The linear resonant excitation of Alfvén waves in a cold plasma permeated by a nonuniform magnetic field is considered. The equilibrium magnetic field is irrotational and possesses an invariant coordinate perpendicular to the direction of the field. By solving for the coefficients in a Generalized Frobenius Series the regular and singular solutions may be generated. The singular solution is logarithmic and produces a net absorption of energy at the resonant field line. The efficiency of coupling between the fast mode and the resonant Alfvén mode is determined by the following overlap integral along the resonant field line, ∫(ξβrbγ0/hβ)dl; ξβr is the resonant eigenfunction, bγ0 is the compressional/parallel magnetic field perturbation, and hβ is proportional to the separation of background lines of force in the invariant direction. The amplitude of the singular solution is proportional to this integral, while the rate of energy absorption at the resonance is proportional to its square. It is also shown how the analytical solution at the resonance may be used to avoid problems encountered in numerical solutions.

1.
Z.
Sedlacek
,
J. Plasma Phys.
5
,
239
(
1971
).
2.
D. J.
Southwood
,
Planet. Space Sci.
22
,
483
(
1974
).
3.
L.
Chen
and
A.
Hasegawa
,
J. Geophys. Res.
79
,
1024
(
1974
).
4.
W.
Allan
,
S. P.
White
, and
E. M.
Poulter
,
Planet. Space Sci.
34
,
371
(
1986
).
5.
W.
Allan
,
E. M.
Poulter
, and
S. P.
White
,
Planet. Space Sci.
34
,
1189
(
1986
).
6.
W.
Allan
,
E. M.
Poulter
, and
S. P.
White
,
Planet. Space Sci.
35
,
1181
(
1987
).
7.
W.
Allan
,
E. M.
Poulter
, and
S. P.
White
,
Planet. Space Sci.
35
,
1193
(
1987
).
8.
W.
Allan
and
D. R.
McDiarmid
,
Planet. Space Sci.
37
,
407
(
1989
).
9.
B.
Inhester
,
J. Geophys. Res.
92
,
4751
(
1987
).
10.
D. J.
Southwood
and
M. G.
Kivelson
,
J. Geophys. Res.
95
,
3201
(
1990
).
11.
L.
Chen
and
S. C.
Cowley
,
Geophys. Res. Lett.
16
,
895
(
1989
).
12.
D. H.
Lee
and
R. L.
Lysak
,
J. Geophys. Res.
94
,
17
,
097
(
1989
).
13.
D. H.
Lee
and
R. L.
Lysak
,
Geophys. Res. Lett.
17
,
53
(
1990
).
14.
B.
Inhester
,
J. Geophys. Res.
91
,
1509
(
1986
).
15.
M.
Mond
,
E.
Hameiri
, and
P. N.
Hu
,
J. Geophys. Res.
95
,
89
(
1990
).
16.
A. N.
Wright
,
Geophys. Res. Lett.
18
,
1951
(
1991
).
17.
A. N.
Wright
,
J. Geophys. Res.
97
,
6429
(
1992
).
18.
A. N.
Wright
,
J. Geophys. Res.
97
,
6439
(
1992
).
19.
J. P.
Goedbloed
,
Phys. Fluids
18
,
1258
(
1975
).
20.
S.
Poedts
and
M.
Goosens
,
Sol. Phys.
133
,
281
(
1991
).
21.
P. J.
Hansen
and
C. K.
Goertz
,
Phys. Fluids B
4
,
2713
(
1992
).
22.
D. J.
Southwood
and
M. G.
Kivelson
,
J. Geophys. Res.
91
,
6871
(
1986
).
23.
X.
Zhu
and
M. G.
Kivelson
,
J. Geophys. Res.
93
,
8602
(
1988
).
24.
M. J.
Thompson
and
A. N.
Wright
,
J. Geophys. Res.
98
,
1554
(
1993
).
25.
M. J.
Thompson
and
A. N.
Wright
, “
Comment on ’Validity of the field line resonance expansion’
,” [
Phys. Fluids B
4
,
2713
(
1992
)] to appear in Phys. Plasmas.
26.
H. F. Davis and A. D. Snider, Introduction to Vector Analysis (Allyn and Bacon, London, 1979).
27.
H. J.
Singer
,
D. J.
Southwood
,
R. J.
Walker
, and
M. G.
Kivelson
,
J. Geophys. Res.
86
,
4589
(
1981
).
28.
D. J.
Southwood
and
W. J.
Hughes
,
Space Sci. Rev.
35
,
301
(
1983
).
29.
A. D. M.
Walker
,
J. Geophys. Res.
92
,
10
,
039
(
1987
).
30.
A. N.
Wright
,
J. Plasma Phys.
43
,
83
(
1990
).
31.
A. N.
Wright
and
P. R.
Smith
,
J. Geophys. Res.
95
,
3745
(
1990
).
32.
H.
Alfvén
,
Ark. Mat. Ast. Fys.
29B
,
1
(
1942
).
33.
Y.-P.
Pao
,
Nucl. Fusion
15
,
631
(
1975
).
34.
M. G.
Kivelson
and
D. J.
Southwood
,
J. Geophys. Res.
91
,
4345
(
1986
).
35.
S.
Fujita
and
V. L.
Patel
,
J. Geophys. Res.
97
,
13
,
777
(
1992
).
36.
D.
Krauss-Varban
and
V. L.
Patel
,
J. Geophys. Res.
93
,
9721
(
1988
).
This content is only available via PDF.
You do not currently have access to this content.