Lectures 2 Extracting simple perturbative quantities using TPSA
Lectures 2 Extracting simple perturbative quantities using TPSA and the standard results of Accelerator Theory
What if we were just opticians? The blue curve represents an interface between a glass medium on the left and air on the right. The shape of the interface is computed so that parallel rays focus exactly at the intersection of the red line and the optic axis. The condition for perfect focusing of parallel rays is a trivial set of conditions on the Taylor series expansion. The Taylor expansion is what we compute directly with a TPSA package. Therefore, are these lectures over…?
We are not just opticians, we also care about dynamics! 10 FODO Cells Iterating produces the black closed curve. The properties of that curve are part of the design criteria of an accelerator. Knowing that curve and how it evolves through a lattice is an important task of lattice design. Understanding the effect of nonlinearities on modifying that curve or even breaking it, is also an important task. This brings us to standard perturbation theory!
Standard Perturbation Results Here I quote results from text books without proof. The assumption is that the reader knows these things already. We then use these results directly with our Toy TPSA in order to extract lattice functions. At the end we discuss the limitations of this haphazard method and prepare the ground for lectures 3, 4 and 5.
Famous Results: 1 The one turn map M can be parameterized as follows if the motion around a ring is derived from some Hamiltonian.
Famous Results 2 This matrix admits a famous quadratic invariant, e, called the Courant-Snyder invariant. This means that:
Extracting Twiss Parameters from M
Tracking Twiss one obvious way Program in html form
- Slides: 9