 
Astron. Astrophys. 364, 931932 (2000)
Erratum
On the steady state of nonlinear quasiresonant Alfvén oscillations in onedimensional magnetic cavity
L. Nocera^{ 1} and
M.S. Ruderman^{ 2}
^{1} Institute of Atomic and Molecular Physics, National Research Council, Via Giardino 7, 56127 Pisa, Italy
^{2} Department of Applied Mathematic, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK
Astron. Astrophys. 340, 287 (1998)
Send offprint requests to: M.S. Ruderman (sheffield.ac.uk)
The following corrections should be instroduced in the paper:

In Sect. 3, lines preceeding Eq. (22), it should be
instead of n.

The sign of the righthand sides of Eqs. (34), (36) and of the
first sum on the righthand side of Eq. (44) has to be changed.

There must be `+' instead of `' between two terms in the large
brackets in Eq. (49).

The quantity has to be substituted
for the quantity in Eqs. (58), and
(64), and on the lefthand side of Eq. (65). The quantity
has to be substituted for the
quantity on the righthand side of
Eq. (65).

The quantity has to be substituted
for the quantity in Eqs. (73), (75),
(76) and (82).

The second sentence in the last paragraph on p. 294 has to be:
"The discriminant of the cubic equation
is
."

The text starting from the second paragraph on p. 295 has to
be:
 . There are three real roots
to Eq. (77). It is obvious that
when either
or
, while
otherwise. Since
, it follows that
, so that always
. Since
(),
we obtain that , while
when
, and
when
. Since
, it follows that
when either
and
, or
and
. Otherwise
.
Summarizing the analysis we state that there are three roots to
Eq. (74) when
Otherwise there is only one real root to
Eq. (74). Examples of unique and triple solutions are shown in
Figs. 4a and 5a respectively.
In terms of and R
conditions (79) are rewritten as
where
are obtained by inverting the relations
Note that the dependences of
on R are given by the
asymptotic formulae
valid for
. The upper bound of R is
necessary since the quasiresonant perturbation scheme adopted in
Eq. (19) requires .
It can be shown that the equation for
has only one positive real root for
all values of R when . The
dependencies of on
, and
and
on R for
, are shown in Figs. 2 and 3
respectively.

The inequality on the line preceeding Eq. (85) has to be
.

The equality on the line preceeding Eq. (88) has to be
.

The interval of variation in
Sect. 5.2 has to be [0.15,0.21] instead of [0.20,0.23].

Sect. 6:

In Sect. 7, p. 298, the second colomn, it has to be

Fig. 2 remains qualitatively the same, but
varies from 0 till 0.70.

The new Fig. 3 is:

Fig. 3. The dependence of and on R for . Unique (triple) solutions exist in the shaded (nonshaded) area.


Fig. 6 is practically the same, but
and
at the horisontal axis has to be
substituted by and
respectively.

Fig. 7 is practically the same, but in the caption it has to be
instead of
.

Fig. 8 is practically the same, but in the caption it has to be
instead of
.
© European Southern Observatory (ESO) 2000
Online publication: January 29, 2001
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