J. Plasma Fusion Res. SERIES, Vol. 8 (2009)

Cosmic Rays in the Dynamic Heliosphere
Marius S. POTGIETER
Unit for Space Physics, North-West University, 2520 Potchefstroom, South Africa(Received: 27 August 2008 / Accepted: 15 December 2008)

The relation between the dynamics of the heliosphere, its shape and geometry, solar activity and cosmic ray
variations is addressed. The global features of the heliosphere influence what happens inside its boundaries on avariety of time-scales. Galactic and anomalous cosmic rays are the messengers that convey vital information on
global heliospheric changes in the manner that they respond to these changes. By observing neutral and charged
particles, including cosmic rays, over a wide range of energies on various spacecraft and at Earth, a better
understanding is gained about heliospheric phenomena including space weather and space climate. Causes of
cosmic ray modulation and variability in the heliosphere are reviewed, with emphasis on the 11-year and 22-year
solar activity cycles, step-modulation, charge-sign dependent modulation and particle drifts. Advances in this field
will be highlighted such as the effects of the solar wind termination shock and the heliosheath on cosmic ray
variability, also related to important recent observations in the heliosheath by the two Voyager spacecraft.
Keywords: Solar activity, solar wind, 22-year cycle, heliosphere, termination shock, heliosheath, cosmic rays.

The heliosphere is considered to be a small but typicalastrosphere. The extent of an astrosphere depends on theram pressure of the stellar wind compared to the totalpressure of the ISM. Because it is moving through the
ISM the heliosphere is asymmetrical with respect to theSun, with the tail region much more extended than thenose region, the direction in which it is moving. It
extends over at least 500 AU in its equatorial regions andat least 250 AU in the polar plane. The main constituentsof this interface with the ISM, shown in Figure 1, are theTS, the HP and a bow shock (BS), with the region
between the TS and the HP defined as the innerheliosheath, with the outer heliosheath located between
the HP and the BS. The latter is expected to be rather
weak. The HP separates the solar wind and ISM so that it
may be considered the outer boundary of the heliosphere.
A prediction of MHD-HD modeling is that the solar windcreates a TS where it goes from supersonic (400�800
km.s–1) to subsonic speeds between ~85 and ~105 AU[e.g. 1-3]. It is predicted that the heliospheric structure is
dynamically asymmetric, yielding a ratio for the
upwind-to-downwind TS distance of ~1:2. However, inthe nose direction the TS movement is relatively limited.
The heliosphere is elongated in its polar directions
because of the latitudinal variation of the solar wind
momentum flux. This asymmetry may become more
pronounced during solar minimum conditions [4]. The TS
position oscillates with solar activity, by as much as 3 AU
in the upwind direction as it is driven outwards and by 5
AU backwards as it tries to recovery; in the tail direction
this will be larger. The TS speed modifies the shock

1. Introduction

This review gives a brief discussion of the featuresof the global heliosphere and the relation between its
dynamics, cosmic ray variations inside its boundaries andheliospace issues such as space climate. The large-scalefeatures of the heliosphere including the termination
shock (TS), the heliopause (HP) and the heliosheath, andin particular the variability of its global structure,
influence what is happening inside its boundaries. This
relates to solar activity and the variability of galactic
cosmic rays (CRs) and anomalous cosmic rays (ACRs).
The origin of the ACRs is briefly discussed withemphasis on their acceleration in the outer heliosphere.
The causes of the CR cycles are reviewed, with emphasison the 11-year and 22-year cycles, step modulation,
charge-sign dependent modulation and particle drifts. The
basic theory for the transport and modulation of CRs is
given, with focus on the compound model for 22-year
modulation. Advances in the field are briefly discussed in
the context of what still are some of the major
uncertainties and issues.

2. The Dynamic Heliosphere

The interstellar space between the Sun and nearbystars is filled with plasmas, magnetic fields, neutral andcharged particles. The Sun moves through the interstellar
medium (ISM) with a velocity of ~26 km.s-1 so that aheliospheric interface with the ISM is formed. The solar
wind prevents this medium from flowing into the large
volume dominated by the Sun, called the heliosphere.
Marius.Potgieter@nwu.ac.za

132©2009 by The Japan Society of Plasma
Science and Nuclear Fusion Research

M.S. Potgieter, Cosmic Rays in the Dynamic Heliosphere

Fig. 1 Illustration of the heliospheric geometry, structure and boundaries using contour plots of the proton number
density in the X-Y and Y-Z planes, obtained with a 3-dimensional HD model with the associated number density
profiles in the heliospheric upwind, downwind, crosswind and polar directions in the lower panels [41].
intensity of 4-5 MeV protons accelerated by the TS near
Voyager 2 was three times that observed concurrently by
Voyager 1, indicating differences in the TS at the two
locations. Companion papers in Nature (July 2008)
reported on the plasma, magnetic field, plasma-wave andlower energy particle observations at the TS. Theseobservations are of major importance and quite anaccomplishment for this 30 year long mission.
Modeling predicts that the interstellar environmentof the heliosphere influences its shape and structure e.g.
[3,9,10] and that the flux of CRs in the heliosphere isaffected by changes of the heliospheric geometry. This is
an interesting contemporary research topic, and relates towhat is called space climate, in additional to thewell-known topic of space weather, which focuses on

strength (indicated by e.g., the compression ratio) by asmuch as 20% [5]. The shape of the HP is highly
asymmetrical as shown in Figure 1; it is well defined in
the nose direction, predicted to be at about 30-50 AU
beyond the TS, but ill defined in the tail direction so that
more modeling is required to understand these features.
The spacecraft Voyager 1 encountered the TS in
December 2004 at a distance of ~94 AU from the Sun, at
a polar angle of ~60º [6,7]. Its twin spacecraft Voyager 2crossed the TS in August 2007 at 83.7 AU in the southernhemisphere, at ~120º and ~10 AU closer to the Sun thanfound by Voyager 1. This asymmetry could indicate an
asymmetric pressure from an interstellar magnetic field,
from transient-induced shock motion, or from the solar
wind dynamic pressure. Stone et al. [8] reported that the133

M.S. Potgieter, Cosmic Rays in the Dynamic Heliosphere

Hermanus NM (4.6 GV) South Africa

Percentage (100% in May 1965)

A<0

A>0

A>0

A<0

A<0

100

95

90

85
22-year cycle

80
1960

77.5

1965

1970

1975

1980

1985

1990

1995

2000

2005

Time (Years)
Fig. 2 The Hermanus Cosmic Ray Monitor in South Africa, illustrating the 11-year and 22-year cycles and the large
step-like decreases and recoveries of galactic cosmic ray intensities at Earth.
(4) The Jovian electrons which dominate the low energy
electron spectrum up to 30 MeV within the first 10 AU
from the Sun.
Anomalous cosmic rays were discovered in the early
1970s, with energies E � 10-100 MeV/nuc [12] and acomposition consisting of hydrogen, helium, nitrogen,oxygen, neon and argon. They get accelerated in the outerheliosphere, at the TS and beyond. For a review of themain features of these ACRs, see [13] and for a review ofenergetic neutral atoms, see [14]. The acceleration
mechanism has become an issue: Immediately uponionization, the interstellar particles are picked up by thesolar wind and acquire energies of about 1 keV/nucleon,
to become ACRs; these pick-up ions must be accelerated
by four orders of magnitude to be observed at thementioned energies. The principal acceleration
mechanism to accomplish this remarkable feature has
been considered to be diffusive shock acceleration [15].
However, at the location of the TS observed by the two
Voyager spacecraft, there was no direct modulation
evidence of this process occurring for ACRs. Thissuggests that the source is elsewhere on the TS or in the
heliosheath, as is further discussed below. The higher
energy ACRs thus seems disappointingly unaffected by
the TS. On the other hand, low-energy ions (E < 3
MeV/nucleon) are clearly accelerated [6,7,8]. These
unmistakably accelerated particles have since become
known as termination shock particles. They are also
expected to originate as interstellar neutral gas but seemto have no obvious connection to the ACRs.

solar and inner heliospheric conditions. In recent years,
the very long-term variability (thousands of years) of the
CR flux has become important for the interpretation of
the abundances of cosmogenic isotopes in cosmochronicarchives (from ice cores) and for its potential impact on
the terrestrial climate. The galactic CR flux is not only
varying due to the solar activity-induced changes of thesolar wind and heliospheric magnetic field (HMF) but
also in response to the changing state of the ISM
surrounding the heliosphere. For detail, the reader isreferred to the comprehensive review by [11].

3. Cosmic Rays in the Heliosphere

Cosmic rays are charged particles with energies
ranging from ~1 MeV to as high as 1021 eV. Charged
particles present in the heliosphere are classified in fourmain populations: (1) Galactic CRs which originated far
outside the heliosphere, probably accelerated during
supernova explosions. When arriving at Earth, theseparticles are composed of ~98% nuclei (mostly protons),
fully stripped of all their electrons, and ~ 2% electrons
and fewer positrons. (2) Solar energetic particles which
originate mainly from solar flares, coronal mass ejections
and shocks in the interplanetary medium. They occur
sporadically, and may have energies up to several GeV,
observed in the inner heliosphere usually only for several
hours mainly during solar maximum activity. These
events are directly linked to what is called space weather.
(3) The anomalous components which were originallyinterstellar neutral atoms that got singly ionized relatively
close to the Sun. They are transported as so-called
pick-up ions to the outer heliosphere where they getaccelerated up to a ~100 MeV through various processes.

3.1 Cosmic ray variabilityLife on Earth is protected against CRs by threespace 'frontiers', the first one arguably the least

134

M.S. Potgieter, Cosmic Rays in the Dynamic Heliospheresignificantly to 11-year modulation during periods ofincreased solar activity in the form of relatively large
discrete steps, increasing the overall amplitude of the
11-year cycle [17].

appreciated: (1) The dynamic heliosphere with the solar
wind and the accompanying turbulent heliosphericmagnetic field (HMF). (2) The Earth's magnetic field,with its dynamic character, e.g., large decreases havebeen occurring over southern Africa over the past decades.
This means that significant changes in the geomagnetic
cut-off rigidity for CRs occur, sufficiently large over the
past 400 years so that the change in CR flux impacting
the Earth may approximate the relative change in flux
over a solar cycle [16]. The magnetosphere withstands
the space weather changes that the Sun produces, andalso reverses its magnetic polarity on a very long-term(the last one was ~780 000 years ago, so that the next
reversal is considered long overdue). (3) The atmospherewith all its complex physics and chemistry. The CR
intensity decreases exponentially with increasing
atmospheric pressure.
The most important variability time scale related tosolar activity is the 11-year cycle. This quasi-periodicity
is convincingly reflected in the records of sunspots since
the early 1600's, and other solar activity indices and also
in the galactic CR intensity observed at ground and sea
level especially since the 1950's when neutron monitors(NMs) as CR detectors were widely deployed as part of
the International Geophysical Year (IGY 1957). This isshown in Figure 2. The period 2006-2008 has beencelebrated as the 50th anniversary of the IGY and is called
the International Heliophysical Year (www.ihy2007.org).
Another important cycle in Figure 2 is the 22-year cycle
shown, directly related to the reversal of the solar
magnetic field during each period of extreme solar
activity. There are several additional short periodicities
evident in NM and other CR data, e.g., the 25-27-day
variation caused by the rotational Sun, and the daily
variation caused by the Earth's rotation. These variations
seldom have magnitudes of more than 1% with respect tothe previous quiet times. The well-studied corotating
effect is caused mainly by interaction regions (CIRs)
created when a faster solar wind overtakes a previously
released slow solar wind. They usually merge as they
propagate outwards to form various types of interaction
regions, the largest ones are known as global mergedinteraction regions (GMIRs), discussed further below.
They are related to what happened to the solar magnetic
field at an earlier stage and are linked to coronal massejections (CMEs) that are always prominent withincreased solar activity but dissipate during solar
minimum. These GMIRs propagate with the solar windspeed into the heliosheath. Isolated GMIRs may causevery large decreases (as shown for 1991 in Figure 2)
superimposed on the 11-year cycle but they usually lasts
only several months. A series of GMIRs may contribute

3.2 Space Climate
The galactic CR flux is also not expected to beconstant along the trajectory of the solar system in thegalaxy. Interstellar conditions, also locally, should differ
significantly over time-scales of millions of years, such as
when the Sun moves in and out of the galactic spiral arms[18]. It is accepted that the concentration of 10Be nuclei inpolar ice exhibits temporal variations in response tochanges in the flux of the primary CRs over hundreds ofyears ([19] and references therein).
Exploring CR modulation over time scales ofhundreds to thousands to millions of years, during times
when the heliosphere was significantly different from thepresent epoch, is a very interesting development andkeenly studied. Marsh and Svensmark [20] found acorrelation between the flux of CRs and the global
average of low cloud cover on Earth. Besides solar
activity as the internal driver of heliospheric dynamics,
and the obvious space weather connection, the structureof the heliosphere is also determined by external factors
caused by a changing interstellar environment [9]. Shaviv[18] speculated that the major ice ages on Earth mighteven be triggered by encounters of the heliosphere with
its galactic environment, given the CR-clouds relation. As
reviewed by [11], computations indicate that the galactic
CR flux reaching the heliosphere is indeed not constantover very long time scales e.g., the galactic spiral arms
crossings where a large number of supernovae occur [21].
This kind of variation in galactic CR intensity issignificant so that it should have a measurable effect on
space climate in the heliosphere and a clear imprint on
the terrestrial archive. A full understanding of CRvariability in this context is a major research goal. It isessential to fully understand the dynamics of theheliosphere, the time variation of local ISM, and beyond,in order to appreciate the variations of the order of
thousands of years, and much longer, that seem to exist in
the flux of galactic CRs. The effects of the dynamics ofthe heliosphere on CR modulation and subsequently on
climate has been studied quantitatively only recently, an
aspect that will become increasingly important.

4. The Theory and Modeling of the Heliospheric
Modulation of Cosmic Rays

Models for the global modulation of CRs in the
heliosphere are based on numerical solutions of Parker’s[22] time-dependent transport equation:

135

M.S. Potgieter, Cosmic Rays in the Dynamic Heliospheremodulation difficult. Nevertheless, there exist several
concepts (not yet fully developed theories) on how
modulation occurs over 11 years, the most recent work by[27]. Fourth, a major issue in modulation modeling is thespatial, energy (or rigidity) and time-dependence of themodulation process as determined by the diffusion
coefficients. As yet, no ab initio modulation theory exists,
one in which the diffusion coefficients are determined on
the basis of our understanding of heliospheric turbulenceand diffusion. For example, the slope of the turbulence
spectrum determines the energy dependence of thescattering mean free path with respect to the background
HMF, obviously of vital importance to CR propagation
studies. The time dependence of the transport of energetic
particles results from the time dependence of the solar
wind and HMF turbulence. Using basic andphenomenological approaches, progress is being made inthis vital important field of heliospheric physics [28,29;
see 23 for a review].
An important advance in the modeling of CR
modulation is the development of self-consistent “hybrid”
models that describe the dynamical structure of theheliosphere embedded in the local ISM andsimultaneously allow for a kinetic treatment of CR
transport and modulation. Much can be learned about
astrospheres in general from these dedicated modelingstudies of the heliosphere [30, 31, 32].

�fp�f
� �(V � � v D � ) ��f � � � (K s ��f ) � (� � V)
�J
, (1)
3
�t
� p source

where f (r,p,t) is the cosmic ray distribution function; p is
momentum, r is position, V is the solar wind velocity andt is time. Terms on the right-hand side represent
respectively convection, gradient- and curvature-drifts,
diffusion, adiabatic energy changes, and a source function
e.g., for the anomalous cosmic ray component or the
Jovian electron source. The tensor Ks consists of aparallel diffusion coefficient (K||) and two perpendicular
diffusion coefficients, one in the radial direction (K�r) and
one in the polar direction (K��). The pitch angle averaged
guiding center drift velocity for a near isotropic cosmic
ray distribution is given by �vD� = � � (KAeB), with eB =B/Bm and Bm the magnitude of the modified background
HMF, with KA the off-diagonal element of the full
diffusion tensor describing gradient and curvature drift.
For detailed information, see the review [23].
Realistic modeling of the modulation of CRs in the
heliosphere requires key but mostly unknown information.
First, the local interstellar spectra for the different CR
species are needed as initial conditions at the assumed
outer heliospheric boundary. Little is known about mostof these galactic spectra at energies below a few GeV
because of heliospheric modulation. Second, thestructural shape and geometry of the heliosphere must be
specified, for example, where the TS and the HP is
located. Third, knowledge is required about the global,
3-dimensional solar wind and HMF profiles. Presently,
the solar wind profile can be specified with detail in the
inner heliosphere, while for the HMF it was realized thatit may not be approximated well enough by a rotating
dipole so that more advanced approaches are exploredwith interesting consequences for CR modulation [24].
The wavy heliospheric current sheet (HCS) has turned
out to be one of the most successful modulation
parameters, once it was realized that gradient andcurvature drifts should play an important role [25]. The“tilt angle” � of the HCS has become a prime indicator ofsolar activity from a CR modulation point of view and it
is widely used in CR data interpretation; for solar
minimum conditions � = 10º and for moderate maximum
conditions � = 75º (quake.stanford.edu/~wso). The twomagnetic polarity cycles are usually indicated by A > 0(1970’s, 1990’s) and A < 0 (1980’s, 2000’s). The
modulation effects of the HCS and drifts, the subsequent22-year cycle and charge-sign dependence have beenstudied in detail [26,27]. Periods of maximum CR
modulation are more complex; they may last only three
years (e.g., 1969–1971), or up to six years (e.g.,
1979–1984), or may temporarily be dominated by amassive CR decrease as in 1991 (see Figure 1).
Underlying patterns are obscured by an apparent
randomness which makes modeling of long-term

4.1 The 11-year and 22-year cycles, and step
modulation
Significant progress has been made in solving
Eq.(1) numerically with increasing sophistication andcomplexity, also time-dependently for both the A > 0
and A < 0 magnetic polarity cycles, using as main input
parameters the time varying HCS tilt angles and the timevarying measured HMF values at Earth (NSSDCCOHOWeb: http://nssdc.gfc.nasa.gov/cohoweb). A basic
departure point for the time-dependence of global,
11-year modulation is that propagating barriers (solar
wind and magnetic field structures inhibiting the easy
access of CRs) are formed and later dissipated in the
heliosphere following the solar activity cycle. This isespecially applicable to the phase of the solar activity
cycle before and after solar maximum conditions whenlarge steps in the particle intensities occurred shown in
Figure 2. As mentioned above, a wide range of interaction
regions occur in the heliosphere with GMIRs being thelargest, introduced by [33]. The paradigm on which thismodulation ‘barrier’ is based is that interaction (andrarefaction) regions form with increasing radial distancefrom the Sun. This happens when two different solar
wind speed regions become radially aligned to form aninteraction region when the fast one runs into the slower
one, resulting in compression fronts with forward and136

M.S. Potgieter, Cosmic Rays in the Dynamic Heliospherebackward shocks. When these narrow interaction regions
propagate outwards and expand, they may wrap almost
around the Sun to become CIRs. When they merge andinteract, merged interaction regions and finally GMIRs
are formed beyond 5-10 AU. Potgieter et al. [34]illustrated that the affects of GMIRs on 11-year
modulation depend on their rate of occurrence, the speedwith which they propagate, their spatial extent andamplitude, especially their latitudinal extent (to disturb
global drifts), and the background modulation conditions
they encounter and importantly on the radius of theheliosphere (i.e., how long they stay inside themodulation volume). Drifts, on the other hand, dominate
the solar minimum modulation periods up to four years sothat during an 11-year cycle a transition must occur(depending on how solar activity develops and declines)
from a period dominated by drifts to a period dominatedby these propagating structures. The largest of the step
decreases and recoveries shown in Figure 2 are caused bythese GMIRs. The 11-year and 22-year cycles together
with the step-like modulation evident in Figure 2 aregood examples of the interplay of the main modulation
mechanisms; global gradient and curvature drifts playing
a dominant role during periods of minimum solar activity
in conjunction with convection, diffusion and adiabatic
energy losses. The role of gradient, curvature and current
sheet drifts in long-term CR modulation was illustratedby [17] who showed that it was possible to simulate, tothe first order, a complete 22-year modulation cycle byincluding a combination of drifts with time-dependent tilt
angles and GMIRs [35, and references therein].
Following up on these earlier modeling efforts, aself-consistent CR hydrodynamic model was used by [36]who showed that GMIRs undergo considerable decay inboth amplitude and width when encountering the solar
wind TS, and that they can exist well into the heliosheath.
This aspect of heliospheric physics is another importantdevelopment. For a recent contribution of what may
happen in the heliosheath, see e.g. [37, 56].
Cane et al. [38] pointed out that the step decreases
observed at Earth could not be primarily caused by
GMIRs because they occurred well before GMIRs could
form. Instead, they suggested that time-dependent globalchanges in the HMF over an 11-year cycle might beresponsible for long-term modulation. Ferreira andPotgieter [27] combined these changes with
time-dependent drifts to simulate 11-year modulation in
the heliosphere, naming it the compound modelingapproach. It was assumed that all the diffusion
coefficients change time dependently proportional toB(t)-n, with B(t) the observed solar magnetic field at Earth,and n(P,t) a function of rigidity and the HCS tilt angle(time dependence related to solar activity). These changes
are then propagated outwards at the solar wind speed toform propagating modulation ‘barriers’ throughout the
heliosphere, changing with the solar cycle. With n = 1,
and B(t) changing by an observed factor of 2 over a solar
cycle, this approach resulted in a variation of the
diffusion coefficients by a factor of 2 only, which isperfect to simulate the 11-year modulation at NM
energies at Earth, as seen in Figure 2, but not at all for
lower rigidities. In order to reproduce spacecraft
observations at E < ~1 GeV, n must depend on time (solar
activity) and rigidity. Using the HCS tilt angles as the
only time-dependent modulation parameter resulted incompatible with solar minimum observations but not forintermediate to solar maximum conditions; the computed
modulation amplitude was too small. They illustrated thatHCS drifts alone cannot be responsible for themodulation of galactic CRs over a complete 11-year cycle.
Using the compound approach resolved this problem.
Applied at Earth and along the Ulysses and Voyager 1
and 2 trajectories, this approach is remarkably successful
e.g., when compared with 1.2 GV electron and helium
observations at Earth, it produces the correct 22- year
modulation amplitude and most of the modulation steps.
Some of the simulated steps did not have the correct
magnitude and phase, indicating that refinement of thisapproach is needed by allowing for merging of the
propagating structures. However, solar maximum
modulation could be largely reproduced for different CR
species using this relatively simple concept, while
maintaining all the other major modulation featuresduring solar minimum, such as charge-sign dependence
will be discussed below.
4.2 Charge-sign dependent modulation
An important accomplishment is that thiscompound modeling approach also explains the observed
charge-sign dependent modulation, from minimum tomaximum solar activity. This type of modulation is one of
the important features of CR modulation because it is adirect indication of gradient, curvature and current sheet
drifts in the heliosphere. It was also found that during
periods of large solar activity, drifts must be reduced
additionally to other time-dependent changes in order todescribe the mentioned observations and the electron to
He intensity ratio at Earth during the period when the
HMF polarity reverses. Ndiitwani et al. [39] calculated
the percentage drifts required over a full modulation
cycle, including extreme solar maximum, to findcompatibility between the compound modeling approachand the observed electron to proton ratio from the KET
on board Ulysses. They found that little drifts are137

M.S. Potgieter, Cosmic Rays in the Dynamic Heliosphererequired during solar maximum activity in contrast to
close to 90% at solar minimum activity. Drifts had to be
reduced from a 50% level at the beginning of 1999 to a
10% level by the end of 1999, to vanish during 2000
(solar maximum). This indicates that in order to produce
realistic charge-sign dependent modulation during
extreme solar maximum conditions, the heliosphere must
become diffusion dominated. For detailed discussions ofthese observations and corresponding modeling, see [23].

5.

Modulation in the heliosheath

Observations by the Ulysses, Pioneer, Voyager, IMP,SOHO and other missions, and now also PAMELA [55],have contributed significantly to understand the spatial
dependence and time evolution of the main modulation
mechanisms. A major contribution was the confirmationthat V is not uniform over all latitudes but that it divides
into the fast and slow wind regions during solar minimum
conditions [40]. The next challenge is to understand thecomplexity of the solar wind flow and the imbedded
magnetic field in the heliosheath, where V obtains strong
latitudinal and azimuthal components. Apart from theconvection caused by the solar wind, the divergence of V
is equally important because it describes the adiabatic
energy changes of CRs. When it is positive, as in most of
the heliosphere, CR ions experience large energy loses
resulting in a characteristic spectral shape below a few

Fig. 4 Computed spectra for singly ionized anomalous
He at the TS (93 AU) and in the heliosheath forthree acceleration scenarios: (1) diffusive shock
acceleration only (dashed dotted line), (2)diffusive shock acceleration and adiabatic
heating (dashed line) and (3) shock
acceleration, heating in the inner heliosheath
and acceleration of a stochastic nature (solidlines) [44].
hundred MeV in the inner heliosphere. Right at the TS it
is negative and beyond the shock it may vary between
positive and negative, with interesting effects for ACRs,such as a significant increasing intensity beyond the TS
caused by adiabatic heating [41]. In Figure 3, an exampleof the numerical solutions of Eq. (1) is shown to illustrate
the radial intensity profiles for anomalous protons,
respectively from the inner to the outer heliosphere withthree scenarios for the divergence of V in the heliosheath.
The solutions are for the equatorial nose direction of theheliosphere during solar minimum activity conditions forthe two magnetic field polarities. The TS position isindicated with a vertical line, black lines represent the2reference solutions with V � 1 / r in the heliosheath,82
red lines for V � 1 / r and blue lines for V � r .
Langner and Potgieter [42] also studied charge-signdependent effects in the outer heliosphere and came to theconclusion that drifts may be significantly altered beyond
the TS, a topic that needs further investigation at both thefundamental and modeling level.
The contribution of additional terms to Eq. (1) also
have to be investigated, e.g., if the Alfven speed would nolonger be negligible compared to the solar wind speed[43] as may happen in the heliosheath. Recently, Ferreira
et al. [44, references herein] illustrated that byconsidering diffusive shock acceleration at the TS,
adiabatic heating and stochastic acceleration together

Fig. 3 Radial intensity profiles for anomalous protons
with three scenarios for the divergence of thesolar wind speed in the heliosheath during solar
minimum conditions in the A > 0 (top panel)and A < 0 (bottom panel) magnetic polarity
epochs [41]. See accompanying text.

138

M.S. Potgieter, Cosmic Rays in the Dynamic Heliosphere

Differential intensity(particles.MeV-1.m-2.s-1.sr-1)

Percentage of modulationin heliosheath to total modulation

beyond the TS, the ACRs may get accelerated up to the
HP and may thus escape the heliosphere to be thedominant low energy (E < 50-100 MeV) CR component
in the local interstellar medium, obscuring the value ofthe galactic CR spectra at these energies for several
particle species inside the heliosphere. Figure 4 depicts
the computed spectra for singly ionized anomalous He at
the TS (93 AU) and beyond for three acceleration
scenarios: (1) Diffusive shock acceleration only
(dashed-dotted line). (2) Diffusive shock acceleration andadiabatic heating (dashed line). (3) Shock acceleration,
adiabatic heating and stochastic acceleration (solid lines),
shown at the shock (bottom solid line), at 100 AU and
120 AU (top solid line). In comparison the observed
Voyager 1 spectra from 16 to 23 January 2005 at theobserved termination shock are shown as the triangles,
and the asterisk symbols are for Voyager 1 observations
at 100 AU http://voycrs.gsfc.nasa.gov).
While the high-energy part of the galactic CR
spectrum is well observed, its spectral shape at E < ~1
GeV.nuc-1 is still not known. Recent in situ measurements
made with the Voyager spacecraft in the heliosheath haveadded further constraints on the local interstellar spectra
for galactic CRs at these low energies. Scherer et al. [45]

101
100

E-2.232
95 AU - case 1
95 AU - case 2

10-1

A>0
Tilt =100
A<0
Tilt =750

0Intensity higher
at TS than LIS

A>0
Tilt =750
A<0Tilt =100

-50
10-2

10-1

100

101

the interstellar spectra can be significant.
Langner and Potgieter [47] showed that theacceleration and modulation effects of a changing radial
perpendicular diffusion as function of latitude in the outerheliosphere and along the TS position could change thespectral indices of the computed TS spectra. It is foundthat although the compression ratio was specified as s =2.5 in the model, the compression ratio calculated fromthe ACR spectral indices is much lower (for ACR HE
spectra, s = 1.2; for ACR proton spectra s = 1.9) whenradial perpendicular diffusion is made strongly latitudedependent. The increasing radial perpendicular diffusion
with heliolatitude results in a spectral break in the
spectrum at the TS at ~6.0 MeV, changing from E-1.38 toE-2.23 for ACR protons, and at ~3.0 MeV, changing fromE-1.38 to E-2.30 for ACR Helium. Shown in Figure 5, thisapproach therefore predicts a definite 'break' in the
spectral power law at an energy at which TS accelerationof ACRs become less effective, as Voyager 1 observations
indicate.
McComas and Schwadron [48] proposed that ACRs
could also be accelerated at the flanks of the TS whereconnection time is sufficient for acceleration to ACR
energies. The injection into the TS may be more efficientat the flanks where the shock angle is less perpendicularthan it is at the nose region. Since ACRs are coming fromthe flanks their flux continues to increase beyond the TS,
and the ACR spectrum must gradually unfold only as
Voyager 1 advances deeper into the heliosheath andbecomes magnetically connected to the flanks [49,50].

E-1.379

10-2

50

Fig. 6 Computed percentage of CR modulation in the
heliosheath with respect to the total modulation(between 120 and 1 AU) as a function of
kinetic energy for the two magnetic polarity
cycles (A > 0 and A < 0), for solar minimum (�= 10º) and for moderate maximum (� = 75º)conditions, in the equatorial plane in the nose
direction of the heliosphere. Negative
percentages mean that the CRs can bereaccelerated at the TS [52].

104

102

>80%

Kinetic energy (GeV)

105

103

100

100

Kinetic Energy (GeV)

Fig. 5 Accelerated ACR protons at the TS position.
Grey lines are normalized power law functions
fitting the spectra at the TS position. Note the‘break’ in the spectrum for case 2 [47].
argued that these observations also suggest how the
low-energy proton part is influenced locally and perhaps
even globally in the Galaxy. The measured flux of ACRs
in the heliosheath is unexpectedly high compared to
expectations before Voyager 1 reached the TS, whichmight be a temporal effect or due to an additional
acceleration beyond the termination shock. Combining
this finding with recent model results for astrospheres[46] immersed in different interstellar environmentsshows that the astrospheric ACR fluxes of solar-type stars
can be a hundred times higher than thought earlier andconsequently their total contribution to the lower end of139

M.S. Potgieter, Cosmic Rays in the Dynamic Heliosphere

physical processes that can be used to gain better
understanding of the features and characteristics ofgeospace and galactic space. The heliosphere is a typicalsmall astrosphere. Cosmic ray variability contributes tothe understanding of the importance of the complex fieldof space weather. Only recently has the dynamics of theheliosphere been studied and appreciated, in particular its
role in cosmic ray variability and ultimately its role inspace climate [11].
Heliospheric physics, and in particular, the outerheliosphere with the solar wind TS and heliosheath, has
become most relevant and is being actively studied. The
recent crossings of the TS by the two Voyager spacecraft
have been a major accomplishment that has renewed theinterest in CR modulation and the physics of theheliosheath. Observations of galactic and anomalous CRs
in the outer heliosphere, together with the solar wind andmagnetic field, have also caused new controversies andscientific issues. The acceleration of the anomalous CRs
at the TS was thought to be caused mainly by diffusive
shock acceleration but new information and modelingshow that neglected mechanisms such as stochastic
acceleration and solar wind adiabatic heating may beequally important.
Several challenges need to be studied: What is theglobal strength and structure of the TS? How areenergetic particles accelerated at and beyond the TS?
What are the global properties of the plasmatic flow
beyond the TS and in the heliotail? How does theinterstellar flow interact with the heliosphere beyond the
HP? Understanding this physics will give the theoreticaland modeling tools to study broader issues in bothheliophysics and astrophysics.
The study of the heliosheath, the heliopause and theheliospheric interface with the local interstellar medium
and how galactic and anomalous cosmic rays respond to
the global dynamics thereof, will be one of the prominent
heliospace research topics for the coming years.

This field of research, with the focus on the outerheliosphere, in particular the inner heliosheath, iscurrently highly relevant, with several issues to beclarified [51].
Considering the modulation shown in Figure 2, thequestion that is relevant within the context of present
Voyager 1 and 2 observations is how much modulation
occurs inside the heliosheath and where does the CR
modulation actually begin? Does it begin at the HP andacts the heliosheath as a kind of modulation 'barrier'? Or
could it be that CR modulation sets on beyond the HP?
The process is of course highly energy dependent so theanswer must depend on the considered energy of the CRs.
Presently, the HP is generally assumed be the 'outerboundary' for CR modulation. An illustrative example of
the amount of modulation that CR protons may
experience in the heliosheath in the nose direction isshown in Figure 6. The percentage of modulation in theequatorial plane in the heliosheath is given with respect tothe total modulation (between 120 AU and 1 AU) as afunction of kinetic energy for both polarity cycles (A > 0
and A < 0), for solar minimum (� = 10�) and moderate
maximum (� = 75�) conditions [52, 53]. Evidently, larger
than 80% modulation may occur in the heliosheath forboth polarity cycles at E < �0.02 GeV. For all four theconditions, the modulation in the heliosheath will
eventually reach 0% (not shown) but at different energies,
indicating that heliosheath modulation may differ
significantly with energy as well as with drift cycles. The
amount of modulation inside the heliosheath will not beknown precisely until the local interstellar spectra arebeing observed. How much gradient and curvature drifts
actually occur in the heliosheath is still unanswered. The
negative percentages indicate that the intensity may
actually increasing in the heliosheath as one moves
inward from the HP toward the TS because of there-acceleration of CRs at the TS. This of course depends
on many aspects, in particular the TS compression ratio.
From this it is clear that the heliosheath, with its
interesting physics, plays an important role in CR
modulation.
Another active field of research is that of energetic
neutral atoms (ENAs) produced by charge exchange
between fast ions and slow neutral atoms. A major part of
the ENA flux comes from regions where both the flux ofparent ions and the neutral atom density are high; at theenergies that will be measured by the IBEX mission, themain contribution is expected from the (inner)
heliosheath [54].

7. Acknowledgements

The financial support by the South African National
Research Foundation (NRF) and the SA Centre for High
Performance Computing (CHPC) is valued. The author isalso grateful for many delightful and informative
discussions on the outer heliosphere with Stefan Ferreira,Ingo Büsching, Klaus Scherer, Horst Fichtner, and Bill
Webber.

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6. Summary

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