This paper describes a double‐stream analysis that can be used to investigate interactions in any finite multiple‐charged drifting particle stream immersed in a finite longitudinal dc magnetic field that is parallel to the drift velocity. The advantages of the analysis are that collisions and longitudinal thermal velocity effects are included along with transverse waves (fast and slow) and space‐charge waves with the only approximations being small‐signal linearization and negligible transverse thermal velocity. In addition, the finiteness of the charged‐particle streams and the boundary conditions are taken into account. The results of the analysis are field expressions which can be used to obtain a determinantal equation in ω by satisfying the appropriate boundary conditions.

1.
I. B.
Bernstein
,
Phys. Rev.
109
,
10
(
1958
).
Google Scholar
Crossref
Search ADS
 
2.
E. G.
Harris
,
J. Nucl. Energy C
2
,
138
(
1961
).
Google Scholar
Crossref
Search ADS
 
3.
A. J.
Lichtenberg
 and
J. S.
Jayson
,
J. Appl. Phys.
36
,
449
(
1965
).
Google Scholar
Crossref
Search ADS
 
4.
B.
Vural
 and
M. C.
Steele
,
Phys. Rev. A
139
,
300
(
1965
).
Google Scholar
Crossref
Search ADS
 
5.
B. J.
Maxum
 and
A. W.
Trivelpiece
,
J. Appl. Phys.
36
,
481
(
1965
).
Google Scholar
Crossref
Search ADS
 
6.
B.
Vural
,
RCA Rev. (Radio Corp. Am.)
22
,
753
(
1961
).
Google Scholar
 
7.
C. H.
Durney
,
D. A.
Christensen
, and
R. W.
Grow
,
IEEE Trans. Electron. Devices
ED‐16
,
609
(
1969
).
Google Scholar
 
8.
R. W. Grow, First Interim Report, Contract No. AF 33(615)‐3686, Microwave Device and Physical Electronics Laboratory, University of Utah, Salt Lake City, Utah (unpublished).
9.
L. C. Goodrich, C. H. Durney, and R. W. Grow (unpublished).
10.
L. C.
Goodrich
,
C. H.
Durney
, and
R. W.
Grow
,
Phys. Fluids
15
,
715
(
1972
).
Google Scholar
Crossref
Search ADS
 
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© 1974 American Institute of Physics.
1974
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