In order to provide scaling formulae for the geodesic acoustic mode (GAM) frequency and damping rate, GAMs are studied by means of the gyrokinetic global particle-in-cell code ORB5. Linear electromagnetic simulations in the low-βe limit have been performed in order to separate acoustic and Alfvénic time scales and obtain more accurate measurements. The dependence of the frequency and damping rate on several parameters such as the safety factor, the GAM radial wavenumber, and the plasma elongation is studied. All simulations have been performed with kinetic electrons with a realistic electron/ion mass ratio. Interpolating formulae for the GAM frequency and damping rate, based on the results of the gyrokinetic simulations, have been derived. Using these expressions, the influence of the temperature gradient on the damping rate is also investigated. Finally, the results are applied to the study of a real discharge of the ASDEX Upgrade tokamak.

1.
W.
Horton
,
Rev. Mod. Phys.
71
,
735
(
1999
).
2.
P.
Manz
,
M.
Ramisch
, and
U.
Stroth
,
Phys. Rev. Lett.
103
,
165004
(
2009
).
3.
A.
Hasegawa
,
C. G.
Maclennan
, and
Y.
Kodama
,
Phys. Fluids
22
,
2122
(
1979
).
4.
M. N.
Rosenbluth
and
F. L.
Hinton
,
Phys. Rev. Lett.
80
,
724
(
1998
).
5.
P. H.
Diamond
,
S. I.
Itoh
,
K.
Itoh
, and
T. S.
Hahm
,
Plasma Phys. Controlled Fusion
47
,
R35
(
2005
).
6.
Ö. D.
Gürcan
and
P. H.
Diamond
,
J. Phys. A: Math. Theor.
48
,
293001
(
2015
).
7.
N.
Winsor
,
J. L.
Johnson
, and
J. M.
Dawson
,
Phys. Fluids
11
,
2448
(
1968
).
8.
F.
Zonca
and
L.
Chen
,
Europhys. Lett.
83
,
35001
(
2008
).
9.
A. I.
Smolyakov
,
M. F.
Bashir
,
A. G.
Elfimov
,
M.
Yagi
, and
N.
Miyato
,
Plasma Phys. Rep.
42
,
407
(
2016
).
10.
Z.
Gao
,
Phys. Plasmas
20
,
032501
(
2013
).
11.
P.
Simon
,
G. D.
Conway
,
U.
Stroth
,
A.
Biancalani
,
F.
Palermo
, and
the ASDEX Upgrade Team
,
Plasma Phys. Controlled Fusion
58
,
045029
(
2016
).
12.
H.
Biglari
,
P. H.
Diamond
, and
P. W.
Terry
,
Phys. Fluids B
2
,
1
(
1990
).
13.
K.
Miki
and
P. H.
Diamond
,
Nucl. Fusion
51
,
103003
(
2011
).
15.
P.
Manz
,
G. S.
Xu
,
B. N.
Wan
,
H. Q.
Wang
,
H. Y.
Guo
,
I.
Cziegler
,
N.
Fedorczak
,
C.
Holland
,
S. H.
Müller
,
S. C.
Thakur
 et al.,
Phys. Plasmas
19
,
072311
(
2012
).
16.
G. D.
Conway
,
C.
Angioni
,
F.
Ryter
,
P.
Sauter
,
J.
Vicente
, and
the ASDEX Upgrade Team,
Phys. Rev. Lett.
106
,
065001
(
2011
).
17.
L.
Schmitz
,
L.
Zeng
,
T. L.
Rhodes
,
J. C.
Hillesheim
,
E. J.
Doyle
,
R. J.
Groebner
,
W. A.
Peebles
,
K. H.
Burrell
, and
G.
Wang
,
Phys. Rev. Lett.
108
,
155002
(
2012
).
18.
M.
Cavedon
,
T.
Pütterich
,
E.
Viezzer
,
G.
Birkenmeier
,
T.
Happel
,
F. M.
Laggner
,
P.
Manz
,
F.
Ryter
,
U.
Stroth
, and
the ASDEX Upgrade Team
,
Nucl. Fusion
57
,
014002
(
2017
).
19.
S.
Jolliet
,
A.
Bottino
,
P.
Angelino
,
R.
Hatzky
,
T. M.
Tran
,
B. F.
Mcmillan
,
O.
Sauter
,
K.
Appert
,
Y.
Idomura
, and
L.
Villard
,
Comput. Phys.
177
,
409
(
2007
).
20.
A.
Bottino
and
E.
Sonnendrücker
,
J. Plasma Phys.
81
,
435810501
(
2015
).
21.
H. S.
Zhang
and
Z.
Lin
,
Phys. Plasmas
17
,
072502
(
2010
).
22.
A.
Biancalani
,
A.
Bottino
,
C.
Ehrlacher
,
V.
Grandgirard
,
G.
Merlo
,
I.
Novikau
,
Z.
Qiu
,
E.
Sonnendrücker
,
X.
Garbet
,
T.
Görler
 et al.,
Phys. Plasmas
24
,
062512
(
2017
).
23.
F.
Palermo
,
A.
Biancalani
,
C.
Angioni
,
F.
Zonca
, and
A.
Bottino
,
Europhys. Lett.
115
,
15001
(
2016
).
24.
A.
Biancalani
,
F.
Palermo
,
C.
Angioni
,
A.
Bottino
, and
F.
Zonca
,
Phys. Plasmas
23
,
112115
(
2016
).
25.
Z.
Qiu
,
F.
Zonca
, and
L.
Chen
,
Plasma Sci. Technol.
13
,
257
(
2011
).
26.
G. D.
Conway
,
C.
Tröster
,
B.
Scott
,
K.
Hallatschek
, and
the ASDEX Upgrade Team,
Plasma Phys. Controlled Fusion
50
,
055009
(
2008
).
27.
F.
Jenko
,
W.
Dorland
,
M.
Kotschenreuther
, and
B. N.
Rogers
,
Phys. Plasmas
7
,
1904
(
2000
).
28.
T.
Görler
,
X.
Lapillonne
,
S.
Brunner
,
T.
Dannert
,
F.
Jenko
,
F.
Merz
, and
D.
Told
,
J. Comput. Phys.
230
,
7053
(
2011
).
29.
N.
Tronko
,
A.
Bottino
, and
E.
Sonnendrücker
,
Phys. Plasmas
23
,
082505
(
2016
).
30.
H.
Sugama
,
Phys. Plasmas
7
,
466
(
2000
).
31.
M.
Miyato
,
B.
Scott
, and
D.
Strintzi
,
J. Phys. Soc. Jpn.
78
,
104501
(
2009
).
32.
H.
Lütjens
,
A.
Bondeson
, and
O.
Sauter
,
Comput. Phys. Commun.
97
,
219
(
1996
).
33.
Z.
Gao
,
Phys. Plasmas
17
,
092503
(
2010
).
34.
Z.
Qiu
,
L.
Chen
, and
F.
Zonca
,
Plasma Phys. Controlled Fusions
51
,
012001
(
2009
).
35.
W. W.
Lee
,
J. Comput. Phys.
72
,
243
(
1987
).
36.
R.
Singh
and
Ö. D.
Gürcan
,
Phys. Plasmas
24
,
022507
(
2017
).
37.
Z.
Gao
,
Plasma Sci. Technol.
13
,
15
(
2011
).
38.
H.
Sugama
and
T. H.
Watanabe
,
J. Plasma Phys.
74
,
139
(
2008
).
39.
M.
Sasaki
,
K.
Itoh
,
A.
Ejiri
, and
Y.
Takase
,
Contrib. Plasma Phys.
48
,
68
(
2008
).
40.
V. I.
Ilgisonis
,
I. V.
Khalzov
,
V. P.
Lakhin
,
A. I.
Smolyakov
, and
E. A.
Sorokina
,
Plasma Phys. Controlled Fusion
56
,
035001
(
2014
).
41.
G.
Merlo
,
S.
Brunner
,
Z.
Huang
,
S.
Coda
,
T.
Görler
,
L.
Villard
,
A.
Bañón Navarro
,
J.
Dominski
,
M.
Fontana
,
F.
Jenko
,
L.
Porte
, and
D.
Told
, “Investigating the radial structure of axisymmetric fluctuations in the TCV tokamak with local and global gyrokinetic GENE simulations,”
Plasma Phys. Controlled Fusion
(submitted).
42.
L.
Chen
,
Z.
Lin
, and
R.
White
,
Phys. Plasmas
7
,
3129
(
2000
).
43.
P.
Manz
,
P.
Lauber
,
V. E.
Nikolaeva
,
T.
Happel
,
F.
Ryter
,
G.
Birkenmeier
,
A.
Bogomolov
,
G. D.
Conway
,
M. E.
Manso
,
M.
Maraschek
,
D.
Prisiazhniuk
,
E.
Viezzer
, and
the ASDEX Upgrade Team
,
Nucl. Fusion
55
,
083004
(
2015
).
44.
G.
Wang
,
W. A.
Peebles
,
T. L.
Rhodes
,
M. E.
Austin
,
Z.
Yan
,
G. R.
McKee
,
R. J.
La Haye
,
K. H.
Burrell
,
E. J.
Doyle
,
J. C.
Hillesheim
 et al.,
Phys. Plasmas
20
,
092501
(
2013
).
45.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes in C: The Art of Scientific Computing
(
Cambridge University Press
,
2002
), p.
683
.
46.
N.
Tronko
,
A.
Bottino
,
T.
Görler
,
E.
Sonnendrücker
,
D.
Told
, and
L.
Villard
,
Phys. Plasmas
24
,
056115
(
2017
).
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