Homework Problems
Homework Problems III
Accelerator Physics
Show that for any smooth scalar field, φ:
∇×∇φ = 0
Solution:
Show that:
Solution:
[pic]
Solution:
A sextupole magnet of 4 cm inner diameter is limited by max field of 1 Tesla at the pole tip. What is the maximum sextupole gradient for this magnet in kGauss/cm2?
2x10 kGauss/(2 cm)2 = 5 kGauss/cm2
Consider a transport system consisting of FODO cells, what phase advance choices would be needed to construct a -I transformation matrix out of this cell.
Two 90 degree cells, or three 60 degree cells, or four 45 degree cells, or … will work
Show that a sextupole pair separated by –I transformation has a complete cancellation of geometric aberrations in both horizontal and vertical planes.
[pic]
[pic]
Construct a “fish” diagram for [pic]. At a minimum, show the separatrix, two constant energy curves inside the separatrix, and one constant energy curve outside of the separatrix. Also, display at least 10 points on each curve. It will be easiest to generate the results with a programmable calculator or simple computer code.
Here is a graph of the phase curves as determined by Excel.
[pic]
The abscissa is [pic] is radians, and I’ve chosen energy units so that the co-efficient in front of the potential term is 1. The green curves are the separatrices of two separate accelerating “buckets”, the purple curves are constant-Hamiltonian curves in the “bound” regions (note, at the same value of the Hamiltonian, there are also non-bound orbits), and the red curves are values of the Hamiltonian that only have non-bound orbits. The corresponding curves are separated by [pic].
-----------------------
[pic]
hKe}h6s¾B*phÿhjN@-jhjN@U[pic]mHnHtH u[pic]-jh6s¾U[pic]mHnHtH u[pic]-jhKe}hD5ÀB*U[pic]mHnHphÿtH u[pic]hKe}hD5ÀB*phÿhD5À
h7!ýOJQJhR(ôh7!ý>*[pic]OJQJhR(ôh7!ýOJ[pic]QJ[pic]h7!ýhÈO
h¿,h¿,
hbG:hÕ&»hO8hÆ L5[pic]
[pic]
[pic]
[pic]
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.