A Smooth Approximation to the Alternating Gradient Orbit Equations
- Wayne State Univ., Detroit, MI (United States); Midwestern Universities Research Association (MURA), Urbana, IL (United States)
We propose to develop an approximate solution to the equation $$\frac{d^2x}{ds^2}=f(x,s)$$ where f(x, s) is periodic in s with period S. The approximation will be based upon the assumption that x changes relatively little within a sector length S, and will be expected to be valid when the betatron wavelength is large in comparison with the sector length S. Under these conditions, we will attempt to replace Eq. (1) by its "smooth" approximation $$\frac{d^2x}{ds^2}=f(x,x')$$ where in nearly all case of interest, the function F will not depend on x1 = dx/ds. The solution of Eq. (2) will indicate the gross features of the betatron oscillations, but will not be expected to reveal details of the motion within a sector, or resonance effects which depend on the sector length.
- Research Organization:
- Wayne State Univ., Detroit, MI (United States); Midwestern Universities Research Association (MURA), Urbana, IL (United States)
- Sponsoring Organization:
- US Atomic Energy Commission (AEC)
- NSA Number:
- NSA-11-003122
- OSTI ID:
- 4358972
- Report Number(s):
- MURA--25; KRS-MURA--1
- Country of Publication:
- United States
- Language:
- English
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