1. ϕ-bending in an infinite solenoid ρ = p T /.3 B α = R c /ρ Δϕ 1 = α/2 Δϕ = Δϕ 1 R c /R d Δϕ = (.3 B/ p T ). R c 2 /R d /2 p T =20 GeV/c B=2T R c =1m D1 : Rd>1.3 m, Δϕ< 11mrad D2 : Rd>2.2 m, Δϕ< 7 mrad D3 : Rd>3.4 m, Δϕ< 4 mrad Solenoid (R c ) Detector (R d ) Δϕ Δϕ 1 α ρ

2. Field model of the real solenoid z1=2m z2=4m B=2T

3. Computing ∫ B z dR Case 1: ∫B z dR = B R c Case 2: ∫B z dR = B (R t + (R c -R t )(2*Z 2 -Z 1 -Z e )/(Z 2 -Z 1 )/2) Case 3: ∫B z dR =B (R t +R e )/2 RcRc Z1Z1 Z2Z2 RtRt 1 2 3 RtRt ZeZe ReRe

4. ∫B z dR as a function of η

5. ϕ-bending as a function of η