1. 1 BetaFunction Void DoIntegration Double GetBeta Double GetAlpha Double GetEmittance Double GetPz Void Print Void AddMaterial Void AddQuadrupole Void AddSolenoid Void SetStepSize Void SetFieldIsFlipped Void ResetField Material Double GetBeta Double GetAlpha Double GetPz Double GetEmittance Double GetLengthGivenEmittance Quadrupole Double GetKappa OpticsFieldManager BeamTools Minimiser Output Public Methods Solenoid Double GetBz Class Diagram1

2. 2 Solenoid Define Builds a vector of BTSheet –Would use BTSolenoid but it needs rewriting –OpticsSolenoid calculates on-axis Bz only BTSolenoid insists on calculating a full field map (slow!!) I have a quicker algorithm anyway which I may use –Returns it to BetaFunction –This should be better integrated with BeamTools

3. 3 Quadrupole Define length, z-position (maybe aperture later) Get kappa w/o fringe fields, i.e. square edge approx –Kappa is focusing strength –Returns kappa or -kappa depending on whether I am looking at x axis or y axis –Should probably include fringe fields at some stage –A neater algorithm would be to calculate dB/dr on-axis from a field map Slower, maybe appropriate for second approximation to linear problem

4. 4 Material Define material, length, position Gives changes in optical functions on passing through a material –Uses linear approximation (fairly good) –This is something Bravar hasn’t done Already beating them –Formulae come from CERN/PS 2001-0013 (AE) DESCRIPTION OF BEAM-MATTER INTERACTION IN THE COVARIANCE MATRIX FORMALISM Beware of binomial approximation in some results! –Works in both directions, forward and backward

5. 5 BetaFunction Builds an optical geometry –AddOpticalComponent type methods –Use a field map –Calculates focusing strength kappa from quadrupole and on-axis Bz Calculates optical functions –Then run DoIntegration() to calculate beta Beta etc stored as array at intervals dZ (dZ +ve or -ve) –Use GetOpticalFunction() to get linear interpolation for the optical functions, pz etc Maybe use BTSpline at some stage

6. 6 Minimiser Under Construction! Need to learn how Minuit works Initial thoughts/aims –Constraints are beta and alpha at various points down the beamline –Variable parameters are optical parameters, e.g. current in solenoids Other possibilities include material thickness, quad dB/dr, etc –Score according to?? Then some sort of manager class/executable?