J. Plasma Fusion Res. SERIES, VSpontan4 4j00t) 536-539

Variation in a Rotating MagnetosphereMIYOSHI Takahiro* and KUSANO Kanyar

Naka Fusion ResearchIGraduate School ofJapan Atomic Energy Research Institute, Ibaraki 311-0193, Japan
Sciences of Matter, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

5 December 2000 / Accepted: 16 August 2001)

AbstractThemagnetohydrodynamic
external plasma flow.
magnetopause, wheretemporally varied evenrelatively low speed
the competitive
dawn sidein a rotating magnetospheric system is investigated by using the global) simulation of the interaction between the rotating magnetosphere and theresults of the simulation indicate that the global structure of the dawn side
external flow collides with the rotating flow in the magnetosphere, isthe condition of the external flow is steady, especially in the case imposing
I flow. The mechanism of the spontaneous variation may be determined bybetween the external flow, the rotating flow, and the magnetic pressure at theKeywords:
magnetosphere, planerotation, spontaneous variation, MHD, numerical simulation

observed for ranges about 50 Ry to more than 100 Rr [5].
Until now the mechanism of the variation has not been

1. lntroduction
The magnetosphere rs

by the nonlinear

interaction between the intri
celestial body and the state of
the Earth's magnetosphere,

magnetic field of therrounding plasmas. In
solar wind, which issupersonic/super-Alfv€nic
the sun, compresses the dipo

flow blowins frommagnetic field of theunt shape, where theEarth and deforms it into a
dynamic pressure of theunderstood completely, although the large variation
more than 50 R.1 may be caused by the large variation of
the dynamic pressureof the solar wind [6]. Since thedistance to the magnetopause, especially in theexpanded state, is inconsistent with estimated Ryp, thescale to the Jovian magnetopause is characterized by theinteraction not only with the solar wind but also with therotation. Thus, the rotation must induce the distinctive
features of the magnetospheric structure and thedynamics. In the rotating magnetospheric system, wecan introduce another characteristic scale, Ra, at which
the kinetic energy of the corotating plasma is equal toflow is balanced withmaenetic field
the magnetic pressure of thecharacteristic
imate
thesimplyThus,
wecan[,2].
scale to the magnetopause, Rr.ap, by the balanced
interface. As for theequation of the pressures atessentially confirmed
Earth's magnetosphere, thisother hand. the Jovian
by the observation [3]. On
by the rapid rotation
magnetosphere is strongly
disc. where dense andof Jupiter. Indeed, thelike region detectedcool plasmas are confined in aformed by the rotation
by in situ observations, mustthe magnetic energy [7]. In the Jovian magnetosphere,
Ra is estimated as a match for Ryp, while Ra is thought

to be extremely greater than Ryp in the Earth's
magnetosphere if the corotation could be assumed.
Thus, the researches of the Jovian magnetosphere will
give new insight of the magnetospheric physics becauseof Jupiter [4]. Furthermore,position of the bow shock

variation of thethe magnetopause was*: miy o s hi @ s ci.hiro s hima-u. ac.j p

C orre sponding autho r' s536

@2001 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchMiyoshi T. et al., Sponraneous Variation in a Rotating Magnetospherethe effects of the rotation, the external flow, and theTable 1 Solar wind parameters in simulation runs.

intrinsic magnetic field are competed with each other.

Although several global models for the Jovian
magnetosphere have been proposed based on local
theories or it situ observations l7-ll), even the global
structure is still uncertain due to the nonlinearity and thecasen(lcmr)% (knV94 (nT)

r(K)

L

0.1-300

04x lff

H

0.1-400

04x lU

three-dimensionality. Recently, first simulation studies

for the global structure of the Jovian magnetosphere,

switched depending on the sign ofthe radial velocity V.,
such that P = nonti,P - Ps for % > 0, and dpldr = 0, dPl

where the interaction between the rotating
magnetosphere and the solar wind is taken into account,have been carried out by two groups independently [12-dr = 0 for V, < 0, where m1 is the mass of proton, n0 =0.1 cm3 and Ps = 1.1 x 10-12 cm3, respectively. These

141. In their models, the magnetospheric structure suchparameters ns and Po are chosen from in situ

as the plasma disc was realized, self-consistently. The

measurements at the middle portion of the Jovian
magnetosphere [6]. The velocity parallel to themagnetic field, Vl1 = V.BIB, at the inner boundary isdetermined such as to satisfy the empirical relationd(f pVfil)r = 0. The velociry perpendicular to thedynamics of the global structure, however, was notclarified completely. Therefore, in this paper, thedynamics of the global structure of the previous model|2,13) is investigated in detail, and the spontaneousvariation model of the rotating magnetosphere ismagnetic field, V1 = V - VnBlB, is determined by V1=proposed.

E x BlB2, where E = -(Oo x 16) x B. The angular

2. Simulation Modelvelocity Oa at rn is set to a half of the Jovian angularvelocity, Q1 = (2n110.0)e,lh, based on the observationfrom the inner to the middle Jovian magnetosphere [4].

The simulation model in the present study is thesame as in the previous papers ll2,l3l. The model with

For these parameters, R1,ap is estimated approximately as

the boundary conditions is summarized as follows: Themagnetohydrodynamic (MHD) equations are adopted as

43.2 & and 47.5 R; in case H and L, respectively. Also,
R4 is evaluated as about 47.9 Rr in both cases. Thus, thethe basic equations since we concentrate our attention
on the global structure and the dynamics at present. The

two characteristic scales are the same order, and thedifference between the parameters for case H and L

MHD equations are numerically solved by employing

seems to be slight.

the total variation diminishing (TVD) scheme based on

the eight-waves characteristic form of the MHD

3. Results and Discussion

equations [15]. Since we focus on the global structure ofThe global structure of the magnetosphere seems toachieve the quasi-steady state in both cases H and L by

the Jovian magnetosphere, the simulation domain isgiven by a large rectangular box, (-350 Rr, -250 Rr, 0)
3 (x,y,z) < (150 Rr, 250 Rr,250 Rr), in which the innerhalf sphere of the radius ro = 30 Ry is clipped off. Herethe elapsed time about 30 to 40 hours. In the previous
papers [12,13], the spatial structure of the rotating
magnetosphere in the quasi-steady state was investigatedin detail. However, the detailed analyses for the time

we use the solar-magnetospheric coordinate, where thex, y, and z point to the sun, the dusk and the north,development of the global structure indicate therespectively. In order to perform the present simulation,

dynamic feature of the rotating magnetosphere although
the fundamental structure, such as the topology of themagnetic field lines of force as seen in Plate I of [13],does not change essentially over in the quasi-steadystate. From the view of the global model proposed asfollowing boundary conditions are imposed: The mirror
boundary condition is adopted at the equatorial plane.
The boundary condition on the top, the side, and the tailwalls is given by the free boundary condition. Theinflow parameters are fixed at the front boundary as

PlateT of [3], the magnetosphere over the dawn to thenoon region shows the complicated structure, where thegiven in Table 1, where no IMF is assumed at present.
Also, since we take an interest in the global structure
and its dynamics of the rotating magnetosphere, theinner boundaty at ro is simply regarded as a plasmabath. Thus, the influence of the plasma source, i.e., Iotorus, is averaged out on the inner sphere. The innerboundary condition of the density and the pressure issolar wind collides with the rotating flow in themagnetosphere. Also in that area, the sponginess of themagnetosphere was observed by in situ observations [5].
Thus, in Fig. I, we show the time evolution of thedistance to the magnetopause Ryp at 0730 LT in case Hand L. It is found, in case L, that the distance to the537

T. et aI., Spontaneous Variation in a Rotating MagnetosphereFig. 3 (a) that the intensity of the magnetic field on themagnetopause at 0730 LT is weakened for the shrinking
phase. Moreover, at the downstream of the rotating flow
(1000 LT), the strong azimuthal flow is detected justafter a little delay from the shrinking phase at 0730 LT.
Thus, the mechanism of the spontaneous variation may
be explained as follows (Fig. 4): As the first stage, incase L, the magnetic field lines of force frozen-in in therotating plasmas are advected toward and accumulated

magnetopause at the prenoon region is temporallyvaried, and rapid shrinkage f the magnetopause

y be recurrent evensubsequent to slow expansion
when the condition of the solar ind is steadv. This mav
on in the Jovian
be one of the causes of the flwn side [5]. On themagnetosphere detected at theother hand, the evident variati
not observed in case H. The di
may arise from the fact that,internal magnetospheric state
dominant state, while the ln

the magnetopause isnce of these results

the former case, thethe dvnamicallv
state is magneticallytosphere in the latterat the dawn side, where the plasma flow is stagnant, due

to the dynamically dominant state (Figs. 7 and 8 of[12]). Therefore, the magnetic pressure at the dawn side

dominant at the day side
papers (see Plate 3 ofcase, as discussed in the previythe process of theclariinordertoHere,[13]).
thestructure of the
spontaneous varlatlon ln case .
the expanded and themagnetic field lines of force. 2. As seen in Fis. 2
shrinking state is displayed in(a), the magnetic field lines
to pile up on the dawn
shrinking state in Fig.
side in the expanded state. Inaccumulated field lines
2 (b), on the other hand,are partly relaxed. As
on the dawn in the expanded
partiala confirmation of thebecomes large and gradually enlarges the magnetopause.
Also for this phase, the magnetic field lines anchored tothe dawn side magnetosphere continue to be bent. Then,

when the direction of the force deviated from theequilibrium on the dawn side magnetopause is changed
from the normal direction to the tangential direction, the(")
1FrrctrLjq4*{b}10ilmFig. 1 Time history of theat 0730 LT in case H andof the magnetopause,ffidhto

J*rordt

LF!0\",1/rr0Fig. 2 Three-dimensionallines of force in case L56.7, respectively.

ilt0*t {tsurt}00

Fig. 3 Time history of (a) the intensity of the magnetic
field at 0730 LT and (b) the azimuthal velocity atof the magnetic field(a) t = SS.Z and (b) t =1000 LT, respectively, just inside themagnetopause.
538

Miyoshi T. et al., Spontaneous Variation in a Rotating Magnetosphere(07s0 tT)solar wind(1000 LTJ : higb magaetic pressw regioo *;{iF : low nagnetic prusre rogioa -.}: plasma flow
: foree deviat€d from equilibrium

Fig. 4 Schematic model for the spontaneous variation in the rotating magnetosphere.

accumulated lines rush into the downstream by themagnetic tension force in the shrinking phase. Here thechange may be related to the structure of the dip at theReference[]

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4. Summary

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