4/3/2017. PHY 712 Electrodynamics 9-9:50 AM MWF Olin 103
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1 PHY 7 Eleodnais 9-9:50 AM MWF Olin 0 Plan fo Leue 0: Coninue eading Chap Snhoon adiaion adiaion fo eleon snhoon deies adiaion fo asonoial objes in iula obis 0/05/07 PHY 7 Sping Leue 0 0/05/07 PHY 7 Sping Leue 0 0/05/07 PHY 7 Sping Leue 0
2 0/05/07 PHY 7 Sping Leue 0 Powe disibuion fo iula aeleaion / 5 / 5 d dp d P d dp adiaion fo haged paile in iula pah 0/05/07 PHY 7 Sping Leue 0 5 Speal oposiion of eleoagnei adiaion -- oninued / : on he following inegal inensi depends he speal When he dus leas, i e d I w w w 0/05/07 PHY 7 Sping Leue 0 6 Snhoon adiaion ligh soue insallaions Snhoon adiaion ene in Madison, Wisonsin E =05 GeV and GeV; l = 0 Å and 0 Å hp://wwwswisedu/
3 SC Aladdin -- Madison Wisonsin 0/05/07 PHY 7 Sping Leue 0 7 Bookhaen Naional Laboao Naional Ligh Soue E =06 GeV; l = 0 Å hp://wwwbnlgo/ps/ 0/05/07 PHY 7 Sping Leue 0 8 Spealinensi elaionship : I w w d Top iew: iw / e sin / os / os / sin / Fo oneniene, hoose: os sin 0/05/07 PHY 7 Sping Leue 0 9
4 sin / os / os / sin / Fo oneniene, hoose: os sin Noe ha we hae peious ε he Poning eo is in he hoose o anale wo ohogonal polaiai on dieions shown ha in he adiaion one, dieion; we an hen ε sin os ε sin / ε sin os / : 0/05/07 PHY 7 Sping Leue 0 0 ε ε ε ε sin os ε sin / ε sin os / d I w dwd iw ( ( )/ ) ( )e d d I w dwd C ( w) d sin( / ) e C ( w) C ( w) C ( w) d sin os( / )e iw ( os sin( / )) iw ( os sin( / )) 0/05/07 PHY 7 Sping Leue 0 We will anale his epession fo wo diffeen ases The fis ase, is appopiae fo an-ade snhoons used as ligh soues In his ase, he ligh is podued b sho buss of eleons oing lose o he speed of ligh ( ( / ( )) passing a bea line po In addiion, beause of he design of he adiaion pos, 0, and he elean inegaion ies ae lose o 0 This esuls in he fo shown in E 79 of ou e I is onenien o ewie his fo in es of a iial feuen w d I w w ( ) K / ( ) dwd w w w K / ( ) w 0/05/07 PHY 7 Sping Leue 0
5 K Soe deails: Modified Bessel funions d os / K d / sin 0 0 Eponenial fao w w os sin / In helii of 0, 0, w w w whee / w 6 and / 0/05/07 PHY 7 Sping Leue 0 d I w w ( ) K / ( ) dwd w w w K/ ( ) w B ploing he inensi as a funion of w, we see ha he inensi is lages nea ω ω The plo below shows he inensi as a funion of ω/ω fo γθ=0, 05 an d : d I dwd γθ= γθ=0 γθ=05 ω/ω 0/05/07 PHY 7 Sping Leue 0 The seond eaple of snhoon adiaion oes fo a disan haged paile oing in a iula ajeo suh ha he speu epesens a supeposiion of ligh geneaed oe an oplee iles In his ase, hee is an inefeene effe whih esuls in he speu onsising of disee uliples of / Fo his ase we need o eonside he analsis Thee is a e onenien Bessel funion ideni of he fo: ia sin i e J ( a)e Hee J ( a) is a Bessel funion of inege ode w In ou ase a o s and C ( w) d sin( / )e de iw os iw ( os sin( / )) iw ( os sin( / )) w = J os ( w ) iw os Sping 0/05/07 PHY Leue 0 5 5
6 Asonoial snhoon adiaion -- oninued: Noe ha: C ( w) d sin os( / )e i ( w ) de ( w ) w C ( w) i J os ( w ), dj ( a) whee J ( a) da Siilal: iw ( os sin( / )) an w = J os ( w ) / 0/05/07 PHY 7 Sping Leue 0 6 Asonoial snhoon adiaion -- oninued: In boh of he epessions, he su oe inludes boh negaie and posiie alues Howee, onl he posiie alues of w and heefoe posiie alues of ae of inees Using he ideni: J ( ) ( ) ( ), he a J a esul beoes: d I dwd w w an w ( w ) J os J os 0 / These esuls wee deied b Julian Shwinge (Phs e 75, 9-95 (99)) The disee ase is siila o he esul uoed in Poble 5 in Jakson's e Fo infoaion on an-ade snhoon soues, he following web page is useful: hp://wwwalslblgo/als/snhoon_soueshl 0/05/07 PHY 7 Sping Leue 0 7 6
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