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Analytical approach to Eigen-emittan...

Nash, Boaz.

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Analytical approach to Eigen-emittance evolution in storage rings.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Analytical approach to Eigen-emittance evolution in storage rings./
作者:	Nash, Boaz.
面頁冊數:	182 p.
附註:	Adviser: Alexander W. Chao.
Contained By:	Dissertation Abstracts International67-05B.
標題:	Physics, Elementary Particles and High Energy. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3219342
ISBN:	9780542707766

Analytical approach to Eigen-emittance evolution in storage rings.
Nash, Boaz.

Analytical approach to Eigen-emittance evolution in storage rings. - 182 p.

Adviser: Alexander W. Chao.

Thesis (Ph.D.)--Stanford University, 2006.

This dissertation develops the subject of beam evolution in storage rings with nearly uncoupled symplectic linear dynamics. Linear coupling and dissipative/diffusive processes are treated perturbatively. The beam distribution is assumed Gaussian and a function of the invariants. The development requires two pieces: the global invariants and the local stochastic processes which change the emittances, or averages of the invariants. A map based perturbation theory is described, providing explicit expressions for the invariants near each linear resonance, where small perturbations can have a large effect. Emittance evolution is determined by the damping and diffusion coefficients. The discussion is divided into the cases of uniform and non-uniform stochasticity, synchrotron radiation an example of the former and intrabeam scattering the latter. For the uniform case, the beam dynamics is captured by a global diffusion coefficent and damping decrement for each eigen-invariant. Explicit expressions for these quantities near coupling resonances are given. In many cases, they are simply related to the uncoupled values. Near a sum resonance, it is found that one of the damping decrements becomes negative, indicating an anti-damping instability. The formalism is applied to a number of examples, including synchrobetatron coupling caused by a crab cavity, a case of current interest where there is concern about operation near half integer betatron tune. In the non-uniform case, the moment evolution is computed directly, which is illustrated through the example of intrabeam scattering. Our approach to intrabeam scattering damping and diffusion has the advantage of not requiring a loosely-defined Coulomb Logarithm. It is found that in some situations there is a small difference between our results and the standard approaches such as Bjorken-Mtingwa, which is illustrated by comparison of the two approaches and with a measurement of Au evolution in RHIC. Finally, in combining IBS with the global invariants some general statements about IBS equilibrium can be made. Specifically, it is emphasized that no such equilibrium is possible in a non-smooth lattice, even below transition. Near enough to a synchrobetatron coupling resonance, it is found that even for a smooth ring, no IBS equilibrium occurs.

ISBN: 9780542707766Subjects--Topical Terms:

1019488
Physics, Elementary Particles and High Energy.

Analytical approach to Eigen-emittance evolution in storage rings.
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245 1 0 $a Analytical approach to Eigen-emittance evolution in storage rings.
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502 $a Thesis (Ph.D.)--Stanford University, 2006.
520 $a This dissertation develops the subject of beam evolution in storage rings with nearly uncoupled symplectic linear dynamics. Linear coupling and dissipative/diffusive processes are treated perturbatively. The beam distribution is assumed Gaussian and a function of the invariants. The development requires two pieces: the global invariants and the local stochastic processes which change the emittances, or averages of the invariants. A map based perturbation theory is described, providing explicit expressions for the invariants near each linear resonance, where small perturbations can have a large effect. Emittance evolution is determined by the damping and diffusion coefficients. The discussion is divided into the cases of uniform and non-uniform stochasticity, synchrotron radiation an example of the former and intrabeam scattering the latter. For the uniform case, the beam dynamics is captured by a global diffusion coefficent and damping decrement for each eigen-invariant. Explicit expressions for these quantities near coupling resonances are given. In many cases, they are simply related to the uncoupled values. Near a sum resonance, it is found that one of the damping decrements becomes negative, indicating an anti-damping instability. The formalism is applied to a number of examples, including synchrobetatron coupling caused by a crab cavity, a case of current interest where there is concern about operation near half integer betatron tune. In the non-uniform case, the moment evolution is computed directly, which is illustrated through the example of intrabeam scattering. Our approach to intrabeam scattering damping and diffusion has the advantage of not requiring a loosely-defined Coulomb Logarithm. It is found that in some situations there is a small difference between our results and the standard approaches such as Bjorken-Mtingwa, which is illustrated by comparison of the two approaches and with a measurement of Au evolution in RHIC. Finally, in combining IBS with the global invariants some general statements about IBS equilibrium can be made. Specifically, it is emphasized that no such equilibrium is possible in a non-smooth lattice, even below transition. Near enough to a synchrobetatron coupling resonance, it is found that even for a smooth ring, no IBS equilibrium occurs.
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