Pickup Ion Acceleration in the Heliosphere: Consequences of
Organized Footpoint Motion on the Sun
N. A. Schwadron
Southwest Research Institute, P.O. Drawer 28510, San Antonio, TX, 78228-0510
Abstract. Suprathermal and pickup ion tails exist ubiquitously in slow solar wind. What is the intrinsic property of slow
solar wind that causes ubiquitous particle acceleration? Observations from Ulysses have shown that statistical acceleration
through transit time damping of fluctuations in field strength is the vehicle by which pickup ion tails are produced. But the
source of compressive fluctuations in slow solar wind has not been established. We show that shearing of magnetic fields by
small-scale fluctuations in the solar wind speed provides a strong and continuous source of compressive fluctuations. This
effect occurs naturally if slow solar wind is generated from material stored in coronal loops and released due to organized
drifts of open magnetic field footpoints on the Sun. Another consequence of these organized footpoint drifts is the creation of
large-scale magnetic field structures that connect fast and slow solar wind – located for example in the outer heliosphere at
the latitudinal boundaries between fast and slow solar wind. These structures are sites for particle acceleration throughout the
heliosphere. In summary, we argue that the organized drifts of open magnetic field footpoints significantly alter the structure
of the heliospheric magnetic field in regions where there are strong changes in the solar wind speed, on small and large spatial
scales, creating a previously unknown role for solar wind shearing, and providing a new and needed vehicle for the particle
acceleration throughout the heliosphere.
It has been well established that particles with energies
of order 1 MeV per nucleon can be accelerated at the
forward and reverse shocks which surround Co-rotating
Interaction Regions (CIR’s), where high and low speed
streams interact in the solar wind [e.g., 1, 2, 3]. [4] and
[5] have suggested a two step acceleration process is
called for. In the first step, pickup ions born with random
speeds up to twice that of the solar wind are accelerated
by transit-time damping of fluctuations in the magnetic
field magnitude within CIRs, achieving random speeds
between four and six times that of the solar wind. In the
second step, these already pre-accelerated ions may efficiently move along magnetic field lines and are thereby
injected into diffusive shock acceleration at the shocks
(particle the reverse shock) that bound CIRs.
Observational evidence for this two-step acceleration
process has not been hard to find. Figure 1 shows the
results of an observational test conducted by [5] in which
the energy in initially accelerated pickup ions was not
found to to be strongly correlated with the presence
shocks. A strong correlation was however found with the
presence of fluctuations in the magnetic field magnitude
that may be transit-time damped by pickup ions.
[7] and [8] show the remarkable ubiquity of acceleration of pickup ions and solar wind suprathermal ions
within slow solar wind as demonstrated through univer-
20
2
〈η 〉
15
10
5
0
Percent of data within one day of a shock
OBSERVATIONAL CONSTRAINTS
E (keV)
FIGURE 1. Evidence that the initial acceleration of pickup
ions in slow solar wind is caused by transit-time damping,
not acceleration near CIR shocks [5]. The x-axis is average
¯ in pickup ion tails (for random speeds from twice
energy, E,
to six times the solar wind speed). The y-axis is the average intensity
of
fluctuations in the magnetic field magnitude,
η2 δ B 2 B 2 , which may be transit time damped by pickup
ions. The data here were taken from Ulysses observations for
150 days during 1992 when Ulysses was at low-latitudes and
encountered 23 shocks associated with CIRs.Plotted as diamonds are the percentage of data within each energy bin that
fall within one day of a shock. Plotted as stars are the average
intensity of fluctuations in field magnitude versus the average
energy in pickup ion tails. Data were binned according to the
energy. The solid line represents the results of an analytic model
presented by [5] that describes transit-time damping by pickup
ions.
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
593
change in the plasma frame given by δE pδp m mδv vph λ λ . Given also that the interaction time is
δt λ v vph λ λ , the diffusion coefficient in momentum (or equivalently, speed) is
D pp
p2 δp 2
p2 δt v
v !
4
η2 %
λ2
v vph λ λ
"$# 4
λ
v2ph
(1)
Detailed quasi-linear calculations of this effect were
performed by, e.g., [12] and [5], and [13]. The form for
the coefficient of momentum diffusion depends critically
on the ion gyroradius and on the nature of the compressive turbulence. [5] found that they could account for observed pickup ion tails in slow solar wind if they assumed
the turbulence was highly elongated (with parallel correlation lengths 30 times those of perpendicular correlation
lengths). Correlation lengths perpendicular to the mean
magnetic field of 0.01 AU were used and are typical of
interplanetary turbulence.
FIGURE 2. Distributions of interstellar pickup He in highlatitude fast solar wind (blue) and in-ecliptic slower solar wind
(red) observed by Ulysses/SWICS [6].
sal presence of pickup ion and solar wind tails (see Figure 2). Comparisons between fast and slow solar wind
are also illuminating, as demonstrated by Figure 2. It appears that the suprathermal and pickup ion tails are significantly stronger in slow solar wind than in fast solar
wind [4, 9, 7, 10, 8]. The comparison begs the question:
what are the properties intrinsic to slow solar wind that
cause the ubiquity of suprathermal ion and pickup ion
tails?
ENERGY SOURCES FOR TRANSIT
TIME DAMPING
Transit time damping is great for producing acceleration,
but acts so quickly that it readily destroys fluctuations in
field strength. It is for precisely this reason that fluctuations in field strength are observed to be small in the solar wind. Nonetheless, if fluctuations in field strength are
observed, even at a low level, there must be a continuous
source that produces them.
We point out here that shearing of the magnetic field
by the solar wind is inherent to the boundaries between
faster and slower streams if there is an organized motion of open magnetic field footpoints on the Sun through
these boundaries. More generally, we show that shearing
of the magnetic field may be an inherent property of slow
solar wind, particularly on small spatial scales. The effect
continuously transfers energy from the solar wind flow
into compression and rarefaction regions. On small spatial scales, the effect helps to explain the general presence
of compressive waves in slow solar wind. On large spatial scales, it suggests a new and different structure to the
boundaries between fast and slow solar wind; structures
that are quite favorable for particle acceleration, even in
the distant heliosphere.
It is clear from solar wind observations that transitions
in speed are ubiquitous. Traditionally it has been thought
the these speed transitions do not shear the magnetic
field since the footpoints of open field lines and solar
wind transition regions rotate bodily with the Sun. It was
realized recently by, e.g., [14], [15] and [16] that the
footpoints of open magnetic field lines are not fixed on
a bodily rotating Sun; instead, field line footpoints move
through coronal hole boundaries, as illustrated in Figure
STATISTICAL ACCELERATION
THROUGH TRANSIT TIME DAMPING
Statistical acceleration through transit time damping was
overviewed recently by [11]. The close parallel was
made to a magnetic pump which can be treated in a very
straightforward manner. Consider an ion that propagates
along a field line in which the field magnitude varies. In
the frame of reference of a compressive fluctuation (moving along the mean magnetic field) the ion’s first adiabatic invariant is preserved. A fluctuation of field magnitude, with amplitude δ B B , results in a change of
the perpendicular ion speed, v , given by δv v δ B 2 B Since we are dealing here with compressive magnetosonic waves which propagate at an angle
with respect to the mean magnetic field, the component
of wave propagation parallel to the mean magnetic field
with speed is vph λ λ , where vph is the phase speed
of the wave and λ and λ are the parallel and perpendicular correlation lengths, respectively. Energy is conserved in the frame moving along the mean field with
the fluctuation so that v δv v vph λ λ δv ,
where v is the ion speed parallel to the mean magnetic
field in the plasma frame. This also yields an energy
594
5. The motion of field line footpoints across a region with
an abrupt change in solar wind speed (for instance, a
coronal hole boundary) leads to strong shearing of the
magnetic field.
[17] considered this shearing effect in co-rotating rarefaction regions (CRRs) which are mapped out from
the trailing edges of coronal holes. In CRRs, the heliospheric magnetic field is strongly underwound if drifts of
open magnetic field footpoints through the coronal hole
boundary are present. The underwinding is caused by solar wind shearing since the faster portions of the stream
draw out the magnetic field more quickly than the slower
portions. The effect may be quantified simply. The tangent of the angle ψ, the field direction relative to the radial direction in the φ r plane, is given by
tan ψ Ω ')( ωφ r sin θ
Bφ
&
Br
V r V u
+* ∇SV
FIGURE 3. An illustration of the motions of the open magnetic field in the solar corona, in the polar corona [20, 14, 15].
The figure is drawn in the frame co-rotating with the equatorial
rotation rate. The axis of expansion symmetry is “M”, the solar
rotation axis is “Ω. Open field lines are shown in green, with
“p” the field line that connects to the heliographic pole. The red
curves are the trajectories of the field lines, the motion of which
is driven by differential rotation of the photosphere. The thick
black curves show the coronal hole boundaries.
(2)
Here, V is the solar wind speed, r is the heliocentric
radius, ∇SV is the gradient in solar wind speed along
source surface, u is the velocity of footpoints along
the source surface (in the frame of reference that corotates with the Sun), Ω ' is the equatorial rotation rate,
and ωφ is the footpoint rotation rate in the azimuth.
The resulting orientation of the underwound heliospheric
magnetic field is shown in Figure 4. At large distances
the field orientation in CRRs becomes fixed, whereas a
Parker spiral becomes increasingly azimuthal. The effect
has been confirmed by observations of the heliospheric
magnetic field [18, 19].
In the case of rarefaction regions, this shearing effect
causes a strong reduction in the field magnitude [17]. In
compression regions, shearing will cause compression of
the magnetic field. These magnitude changes are due to
more than the mere compression of the plasma. This is
exemplified by considering the magnetic field generated
in heliospheric space when footpoints move across a
latitudinal transition in the wind speed, such that the
wind speed, V V θ , is given as a function of colatitude, θ. In this case, the magnetic field can be solved
exactly
FIGURE 4. The orientation of the magnetic field in rarefaction regions under the influence of shearing and footpoint motion. Streamlines are shown by the solid spiral lines (black),
and segments (blue) show the field orientation in the rarefaction regions. The speed gradient is given by a 300 km/s speed
change over a 5 degree transition region.
R2SS
rωθ ∂V
rωθ
Ω' r sin θ
êθ êφ 0
1
êr .
,
2
2
r
V ∂θ /
V
V
(3)
where êr , êθ , and êφ are the unit vectors in the radial, colatitude and azimuthal directions, respectively. The radial
position of the source surface is RSS . The term caused
by shearing, 1 BSS R2SS ωθ 2 rV 2 435 ∂V ∂θ êr , leads to an
additional component of the field in the radial direction
which may either add to or subtract from the nominal radial component (depending on the direction of the speed
gradient relative to the direction of footpoint motions). In
this case, the plasma itself experiences no compression or
B BSS
rarefaction since the speed transitions occur across latitude. The fluctuations in magnitude arise because of the
additional radial shearing term.
In the outer heliosphere, at boundaries between fast
and slow solar wind, the shearing induces large-scale regions where the field is strongly perturbed (and more
radial). The fact that these transition regions are magnetically connected implies that, along a given field line,
595
ACKNOWLEDGMENTS
there is a speed gradient from slow to fast wind speeds.
As ions propagate and scatter along the field lines, they
diffuse in energy (or equivalently, momentum) by interacting with the speed gradients. Hence, these are important sites for acceleration.
This work was supported by NSF grant ATM 0100659. I
wish to thank Dave McComas, Heather Elliott, Len Fisk
and George Gloeckler for useful discussions.
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1.
2.
3.
4.
5.
FIGURE 5. Fluctuations in the magnetic field strength produced by shearing.
6.
7.
The effects of shearing have been applied above to
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Small-scale speed fluctuations are observed to be larger
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