A detailed investigation of rescaled range (R/S) analysis to search for long-time correlations (via the Hurst exponent, H) in plasma turbulence is presented. In order to elucidate important issues related to R/S analysis, structure functions (SFs), one of several techniques available for calculating H, are also applied, and comparisons between the two methods are made. Time records of both simulated data and fluctuation reflectometry data from the DIII-D tokamak [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] are analyzed. It is found that the R/S method can be used to accurately determine H, provided a long enough data record is used, and that H is an indicator of persistence in the data. In addition, subtleties of the correct application of both methods are discussed, and potential advantages of SFs are pointed out.

1.
D. E.
Newman
,
B. A.
Carreras
,
P. H.
Diamond
, and
T. S.
Hahm
,
Phys. Plasmas
3
,
1858
(
1996
).
2.
J. A.
Krommes
,
Phys. Plasmas
7
,
1752
(
2000
).
3.
B. A.
Carreras
,
B. Ph.
van Milligen
,
M. A.
Pedrosa
et al.,
Phys. Plasmas
5
,
3632
(
1998
).
4.
H. E.
Hurst
,
Trans. Am. Soc. Civ. Eng.
116
,
770
(
1951
).
5.
B. B.
Mandelbrot
and
J. R.
Willis
,
Water Resour. Res.
4
,
909
(
1968
).
6.
G.
Wang
,
G.
Antar
, and
P.
Devynck
,
Phys. Plasmas
7
,
1181
(
2000
).
7.
G.
Antar
,
P.
Devynck
, and
G. D.
Wang
,
Phys. Plasmas
7
,
5269
(
2000
).
8.
A.
Davis
,
A.
Marshak
,
W.
Wiscombe
, and
R.
Calahan
,
J. Geophys. Res.
99
,
8055
(
1994
).
9.
M. J.
Cannon
,
D. B.
Percival
,
D. C.
Caccia
,
G. M.
Raymond
, and
J. B.
Bassingthwiaghte
,
Physica A
241
,
606
(
1997
).
10.
J. B.
Bassingthwaighte
and
G. M.
Raymond
,
Ann. Biomed. Eng.
23
,
491
(
1995
).
11.
P.
Flanrin
,
IEEE Trans. Inf. Theory
35
,
197
(
1989
).
12.
J. Beren, Statistics for Long-Memory Processes (Chapman and Hall, New York, 1994), pp. 41–45.
13.
R. B.
Davies
and
D. S.
Harte
,
Biometrika
74
,
95
(
1987
).
14.
D. B.
Percival
,
Comput. Sci. Statistics
24
,
534
(
1992
).
15.
E. J.
Doyle
,
T.
Lehecka
,
N. C.
Luhmann
, Jr.
,
W. A.
Peebles
,
R.
Philipona
,
K. H.
Burrell
,
R. J.
Groebner
,
H.
Matsumoto
, and
T. H.
Osborne
,
Rev. Sci. Instrum.
61
,
3016
(
1990
).
16.
B. A.
Carreras
,
D. E.
Newman
,
B. P.
van Milligen
, and
C.
Hidalgo
,
Phys. Plasmas
6
,
485
(
1999
).
17.
B. Ph.
van Milligan
,
C.
Hidalgo
, and
B. A.
Carreras
,
Phys. Plasmas
7
,
5267
(
2000
).
This content is only available via PDF.
You do not currently have access to this content.