Class Review. Content

Transcription

1 193 Cla Review Content 1. A Hitory of Particle Accelerator 2. E & M in Particle Accelerator 3. Linear Beam Optic in Straight Sytem 4. Linear Beam Optic in Circular Sytem 5. Nonlinear Beam Optic in Straight Sytem 6. Nonlinear Beam Optic in Circular Sytem 7. Accelerator Meaurement 8. RF Sytem for Particle Acceleration Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

2 194 The Van de Graaff Accelerator The Tandem Accelerator USPAS Advanced Accelerator Phyic June 26

3 195 The Cockcroft-Walton Accelerator USPAS Advanced Accelerator Phyic June 26

4 196 Three hitoric line of accelerator Direct Voltage Accelerator Reonant Accelerator Tranformer Accelerator The Cyclotron The microtron USPAS Advanced Accelerator Phyic June 26

5 197 Wideroe or drift tube linear accelerator Traveling wave cavity: Pae focuing Standing wave cavity: π ψ, 2 Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

6 198 The RF quadrupole RFQ 197: Kapchinkii and Teplyakov invent the RFQ USPAS Advanced Accelerator Phyic June 26

7 199 Betatron USPAS Advanced Accelerator Phyic June 26

8 2 The Synchrotron USPAS Advanced Accelerator Phyic June 26

9 21 Ellement of a Collider Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

10 22 ev The Livington Chart USPAS Advanced Accelerator Phyic June 26

11 23 3 Generation of Light Source Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

12 24 B Fringe Field and Main Field Main field Fringe field ν iν ϕ ϑν Ψν Im{ r e } + Ψ ν 1 ν 1 ν ψ r, ϕ Im{ Ψ w } + Ψ ν Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

13 25 Where i the vertical Dipole? HERA Tunnel Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

14 26 Real Quadrupole SLAC The coil how that thi i an upright quadrupole not a rotated or kew quadrupole. PETRA Tunnel Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

15 27 The CESR Tunnel USPAS Advanced Accelerator Phyic June 26

16 28 Real Air-coil Multipole Quadrupole corrector RHIC Tunnel LHC dipole USPAS Advanced Accelerator Phyic June 26

17 29 LHC double quadrupole Special SC Air-coil Magnet Accuracy RHIC Siberian Snake dipole USPAS Advanced Accelerator Phyic June 26

18 21 Lioville Theorem A phae pace volume doe not change when it i tranported by Hamiltonian motion. M with det[ M ] + 1 ' x x' x x V n n n d d M d d Volume V V V V n V Hamiltonian Motion V V But Hamiltonian require ymplecticity, which i much more than jut det[ M ] + 1 Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

19 211 Symplectic Repreentation ' Hamiltonian J H, ODE T ' F, F J + J F Generating Function p, p J F1 q, q, [from note] Symplectic tranport map M J M T J Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

20 212 r The comoving Coordinate Sytem R + xe + ye x y d R e d R d d R The time dependence of a particle motion i often not a intereting a the trajectory along the accelerator length. Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

21 213 Linear equation of motion: ' F Matrix olution of the tarting condition M Matrix Solution L4 M drift L3 M quad L2 M drift L1 M bend drift L3 M quad L2 M drift L1 Bend Quadrupole M M L M L quad 2 drift 1 drift L1 Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

22 USPAS Advanced Accelerator Phyic June , ' f, ' f L + a M L a M M L H H H H with ' ', ' ' ' f L a M a M a M + + d f M a ˆ ˆ ˆ, ˆ 1 + d f M d f M M H ˆ ˆ ˆ, ˆ ˆ ˆ ˆ, ˆ Field error, nonlinear field, etc can lead to, f Perturbation are propagated from to Variation of Contant

23 215 Beta Function and Betatron Phae x'' x k y'' y k x x M 11 x + M 12 x ' 2J in ψ + φ Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

24 216 Twi Parameter ' 2α α' k γ ψ 1 ' d' γ x, x' α α x x' 2J Area: 2π J x J / ε π ε 2J inφ e djdφ ε 2 x' εγ xx' ε 1 π ε α in 2 J / 2 2J φ e djdφ εα ε x 2 2 x' xx' 2 i called the emittance. Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

25 USPAS Advanced Accelerator Phyic June T M M γ α α γ α α Propagation of Twi Parameter + + ] in [co ] in 1 co [ in ] in [co co in in co ψ α ψ ψ α α ψ α α ψ ψ α ψ ψ ψ ψ ψ α α M

26 218 Cloed Orbit Correction and Bump x co ϑ 2 ϑ3 1 ϑ Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

27 219 The Periodic Diperion Poincare Section η USPAS Advanced Accelerator Phyic June 26

28 22 The FODO Cell USPAS Advanced Accelerator Phyic June 26

29 221 Quadrupole Error and Tune Shift One quadrupole error: ν 4 π k One quadrupole error: kˆ ˆ co2ψˆ ψ 2 in µ µ Chromaticity: 1 ξ x x k1 xk 4 + η π 2 dˆ Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

30 222 The Dynamic Aperture Stable and untable fixed point!.4 υ Caotic motion cloe to fixed point! -8-1 υ Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

31 223 Reonance n for υ 3 υ n 4 υ υ + H J n + m υ, J J ϕ ϑ Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

32 224 n + m x υx + myυ y Reonance Diagram mean that ocillation in y can drive ocillation in x in ν y ν x Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

33 225 Diperion relation and Cavitie ω k k Georg.Hofftaetter@Cornell.edu USPAS Advanced Accelerator Phyic June 26

34 226 USPAS Advanced Accelerator Phyic June 26