Shot Pulses in Rings Mico-bunching: Longitudinal Bunch Pofile Measuements at TTF ) The time vaying fields in a tansvese mode cavity kick the font of a bunch up, and the back of the bunch don. ) A betaton phase advance of π late, the bunch adiates in an undulato 3) The vetical photon angles ae coelated ith the souce point Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
Shot Pulses in Rings Mico-bunching: Longitudinal Bunch Pofile Measuements at TTF ) The time vaying fields in a tansvese mode cavity kick the font of a bunch up, and the back of the bunch don. ) A betaton phase advance of π late, the bunch adiates in an undulato 3) The vetical photon angles ae coelated ith the souce point 4) A slit, selecting only a shot ange of vetical angles, selects photons fom a small ange of souce points along the bunch. 5) A second cab cavity, a betaton phase advance of p afte the fist, kicks the tail up and the font don, compensating the vetical oscilations. 6) The bunch is typically about ps long, selecting ps educes the intensity to appoimately %. Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
3 Shot Pulses in Rings Mico-bunching: Longitudinal Bunch Pofile Measuements at TTF ) Instead of a slit, one can use an -ay bunch compesso. It poduces a time of flight that depends on the vetical angle to eliminate the coelation beteen vetical angle and souce point location. X-ay compession in asymmetic-cut cystals ) Realistically: tansmits up to 5% of beam due to collimation and losses. Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
4 Optics : Whee is the vetical Dipole? HERA Tunnel Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
5 Optics : Real Quadupoles SLAC The coils sho that this is an upight quadupole not a otated o ske quadupole. PETRA Tunnel Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
6 Optics 3: Real Setupoles ESRF Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
7 B Finge Fields and Main Fields 443 443 Main field Finge field Only the finge field egion has tems ith ψ z Main fields in acceleato physics: z ψ Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
8 Comple Potentials + iy, iy + + y, + z y i ( i + ) i( ( ) ) + z 4 + z ψ Im{ ψ Im{ λ, λ a, λ 4a ( z) λ λ ( ) } Im{ a ( ) ( λ + ) λ( ) λ λ, λ } λ } Iteation equation: a λ fo λ, a Ψ The functions Ψ detemine the complete field inside a magnet. Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
9 Finge Fields and Main z ψ Fields Only the finge field egion has tems ith ψ z Main fields in acceleato physics: z ψ Im{ ψ Ψ } Nice ay to deive multipole fields ψ (, ϕ) Ψ Im{ e i ( ϕ ϑ ) } Relation beteen adial poe and azimuthal symmety! The inde descibes C Symmety aound the z-ais e z due to a sign change afte ϕ π 3 Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8 S N N S S N
3 ψ Ψ Im{ iy Ψ y B ψ Ψ } C Symmety Multipoles in Acceleatos : Dipoles - (+,-) in Ψ e y + (S,N) in B + - Equipotential y const. B dp dt q v B Dipole magnets ae used fo steeing the beams diection dϕ Bending adius: dp dt ρ ρ p qvb p qb dp p dϕ ρ dl dϕ vdt dp / p p qb Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
3 Multipoles in Acceleatos : Quadupoles ψ Ψ Im{( iy) } Ψ y B Ψ ψ y - + C Symmety + - - + + - y z In a quadupole paticles ae focused in one plane and defocused in the othe plane. Othe modes of stong focusing ae not possible. Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
3 3 3 y ψ Ψ3 Im{( iy) } Ψ3 ( y 3 y) B ψ Ψ3 3 y C 3 Symmety S N Nonlinea Optics - Setupoles S i) Setupole fields hadly influence the paticles close to the cente, hee one can lineaize in and y. B B Ψ N N 3 S ψ Ψ a + 3 3 y 3 y y + y 6Ψ3 ii) iii) y + In linea appoimation a by shifted setupole has a quadupole field. When depends on the enegy, one can build an enegy dependent quadupole. O( ) k 3 Ψ3 k k! Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8
33 '' + ( k + κ ) Second-Ode Dispesion Fist ode in, '' + ( k κ f f ( δ ) κδ + ) Fist ode in,, δ D'' δ + K Dδ D s ˆ κ ββˆ sin( ψ k + ) '' + ( κ f + f ( δ ) f ψˆ) dsˆ D'' + K D κ Second ode in,, δ f κ ( δ ' κδ + κ ) + k( δ κ) k f(, ', δ ) The enegy dependent dispeion: D D '' + K D s Geog.Hoffstaette@Conell.edu Class Phys 488/688 Conell Univesity 4//8 f ( D, D',) [ f ] ββˆ sin( ψ ψˆ) dsˆ