First‐Order Space‐Charge Correction

1963 ◽  
Vol 34 (5) ◽  
pp. 1568-1569 ◽  
Author(s):  
D. S. Colburn ◽  
G. S. Kino
Keyword(s):  
Space Charge ◽  
First Order

First-order covariant treatment of the influence of space charge and external fields on finite-emittance relativistic beams of charged particles in generalized curvilinear coordinates

1989 ◽  
Vol 67 (7) ◽  
pp. 678-685
Author(s):  
Giulio Bosi
Keyword(s):  
Distribution Function ◽  
Space Charge ◽  
Charged Particles ◽  
Curvilinear Coordinates ◽  
Coordinate Space ◽  
Transverse Motion ◽  
Metric Tensor ◽  
First Order ◽  
Dimensional Phase Space ◽  
Principal Axes

A first-order covariant treatment of space-charge effects on relativistic beams of charged particles under the influence of applied fields of arbitrary forms is presented. The beams and fields are assumed to fulfill no particular symmetry conditions, and curvilinear orthogonal coordinates are used. Relative to a given distribution function, a suitable choice of both metric tensor and optical axis allows for the selection of appropriate coordinates, reducing the overall transverse motion of a charged particle to a pair of independent motions along the principal axes of a tensor that is related to both geometry and field. Detailed formulas applying to a microcanonical distribution in an eight-dimensional phase space are worked out, and the envelope equations for a monokinetic beam are carried out explicitly. The distribution function is shown to separate into the product of a stationary distribution in transverse-coordinate space and momentum space by using factors carrying the relativistic corrections. As a result, the envelope equations are formally identical to the customary equations describing the envelope of a nonrelativistic beam under the influence of merely transverse forces. A few numerical applications are finally presented; the behavior of beams moving through a magnetic prism and through a cycloidal analyzer is displayed graphically.

Die Raumladungsbremsung von Elektronenlawinen

1959 ◽  
Vol 14 (11) ◽  
pp. 989-994
Author(s):  
K. J. Schmidt-Tiedemann
Keyword(s):  
Electric Field ◽  
Space Charge ◽  
Electron Avalanche ◽  
Homogeneous Electric Field ◽  
First Order ◽  
Charge Field ◽  
The Common ◽  
Negative Space ◽  
Theoretical Results ◽  
First Order Perturbation

The electric field generated by the positive and negative space charge of a single electron avalanche moving in a homogeneous electric field is calculated. Treating the interaction of the avalanche with its own space charge field as a first order perturbation, a growth formula is obtained which differs markedly from the common TOWNSEND formula. The theoretical results fit well with experimental data on avalanche statistics reported in the literature.

A First Order Space Charge Option for TRANSOPTR

1983 ◽  
Vol 30 (4) ◽  
pp. 2666-2668 ◽  
Author(s):  
M. S. de Jong ◽  
E. A. Heighway
Keyword(s):  
Space Charge ◽  
First Order

Temperature Dependence of a-Si:H Nip Diodes

1991 ◽  
Vol 219 ◽  
Author(s):  
C. van Berkel ◽  
M. J. Powell ◽  
I. D. French
Keyword(s):  
Activation Energy ◽  
Space Charge ◽  
Temperature Dependence ◽  
Quality Factor ◽  
Physical Interpretation ◽  
Linear Dependence ◽  
Space Charge Limited Current ◽  
Temperature Expansion ◽  
First Order ◽  
Hole Recombination

ABSTRACTWe analyse the temperature dependence of the forward characteristics of a-Si:H nip diodes, which are characterised by a well defined exponential region at low bias and space charge limited current at higher bias. At each bias, the temperature dependence of the diodes shows a well defined activation energy and a linear dependence on bias exists for both the activation energy and exponential prefactor. We describe these phenomena with a first order temperature expansion of the diode quality factor n and present a physical interpretation in terms of electron and hole recombination in the i-layer.

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