ビーム物理_第４回.key
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1 !
2 !
3 PART IV Synchrotron Radiation 1. Generation of Synchrotron Radiation! 2. Effects of Synchrotron Radiation on Beams
4 I. Generation of synchrotron radiation I. Maxwell Feynmann II. Syncrotron III. II. Effects of synchrotron radiation on beams I. II. III.
5 K-J.Kim s text book アメリカ物理学会加速器学校のテキスト シンクロトロン放射を真 面 目に取り扱う 位相の取り扱いに取り組むも 未完のようだ J.Schwinger s paper 1948~9 Schwinger Classical Electrodynamics (Jackson) Kim K.J., Characteristics of Synchrotron Radiation, AIP Conference Proceedings 184, vol. 1 p567 (American Institute of Physics, NewYork, 1989). PhysRev pdf Notes M. Sands slac-r-121.pdf Notes.pdf Notes
6 I. Maxwell Feynman 1.Maxwell 2. Feynman
7 Maxwell Maxwell
8 Lorentz
9 Green s δ
10 unit aming vector
11 t : " t :
12 t t (t)
13 Heaviside-Feynmann Coulomb Mixture " unit aiming vector n
14 II. Syncrotron 1. " 2.
15 8tp, -tst, tst<, A PlotRange Æ 880, r<, 8-r, r<<d 10 r@tp_d := 8r H1 - Cos@Cmov tp ê rdl, r Sin@Cmov tp ê rd<; H* curvature,observer,energy *L r = 10; robs = 80, 100<; grel = 50; H* physical consts.*l Clv = ; 1 e 0 = 4 Pi 10 ^H-7L Clv ; 2 qelec = ^-H19L; H* particle velocity *L 1 Cmov = Clv SqrtB 1 - grel F; 2 tst = HPi ê 4L r ê Clv; n
16 := - - tobs@tp_d := tp + R@tpD ê Clv; Plot@tobs@tpD, 8tp, -tst, tst<, PlotRange Æ AllD n@tp_d := Hrobs - r@tpdl ê R@tpD; ParametricPlot@8tp, n@tpd@@1dd<, 8tp, -tst, tst <, PlotRange Æ All, AspectRatio Æ 1D k@tp_d = D@tobs@tpD, tpd; Plot@k@tpD, 8tp, -tst, tst<d 0.30 ParametricPlot@8tobs@tpD, n@tpd@@1dd<, 8tp, -tst, tst <, PlotRange Æ All, AspectRatio Æ 1D n x n x
17 8tp, -tst, tst <, PlotRange Æ All, AspectRatio Æ 1D n x n x H* dnht'l dt = 1 kht'l dndt@tp_d = dnht'l dt' *L 1 k@tpd D@n@tpD, tpd; H* d2 nht'l 1 d dt 2 = 2 nht'l HkHt'LL 2 dt' 2 - k' dnht'l HkHt'LL 3 *L dt' d2ndt2@tp_d = 1 D@k@tpD, tpd D@n@tpD, 8tp, 2<D - Hk@tpDL2 Hk@tpDL D@n@tpD, tpd; ParametricPlot@8tobs@tpD, dndt@tpd@@1dd<, 8tp, -tst, tst <, AspectRatio Æ 1D ParametricPlot@8tobs@tpD, d2ndt2@tpd@@1dd<, 8tp, -tst ê 10, tst ê <, PlotRange Æ All, AspectRatio Æ 1D n x
18 Feynmann H* EHx,tL= q 4pe 0 : n R 2 + R c d J n dt R 2 N+ 1 d 2 n c 2 dt 2 > *L dnr2dt@tp_d = DB n@tpd, tpf ì k@tpd; R@tpD2 Efield@tp_D = qelec n@tpd 4 Pi e 0 R@tpD + R@tpD 2 Clv dnr2dt@tpd + 1 Clv d2ndt2@tpd ; 2 Table@ParametricPlot@8tobs@tpD, Efield@tpD@@iDD<, 8tp, -tst ê 10, tst ê 10 <, PlotRange Æ All, PlotPoints Æ 1000, AspectRatio Æ 1D, 8i, 1, 2<D
19
20 Fourier Nbin = 2^10; eqtime = Table@ FindRoot@ tobs@tpd ä Htobs@-tst ê 10D H1 - i ê NbinL + tobs@tst ê 10D Hi ê NbinLL, 8tp, -tst ê 10, tst ê 10<, AccuracyGoal Æ 24, WorkingPrecision Æ 34, MaxIterations Æ 50D, 8i, 0, Nbin<D; Edata = Efield@tpD ê. eqtime; ListPlot@Transpose@EdataD@@1DD, PlotRange Æ AllD Fdata = Fourier@Transpose@EdataD@@1DDD; ListPlot@Abs@FdataD, PlotRange Æ 880, Nbin ê 10<, All<D
21
22 z t << "FourierSeries`" r@tp_d := :- K und Clv Sin@w u tpd grel w u, K 2 und 2 Clv tp - K 2 und Clv Sin@2 w u tpd >; 2 grel 2 I8 grel 2 M w u z H* curvature,observer,energy *L K und = 1; l u = 0.04; N u = 10; robs = 80, 100<; grel = 50; H* physical consts.*l Clv = ; 1 e 0 = ; 4 Pi 10^H-7L Clv 2 qelec = ^-H19L; H* undulater frequency, velocity of moving charge, time duration of observation *L 2 Pi Clv w u = ; Cmov = Clv SqrtB 1 - l u tst = l u N u ê Cmov; 1 F; grel 2 x ParametricPlot@r@tpD, 8tp, 0, tst<, AspectRatio Æ 2, PlotRange Æ All, PlotPoints Æ 5000D
23 := - - tobs@tp_d := tp + R@tpD ê Clv; Plot@tobs@tpD, 8tp, 0, tst ê N u <, PlotRange Æ AllD t t k@tp_d = D@tobs@tpD, tpd; Plot@k@tpD, 8tp, 0, tst ê N u <, PlotPoints Æ 1000D κ t
24 unit aiming vector := Hrobs - r@tpdl ê R@tpD; Table@ParametricPlot@8tp, n@tpd@@idd<, 8tp, 0, tst ê N u <, AspectRatio Æ 1, PlotRange Æ AllD, 8i, 1, 2<D n x Table@ParametricPlot@8tobs@tpD, n@tpd@@idd<, 8tp, 0, tst ê N u <, AspectRatio Æ 1, PlotRange Æ All, PlotPoints Æ 1000D, 8i, 1, 2<D n x t t n z n1 z t t
25 Feynmamm E Hx, tl = q 4 pe 0 : n R 2 + R c d dt n + 1 d2 n > R 2 c 2 dt 2 Ex Ex Ex Ez Ez Ez
26 Nbin = 2^15; eqtime = Table@FindRoot@tobs@tpD ä Htobs@0D H1 - i ê NbinL + tobs@tstd Hi ê NbinLL, 8tp, 0, tst<, AccuracyGoal Æ 14, WorkingPrecision Æ 24, MaxIterations Æ 50D, 8i, 0, Nbin<D; Edata = Efield@tpD ê. eqtime; ListPlot@Transpose@EdataD@@1DD, PlotRange Æ All, Joined Æ TrueD Fdata = Fourier@Transpose@EdataD@@1DDD; ListPlot@Log@Abs@FdataDD, PlotRange Æ 880, Nbin ê 50<, All<, Joined Æ TrueD
27 Nbin = 2^15; eqtime = Table@FindRoot@tobs@tpD ä Htobs@0D H1 - i ê NbinL + tobs@tstd Hi ê NbinLL, 8tp, 0, tst<, AccuracyGoal Æ 14, WorkingPrecision Æ 24, MaxIterations Æ 50D, 8i, 0, Nbin<D; Edata = Efield@tpD ê. eqtime; ListPlot@Transpose@EdataD@@1DD, PlotRange Æ All, Joined Æ False, PlotStyle Æ [email protected] Fdata = Fourier@Transpose@EdataD@@1DDD; ListPlot@Log@Abs@FdataDD, PlotRange Æ 880, Nbin ê 100<, All<, Joined Æ FalseD
28 III. 1. " 2.
29 Analytical method of radiation calculation General formula(another expression) Far-field approximation
30 Acceleration gives electric field far from the source where in other form
31 Power and spectrum Power Spectrum where
32 Photon number Amplitude of electric field E^2 gives finding probability of photons.
33 Polarization vector
34 Electric field of each polarization in time domain
35 Electric field calculated in frequency domain
36 Analytic calculation of radiation from bending Emitter time t and observer time t.
37 Power spectrum of bending radiation where e^2 N N (Ne)^2 Ne^2 "
38 σ-polarization %-polarization Total
39
40 IV. Effects of Synchrotron Radiation on Beams" 1. " 2. " 3.
41 Transfer matrix
42 Transfer matrix Transfer matrix Transfer matrix
43 Determinant
44 "
45 u i ( ) t i ( )
46 t t t
47 FEL i, j
48
49
50 emittance
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