s L T e ae L T Mea oma : damea o s mode mos doma See Tae 5. o eoo o aae coss-secos.
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T T T T cos cos d a a cos a cos T a cos cos d T L d To cacae a T T cos cos cosd T T a T T a a a cos a cos d cos L cosd T a cos cos cosd T Sma a T T cos cos cos d Eaa e eas a a 3π a a a 3 5π 5 a 4 M Keep o e s em
m m π π 3 cos 3 c s o ea. Te eazed eqao o moo s o m z π 3 ee 3 << m π o eqao: O a oom Deea... me Ss e eqao o moo
s om co eqao e ae Ts s e ae eqao oom co. Te secod em s e co em. ompae s Eq. 5.3 o eoo. ssme a ep[ ]. Ss o e ae eqao Te ae me s compe. Dee as e ae me o damp: π L Te ee
ae me o damp ae me damp o c e ae Le. Te maa pa es Rea pa es Fom ese o eqaos
4 So e qadac eqao ± Noe a ε ε << ε. Sce << e ae s oom co ceases L ad. O e oe ad No e ae ae ae Ts e ae ampde decas epoea.
[ ] ep ep ep ep ep ep π π π L L L
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co eq: Smpe case: θ -D poem ad sead sae Eqao o moo es Le ;.5 ~.3 Noe a s eae Te
osa dep: d d s e oda codo a e ae. Teeoe Le e ae <<
Sop oom: d d d d s d d d d d d Reca ad ea ae sso o s e oda codo ad a e ae [ ]
Teeoe cosa as
cd oos oce [ ] z z [ ] z z ee ω sφ oos paamee ω ea s oao speed π 4s 7.7 5 ads φ ade pose oe emspee eae soe emspee ssme a o sa coase so a ad eeee c s e o eqm sae. so assme a ds sa o o a -momem eqao es. Te e sθ >> W sθ
ssme a B so a d d Bsec B. Te Bsec Bsec B B B a a W sθ B W sθ B We ae oe eqao o o os ad B. To soe s eqao e B. Te B cos s B cos B B W sθ s e eaosp cos s W sθ B W sθ B Reca B W B sθ B B W sθ ad W sθ W sθ W W 4 s θ sθ W sθ
Fa W W s a s θ θ We sead sae s aceed ae a o me W S sθ No S S a odc o -momem eqao S S a cos θ S S θ cos a So o e assmpo o cosa sope.e. * * * * ee ad * * ae e Eq. 5. o eoo.