Analysis of the dynamic behavior of an intense charged particle beam using the semigroup approach

Thesis/Dissertation · Sun Jan 01 00:00:00 EST 1984

OSTI ID:7021638

Stafford, M A

Dynamic models of a charged particle beam subject to external electromagnetic fields are cast into the abstract Cauchy problem form. Various applications of intense charged particle beams, i.e., beams whose self electromagnetic fields are significant, might require, or be enhanced by, the use of dynamic control constructed from suitably processed measurements of the state of the beam. This research provides a mathematical foundation for future engineering development of estimation and control designs for such beams. Beginning with the Vlasov equation, successively simpler models of intense beams are presented, along with their corresponding assumptions. Expression of a model in abstract Cauchy problem form is useful in determining whether the model is well posed. Solutions of well-posed problems can be expressed in terms of a one-parameter semigroup of linear operators. The semigroup point of view allows the application of the rapidly maturing modern control theory of infinite dimensional system. An appropriate underlying Banach space is identified for a simple, but nontrivial, single degree of freedom model (the electrostatic approximation model), and the associated one-parameter semigroup of linear operators is characterized.

• Research Organization: Air Force Inst. of Tech., Wright-Patterson AFB, OH (USA)
• OSTI ID: 7021638
• Resource Relation: Other Information: Thesis (Ph. D.)
• Country of Publication: United States
• Language: English

Related Subjects

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GENERAL PHYSICS
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ELECTRON BEAMS
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ION BEAMS
BANACH SPACE
BOLTZMANN-VLASOV EQUATION
CAUCHY PROBLEM
ELECTROMAGNETIC FIELDS
LINEAR MOMENTUM OPERATORS
MATHEMATICAL MODELS
BEAMS
DIFFERENTIAL EQUATIONS
EQUATIONS
LEPTON BEAMS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
QUANTUM OPERATORS
RADIATION TRANSPORT
SPACE
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