TraceWin study

Dipole Magnet with edges.
Reference:

[1] High energy ring accelerator physics 

[2]  TraceWin manual files

Magnetic Rigidity: Bρ =p/e

• Bρ=E(GeV)/0.29979(e)
• Bρ=3.1297βγ(p)

Quadrupole Focal Length:
1/f=B'l/Bρ

Edge focusing of rectangle dipole:

• Medge,x =(1,0;tanε/ρ,1） defocusing
• Medge,y=(1,0;-tanε/ρ,1） focusing
• sector dipole:=0

z''+K(s)z=0

Type of Elements	Kx	Ky
Drift	0	0
Vertical Dipole	1/ρx2	0
Horizontal Dipole	0	1/ρy2
Quadrupole	-k	k
Vertical Dipole with Q	1/ρx2-k	k
Horizontal Dipole with Q	-k	1/ρx2+k

Courant-Snyder Parameters

x(s)=Asqrt(β(s))cos[Φ(s)+δ]

Dispersion Function
x=D(p,s)Δp/p