Physics 417517 Introduction to Particle Accelerator Physics G
- Slides: 10
Physics 417/517 Introduction to Particle Accelerator Physics G. A. Krafft Jefferson Lab Professor of Physics Old Dominion University Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
Solutions Homogeneous Eqn. Dipole Drift Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
Quadrupole in the focusing direction Quadrupole in the defocusing direction Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
Transfer Matrices Dipole with bend Θ (put coordinate of final position in solution) Drift Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
Quadrupole in the focusing direction length L Quadrupole in the defocusing direction length L Wille: pg. 71 Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
Thin Lenses –f f Thin Focusing Lens (limiting case when argument goes to zero!) Thin Defocusing Lens: change sign of f Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
Composition Rule: Matrix Multiplication! Element 1 Element 2 More generally Remember: First element farthest RIGHT Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
Some Geometry of Ellipses y Equation for an upright ellipse b a x In beam optics, the equations for ellipses are normalized (by multiplication of the ellipse equation by ab) so that the area of the ellipse divided by π appears on the RHS of the defining equation. For a general ellipse Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
The area is easily computed to be Eqn. (1) So the equation is equivalently Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
When normalized in this manner, the equation coefficients clearly satisfy Example: the defining equation for the upright ellipse may be rewritten in following suggestive way β = a/b and γ = b/a, note Physics 417/517 Introduction to Particle Accelerator Physics 9/20/2007
