PAC09 - List of Authors (Anderson, O.A.)

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Anderson, O.A.

Paper	Title	Page
FR5PFP007	Analytic Solution of the Envelope Equations for an Undepressed Matched Beam in a Quadrupole Doublet Channel	4320
	O.A. Anderson LBNL, Berkeley, California L.L. LoDestro LLNL, Livermore, California
	Funding: Supported in part by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. In 1958, Courant and Snyder analyzed the problem of alternating-gradient beam transport and treated a model without focusing gaps or space charge.* We extend their work to include the effect of gaps (still neglecting space charge) and obtain exact solutions for the matched envelopes. We assume a periodic lattice of quadrupole doublets. The focus sections have piecewise-constant field strength and equal lengths, but the zero-field drift sections have arbitrary length ratio. We obtain and show the exact envelope results as functions of z for various field strengths, occupancies (eta), and gap-length ratios. We show the peak envelope excursion as a function of field strength or phase advance (σ) for various cases. There is a broad σ range over which the minimum peak varies less than ± 1%. For eta = 1, this range is 64 to 98 degrees; for eta = 0.5, it is 62 to 96 degrees. In the lowest stable band, the optimum field strength rises by 37.6% when eta is reduced from 1.0 to 0.5 and rises by 76.0% if also one gap has zero length. In the second stable band, the higher field strength accentuates the remarkable compression effect predicted for the FD (gapless) model. E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958). *The present work extends a recent envelope analysis carried out without gaps (O.A. Anderson and L.L. LoDestro, submitted to Phys. Rev. ST-AB).

Paper

Title

Page

FR5PFP007

Analytic Solution of the Envelope Equations for an Undepressed Matched Beam in a Quadrupole Doublet Channel

4320

O.A. Anderson
LBNL, Berkeley, California
L.L. LoDestro
LLNL, Livermore, California

Funding: Supported in part by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

In 1958, Courant and Snyder analyzed the problem of alternating-gradient beam transport and treated a model without focusing gaps or space charge.* We extend their work to include the effect of gaps (still neglecting space charge) and obtain exact solutions for the matched envelopes.** We assume a periodic lattice of quadrupole doublets. The focus sections have piecewise-constant field strength and equal lengths, but the zero-field drift sections have arbitrary length ratio. We obtain and show the exact envelope results as functions of z for various field strengths, occupancies (eta), and gap-length ratios. We show the peak envelope excursion as a function of field strength or phase advance (σ) for various cases. There is a broad σ range over which the minimum peak varies less than ± 1%. For eta = 1, this range is 64 to 98 degrees; for eta = 0.5, it is 62 to 96 degrees. In the lowest stable band, the optimum field strength rises by 37.6% when eta is reduced from 1.0 to 0.5 and rises by 76.0% if also one gap has zero length. In the second stable band, the higher field strength accentuates the remarkable compression effect predicted for the FD (gapless) model.**

*E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958).
**The present work extends a recent envelope analysis carried out without gaps (O.A. Anderson and L.L. LoDestro, submitted to Phys. Rev. ST-AB).