A stochastic differential equation for intermittent plasma density dynamics in magnetic fusion edge plasma is derived, which is consistent with the experimentally measured gamma distribution and the theoretically expected quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. The sensitivity of intermittency to the nonlinear dynamics is investigated by analyzing the nonlinear Langevin representation of the beta process, which leads to a root-square nonlinearity.

1.
B. A.
Carreras
,
J. Nucl. Mater.
337
,
315
(
2005
).
2.
D. A.
D'Ippolito
,
J. R.
Myra
, and
S. J.
Zweben
,
Phys. Plasmas
18
,
060501
(
2011
).
3.
J. A.
Krommes
,
Phys. Rep.
360
,
1
(
2002
).
4.
J. A.
Krommes
,
Phys. Plasmas
15
,
030703
(
2008
).
5.
I.
Sandberg
,
S.
Benkadda
,
X.
Garbet
,
G.
Ropokis
,
K.
Hizanidis
, and
del-Castillo-Negrete
,
Phys. Rev. Lett.
103
,
165001
(
2009
).
6.
J. P.
Graves
,
J.
Horacek
,
R. A.
Pitts
, and
K. I.
Hopcraft
,
Plasma Phys. Controlled Fusion
47
,
L1
(
2005
).
7.
B.
Labit
,
I.
Furno
,
A.
Fasoli
,
A.
Diallo
,
S. H.
Müller
,
G.
Plyushchev
,
M.
Podest
, and
F. M.
Poli
,
Phys. Rev. Lett.
98
,
255002
(
2007
).
8.
E.
Jakeman
and
P. N.
Pusey
,
Phys. Rev. Lett.
40
,
546
(
1978
).
9.
O. E.
Garcia
,
Phys. Rev. Lett.
108
,
265001
(
2012
).
10.
S. O.
Rice
,
Bell Syst. Tech. J.
23
,
282
(
1944
).
11.
E.
Jakeman
,
J. Phys. A: Math. Gen.
13
,
31
(
1980
).
12.
C.
Gardiner
,
Stochastic Methods
(
Springer
,
2009
).
13.
A.
Mekkaoui
,
Y.
Marandet
,
D.
Reiter
,
P.
Boerner
,
P.
Genesio
,
J.
Rosato
,
R.
Stamm
,
H.
Capes
,
M.
Koubiti
, and
L.
Godbert-Mouret
,
Phys. Plasmas
19
,
060701
(
2012
).
14.
H.
Cramér
,
Mathematical Methods of Statistics
(
Asia Publishing House
,
1961
).
15.
T.
Ozaki
, “
Nonlinear time series models and dynamical systems
,” in
Handbook of Statistics
(
Elsevier, North-Holland
,
Amsterdam
,
1985
), Vol.
5
.
16.
T.
Ozaki
,
Stat. Sin.
2
,
113
(
1992
).
17.
J. C.
Cox
,
J. E.
Ingersoll
, and
J. S. A.
Ross
,
Econometrica
53
,
385
(
1985
).
18.
N. H.
Bian
,
Phys. Plasmas
17
,
044501
(
2010
).
19.
P.
Krishnaiah
and
M.
Rao
,
Am. Math. Monthly
68
,
342
(
1961
).
20.
S.
Kotz
,
N.
Balakrishnan
, and
N. L.
Johnson
,
Continuous Multivariate Distributions
(
John Wiley & Sons
,
2000
).
21.
E.
Lukacs
,
Ann. Math. Stat.
26
,
319
(
1955
).
22.
E.
McKenzie
,
J. Appl. Prob.
19
,
463
(
1982
).
23.
A. M.
Kagan
,
Y. V.
Linnik
, and
C. R.
Rao
,
Characterization Problems in Mathematical Statistics
(
John Wiley & Sons
,
New York
,
1973
).
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