Historical (Hysterical?) Background Three schools of thought on codes & machine design –Quartermaster –Hacker –Curmudgeon

Quartermaster develop codes & design machines like you’d run the the Normandy invasion proposals, grants, reviews, lots of staff (2 or more people) often at academic institutions (MARYLIE, COSY∞) or at large labs (MAD) physics models often complex &/or detailed user interface often most charitably described as “idiosyncratic”

Hacker Based on the latest whiz-bang coding or computational paradigm Often developed by commercially or consulting oriented people Either very proprietary (e.g. LATTICE, PBO lab) or open source (CLASSIC) Can, in principle “do it all” but typically have limited range of applicability & you must bring your checkbook each time you want some additional capability

Curmudgeon “Just tell me what you want, kid, and I’ll figure out a way to deal with it” “Just in time programming” Codes not formalized, typically tied to particular problem but may be generalized over the course of time (e.g. DIMAD) to do “most” problems “mostly” right May be spreadsheet, handheld, or PDA based Can be very idiosyncratic Can be very easy or very hard to use

Legends of Ancient Mariners Brown/TRANSPORT Garren/SYNCH Crosby Collins Codes tend to emphasize the needs/interest of their prime movers Hep labs – small bend angle approximations Academic – very mathy

The problem All are “wrong” in some situation or another, usually the situation I want to be in! Most use questionable models/methods with acceleration (or, amusingly, don’t do acceleration,evn though we design accelerators!) Few allow fully coupled (H/V/synchrobetatron) modeling

Examples: I’ll pick on DIMAD “Way back in 82…” –Tracking with nonsymplectic Taylor’s series in Kaon factory lattice:

–Go to generating function approx –Adds in higher order terms to make symplectic – but are they the “right ones”? –Result: Much furor, new codes, lots of workshops… IR Demo –2 nd order transform not symplectic – blows phase space off-momentum –“TURTLE” mode tracking “just fine”

Compare integration/DIMAD, IR Upgrade

The bottom line As we go to larger acceptances, higher performance, perturbative methods become harder & harder to apply Other than applying Brown’s principle (“don’t mess with the beam”) how to we then get guidance?

The Pitch Beam optics is just circles & straight lines (actually, just circles – straight lines are circles of ∞ radius) Perturbation approach can be misleading – fix problems of linear optics (chromatics, aberrations – e.g., CEBAF T 126, etc ) with sextupoles, fix aberrations with octupoles, etc. Can’t we do it all geometrically instead?

Example: Mirror Bend Achromat hard to find, perturbatively, obvious, geometrically

  p  p   p  p    B ≠ 0 B =0  sin   sin  tan 

DIMAD “integrated” analysis misleading:

But this DOES give the higher order terms! Can we systematically extract the high order stuff by looking at residuals in comparison to exact solutions? Couldn’t we define an “action” that is minimized for the actual trajectory, then optimize by finding the “minimum action trajectory? (Brown’s maxim – “Don’t **** with the beam”) Any takers?