The paper describes the occurrence of stochastic heating of dust particles in dusty plasmas as an energy instability due to the correlations between dust grain charge and electric field fluctuations. The possibility that the mean energy (“temperature”) of dust particles can grow in time has been found both from the self-consistent kinetic description of dusty plasmas taking into account charge fluctuations [U. de Angelis, A. V. Ivlev, V. N. Tsytovich, and G. E. Morfill, Phys. Plasmas 12(5), 052301 (2005)] and from a Fokker-Planck approach to systems with variable charge [A. V. Ivlev, S. K. Zhdanov, B. A. Klumov, and G. E. Morfill, Phys. Plasmas 12(9), 092104 (2005)]. Here, a different derivation is given by using the mathematical techniques of the so called multiplicative stochastic differential equations. Both cases of “fast” and “slow” fluctuations are discussed.

1.
A. M.
Ignatov
,
Fiz. Plazmy
31
(
1
),
52
(
2005
)
A. M.
Ignatov
, [
Plasma Phys. Rep
.
31
(
1
),
46
(
2005
)].
2.
S. A.
Khrapak
and
G. E.
Morfill
Phys. Plasmas
9
(
2
),
619
(
2002
).
3.
G. E.
Morfill
,
A. V.
Ivlev
, and
J. R.
Jokipii
,
Phys. Rev. Lett.
83
(
5
),
971
(
1999
).
4.
O. S.
Vaulina
,
S. A.
Khrapak
,
A. P.
Nefedov
, and
O. F.
Petrov
,
Phys. Rev. E
60
(
5
),
5959
(
1999
)
5.
U.
de Angelis
,
A. V.
Ivlev
,
V. N.
Tsytovich
, and
G. E.
Morfill
,
Phys. Plasmas
12
(
5
),
052301
(
2005
).
6.
A. V.
Ivlev
,
S. K.
Zhdanov
,
B. A.
Klumov
, and
G. E.
Morfill
,
Phys. Plasmas
12
(
9
),
092104
(
2005
).
7.
A. V.
Ivlev
,
A.
Lazarian
,
V. N.
Tsytovich
,
U.
de Angelis
,
T.
Hoang
, and
G. E.
Morfill
,
Astrophys. J.
723
,
612
(
2010
).
8.
C.
Marmolino
,
U.
de Angelis
,
A. V.
Ivlev
, and
G. E.
Morfill
,
AIP Conf. Proc.
1061
,
105
(
2008
).
9.
C.
Marmolino
,
U.
de Angelis
,
A. V.
Ivlev
, and
G. E.
Morfill
,
Phys. Plasmas
16
,
033701
(
2009
).
10.
M.
Gitterman
,
The Noisy Oscillator. The First Hundred Years, From Einstein Until Now
(
World Scientific
,
New Jersey
,
2005
)
11.
N. J.
Van Kampen
,
Phys. Rep.
24
(
3
),
171
(
1976
).
12.
N. J.
Van Kampen
,
Stochastic Processes in Physics and Chemistry
, (
Elsevier
,
Amsterdam
,
2007
), Chap. XVI.
13.
T.
Matsoukas
and
M.
Russell
,
J. Appl. Phys.
77
(
9
),
4285
(
1995
).
14.
T.
Matsoukas
,
M.
Russell
, and
M.
Smith
,
J. Vac. Sci. Technol. A
14
(
2
),
624
(
1996
).
15.
P. K.
Shukla
and
B.
Eliasson
Rev. Mod. Phys.
81
(
1
),
25
(
2009
).
16.
V. E.
Fortov
,
A. G.
Khrapak
,
S. A.
Khrapak
,
V. I.
Molotkov
, and
O. F.
Petrov
,
Phys.Usp.
47
(
5
),
447
(
2004
).
17.
G. E.
Morfill
and
A. V.
Ivlev
,
Rev. Mod. Phys.
81
(
4
),
1353
(
2009
).
18.
S. C.
Harvey
,
R. K. -Z.K.-Z.
Tan
, and
T. E.
Cheatham
 III
,
J. Comput. Chem.
19
(
7
),
726
(
1998
).
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