Electromagnetic Ion/Beam Instabilities In The Fast Solar
Wind: Proton Core Temperature Anisotropy Effects On
The Relative Drift Speed And Ion Heating
Jaime A. Araneda1, Adolfo F.-Viñas2, and Hernán F. Astudillo1
1
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas,
Universidad de Concepción, Casilla 160-C, Chile
2
Laboratory for Extraterrestrial Physics, Mail Code 692, NASA Goddard Space Flight Center,
Greenbelt, MD 20771, USA
Abstract. Ion velocity distributions in the fast solar wind are usually characterized by nonthermal features such as
multicomponent ions, temperature anisotropies and average relative drifts. These nonthermal features lead to the growth
of several electromagnetic instabilities. Here, two-dimensional hybrid simulations are used to study these instabilities in
a homogeneous, magnetized collisionless plasma model. We show that for conditions typical of the fast solar wind the
proton core temperature anisotropy plays a significant role in modifying the wave-particle scattering of each proton
component as compared to the isotropic cases. As a consequence, the scattering reduces both the heating and anisotropy
enhancement of the proton beam and decreases the relative proton/ion flow speed below the corresponding isotropic
instability thresholds in agreement with recent observations and with our previous one-dimensional study. Our results
are consistent with recent satellite observations and provide support to the physical scenario in which core temperature
anisotropies play a regulating effect on the instability thresholds.
INTRODUCTION
Although electromagnetic ion/ion instabilities have
been studied extensively in the context of several
plasma environments [e.g., Ref. 4], fewer
investigations have been concerned with instabilities
derived from typical fast solar wind parameters. Based
upon model distribution functions of plasma
observations near 1 AU and linear theory,
Montgomery et al., [5-6] found that if the
proton/proton relative drift speed approaches the
Alfvén speed two modes become unstable: A
magnetosonic and several oblique Alfvén modes. The
proton/proton magnetosonic instability has the larger
growth rate in the direction parallel to the background
magnetic field with a weak beam density, whereas the
oblique Alfvén modes are more unstable at sufficiently
large beam density and relatively small core [7].
Helios and Ulysses in situ plasma measurements in
the fast solar wind (Usw 600 km/s) have revealed a
variety of nonthermal features in the ion velocity
distributions [See e.g., Refs.1-3]. Proton distributions
exhibit two ubiquitous characteristics: double-peaked
streams with a typical relative drift speed of Upp/VA
3, and core temperature anisotropies with temperatures
ratios of T /T 1-4. Each ion component, (core and
beam) is usually modeled by a bi-Maxwellian
distribution with a density nj, a flow speed Uj, and T||j
and T j, temperatures parallel and perpendicular to B0,
the background magnetic field. In addition, minor ions
such as alpha particle are observed to flow faster than
protons with drift speeds which, on average, follow the
local Alfvén speed (U p
1.0 VA). Furthermore, the
alpha particles are also typically observed to be hotter
(T ≈ 2-4 Tp). Each of these nonthermal characteristics
can trigger a number of electromagnetic ion/ion
instabilities such as the magnetosonic and
Alfvén/cyclotron instabilities.
Linear Vlasov theory predicts that threshold
conditions for the magnetosonic instability correspond
to Upp/VA
2 [6,7]. Nevertheless, Helios data
analysis of Marsch and Livi [8] showed a number of
observations matching 2 Upp/VA 4, with a large
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
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the wavelength of the fastest growing mode and an
integration time step of p t = 0.05. Charge neutrality
and the zero current condition were imposed at t = 0.
We use the subscripts c to denote the more dense
proton component and b for the less dense beam.
number corresponding to apparently unstable cases. In
contrast, Ulysses observations of the proton/proton
relative drift speed reported by Goldstein et al. [3] lie
below the predicted threshold with mean values
considerable smaller. Because the two data sets were
obtained at different distances from de Sun, there must
be some regulating mechanism for the differential
streaming and probably ion heating. Recently, the
effect of a proton core anisotropy on the relative drift
speed and beam heating was investigated by Araneda
et al., [9]. Using linear Vlasov theory and onedimensional hybrid simulations, these authors found
that a proton core temperature anisotropy T c/T||c > 1
play a key regulator for the relative streaming and
preferential heating of the more tenuous proton
component. The wave-particle scattering by
electromagnetic fluctuations from the proton cyclotron
instability not only reduces the relative streaming
speed but also constraint the proton beam anisotropy
to T b/T||b 1 values. Moreover, although a T /T|| < 1
anisotropy can significantly increase the growth rate of
the alpha/proton magnetosonic instability [10], they
shown that the same mechanism reduces the
alpha/proton relative flow and constrains also the
enhancements of the temperature ratio of the alphas
T /T|| . Simulations with initial isotropic components
reduce also the core/beam relative drift but yields to a
strong heating of the more tenuous beam component
temperature perpendicular to B0 [11-13].
We first describe results from run I for which we
assume
that β ||c
= 8πne k BT||c / B02 = β ||b = 1.0 and
Tc ⊥ / T||c = Tb⊥ / Tb|| = 1.0 . Other initial parameters
are nb/ne = 0.05, and Ubc/VA = 2.63. These parameters
are similar to those of the simulation of the
magnetosonic instability illustrated in Figure 1 of Ref.
11 and the results are analogous. The time histories of
the beam and core anisotropies, the beam/core relative
drift speed, and the beam/core temperature ratio are
shown in Figure 1. The less dense beam component
develops a relative strong temperature anisotropy
Ab ≡ Tb⊥ / T||b , whereas T||b / T||c decreases, and
Ac ≡ Tc ⊥ / T||c
remain
approximately
without
variations. Note that the relative drift speed exhibit
also a moderate reduction indicating that the
magnetosonic instability alone is inefficient to produce
significant changes in Ubc.
The purpose of this paper is to extend the nonlinear
study of the proton/proton instabilities of Ref. [9] by
using two-dimensional simulations. We examine the
effect of an initial proton core temperature anisotropy
on the magnetosonic instability under conditions in
which this instability has the largest growth rate in the
1-D case.
COMPUTER SIMULATIONS
We have used a two-dimensional hybrid code that
treats the ions as discrete particles and the electrons as
a massless fluid. In order to verify our calculations we
have employed two codes with completely different
schemas obtaining similar results. The simulations are
performed in the center of mass frame. At t = 0, the
core and proton beam components, each assumed to be
a drifting bi-Maxwellian distribution, stream parallel
to B0 (the x direction) and with relative velocity Uj.
Each ion distribution is represented by a fixed number
of superparticles. On average, about 256 particles per
cell are used for each component. For each simulation
we used a 128
64 computational grid with the
simulation system length chosen to be about 8 times
FIGURE 1. Time histories for run I: The relative drift speed
indicated by heavy dotted lines. The solid lines represent the
beam proton anisotropy, the thin dotted lines the
beam/proton temperature ratio, and the dashed lines the core
temperature anisotropy.
We now examine the consequences of a initial core
temperature anisotropy on the magnetosonic
instability. Specifically, our run II used the same
parameters as in run I, except that Tc ⊥ / T||c = 3.0 .
Under these parameters the magnetosonic instability
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quench significantly whereas the proton cyclotron
modes (both forward and backward) dominate [9].
the maximum proton anisotropy observed in the solar
wind from the Helios spacecraft [8].
The time histories for this case are shown in Figure
2 in the same format as Figure 1. Between t = 0 and
40, we observe the same characteristic increase of the
beam temperature anisotropy, similar to the isotropic
case of run I. However, afterward a substantial
slowdown of both the relative drift speed and beam
temperature anisotropy takes place. Following
saturation, the normalized values for these parameters
drop around 1 in agreement with Ulysses observations
[3]. The tendency toward an isotropic proton beam
distribution is due to the scattering from the backwardpropagating ion cyclotron waves resulting from the
relaxation of the anisotropic proton core. In fact,
observing the individual particles in the phase-space
(not shown) it can be seen that beam particles
localized on the negative tail of the distribution (as
seen in the beam frame) experience a
force δv ⊥ × δB ⊥ in the parallel direction. This causes
an increase in the proton beam parallel temperature
and also contributes to reduce the proton/proton
relative drift speed. Because the Doppler effect, the
only waves able to resonate with the beam proton in
this range of velocities are the backward propagating
ion cyclotron waves. Since the magnetosonic waves
will tend to heat the beam proton distribution in the
perpendicular direction, the net effect is an almost
isotropic heating of the beam.
Figure 3 shows the time histories for run III in the
same format as Figure 2. As in run II, we note the
initial perpendicular heating of the beam followed by a
decrease, continuing almost constant below Ab = 1 .
For this extreme case, we note a strong reduction of
the relative drift speed and the evolution of the plasma
toward a stable configuration with Ac 1.
FIGURE 3. Time history for run III: The dotted lines
represent the relative drift speed. The solid lines represent
the beam proton anisotropy, and the dashed lines the core
temperature anisotropy.
CONCLUSIONS
We used two-dimensional hybrid simulations of the
proton/proton and proton core driven Alfvén/cyclotron
instabilities using initial conditions similar to those
observed in the fast solar wind near 0.3 AU. The 2D
simulations confirm previous results from onedimensional hybrid simulations that the proton core
temperature anisotropy play a key regulator of both the
perpendicular heating of streaming protons and the
relative drift speed. This implies that a statistical study
on correlations of observed core/beam distributions
with theoretical threshold conditions must include the
effects of the proton core anisotropy and probably also
the beam temperature anisotropy.
FIGURE 2. Time history for run II: The dotted lines
represent the relative drift speed. The solid lines represent
the beam proton anisotropy, and the dashed lines the core
temperature anisotropy.
The last simulation that we examine (run III) is one
in which the initial parameter are again the same, but
now with Tc ⊥ / T||c = 4.0 . This value corresponds to
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ACKNOWLEDGMENTS
This work was partially supported by Fondecyt
grant 1000/7000320 and by the University of
Concepción. A. F. Viñas thanks the NASA Theory
Program at GSFC for his support.
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