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1 SPring-8 RFgun JASRI/SPring
2 Contents
3 . 3 cavity γ E A = er 3 πε γ vb r B = v E c r c A B A ( ) F = e E + v B A A A A B dp e( v B+ E) = = m d dt dt ( γ v) dv e ( ) dt v B E v E = + v γm c Runge-Kutta method
4 6 ε x βγ = < x >< x > < x x > Cavity MAFIA cavity
5 . Envelop equation Lawson s equation r d = ei dz ßffl m C 3 fl 3 fi 3 r CW
6 Transverse x r e- z Ex E Pencil beam Ez v E = πɛ γ Longitudinal er [ ] 3/ r v r c E x = x Q πɛ x Ex By. v z= l + x γ v z z E z = ρ ɛ ( ) z + R γ R γ z Envelop equation dv dt = e γm ( v B + E s (v E) c v ) d x ds = d z ds = eq πɛ mc γ 3 β x q z + x eq πɛ m c γ 3 β x z ( γ ) z + x γ x γ z
7 envelop equation Transverse Longitudinal Energy = MeV, φ = mm, pulse width = 3 mm Energy = MeV, φ = mm, pulse width = 3 mm Beam Radius (mm) Envelop equation Simulation code Pulse Width (mm) Envelop equation Simulation code Longitudinal Traveling length (m) Longitudinal Traveling length (m)
8 RFgun envelop equation d x dt = eq πɛ m γ 3 x E x rf = E cos (ωt φ) B y rf = r c ωe sin (ωt φ) e β (t) = r γ (t) = m E (sin(ωt φ)+sin φ) c ω + β(t) + l + x γ eβc γm B y rf + e (sin(ωt φ)+sin m E φ) eβ γm c E z rf dx dt Transverse Longitudinal B z field Real Cavity Perfect pillbox type z (mm) cavitybz cavity pillbox Beam size (mm) Energy = -3.6 MeV, φ = mm, pulse width = 3mm 8 6 Envelop equation Simulation Time (nsec)
9 3. To dummy load Solenoid coil Screen monitor Faraday cup RF Cavity Bending magnet Cu-Cathode degrees X-Y slit Wall-current monitor UV-Laser path cm
10 Emittance (πmm mrad) Data No. (X emittance) Data No. (Y emittance) Data No. (X emittance) Data No. (Y emittance) X emittance(simulation) Y emittance(simulation) Parameters (for both experiment & our simulation ) Maximum field on the cathode 35 MV/m Initial RF phase 85 degree First solenoid coil 56 Gauss Second solenoid coil 78 Gauss Laser incident angle 66 degrees Laser spot distribution Gaussian like figure Laser spot radius.3 mm (σ) Laser temporal length 5 ps (FWHM) Charge of electron beam (nc/bunch).8nc/bunch.8nc/bunch Charge
11 Emittance (πmm mrad) x y (<x> +<y> )/ Charge (nc/bunch) Emittance (πmm mrad) x y Longitudinal position (m) X,Y
12 cavity
13 . Charge Beam radius Bunch length : C/bunch : 6 mm uniform : ps Emittance (πmm.mrad) Distance from Cathode (mm) Emittance (πmm.mrad) Particle Number x y 5 5mm 7 Grape term nc 3 E A = πε γ r er v B r c 3
14 5. Surface of the Cathode Traveling length from the cathode (mm) E = 5 MV/m E = MV/m E = 5 MV/m Time (ps) Transverse position (mm) dv dt = e γm Longitudinal position from Cathode (mm) ( v B + E ) (v E) c v E e (sin (ωt φ)+sinφ) v(t) = c c ω + E e (sin (ωt φ)+sinφ)
15 3 radial Emittance (πmm mrad) Image On.nC/bunch Image Off.nC/bunch 5 5 Longitudinal position (mm)
16 Transverse position (mm) Longitudinal position from Cathode(mm)
17 E = er n πɛ γn [ ] 3/ R n V n R n c VrΔt cδt -vn -vr -vr vn E = πɛ γ r er r [ ] 3/ R r V r R r c Rr Rn RF DC Emittance (πmm mrad) Normal.nC/bunch Retarded point.nc/bunch Normal.nC/bunch Retarded point.nc/bunch Longitudinal position (m)
18 6. Emittance (πmm mrad) 6 8 Our code - with random PARMELA Our code - even intervals..8. Charge of electron beam (nc/bunch) x (mm) Initial Particle Position with Random Numbers z (m) x (mm) Output Particle Position with Random Numbers z (m) x (mm) Initial Particle Position aligned at even intervals z (m) x (mm) Output Particle Position alined at even intervals z (m)
19 7. Keeping particle numbers of Increasing particle numbers as charge grows Emittance (πmm mrad) 8 6.nC.nC.nC Charge (nc)
20 Weak Field
21 8. SPring-8 RFgun 3
18 2 F 12 r 2 r 1 (3) Coulomb km Coulomb M = kg F G = ( ) ( ) ( ) 2 = [N]. Coulomb
r 1 r 2 r 1 r 2 2 Coulomb Gauss Coulomb 2.1 Coulomb 1 2 r 1 r 2 1 2 F 12 2 1 F 21 F 12 = F 21 = 1 4πε 0 1 2 r 1 r 2 2 r 1 r 2 r 1 r 2 (2.1) Coulomb ε 0 = 107 4πc 2 =8.854 187 817 10 12 C 2 N 1 m 2 (2.2)
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