Description:  Spacecharge effects play a dominant role in many areas of physics. In highpower microwave devices using highcurrent, relativistic electron beams, it places a limit on the amount of radiation a device can produce. Because the beam's spacecharge can actually reflect a portion of the beam, the ability to accurately predict the amount of current a device can carry is needed. This current value is known as the spacecharge limited current. Because of the mathematical difficulties, this limit is typically estimated from a onedimensional theory. This work presents a twodimensional theory for calculating an upperbound for the spacecharge limited current of relativistic electron beams propagating in grounded coaxial drift tubes. Applicable to annular beams of arbitrary radius and thickness, the theory includes the effect introduced by a finitelength drift tube of circular crosssection. Using Green's second identity, the need to solve Poisson's equation is transferred to solving a SturmLiouville eigenvalue problem, which is easily solved by elementary methods. In general, the resulting eigenvalue, which is required to estimate the limiting current, must be numerically determined. However, analytic expressions can be found for frequently encountered limiting cases. Spacecharge effects also produce the fundamental collective behavior found in plasmas, especially in plasma sheaths. A plasma sheath is the transition region between a bulk plasma and an adjacent plasmafacing surface. The sheath controls the loss of particles from the plasma in order to maintain neutrality. Using a fully kinetic theory, the problem of a planar sheath with a singleminimum electric potential profile is investigated. Appropriate for single chargestate ions of arbitrary temperature, the theory includes the emission of warm electrons from the surface as well as a net current through the sheath and is compared to particleincell simulations. Approximate expressions are developed for estimating the sheath potential as well as the transition to spacecharge saturation. The case of a spacecharge limited sheath is discussed and compared to the familiar ChildLangmuir law. 

Creator(s):  Stephens, Kenneth Frank 
Creation Date:  August 2000 
Partner(s): 
UNT Libraries

Collection(s): 
UNT Theses and Dissertations

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Publisher Info: 
Publisher Name: University of North Texas
Place of Publication: Denton, Texas


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Description:  Spacecharge effects play a dominant role in many areas of physics. In highpower microwave devices using highcurrent, relativistic electron beams, it places a limit on the amount of radiation a device can produce. Because the beam's spacecharge can actually reflect a portion of the beam, the ability to accurately predict the amount of current a device can carry is needed. This current value is known as the spacecharge limited current. Because of the mathematical difficulties, this limit is typically estimated from a onedimensional theory. This work presents a twodimensional theory for calculating an upperbound for the spacecharge limited current of relativistic electron beams propagating in grounded coaxial drift tubes. Applicable to annular beams of arbitrary radius and thickness, the theory includes the effect introduced by a finitelength drift tube of circular crosssection. Using Green's second identity, the need to solve Poisson's equation is transferred to solving a SturmLiouville eigenvalue problem, which is easily solved by elementary methods. In general, the resulting eigenvalue, which is required to estimate the limiting current, must be numerically determined. However, analytic expressions can be found for frequently encountered limiting cases. Spacecharge effects also produce the fundamental collective behavior found in plasmas, especially in plasma sheaths. A plasma sheath is the transition region between a bulk plasma and an adjacent plasmafacing surface. The sheath controls the loss of particles from the plasma in order to maintain neutrality. Using a fully kinetic theory, the problem of a planar sheath with a singleminimum electric potential profile is investigated. Appropriate for single chargestate ions of arbitrary temperature, the theory includes the emission of warm electrons from the surface as well as a net current through the sheath and is compared to particleincell simulations. Approximate expressions are developed for estimating the sheath potential as well as the transition to spacecharge saturation. The case of a spacecharge limited sheath is discussed and compared to the familiar ChildLangmuir law. 

Degree: 
Name:
Doctor of Philosophy
Level:
Doctoral
Discipline:
Physics
Department:
Department of Physics
Grantor:
University of North Texas


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Keyword(s):  spacecharge limited  ChildLangmuir  plasma sheath  fully kinetic sheath theory  particle simulation  
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Partner: 
UNT Libraries


Collection: 
UNT Theses and Dissertations


Identifier:  
Resource Type:  Thesis or Dissertation  
Format:  Text  
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Public
License:
Copyright
Holder:
Stephens, Kenneth Frank II
Statement:
Copyright is held by the author, unless otherwise noted. All rights reserved.
