Time independent states are explored theoretically for generalized Pierce diode (non-neutral plasma diode with ionic background), which is driven by a cold relativistic electron beam. The region between the electrodes is assumed to be filled uniformly with static ions. Injected beam is monochromatic, i.e., all the electrons are emitted with the same kinetic energy (relativistic). Relativistic effects are explored both for collisionless and collisional systems. The formulation of the model is based on the fluid-Maxwell's equations and it is solved by two methods: in the absence of any dissipative source, Eulerian description is employed, whereas to incorporate the effects of collisional drag Lagrangian formulation is found to be useful. The steady-state solutions are visualized through the “Bursian” and “Non-Bursian” branches in a parametric plane. It is observed that the magnitude of the maximum current density of a Pierce diode increases with the relativistic factor of the injected beam. Other factors like the density of background ions and particle collision also have significant influence on the space-charge-limited flow and other steady state properties. Obtained results are relevant to comprehend the working mechanism of many diode-based instruments such as thermionic energy converters, microwave emitter, Q-machines, etc.

1.
H.
Sze
,
J.
Benford
, and
B.
Harteneck
,
Phys. Fluids
29
,
5875
(
1986
).
2.
J.
Benford
,
J. A.
Swegle
, and
E.
Schamiloglu
,
High Power Microwaves
(
CRC Press, Taylor and Francis
,
2007
).
3.
V. I.
Babanin
,
I. N.
Kolyshkin
,
V. I.
Kuznetsov
,
V. I.
Sitnov
, and
A. Ya.
Ender
, “
Physics of thermionic energy converters
,” in
Proceedings of 2nd Intersociety Conference on Nuclear Power Engineering in Space
, Sukhumi, Georgia (
Vekua Institute of Physics and Technology
,
Sukhumi
,
1991
), p.
9
.
4.
R. W.
Motley
,
Q-Machine
(
Academic Press
,
1975
).
5.
D. J.
Sullivan
,
J. E.
Walsh
, and
E. A.
Coutsias
,
Virtual Cathode Oscillator (Vircator) Theory
, High Power Microwave Sources Vol.
13
(
Artech House Microwave Library
,
NY
,
1987
).
6.
R. A.
Mahaffey
,
P. A.
Sprangle
,
J.
Golden
, and
C. A.
Kapetanakos
,
Phys. Rev. Lett.
39
,
843
(
1977
).
7.
R. A.
Filatov
,
A. E.
Hramov
,
Y. P.
Bliokh
,
A. A.
Koronovskii
, and
J.
Felsteiner
,
Phys. Plasmas
16
,
033106
(
2009
).
8.
V. I.
Kuznetsov
,
A. V.
Solov'ev
, and
A. Ya.
Ender
,
Tech. Phys.
38
,
1207
(
1994
).
9.
A. Ya.
Ender
,
H.
Kolinsky
,
V. I.
Kuznetsov
, and
H.
Schamel
,
Phys. Rep.
328
,
1
(
2000
).
10.
Y. A.
Kalinin
,
A. A.
Koronovskii
,
A. E.
Khramov
,
E. N.
Egorov
, and
R. A.
Filatov
,
Plasma Phys. Rep.
31
,
938
(
2005
).
11.
V. I.
Kuznetsov
and
A. Ya.
Ender
,
Plasma Phys. Rep.
36
,
236
(
2010
).
12.
J.
Frey
and
C. K.
Birdsall
,
J. Appl. Phys.
36
,
2962
(
1965
).
13.
I. G.
Gverdtsiteli
,
V. Ya.
Karakhanov
,
E. A.
Kashirskii
,
R. Ya.
Kucherov
, and
Z. A.
Oganezov
,
Sov. Phys. - Tech. Phys.
17
,
78
(
1972
).
14.
V. I.
Babanin
,
I. N.
Kolyshkin
,
V. I.
Kuznetsov
,
A. S.
Mustafiev
,
V. I.
Sitnov
, and
A. Ya.
Ender
,
Sov. Phys. - Tech. Phys.
27
,
793
(
1982
).
15.
V. I.
Babanin
,
A. Ya.
Ender
,
I. N.
Kolyshkin
,
V. I.
Kuznetsov
,
V. I.
Sitnov
, and
D. V.
Paramonov
, “
Next generation solar bimodal systems
,” in
Proceedings of 32rd IECEC
(AIChE,
1997
), Vol. 427.
16.
17.
Yu. N.
Garstein
and
P. S.
Ramesh
,
J. Appl. Phys.
83
,
2958
(
1998
).
18.
V. R.
Bursian
and
V. I.
Pavlov
,
Zh. Russ. Fiz.-Khim. O-va.
55
,
71
(
1923
) (in Russian).
19.
J. R.
Pierce
,
J. Appl. Phys.
15
,
721
(
1944
).
20.
B. B.
Godfrey
,
Phys. Fluids
30
,
1553
(
1987
).
21.
W. S.
Lawson
,
Phys. Fluids B
1
,
1483
(
1989
).
22.
J. E.
Boers
and
D.
Kelleher
,
J. Appl. Phys.
40
,
2409
(
1969
).
23.
H.
Schamel
and
V.
Maslov
,
Phys. Rev. Lett.
70
,
1105
(
1993
).
24.
H.
Kolinsky
and
H.
Schamel
,
Phys. Plasmas
1
,
2359
(
1994
).
25.
P. V.
Akimov
,
H.
Schamel
,
H.
Kolinsky
,
A. Ya.
Ender
, and
V. I.
Kuznetsov
,
Phys. Plasmas
8
,
3788
(
2001
).
26.
P. V.
Akimov
,
H.
Schamel
,
A. Ya.
Ender
, and
V. I.
Kuznetsov
,
J. Appl. Phys.
93
,
1246
(
2003
).
27.
A. Ya.
Ender
,
V. I.
Kuznetsov
,
H.
Schamel
, and
P. V.
Akimov
,
Phys. Plasmas
11
,
3212
(
2004
).
28.
Y.
Feng
and
J. P.
Verboncoeur
,
Phys. Plasmas
15
,
112101
(
2008
).
29.
X.
Tang
and
P. K.
Shukla
,
Phys. Plasmas
15
,
023702
(
2008
).
30.
A.
Pedersen
,
A.
Manolescu
, and
A.
Valfells
,
Phys. Rev. Lett.
104
,
175002
(
2010
).
31.
V. I.
Kuznetsov
and
A. Ya.
Ender
,
Plasma Phys. Rep.
36
,
226
(
2010
).
32.
A. Y.
Ender
,
V. I.
Kuznetsov
, and
H.
Schamel
,
Phys. Plasmas
18
,
033502
(
2011
).
33.
V. I.
Kuznetsov
and
A. Ya.
Ender
,
Tech. Phys.
58
,
1705
(
2013
).
34.
S. A.
Kurkin
,
A. E.
Hramov
, and
A. A.
Koronovskii
,
Appl. Phys. Lett.
103
,
043507
(
2013
).
35.
M. S.
Rosin
and
H.
Sun
,
Phys. Rev. E
87
,
043114
(
2013
).
36.
S.
Pramanik
,
A. Ya.
Ender
,
V. I.
Kuznetsov
, and
N.
Chacrabarti
,
Phys. Plasmas
22
,
042110
(
2015
).
37.
S.
Pramanik
,
V. I.
Kuznetsov
,
A. B.
Gerasimenko
, and
N.
Chakrabarti
,
Phys. Plasmas
23
,
062118
(
2016
).
38.
A. Ya.
Ender
,
S.
Kuhn
, and
V. I.
Kuznetsov
,
Phys. Plasmas
13
,
113506
(
2006
).
39.
V. I.
Kuznetsov
,
A. Ya.
Ender
, and
V. I.
Babanin
,
J. Appl. Phys.
124
,
044502
(
2018
).
40.
P. V.
Akimov
and
H.
Schamel
,
J. Appl. Phys.
92
,
1690
(
2002
).
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