1. Joel Brock, Georg Hoffstaetter, David Sagan, Karthik Narayan

2.  Subroutine library for Accelerator Beam Physics  Used by Tao (Tool for Accelerator Optics)

3.  Variable local reference coordinates  Locally, in flat orbits

4.  Attributes  Graze angle  X-offset  Y-offset  Graze angle error  Graze curvature  Transverse curvature  Tilt  Tilt error  X-pitch  Y-pitch  Beam Attributes (Six Vector)  X  Px  Y  Py  Z  Pz

7. XOffset and GAE Verification The following variables are ideally very small: X_offset graze_angle_err beam_start x beam_start px PropertyValue Graze angle40.07623° Graze angle error13.76028 ° X_Offset7.11982 mm Beam x offset14.77663 mm Beam px0.85002 Final x orbit6.39 082mm

8. COMPLETED  Graze angle  X offset  Graze angle error  Graze curvature  X-pitch  Transfer matrix for graze angle, x offset, and graze angle error TO BE COMPLETED  Y-offset  Transverse curvature  Tilt  Tilt error  Y-pitch  Transformation matrix with all offsets and errors  Higher order non-linear terms  Canonical z-coordinate equations

9.  The Physics of Particle Accelerators by Klaus Wille  General accelerator physics concepts  Particle Accelerator Physics by Helmut Wiedemann  Transfer matrices, deeper concepts  The BMAD Reference Manual by David Sagan  Coordinate systems, element attributes  The Tao Reference Manual by David Sagan, Jeffrey Smith  Lattice configuration, element configuration

10.  BMAD (baby/better/be) Subroutine Library  Back end testing purposes  Tao (Tool for Accelerator Optics)  Front end testing purposes  The Geometer’s Sketchpad  2D drawing environment

11. Questions? Comments? Concerns?