Analysis of the dynamic behavior of an intense charged-particle beam using the semigroup approach. Doctoral thesis

Technical Report · Wed May 01 00:00:00 EDT 1985

OSTI ID:6276463

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 state transition matrix for a system of linear, ordinary, first-order, constant coefficient differential equations is a special case of such a semigroup.) The semigroup point of view allows the application of the rapidly maturing modern control theory of infinite-dimensional systems. An appropriate underlying Banach space is identified for a simple, but non-trivial, 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). School of Engineering
• OSTI ID: 6276463
• Report Number(s): AD-A-159247/6/XAB; TRN: 86-005205
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
42 ENGINEERING
CHARGED PARTICLES
PARTICLE BEAMS
CAUCHY PROBLEM
CONTROL THEORY
BANACH SPACE
DIFFERENTIAL EQUATIONS
DYNAMICS
ELECTROMAGNETIC FIELDS
ELECTROSTATICS
MATHEMATICAL MODELS
BEAMS
EQUATIONS
MATHEMATICAL SPACE
MECHANICS
SPACE
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