We investigate the interaction of electromagnetic waves and electron beams in a 4 m long traveling wave tube (TWT). The device is specifically designed to simulate beam-plasma experiments without appreciable noise. This TWT presents an upgraded slow wave structure (SWS) that results in more precise measurements and makes new experiments possible. We introduce a theoretical model describing wave propagation through the SWS and validated by the experimental dispersion relation, impedance, and phase and group velocities. We analyze nonlinear effects arising from the beam–wave interaction, such as the modulation of the electron beam and the wave growth and saturation process. When the beam current is low, the wave growth coefficient and saturation amplitude follow the linear theory predictions. However, for high values of current, nonlinear space charge effects become important and these parameters deviate from the linear predictions, tending to a constant value. After saturation, we also observe trapping of the beam electrons, which alters the wave amplitude along the TWT.

1.
P. K.
Shukla
,
N. N.
Rao
,
M. Y.
Yu
, and
N. L.
Tsintsadze
,
Phys. Rep.
138
,
1
(
1986
).
2.
Y.
Elskens
and
D. F.
Escande
,
Microscopic Dynamics of Plasmas and Chaos
(
IOP Publishing
,
Bristol
,
2003
).
3.
J. T.
Mendonça
,
Theory of Photon Acceleration
(
IOP Publishing
,
Bristol
,
2001
).
6.
A. J.
Lichtenberg
and
M. A.
Lieberman
,
Regular and Chaotic Dynamics
, 2nd ed. (
Springer
,
New York
,
1992
).
7.
R.
Pakter
and
G.
Corso
,
Phys. Plasmas
2
,
4312
(
1995
).
8.
M. C.
de Sousa
,
F. M.
Steffens
,
R.
Pakter
, and
F. B.
Rizzato
,
Phys. Rev. E
82
,
026402
(
2010
).
9.
M. C.
de Sousa
,
I. L.
Caldas
,
F. B.
Rizzato
,
R.
Pakter
, and
F. M.
Steffens
,
Phys. Rev. E
86
,
016217
(
2012
).
10.
M. C.
de Sousa
and
I. L.
Caldas
,
Phys. Plasmas
25
,
043110
(
2018
).
11.
C. F. F.
Karney
,
Phys. Fluids
21
,
1584
(
1978
).
12.
T. M.
Corrêa da Silva
,
R.
Pakter
,
F. B.
Rizzato
,
M. C.
de Sousa
,
I. L.
Caldas
, and
F. M.
Steffens
,
Phys. Rev. E
88
,
013101
(
2013
).
13.
N. J.
Fisch
,
Rev. Mod. Phys.
59
,
175
(
1987
).
14.
H. L.
Berk
,
B. N.
Breizman
, and
H.
Ye
,
Phys. Rev. Lett.
68
,
3563
(
1992
).
15.
R. C.
Davidson
and
H.
Qin
,
Physics of Intense Charged Particle Beams in High Energy Accelerators
(
World Scientific
,
London
,
2001
).
16.
D. A.
Edwards
and
M. J.
Syphers
,
An Introduction to the Physics of High Energy Accelerators
(
Wiley-VCH
,
Weinheim
,
2004
).
17.
A. S.
Gilmour
, Jr.
,
Klystrons, Traveling Wave Tubes, Magnetrons, Cross-Field Amplifiers, and Gyrotrons
(
Artech House Radar Library
,
Boston
,
2011
).
18.
J. R.
Pierce
,
Traveling Wave Tubes
(
Van Nostrand
,
New York
,
1950
).
19.
A. S.
Gilmour
, Jr.
,
Principles of Traveling Wave Tubes
(
Artech House
,
London
,
1994
).
20.
G.
Faillon
,
G.
Kornfeld
,
E.
Bosch
, and
M. K.
Thumm
, “Microwave tubes,” in
Vacuum Electronics
(
Springer
,
Berlin
,
2008
), pp.
1
82
.
21.
D. F. G.
Minenna
,
F.
André
,
Y.
Elskens
,
J.-F.
Auboin
,
F.
Doveil
,
J.
Puech
, and
É.
Duverdier
,
Eur. Phys. J. H
44
(
1
),
1
(
2019
).
22.
G.
Dimonte
and
J. H.
Malmberg
,
Phys. Rev. Lett.
38
,
401
(
1977
).
23.
G.
Dimonte
and
J. H.
Malmberg
,
Phys. Fluids
21
,
1188
(
1978
).
24.
S. I.
Tsunoda
,
F.
Doveil
, and
J. H.
Malmberg
,
Phys. Rev. Lett.
58
,
1112
(
1987
).
25.
S. I.
Tsunoda
,
F.
Doveil
, and
J. H.
Malmberg
,
Phys. Fluids B
3
,
2747
(
1991
).
26.
D. A.
Hartmann
,
C. F.
Driscoll
,
T. M.
O'Neil
, and
V. D.
Shapiro
,
Phys. Plasmas
2
,
654
(
1995
).
27.
D.
Guyomarc'h
, “
Un tube à onde progressive pour l'étude de la turbulence plasma
,” Ph.D. thesis (
Université de Provence
, Marseilles, France,
1996
).
28.
F.
Doveil
,
D. F.
Escande
, and
A.
Macor
,
Phys. Rev. Lett.
94
,
085003
(
2005
).
29.
F.
Doveil
,
A.
Macor
, and
K.
Auhmani
,
Plasma Phys. Controlled Fusion
47
,
A261
(
2005
).
30.
A.
Macor
, “
D'un faisceau test à l'auto-cohérence dans l'interaction onde-particule
,” Ph.D. thesis (
Université de Provence
, Marseilles, France,
2007
).
31.
F.
Doveil
and
A.
Macor
,
Phys. Rev. E
84
,
045401
(
2011
).
33.
34.
T. M.
O'Neil
,
J. H.
Winfrey
, and
J. H.
Malmberg
,
Phys. Fluids
14
,
1204
(
1971
).
35.
T. M.
O'Neil
and
J. H.
Winfrey
,
Phys. Fluids
15
,
1514
(
1972
).
36.
C.
Chandre
,
G.
Ciraolo
,
F.
Doveil
,
R.
Lima
,
A.
Macor
, and
M.
Vittot
,
Phys. Rev. Lett.
94
,
074101
(
2005
).
37.
F.
Doveil
,
A.
Macor
, and
Y.
Elskens
,
Chaos
16
,
033103
(
2006
).
38.
A.
Macor
,
F.
Doveil
,
C.
Chandre
,
G.
Ciraolo
,
R.
Lima
, and
M.
Vittot
,
Eur. Phys. J. D
41
,
519
(
2007
).
39.
A.
Macor
,
F.
Doveil
, and
E.
Garabedian
,
Nonlinear Phenom. Complex Syst.
10
,
180
(
2007
).
40.
J. L.
Tennyson
,
J. D.
Meiss
, and
P. J.
Morrison
,
Physica D
71
,
1
(
1994
).
41.
D.
del Castillo-Negrete
and
M.-C.
Firpo
,
Chaos
12
,
496
(
2002
).
42.
A. A.
Vedenov
,
E. P.
Velikhov
, and
R. Z.
Sagdeev
,
Nucl. Fusion, Suppl.
2
,
465
(
1962
).
43.
W. E.
Drummond
and
D.
Pines
,
Nucl. Fusion, Suppl.
3
,
1049
(
1962
).
44.
A. A.
Vedenov
,
J. Nucl. Energy, Part C
5
,
169
(
1963
).
45.
Y.
Elskens
,
Phys. AUC
17
,
109
(
2007
).
46.
Y.
Elskens
,
Commun. Nonlinear Sci. Numer. Simul.
15
,
10
(
2010
).
47.
Y.
Elskens
and
E.
Pardoux
,
Ann. Appl. Probab.
20
,
2022
(
2010
).
48.
N.
Besse
,
Y.
Elskens
,
D. F.
Escande
, and
P.
Bertrand
,
Plasma Phys. Controlled Fusion
53
,
025012
(
2011
).
49.
Y.
Elskens
,
J. Stat. Phys.
148
,
591
(
2012
).
50.
F.
André
,
P.
Bernardi
,
N. M.
Ryskin
,
F.
Doveil
, and
Y.
Elskens
,
Europhys. Lett.
103
,
28004
(
2013
).
51.
D. F. G.
Minenna
,
Y.
Elskens
,
F.
André
, and
F.
Doveil
,
Europhys. Lett.
122
,
44002
(
2018
).
52.
D. F. G.
Minenna
,
Y.
Elskens
,
F.
André
,
A.
Poyé
,
J.
Puech
, and
F.
Doveil
,
IEEE Trans. Electron Devices
66
,
4042
(
2019
).
53.
D.
Guyomarc'h
and
F.
Doveil
,
Rev. Sci. Instrum.
71
,
4087
(
2000
).
54.
H.
Spohn
,
Dynamics of Charged Particles and Their Radiation Fields
(
Cambridge University Press
,
Cambridge
,
2004
).
55.
J. D.
Jackson
,
Classical Electrodynamics
, 3rd ed. (
Wiley
,
New York
,
1999
).
56.
J. H.
Malmberg
and
C. B.
Wharton
,
Phys. Fluids
12
,
2600
(
1969
).
57.
R.
Kompfner
,
J. Br. Inst. Radio Eng.
10
,
283
(
1950
).
58.
59.
C. K.
Birdsall
and
G. R.
Brewer
,
IRE Trans. Electron Devices
4
,
1
(
1954
).
60.
G. M.
Branch
and
T. G.
Mihran
,
IRE Trans. Electron Devices
2
,
3
(
1955
).
61.
D. F. G.
Minenna
,
A. G.
Terentyuk
,
F.
André
,
Y.
Elskens
, and
N. M.
Ryskin
,
Phys. Scr.
94
,
055601
(
2019
).
You do not currently have access to this content.