Ebook: Stochastic Cooling of Particle Beams

This lecture note describes the main analytical approaches to stochastic cooling. The first is the time domain picture, in which the beam is rapidly sampled and a statistical analysis is used to describe the cooling behaviour. The second is the frequency domain picture, which is particularly useful since the observations made on the beam are mainly in this domain. This second picture is developed in detail to assess key components of modern cooling theory like mixing and signal shielding and to illustrate some of the diagnostic methods. Finally the use of a distribution function and the Fokker-Plank equation, which offer the most complete description of the beam during the cooling, are discussed.

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This lecture note describes the main analytical approaches to stochastic cooling. The first is the time-domain picture, in which the beam is rapidly sampled at a high rate and a statistical analysis is used to describe the cooling behaviour. The second is the frequency-domain picture, which is particularly useful since the observations made on the beam and the numerical cooling simulations are mainly in this domain. This second picture is developed in detail to assess key components of modern cooling theory like mixing and signal shielding and to illustrate some of the diagnostic methods. Finally the use of a distribution function and the Fokker-Plank equation, which offer the most complete description of the beam during the cooling, are discussed.

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This lecture note describes the main analytical approaches to stochastic cooling. The first is the time-domain picture, in which the beam is rapidly sampled at a high rate and a statistical analysis is used to describe the cooling behaviour. The second is the frequency-domain picture, which is particularly useful since the observations made on the beam and the numerical cooling simulations are mainly in this domain. This second picture is developed in detail to assess key components of modern cooling theory like mixing and signal shielding and to illustrate some of the diagnostic methods. Finally the use of a distribution function and the Fokker-Plank equation, which offer the most complete description of the beam during the cooling, are discussed.

Content:
Front Matter....Pages I-X
Stochastic Cooling of Particle Beams....Pages 1-3
Simplified Theory, Time-Domain Picture....Pages 5-34
Pickup and Kicker Impedance....Pages 35-45
Frequency-Domain Picture....Pages 47-60
A More Detailed Derivation of Betatron Cooling....Pages 61-77
Feedback via the Beam-Signal Shielding....Pages 79-90
The Distribution Function and Fokker-Planck Equations....Pages 91-104
Other Special Applications....Pages 105-113
Back Matter....Pages 115-139

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This lecture note describes the main analytical approaches to stochastic cooling. The first is the time-domain picture, in which the beam is rapidly sampled at a high rate and a statistical analysis is used to describe the cooling behaviour. The second is the frequency-domain picture, which is particularly useful since the observations made on the beam and the numerical cooling simulations are mainly in this domain. This second picture is developed in detail to assess key components of modern cooling theory like mixing and signal shielding and to illustrate some of the diagnostic methods. Finally the use of a distribution function and the Fokker-Plank equation, which offer the most complete description of the beam during the cooling, are discussed.

Content:
Front Matter....Pages I-X
Stochastic Cooling of Particle Beams....Pages 1-3
Simplified Theory, Time-Domain Picture....Pages 5-34
Pickup and Kicker Impedance....Pages 35-45
Frequency-Domain Picture....Pages 47-60
A More Detailed Derivation of Betatron Cooling....Pages 61-77
Feedback via the Beam-Signal Shielding....Pages 79-90
The Distribution Function and Fokker-Planck Equations....Pages 91-104
Other Special Applications....Pages 105-113
Back Matter....Pages 115-139
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