We study large-amplitude, very oblique Alfvén waves at low β, with small gradient length scales, comparable to the ion inertial scale di. Such waves have large density fluctuations and slight dispersion from finite-frequency and finite-ion sound radius effects. We derive a weakly nonlinear evolution equation governing the behavior of the waves in one dimension and categorize the different solitons appearing in different regimes: the regular solitons involve full rotations of the transverse magnetic field similar to modified Korteweg–de Vries (mKdV) solitons (our nonlinear equation reduces to the mKdV equation in the long-wavelength limit). However, for sufficiently small soliton widths, some become singular, small-amplitude solitons with density discontinuities and, are, thus expected to become strongly dissipative in a real plasma. These solutions may be useful in explaining some aspects of the sharp, ion-scale magnetic field rotations (switchbacks) observed in the near-Sun solar wind by Parker Solar Probe.

1.
M. L.
Goldstein
,
A.
Klimas
, and
F.
Barish
, in
Solar Wind III, Proceedings of the 3rd Conference
(
University of California
,
Los Angeles
,
1974
), p.
385
.
2.
A.
Barnes
and
G. C.
Suffolk
,
J. Plasma Phys.
5
,
315
(
1971
).
3.
A.
Barnes
and
J. V.
Hollweg
,
J. Geophys. Res.
79
,
2302
, https://doi.org/10.1029/JA079i016p02302 (
1974
).
4.
A. A.
Schekochihin
,
S. C.
Cowley
,
W.
Dorland
,
G. W.
Hammett
,
G. G.
Howes
,
E.
Quataert
, and
T.
Tatsuno
,
Astrophys. J. Supp. Ser.
182
,
310
(
2009
).
5.
J. W.
Belcher
and
L.
Davis
, Jr.
,
J. Geophys. Res.
76
,
3534
, https://doi.org/10.1029/JA076i016p03534 (
1971
).
6.
S.
Bale
,
S.
Badman
,
J.
Bonnell
,
T.
Bowen
,
D.
Burgess
,
A.
Case
,
C.
Cattell
,
B.
Chandran
,
C.
Chaston
,
C.
Chen
et al,
Nature
576
,
237
(
2019
).
7.
J.
Kasper
,
S.
Bale
,
J. W.
Belcher
,
M.
Berthomier
,
A.
Case
,
B.
Chandran
,
D.
Curtis
,
D.
Gallagher
,
S.
Gary
,
L.
Golub
et al,
Nature
576
,
228
(
2019
).
8.
T. S.
Horbury
,
T.
Woolley
,
R.
Laker
,
L.
Matteini
,
J.
Eastwood
,
S. D.
Bale
,
M.
Velli
,
B. D.
Chandran
,
T.
Phan
,
N. E.
Raouafi
et al,
Astrophys. J. Suppl. Ser.
246
,
45
(
2020
).
9.
R.
Laker
,
T. S.
Horbury
,
S. D.
Bale
,
L.
Matteini
,
T.
Woolley
,
L. D.
Woodham
,
S. T.
Badman
,
M.
Pulupa
,
J. C.
Kasper
,
M.
Stevens
et al, arXiv:2010.10211 (
2020
).
10.
V.
Krasnoselskikh
,
A.
Larosa
,
O.
Agapitov
,
T. D.
de Wit
,
M.
Moncuquet
,
F.
Mozer
,
M.
Stevens
,
S.
Bale
,
J.
Bonnell
,
C.
Froment
et al,
Astrophys. J.
893
,
93
(
2020
).
11.
A.
Larosa
,
V.
Krasnoselskikh
,
T. D.
de Wit
,
O.
Agapitov
,
C.
Froment
,
V. K.
Jagarlamudi
,
M.
Velli
,
S. D.
Bale
,
A. W.
Case
,
K.
Goetz
,
K. P.
Harvey
,
J. C.
Kasper
,
K. E.
Korreck
,
D. E.
Larson
,
R. J.
MacDowall
,
D.
Malaspina
,
M.
Pulupa
,
C.
Revillet
, and
M. L.
Stevens
, “
Switchbacks: Statistical properties and deviations from Alfvénicity
,” arXiv:2012.10420 (
2020
).
12.
S.
Bale
,
T.
Horbury
,
M.
Velli
,
M.
Desai
,
J.
Halekas
,
M.
McManus
,
O.
Panasenco
,
S.
Badman
,
T.
Bowen
,
B.
Chandran
et al,
Astrophys. J.
923
,
174
(
2021
).
13.
A.
Tenerani
,
N.
Sioulas
,
L.
Matteini
,
O.
Panasenco
,
C.
Shi
, and
M.
Velli
,
Astrophys. J. Lett.
919
,
L31
(
2021
).
14.
J.
Squire
,
B. D.
Chandran
, and
R.
Meyrand
,
Astrophys. J. Lett.
891
,
L2
(
2020
).
15.
G.
Zank
,
M.
Nakanotani
,
L.-L.
Zhao
,
L.
Adhikari
, and
J.
Kasper
,
Astrophys. J.
903
,
1
(
2020
).
16.
J. F.
Drake
,
O.
Agapitov
,
M.
Swisdak
,
S. T.
Badman
,
S. D.
Bale
,
T. S.
Horbury
,
J. C.
Kasper
,
R. J.
MacDowall
,
F. S.
Mozer
,
T. D.
Phan
,
M.
Pulupa
,
A.
Szabo
, and
M.
Velli
, arXiv:2009.05645 (
2020
).
17.
A.
Tenerani
,
M.
Velli
,
L.
Matteini
,
V.
Réville
,
C.
Shi
,
S. D.
Bale
,
J. C.
Kasper
,
J. W.
Bonnell
,
A. W.
Case
,
T. D.
de Wit
et al,
Astrophys. J. Suppl. Ser.
246
,
32
(
2020
).
18.
J.
Drake
,
O.
Agapitov
,
M.
Swisdak
,
S.
Badman
,
S.
Bale
,
T.
Horbury
,
J. C.
Kasper
,
R.
MacDowall
,
F.
Mozer
,
T.
Phan
et al,
Astron. Astrophys.
650
,
A2
(
2021
).
19.
A.
Mallet
,
J.
Squire
,
B. D. G.
Chandran
,
T.
Bowen
, and
S. D.
Bale
,
Astrophys. J.
918
,
62
(
2021
).
20.
N.
Schwadron
and
D.
McComas
, arXiv:2102.03696 (
2021
).
21.
Z.
Johnston
,
J.
Squire
,
A.
Mallet
, and
R.
Meyrand
,
Phys. Plasmas
29
,
072902
(
2022
).
22.
J.
Squire
,
Z.
Johnston
,
A.
Mallet
, and
R.
Meyrand
,
Phys. Plasmas
29
,
112903
(
2022
).
23.
J.
Squire
and
A.
Mallet
,
J. Plasma Phys.
88
,
175880503
(
2022
).
24.
W. M.
Farrell
,
R. J.
MacDowall
,
J.
Gruesbeck
,
S.
Bale
, and
J. C.
Kasper
,
Astrophys. J. Suppl. Ser.
249
,
28
(
2020
).
25.
W.
Farrell
,
A.
Rasca
,
R.
MacDowall
,
J.
Gruesbeck
,
S.
Bale
, and
J.
Kasper
,
Astrophys. J.
915
,
68
(
2021
).
26.
A.
Hasegawa
,
J. Geophys. Res.
81
,
5083
, https://doi.org/10.1029/JA081i028p05083 (
1976
).
27.
R. L.
Lysak
and
W.
Lotko
,
J. Geophys. Res.: Space Phys.
101
,
5085
, https://doi.org/10.1029/95JA03712 (
1996
).
28.
K.
Stasiewicz
,
P.
Bellan
,
C.
Chaston
,
C.
Kletzing
,
R.
Lysak
,
J.
Maggs
,
O.
Pokhotelov
,
C.
Seyler
,
P.
Shukla
,
L.
Stenflo
et al,
Space Sci. Rev.
92
,
423
(
2000
).
29.
J. V.
Hollweg
,
J. Geophys. Res.: Space Phys.
104
,
14811
, https://doi.org/10.1029/1998JA900132 (
1999
).
30.
Loosely, since we do not here study the interactions between them to prove that they survive unscathed, part of the usual definition.
31.
A.
Zocco
and
A. A.
Schekochihin
,
Phys. Plasmas
18
,
102309
(
2011
).
32.
C. H. K.
Chen
,
S.
Boldyrev
,
Q.
Xia
, and
J. C.
Perez
,
Phys. Rev. Lett.
110
,
225002
(
2013
).
33.
D.
Duan
,
J.
He
,
T. A.
Bowen
,
L. D.
Woodham
,
T.
Wang
,
C. H.
Chen
,
A.
Mallet
, and
S. D.
Bale
,
Astrophys. J. Lett.
915
,
L8
(
2021
).
34.
D.
Grošelj
,
A.
Mallet
,
N. F.
Loureiro
, and
F.
Jenko
,
Phys. Rev. Lett.
120
,
105101
(
2018
).
35.
R. H.
Cohen
and
R. M.
Kulsrud
,
Phys. Fluids
17
,
2215
(
1974
).
36.
A.
Rogister
,
Phys. Fluids
14
,
2733
(
1971
).
37.
E.
Mjølhus
and
J.
Wyller
,
Phys. Scr.
33
,
442
(
1986
).
38.
A.
Hasegawa
and
K.
Mima
,
Phys. Rev. Lett.
37
,
690
(
1976
).
39.
P.
Shukla
,
H.
Rahman
, and
R.
Sharma
,
J. Plasma Phys.
28
,
125
(
1982
).
40.
M.
Berthomier
,
R.
Pottelette
, and
R. A.
Treumann
,
Phys. Plasmas
6
,
467
(
1999
).
41.
D.-J.
Wu
,
G.-L.
Huang
,
D.-Y.
Wang
, and
C.-G.
Fälthammar
,
Phys. Plasmas
3
,
2879
(
1996
).
42.
D.
Wu
,
Phys. Plasmas
10
,
1364
(
2003
).
43.
D.
Wu
and
J.
Chao
,
Nonlinear Processes Geophys.
11
,
631
(
2004
).
44.
C.
Seyler
and
R.
Lysak
,
Phys. Plasmas
6
,
4778
(
1999
).
45.
A.
Mallet
,
S.
Dorfman
,
M.
Abler
,
T.
Bowen
, and
C. H.
Chen
, arXiv:2303.10192 (
2023
).
46.
T.
Kakutani
and
H.
Ono
,
J. Phys. Soc. Jpn.
26
,
1305
(
1969
).
47.
T.
Kawahara
,
J. Phys. Soc. Jpn.
27
,
1331
(
1969
).
48.
E.
Dubinin
,
K.
Sauer
, and
J.
McKenzie
,
J. Geophys. Res.: Space Phys.
110
,
A10S04
, https://doi.org/10.1029/2004JA010770 (
2005
).
50.
Mathematically, the inertial dispersion can be included without too much trouble, but since when ρ s d e kinetic effects like Landau damping become important we will neglect it.
51.
J. V.
Hollweg
,
J. Geophys. Res.
79
,
1539
, https://doi.org/10.1029/JA079i010p01539 (
1974
).
52.
M. V.
Medvedev
and
P. H.
Diamond
,
Phys. Plasmas
3
,
863
(
1996
).
53.
We could force this to be the case; it amounts to redefining v A and θ while keeping the phase speed v A cos θ constant, but it has no dynamical significance.
54.
R.
Sagdeev
,
Sov. Phys.-Tech. Phys.
6
,
867
(
1962
).
55.
F. F.
Chen
,
Introduction to Plasma Physics and Controlled Fusion
(
Springer
,
1984
), Vol. 1, Chap. 8.
56.
D.-J.
Wu
,
D.-Y.
Wang
, and
C.-G.
Fälthammar
,
Phys. Plasmas
2
,
4476
(
1995
).
57.
E.
Mjølhus
and
J.
Wyller
,
J. Plasma Phys.
40
,
299
(
1988
).
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