scholarly journals SOTRM: A PROGRAM TO GENERATE FIRST AND SECOND ORDER MATRIX ELEMENTS BY TRACKING CHARGED PARTICLES IN A SPECIFIED MAGNETIC FIELD.

1970 ◽  
Author(s):  
E.R. Close
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Second Order ◽  
Matrix Elements ◽  
Order Matrix

Second-order energies and third-order matrix elements of alkali-metal atoms

1987 ◽  
Vol 35 (8) ◽  
pp. 3218-3226 ◽  
Author(s):  
W. R. Johnson ◽  
M. Idrees ◽  
J. Sapirstein
Keyword(s):  
Alkali Metal ◽  
Second Order ◽  
Matrix Elements ◽  
Third Order ◽  
Metal Atoms ◽  
Order Matrix

Second-order treatment of the influence of space charge and external fields on rotationally symmetric finite-emittance relativistic beams of charged particles

1985 ◽  
Vol 63 (8) ◽  
pp. 1092-1097
Author(s):  
Giulio Bosi
Keyword(s):  
Magnetic Field ◽  
Space Charge ◽  
Charged Particles ◽  
External Electromagnetic Field ◽  
Second Order ◽  
Longitudinal Motion ◽  
Standard Geometry ◽  
Rotationally Symmetric ◽  
Longitudinal Effects ◽  
Suitable Generalization

The present paper reports a relativistic treatment of space-charge effects on rotationally symmetric beams of charged particles under the influence of an external electromagnetic field. The general form of a stationary distribution describing a homogeneous, monokinetic beam is suggested, and the details of a suitable generalization of the Kapchinskij–Vladimirskij distribution are fully developed. It is shown that if second-order terms, which mainly affect the longitudinal motion, are retained, the given distribution actually provides a parabolic charge density throughout a beam cross section while the longitudinal current density remains uniform, as is usually assumed. The relativistic version of the envelope equation, including the magnetic field, is also calculated and its classical limit is compared with an available equation applicable to a beam under the influence of merely an electric field. Emittance-dependent discrepancies, related to the longitudinal effects of the space charge, are detected. The standard geometry of a rotationally symmetric Pierce gun is finally revised to allow for the addition of an external magnetic field.

Matrix Representation for Calculation of the Second-Order Aberration in Ion Optics

1966 ◽  
Vol 21 (1-2) ◽  
pp. 9-14
Author(s):  
Isao Takeshita
Keyword(s):  
Magnetic Field ◽  
Matrix Method ◽  
Arbitrary Shape ◽  
Matrix Representation ◽  
Homogeneous Magnetic Field ◽  
Second Order ◽  
Matrix Elements ◽  
Ion Trajectory ◽  
Ion Optics ◽  
The Matrix

The matrix representation for calculating the ion trajectory is extended to include the secondorder aberration terms.Properties of the matrix and relations between its elements are discussed.As an example of the application of the matrix method, the second-order coefficients of a homogeneous magnetic field of arbitrary shape are derived and the relations between the matrix elements and Hinterberger's notations are shown.

scholarly journals 46. The störmertron

1958 ◽  
Vol 6 ◽  
pp. 446-447
Author(s):  
Willard H. Bennett
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Mercury Vapor ◽  
Electron Gun ◽  
Conducting Film ◽  
New Developments ◽  
Electrically Conducting ◽  
The Earth ◽  
Magnetic Dipole Field ◽  
Glass Tubes

A tube has been developed in which the shapes of streams of charged particles moving in the earth's magnetic field can be produced accurately to scale. The tube has been named the Störmertron in honor of Carl Störmer who calculated many such orbits. New developments which have made this tube possible include a method for coating the inside of large glass tubes with a transparent electrically conducting film, and an electron gun producing gas-focused streams in less than ½ micron of mercury vapor, a nearly vapor-free grease joint, and a nearly vapor-free carbon black. The magnetic dipole field of the earth is simulated with an Alnico magnet capped with properly shaped soft iron caps. The stream is deflected using two pairs of yoke coils near the gun.

scholarly journals A Markovian canonical form of second-order matrix-exponential processes

2008 ◽  
Vol 190 (2) ◽  
pp. 459-477 ◽  
Author(s):  
L. Bodrog ◽  
A. Heindl ◽  
G. Horváth ◽  
M. Telek
Keyword(s):  
Canonical Form ◽  
Second Order ◽  
Matrix Exponential ◽  
Order Matrix
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