3D-Streaming Operator with Multiplying Boundary Conditions: Semigroup Generation Properties

Giovanni Borgioli; Silvia Totaro

doi:10.1007/pl00005905

3D-Streaming Operator with Multiplying Boundary Conditions: Semigroup Generation Properties

Semigroup Forum ◽

10.1007/pl00005905 ◽

1997 ◽

Vol 55 (1) ◽

pp. 110-117 ◽

Cited By ~ 15

Author(s):

Giovanni Borgioli ◽

Silvia Totaro

Keyword(s):

Boundary Conditions ◽

Semigroup Generation ◽

3D Streaming

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Semigroup generation properties of the streaming operator in dependence of the boundary conditions

Transport Theory and Statistical Physics ◽

10.1080/00411459608220716 ◽

1996 ◽

Vol 25 (3-5) ◽

pp. 491-502 ◽

Cited By ~ 4

Author(s):

Giovanni Borgioli ◽

Silvia Totaro

Keyword(s):

Boundary Conditions ◽

Semigroup Generation

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Semigroup generation propertiesof streaming operators with noncontractive boundary conditions

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2004.12.007 ◽

2005 ◽

Vol 42 (13) ◽

pp. 1441-1462 ◽

Cited By ~ 14

Author(s):

B. Lods

Keyword(s):

Boundary Conditions ◽

Semigroup Generation

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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