A direct-current pion focusing magnet for low energy in-flight muon-neutrino beams

Accelerator neutrino beams

“…The authors of [135] note that the required B · dℓ to focus pions grows ∝ r as a function of the pion production angle off the target. For a cylindrical lens, whose focusing length ℓ doesn't vary with r, this criterion requires B ∝ r. Given that Bµ 0 (NI)/(2πr), the authors of [135] chose a current distribution NI = (0.5)njr 2 θ, where the current is achieved by mounting conductors on n wedged-shaped "fins" (see Figure 29), each with opening angle θ, and carrying a uniform current density j down each side of the fins.…”

“…For a cylindrical lens, whose focusing length ℓ doesn't vary with r, this criterion requires B ∝ r. Given that Bµ 0 (NI)/(2πr), the authors of [135] chose a current distribution NI = (0.5)njr 2 θ, where the current is achieved by mounting conductors on n wedged-shaped "fins" (see Figure 29), each with opening angle θ, and carrying a uniform current density j down each side of the fins. With j uniform, then NI ∝ r 2 is achieved by having the number of conductors increase as r 2 .…”