Appendix
Appendix A:
A.1 Exploration of α-effect and turbulent diffusion
While it is generally accepted that differential rotation is the main player transforming poloidal into
toroidal field the details of the processes rebuilding the poloidal field from toroidal field are still
uncertain. In the mean-field language these processes are formally described as α-effect. In the nearsurface layers it is in principle possible to observationally constrain the amplitude of turbulent flux
dispersal from models that describe the surface evolution of magnetic field.
In the context of solar dynamo models the following mechanisms for the α-effect are generally
considered: 1. Helical turbulence, 2. MHD shear flow instabilities in the tachocline, 3. Rising flux
tubes in the convection zone influenced by Coriolis force and convection (Babcock-Leighton).
While all these processes are likely to contribute, their amplitude and spatial distribution is notknown well enough to clearly quantify their individual role. Furthermore, recent research points
toward a highly non-linear and also time dependent α-effect resulting from additional constraints
due to conservation of magnetic helicity.
In general it is not possible to verify or rule out α-effect mechanisms within the convection zone
through photospheric observations. However, some insight into the poloidal field generation
mechanism might be possible. In particular measurements of the transport of magnetic flux in thepolar regions by super-granular flows and meridional circulations will provide insight into
efficiency of the Babcock-Leighton mechanism. Note that there is a strong correlation between theway the surface Babcock-Leighton term is modeled and quenched (in 2-D mean field models) andthe resulting amplitude of the poloidal field near the poles. Precise observations of the timing,
structure and strength of the poloidal field is thus key to constrain this fundamental ingredient insolar dynamo models.

A.2 Flows associated with flux emergence
An integral part of the current paradigm is the flux emergence process which consists of thebuoyant rise of strong field from the base of the convection zone toward the solar surface andultimately the formation of active regions.
Direct observations to confirm or disprove this picture are still rare but are of fundamental
importance and need to be improved systematically with SOLAR-C In addition to jet like flows ofa few 100 m/s that might be present at the base of the convection zone, a rising flux tube in theconvective envelope induces additional motions with speeds in excess of 100 m/s based on thintube simulations as well as more recent 3D simulations. This flow is a superposition of theemerging upward motion and the downdraft due to the gravity and has slightly asymmetricstructure in the east-west directions. A flux tube is expected to spend most of the time (about 1
month) in the lower part of the convection zone and only a few days in the upper most 20 Mm.
63However, the rise speed in the near surface layers can reach values of about 1 km/s and is therefore
more likely detectable.
Helioseismic signatures of sunspots have a large contribution from the near surface regions, where
the relative perturbations of wave speeds are maximal. Our ability to seismically image thesubsurface structure of sunspots depends strongly on a good understanding of near surface effects.
The primary source of near surface thermal perturbations is caused by the Wilson depression.
Independent measurements of this contribution in the near surface layers allows us to refine
helioseismic tools and improve their focus on magnetic perturbations in the deeper layers. The
second vantage point of a high latitude mission would allow for stereoscopic measurements of the
Wilson depression, provided the imaging quality of the telescope is sufficient to resolve umbral dot
like features in a sunspot umbra.
Helical turbulence generates helical mean fields. Since magnetic helicity is conserved in highly
conductive fluids, small-scale magnetic helicity of the opposite sign must be shed through thephotosphere or dissipated through Ohmic diffusion in order to sustain the large-scale dynamo.
Evidence for helical field topologies or small-scale magnetic helicity flux through the photospheremight therefore be construed as an observational signature of the turbulent α-effect.
Vector magnetograms will also help quantify the global distribution and flux of magnetic helicity inand through the photosphere which has profound implications for the operation of the turbulent
dynamo (Section3.3). High-latitude magnetograms will also enable a more thorough evaluation of
the effects of surface magnetism on global oscillation frequencies, potentially improving thesensitivity of global rotational inversions. This is crucial for detecting the subtle signatures of zonal
flows possibly associated with subsurface toroidal magnetic flux. In addition, observations of polar
magnetism and related emission on the Sun will help interpret stellar observations by calibratingproxies used to infer magnetic activity.
Magnetic helicity is thought to play a key role on the operation of small versus large scale dynamo
in the Sun. It can be demonstrated that for fast processes with respect to magnetic diffusion and bydefining a reference magnetic field, a gauge invariant magnetic helicity can be defined in diffusive
open system such as the Sun. It is also well known that stability conditions of the surface magnetic
structures are dependent on their magnetic helicity budget and the injection of magnetic flux andhelicity by the convection. This quantity can thus serve a very important role since it can relate
inner and outer magnetism helping us to draw and improve our theoretical view of the solar
magnetism in a more integrated way.
While it is in principle possible to detect helical flows in the convection zone or nonaxisymmetricflows resulting from MHD instabilities in the tachocline, it is not clear how to relate these flows toan α-effect without making very strong assumptions (first order smoothing, second ordercorrelation approximation), which cannot be justified for the solar parameter range from firstprinciples. In that sense a measurement of these flows can be taken only as an indication for apotential α-effect in these regions. On the other hand the contribution from the Babcock-Leighton
α-effect can be constrained by observations of the flux-budget in the photosphere. Pure BabcockLeighton flux-transport dynamo models typically lead to a polar (mean) field strength of about 100
Gauss (if solutions are normalized to about 104 Gauss at the base of the convection zone) clearly inexcess of the observational constraints around 10 Gauss. The latter shows that likely additional αeffects within the convection zone or tachocline exist and it has been shown that their inclusion
64

leads to models consistent with surface observations. A detailed study of the surface flux budget at
all latitudes will promote a better understanding of the mechanisms of poloidal field regeneration in
the sun. In particular, a quantitative determination of the contribution from Babcock-Leighton
sources will impose additional constraints on (unobservable) sources within the convection zone
and tachocline. Meanwhile, observations of magnetic helicity may be used to help assess the role ofthe turbulent α−effect (Section 3.3).

A.3 The inclination requirement

Figure 30. Travel-time perturbation 2δτ computed for various combination of position and thickness ofsoundspeed perturbation of the size 10-5, against full skip angle 2Φ.

We have so far established that observing the sun from a high-inclination orbit may well be
desirable in our attempt to study dynamical processes in the solar interior and ultimately understandthe solar dynamo. The advantage we will have, however, would not be by orders of magnitude interms of our primary observables such as, say, travel-time measurement, because projection effectis just a matter of a factor except near the very edge, where Doppler signal would be dominated byhorizontal motion brought about by convection. Let us look at an example.
According to the ray theory, a ray that reaches tachocline, around r/Rsun~0.7 has a skip angle of~45. If one is aiming at observing tachocline at the solar equator and immediately beneath the disccentre, the product of two foreshortening factors, by which we lose special resolution and thevertical component of velocity, is only cos2(22.5) ~ 0.85. It is generally believed, however, that atleast some of the key dynamical features are at higher latitudes. For a ray that begins at 7.5latitude, travels down to tachocline at 30 latitude and returns to the surface at latitude 52.5, during
all which staying within the meridian, the product is cos (7.5) cos2(52.5) ~ 0.6. For a feature athigher latitudes, the figure will be worse but, it is clear that we are talking only about improvement
by a factor 2 or 3. We would like to point out, however, that even a factor of 2 may turn out to be
crucial at the end of the line of our investigation into the deep interior.
65

More complete analysis of detection capability for a certain signature in the solar interior, by timedistance helioseismology, should take the following steps.
1. Travel-time perturbation: calculate the magnitude of travel-time perturbation for a given pair ofpoints on the solar surface for which cross-correlation function is computed. This can be done by asimple ray approximation, by a more sophisticated method such as Born approximation, or bydirect numerical simulation of wave propagation.
An example-- travel-time perturbation due to sound speed anomaly near the base of the solar
convection zone (Figure 30). Perturbation to travel time 2τ (here τ is the travel time from thesurface to the inner turning points) has been computed for the relative sound speed perturbationΔc/c = 10−5, and various position and thickness, by ray approximation. The ray path Γ isdetermined by local group velocity dω/dk of pure acoustic waves for which local dispersion
relation ω=kc holds. Then soundspeed anomaly Δc/c is integrated over the path Γ. For flow of asimilar size, measured in v/c, the integration has to be done for v cos μ/c, where μ is the angle
between the path and the flow velocity. There is the reduction factor |cos μ | but if integrated overtheta (see Averaging below), by rotating ray path, and if we optimize the signal, the integrated
reduction factor would be just 2/π.
2. Uncertainty: calculate the uncertainty in travel time obtained for a given pair. If the pair is close
to the disc centre, it is known that the so-called realization noise, caused by stochastic excitation, isthe dominant source of contribution. Closer to the limb, however, and particularly if the oscillation
measurement is done in Doppler, granulation noise can be important. Other quantities that are ofimportance to uncertainty are spatial resolution, cadence and length of observations.
The way a poor spatial resolution degrade the travel-time measurement, for example, is not througha straightly enhanced statistical uncertainties, which in fact would generally be decreased. When agroup of travelling wave packets is measured with a poor resolution, there would be many
components travelling between a given pair of pixels, with widely different travel time. As thedispersion in the travel time increase, the travel time between the pixels becomes increasingly illdefined and therefore difficult to measure.
3. Averaging: Most of the time, a single measurement for just a pair of point is unlikely to yield
sufficient signal-to-noise ratio. The averaging may be done in space, or in direction. To account of
the effect of averaging we need to know error correlation between quantities that are (probably
weighted-)summed.
A note on the direction average -- this is averaging the signal over a ray path that is rotated aroundthe target point. Part of the averaging is about averaging product of projection factor for the pair ofsurface points where the individual ray begins and ends. As is seen in Figure 31, for annuli of themoderate size, it is adequate to approximate this by squaring the projection factor for the mid point(the surface point directly above the target), or a certainly point close by.
On the other hand, one can produce a fairly robust argument for the inclination requirement bylimiting the objective to detection of meridional flow. The meridional flow velocity below 60
degree latitude has been measured by SOHO/MDI. From 30 latitude, therefore, one would be able
to measure meridional flow up to the pole, one might think. It is true that from 30 latitude we66

observe a surface element at the pole as well as we would a surface element at 60 latitude from theecliptic plane. As has already been mentioned in the above, however, there is an issue of averaging.
The result obtained by Giles et al (1997) was produced by a longitudinal average within 50 fromthe central meridian. With the increasing latitude μ, the amount of averaging one can carry out
would decrease as cos μ even if we keep the longitudinal resolution, which we will not. Let us say
we would like to do at 80 latitude as well as SOHO/MDI did at the 60 latitude. By noting(cos(60)/cos(80)1/2 ~ 1.7, we can conclude that we will fall short by a factor of at least 1.7; goingto 30 latitude may not be enough for measuring meridional flow close to the pole.

Figure 31. (left:) The path of ray-path end points when a ray with the skip angle of 45, centeredaround a point at 30 latitude(60 co-latitude) is rotated. (right:) The projection factors at the end
points (dashed) as function of , the angle of the path to the local meridian, and its product which isnearly constant (solid)

67

Appendix B: Jupiter Option

Jupiter option that is described in Section 3.2 cannot reach high latitudes before the solar maximum
near the early 2020’s. However, the option gives an opportunity to go to high latitudes withincurrent technology if the kick-motor for H-IIA launch vehcle is availabe. When a longer mission
duration than the current Jupitor option is acceptable, there are solutions of spacecraft orbit with ahigher inclination. The Jupiter option whose final orbit is similar to that of the SEP option in
Sections 3.2 and 3.3 is briefly inroduced here.

B.1 Orbit Trajectory
Figure 32 shows the orbit trajectory for the Jupiter option that satisfy both the short cruise time andthe maximum orbit inclination. This is essentially a balistic orbit using conventional technology.
Minimum distance to the Jupiter is ~60 RJ, so that the radiation environment near the Jupiter is notsevere.

Figure 32. Trajectory profile of Jupiter option

B.2 Mission Profile
The sequence of events of Jupiter option is shown in Table 12. In this sequence, one Jupiterswingby and two Earth swingby operations form the final circular orbit of 1 AU distance from theSun. A similar orbit is possible for the launch opportunity every ~1.1 year but the maximum orbit
inclination is slitly diferent. In the case of 2019 launch, the maximum orbit inclination to the solar
ecliptic plane is 36.6

68

Table 12. Sequence of events of Jupiter Option
Date

Event

v

iSEQ

2018/01/12
2020/02/05
2022/12/30
2024/12/30

LaunchJupiter Swingby
Earth Swingby
Earth Swingby

8.9 km/s
7.3 km/s
17.0 km/s
17.0 km/s

7.1
31.4
35.6
39.5

Figure 33. Mission profile of Jupiter option (to be replaced into English version)

Figure 33 shows the mission profile of Jupiter option. This indicates that the first high-data rate
observations starts > 4.5 years after the launch. It takes 7 years to reach the final orbit.

B.3 Mass and Power Budget
The mass and power budget are shown in Table 13 and Table 14, respectively.

69

Table 13. Spacecraft mass budget of Jupiter Option

Table 14. Spacecraft power budget of Jupiter option
Power (W)
Item
Near Jupiter
1 AU from Sun
Mission payload
α (TBD; heater)
150
Data hadling system
21.8
21.8
Communication system
79.0
211.3
Power supply system
37.0
51.0
Attitude control system
99.0
106.7
Chemical thruster system
250.0
4.0
Total Power486.8+α70

544.8

Appendix C: References
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Gabriel, A. H., 1971, Solar Phys., 21, 392
Giles, P. M., Duvall Jr, T. L., Scherrer, P. H. & Bogart, R. S. 1997, Nature, 390, 52
Haber, D. A. et al. 2002, ApJ, 570, 855
Harrison, R. A. et al. 2009, Solar Phys., 256, 219
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Knaack, R. et al. 2001, A&A, 376, 1080
Kohl, J. et al. 1980, ApJ, 241, L117
Kohl, J. et al. 2006, Astron. Astrophys., Rev., 13, 31
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Lockwood, G. W., Skiff, B. A., Baliunas, S. L., and Radick, R. R. 1992, Nature, 360, 653
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71

Appendix D: Acronyms
ACE
ACS
AR
ARD
BAT
CCD
CFRP
CH
CIR
CME
CMOS
CZ
DHU
DIM
DPCM
DSN
EAI
EDVEGA
EGA
EIS
EM
ESA
ESS
EUV
EUVI
FOV
FWHM
GCR
GONG
HAI
HCE
HK
HMI
HS
ICME
IEM
IES
IHI
IPM
IPS
IPU
ISAS
ISP
ITA

Advanced Composition Exploler (spacecraft)
Attitude Control System
Active Region
Aerospace Research and development Directorate
Battery
Charge Coupled Device
Carbon Fiber Reinforced Plastic
Coronal Hole
Co-rotation Interaction Region
Coronal Mass Ejection
Complementary Metal Oxide Semiconductor
Convection Zone
Data Handling Unit
Direct Inclining Method
Differential Pulse Code Modulation (,a type of digital communications method)
Deep Space Network
EUV Activity Imager proposed for SOLAR-C Plan-A
Electric Propulsion Delta-V Earth Gravity Assist
Earth Gravity Assist
EUV Imaging Spectrometer (on Hinode spacecraft)
Engineering Model
European Space Agency
EUV Scanning Spectrometer proposed for SOLAR-C Plan-A
Extreme UltraViolet
EUV Imager (on STEREO spececrafts)
Field Of View
Full Width at Half Maximum
Galactic Cosmic Rays
Global Oscillation Network Group (by observing the Sun with six ground-based
observatories for helioseismology)
Helioseismic Activity Imagier proposed for SOLAR-C Plan-A
HouseKeeing Electronics
HouseKeeping
Helioseismic Magnetic Imager (on Solar Dynamics Observatory)
HelioSeismology
Interplanetary Coronal Mass Ejection a type of digital communications method
Ion Engine Module
Ion Engine System
Inner Heliospheric Imager proposed for SOLAR-C Plan-A
IES Pointing Mechanism
InterPlanetary Scintillation
IES Power Unit
Institute of Space and Astronautical Science
SPecific Impulse
Ion Thruster Assembly
72

ITCU
JAXA
JGA
JPEG
JPL
LASP
LIM
MDI
MHD
MLI
MMO
MSU
NAOJ
NASA
PCU
PMOD
PMU
PREMOS
PYC
QS
RW
RZ
SAP
SDO
SEM
SEP
SOHO
SORCE
SOT
SSR
STEREO
TCIM
TIM
TR
TRL
TSI
UV
UVCS
VGA
VIRGO
XRT

Ion Thruster Control Unit
Japanese Aerospace Exploration Agency
Jupiter Gravity Assist
Joint Photographic Experts Group (, a group which created a data compression)
Jet Propulsion Laboratory
Laboratory for Atmospheric and Space Physics
Luminosity and Irradiance Monitor proposed for SOLAR-C Plan-A
Michelson Doppler Imager (on SOHO)
Magneto-HydroDynamics
Multi-Layer Insulator
Mercury Magnetospheric Orbiter
Microwave Supply Unit
National Astronomical Observatory of Japan
National Aereopace Agency
Power Control Unit
Physikalisch-Meteorologisches Observatorium Davos
Propellant Management Unit
PREcision MOnitor Sensor on PICARD spacecraft for monitring TSI
Pyrotechnic Controller
Quiet Sun
Reaction Wheel
Radiative Zone
Solar Array Panel
Soalr Dynamics Observatory (spacecraft)
Sequential EDVEGA Method
Solar Energetic Particle in science part or Solar Electric Propulsion in engineering
Solar and Heliospheric Observatory (spacecraft)
SOlar Radiation and Climate Experiment (spacecraft)
Solar Optical Telescope on Hinode spacecraft
Serieis Switching Regulator
Solar TErrestrial RElations Observatory (spacecrafts)
Telemetry Command Interface Module
Total Irradiance Monitor (on SORCE)
Transition Region
Technical Readiness Level
Total Solar Irradiance (on SORCE spacecraft)
UltraViolet
UltraViolet Coronagraph Spectrometer (on SOHO)
Venus Gravity Assist
Variability of solar IRradiance and Gravity Oscillations (on SOHO)
X-Ray Telescope (on Hinode spacecraft)73