on the formation of io-induced acceleration regions related to jovian aurora

Pergamon Planet. Spucr Sci.. Vol. 46, No. 4. pp. 405-415. 1998

c_‘ 199X Elsevier Science Ltd

PII: SOO32-0633(97)00114-1

All rights reserved. Printed in Great Britain 0032-0633198 $19.00+0.00

On the formation of IO-induced acceleration regions related to Jovian aurora

Andreas Kopp,* ’ Guido T. Birk?’ and Antonius Otto’

‘Theoretische Physik IV. Ruhr-Universitat Bochum D-44780 Bochum, Germany ‘Geophysical Institute. University of Alaska, Fairbanks, AK 99775-7320. U.S.A.

Received 23 March 1996: revised 1 April 1997: accepted 6 May 1997

Ahatraet. By means of 3D resistive MHD simulations we present an effective mechanism to accelerate charged particles which may contribute to the Jovian aur- oral luminosity. We restrict ourselves to the lo-induced part, the so-called 10 footprint. We apply the present knowledge about the terrestrial aurora to Jupiter and perform in a first step global simulations of the Jovian magnetosphere in order to investigate the generation of a field-aligned current system by 10 with particular stress on the intluence of mass loading effects. The MHD modes excited by this interaction transport the velocity shear and magnetic perturbations into the Jov- ian ionosphere, thereby establishing a current system similar to the Birkeland currents in the Earth’s magnetosphere-ionosphere system. In a second step we perform local simulations of the Jovian magnetosphere-ionosphere system. In the considered latitudes in consequence of the velocity shear the current density is expected to rise up to supercritical values exciting microinstabilities which lead to anomalous resistivity. This resistivity gives rise to macroscopic resistive instabilities which in their nonlinear evolution result in considerably enhanced parallel electric fields. Thus, a field-aligned potential can be built up in these resistive regions accelerating charged particles to energies of several keV. 0 1998 Elsevier Science Ltd. All rights reserved

Introduction

The decametric radiation is one of the most impressive indications for the powerful electrodynamic interaction

Corrrspondrwe to: A. Kopp *Present address : Max-Planck Institut fur Aeronomie. D-37 19 I Katlenburg-Lindau, Germany. +Present address : Institut fur Astronomie und Astrophysik, Universitat Miinchen. D-81679 Mtinchen. Germany.

between Jupiter and IO. Already the earliest models (Piddington and Drake, 1968 ; Goldreich and Lynden- Bell, 1969) recognized a field-aligned current system between Jupiter and IO to be the key in order to under- stand the generation of electromagnetic radiation of mag- netospheric origin. These models. however, turned out to be too much idealized, and due to the enhanced plasma density in the 10 plasma torus the Alfven velocity was overestimated. Consequently, a so-called “lo flux tube” cannot form, but, as improved models (Neubauer, 1980; Goertz, 1980) could show, the lo-magnetosphere interaction can rather be understood as a wave phenomenon resulting in the formation of AlfvCn wings (Drell et ul.. 1965) carrying the field-aligned electric current. These models were supplemented by Gurnett and Goertz ( 198 1). who suggested a model of multiple reflected AlfvCn waves leading to current loops surrounding the entire IO plasma torus. Although analytical studies (Wright and South- wood. 1987. Wright and Schwartz, 1990 : Bagenal, 1994) and numerical simulations (Linker c’t al., 1991 ; Kopp. 1996) could contribute to a closer understanding of the current system and its generation mechanisms, our knowledge about the acceleration process, leading to the observ- able radiation itself, is far away from a comprehensive model.

Besides the predominating decametric radiation space- borne observations revealed a large manifold of further Jovian radiation of which the aurora1 hiss occurring at the inner boundary of the warm torus (Morgan et ul., 1994) and the Jovian aurora (e.g. Herbert et al., 1987) are the most important features. Recent observation with the Hubble Space Telescope (HST) revealed a bright aurora1 oval consisting on an equatorward part belonging to L- shells slightly outside the IO plasma torus (Caldwell et ~1.. 1992) and a poleward part associated with the boundary between open and closed magnetic field lines at about 65 Jovian radii (1 RJ = 7.14 x 1O’m) (Farrell et NI.. 1993). The origin of these phenomena, not least because of our very insufficient knowledge about convection patterns in the Jovian magnetosphere (Vasyliunas, 1983 ; C‘heng. 1992).

406 A. Kopp et al. : On the formation of lo-induced acceleration regions related to Jovian aurora

could, however. not be clarified up to now. HST observations (Connerney et al., 1993 ; Prange et al., 1996) dis- covered an additional bright spot in the Jovian aurora which is proved to be associated with lo, the so-called lo footprint. At least in this case, to which we restrict ourselves in this paper, the basic mechanism is well known : The lo-magnetosphere interaction generates a field-aligned current system along which particles are accelerated in aurora1 region. The latter point, however, the formation of acceleration zones and the acceleration itself are only poorly understood so far. Since merely the mechanisms generating the field-aligned current system differ, the Jovian aurora and the aurora1 hiss can be treated quite similar to the terrestrial aurora. which supplies us with much more observational data.

current system and use subsequently local simulations to investigate the formation of acceleration zones in detail. In both cases we use the basic equations of resistive MHD according to Otto (1990) in normalized units :

(14

cl!(p)

?t - -V-T = -v.[~~-BB+ (,;+ iBz)l]

(lb) l3B -= Vx(rxB)-iVqxj+iAB at

(ICI

In the following we briefly outline some features of the Earth’s aurora1 phenomena relevant for our purposes. As first suggested by Bostrom (1964) and confirmed by MHD simulations (e.g. Ogino, I986 ; Kopp, 1995) the convection flow developing in consequence of magnetosphere-solar wind interaction generates the system of field-aligned Birkeland currents (Cummings and Dessler, 1967) the existence of which is commonly regarded as a necessary condition for the occurrence of discrete aurora1 phenomena (e.g. Akasofu, 1981). These are characterized by highly varying spatial and temporal scales, and although a unifying description of their origin seems not to be admissible. considerable progress in understanding of aurora1 acceleration processes has been achieved (cf. Zmuda and Armstrong. 1974. Chiu and Cornwall, 1980 ; Borovsky, 1993). Recently. Otto and Birk (1993) pointed out the importance of macroscopic resistive instabilities operating in the magnetosphere-ionosphere current system and could show that resistive instabilities or more generally localized magnetic reconnection play an important role in the formation of thin, elongated aurora1 acceleration regions. In this paper we follow these ideas and demonstrate how, similar to the terrestrial aurora, resistive instabilities occurring along the lo-induced current system (cf. Machida pt al.. 1988) may account for the generation of field-aligned electric fields and thus. for discrete aurora1 phenomena in the Jovian ionosphere. as discussed for the case of the lo footprint.

The paper is organized in the following way : In Section 2 we describe the basic equations and our numerical tech- niques. outline our model of the formation of the lo- related current system and discuss consequences of resistive instabilities that disrupt field-aligned current sheets being unstable due to supercritical current densities. In Section 3 and Section 4 we explain the numerical realization and present our results concerning the generation of the field-aligned current system and aurora1 acceleration regions. respectively. Finally. we sum up our results in Section 5.

2. The model

Here B denotes the magnetic field and p the plasma density. v denotes the plasma velocity, q the resistivity, S the Lundquist number and U: = (P/2)” is an auxiliary function to describe the plasma pressure P (with the adia- batic index y), j is the current density, and 1 is the unit tensor. The numerical codes used are based on a code developed by Otto (1990) employing a leapfrog scheme for the hyperbolic balance equations (equation (la), equation (lb), equation (Id)) and the semi-implicit Dufort- Frankel scheme for the parabolic induction equation (equation (1~)). An artificial viscosity is used to suppress the odd-even instability (cf. Potter (1973) where also a description of the numerical schemes can be found). Some details of the model and the normalization of the basic equations are given in the appendix. If we neglect the corotation lag of the lo plasma torus (Pontius and Hill, 1982) IO is a conducting body moving with a velocity of

L‘XI = 57 km s-’ relative to the torus plasma and Jupiter’s magnetic field. The resulting magnetic field perturbation excites different MHD modes of which we consider here the Alfven mode. As MHD simulations (Linker et al., 1991; Kopp, 1996) could show, a current loop forms which closes in IO’S atmosphere and flows aligned to the AlfvCn characteristics cA = v,,,&B/&. This leads to the formation of AlfvCn wings above and below lo’s orbital plane, respectively, as first suggested by Neubauer (1980). This model, however, does not include IO’S intense plasma production leading to the formation of the 10 plasma torus. In the first part of this paper we model the generation of the field-aligned current system by the IO/torus interaction which finally is associated the Io- footprint in the Jovian aurora observed by Connerney et al. (1993) and Prange et al. (1996). The question arises of how far this current system is altered or whether additional effects occur if IO’S plasma production in taken into account. In the following we consider only plasma production from IO’S atmosphere and refer to the litera- ture (Brown, 1994, 1995, Schneider and Trauger, 1995) for the observations of plasma and neutral particles in lo’s direct environment as well as in the IO plasma torus.

In order to obtain appropriate simulation results of the Concentrating first on basic effects we observe that IO, generation as well as for the acceleration process we split by its relative motion causes the Jovian magnetosphere to the problem into separate parts and perform global simu- deviate from rigid rotation. Rigid corotation is a special lations demonstrating the generation of a field-aligned case of the isorotation, where the angular velocity Q is

A. Kopp et al. : On the formation of IO-induced acceleration regions related to Jovian aurora 407

constant on the magnetic field lines as required by Ferraro’s theorem. Deviations from isorotation were studied in a more general frame by Schindler et al. (1991) who could show a field-aligned current to develop in this case. The poloidal current arising from the toroidal magnetic field evolving due to a non-isorotating flow is directed field-aligned in stationary state. In the case of a localized resistivity, as discussed below, Schindler et al. (199 1) established a relation between the difference in the angular velocity on both sides of the resistive region and the resulting generalized electric potential U = -SE,, ds, which is obtained by integration of the parallel electric field E,, along the magnetic field with are length s. In this potential structure charged particles can be efficiently accelerated.

The field-aligned electric currents can also be regarded as a result of sheared plasma flows around 10, which also propagate along the Alfven characteristics (Barnett, 1986). If the time scales are too short for the Jovian ionosphere to respond by a slippage of magnetic field lines, the field-aligned current densities may exceed a critical value and microinstabilities, which may also be excited by steep pressure gradients (Machida ef al., 1988) lead to the formation of localized dissipative regions. In fact, there is observational evidence for turbulent wave spectra associated with field-aligned currents (Barbosa et al., 198 1). Under this condition the system may depart from this imposed configuration by a macroscopic resistive instability (cf. Otto and Birk, 1993). However, we note that, in principle, any significant violation of ideal Ohm’s law due to electron inertia (Seyler, 1990) stochastic electrostatic double layers (Block, 1975) or electrostatic shocks (Kan, 1975) processes discussed for the terrestrial aurora, may lead to a macroscopic instability process. During the dynamical evolution of this instability, localized regions of significant El that causes aurora1 particle acceleration form.

3. The IO-generated field-aligned current system in the Jovian magnetosphere

We begin with global simulations of the Jovian magnetosphere, where Jupiter is modeled as an aligned rotator located in the center of a cylindrical coordinate system. The numerical code is a cylindrical version (Kopp. 1996) of the original code (Otto, 1990). The computational area is a torus with rectangular cross section which encloses IO’S orbit. IJtilizing symmetry conditions only the upper half = 3 0 is computed. The area ranges in radial direction from r,,, = 1OL to rrnar = 15L and in -_-direction from

--m,n = 0 (equatorial plane) to lman = SL, leading to a length scale L = (1/2)R, = 3.6 x IO’m. The numerical grid resolution is 51 grid points in r and z and 93 grid points in cp-direction. Typical values for the IO plasma torus used in our simulations are (e.g. Bagenal, 1994) :

Q= 1.5x 10ym-3 &= 1.9x 10mhT

T, = 5.5eV(6.4x 104K) T, = 65eV(7.5x 1O’K)

with n,, denoting the particle density and T, (T,) the electron (ion) temperature. The resulting Alfven velocity and time are I’,, = 220 km SC’ and tA = 160 s, respectively,

where an averaged mass number of 23 has been used. The normalized value for the current density is j, = 4.2 x lo-” A mP2.

If Jupiter’s dipole tilt is neglected the initial magnetic field is :

B, = b,, 3rz

Jr’+ (24

G’b)

with b,, > 0. The whole magnetosphere rotates with constant angular velocity R, around the z-axis. In order to satisfy the equation for a stationary equilibrium (the factor l/2 occurs due to normalization, see Appendix A)

jxB-iVP+pR2r = 0

density and pressure are chosen as :

(3)

P = p. ew (r2Q$T,,) (44

P = P, exp (&i/T,) (4b)

where r, = PO/p0 is the temperature which is assumed to be constant. In normalized units we use P,, = p. = 1. The resulting plasma D of order 1 is artificially large, but required from numerical constraints (cf. discussion in Kopp, 1996). We consider IO’S rest frame in which the torus plasma streams in counterclockwise direction with a normalized angular velocity !& = 0.025. 10 is kept fixed at r10 = (yo, ‘pO = 0, i0 = 0), where Y() : = (rmax + r&/2. Now we define two spheres around IO’S center (Fig. 1): within the inner one (R,,) representing lo’s surface, the angular velocity vanishes ; within the outer one (RA) representing IO’S atmosphere new plasma is ejected into the system. For numerical reasons the final values for the angular velocity and the plasma density near 10 are reached after a given time r = 807,. The numerical realization is the following : We use time-dependent boundary conditions for the plasma density as well as for the angular

Fig. 1. Illustration of the numerical model for lo. The figure shows an excerpt of the numerical box near 10, u hich has been resealed to a unit cube (with r,,,,” = 0. I j for better illustration. The lines indicated Jupiter’ dipole field. The dark gray represents IO’S surface within which the angular velocity vanishes, the density is enhanced within the light gray sphere. IO’S atmosphere

408 A. Kopp c’t (11. : On the t’ormation of lo-induced acceleration regions related to Jovian aurora

velocity where the “boundary” extends in the computational area, since it contains lo’s surface and atmosphere. respectively. The values on these boundaries are computed by the following expressions

(5a)

R(r. 1. I -(jr)

= O(r. z, O){, -I<[($]~os’[;K(~)]] (5b)

where in this a(~, -_, 0) is simply the initial value Q,,. The auxiliary function x is defined by ti(.v.) : = min(.\-. 1). Thus. the expression in curled brackets on the rhs. of equation (5a) increases from 0 to 1 for small Ir - r,,,] and remains 0 outside; t -(St indicates the previous time step in equation (5b). Thus. a gradual fill up of the plasma torus may be modeled. Due to our grid resolution. R,,, = 1.4 and RA = 1.6 have to be chosen artificially large, corresponding to 27 and 3 1 lo radii (I R,,, = I .82 x IOhm). respectively. Consequently, at the current state the numerical results in this case can hardly be compared quantitatively with observational date. Since displaying our results in physical length scales would be more con- fusing than useful, numerical units are used in the figures of this section. The qualitative statements. however, are not affected.

In the following we compare the cases with and without plasma production from IO’S atmosphere according to equation (5b). In Figs 3-4 the first case is always shown on the left-hand side. the second on the right-hand side. In Fig. 2 isosurfaces of different quantities are shown in a plane approximately 0.3 above the equatorial plane. The coordinates have been transformed to a Cartesian coordinate system. The circle indicates IO’S surface. in the case with plasma production a second circle outside of the first one indicates lo’s atmosphere. From top to bottom (a) the plasma density p. (b) the angular velocity R and (c) the normal component ofthe current density,j, are plotted. In each diagram five gray tones are used to indicate the values, ranging from black (minimum) to white (maximum). where p ,,,,,, = 0.45 (0.9) and pII,.,, = 1.25 (2.3) for the case without (with) plasma production. In Figures (b) and (c) we use the same values for both cases : a,,,,,, = 0 and Q,,,, = 0.12, and .il _,,,,,, = -0.45 and .i;.[ ,,,,, = 0.45. so that the gray tone also indicates the sign.

In the case with no plasma production we obtain a slight density increase in front of IO and a slight decrease behind. whereas we observe that the newly created plasma is swept away by the streaming torus plasma at the outer surfaces forming a tail-like structure. In addition. the anguIar velocity shows a considerable increase which con- tinues into the wake. The increase in the case without plasma production taken into account. on the other hand, is negligibly small. As the bottom diagrams reveal, the current structure is considerably influenced by this flow pattern. In the first case we obtain a behavior as expected, the current is directed downward at IO’S inner border and upward at the outer one. Due to the increase in the angular

velocity when IO ejects plasma B* VQ changes sign at IO’S inner and outer border and consequently two oppositely directed current systems develop outside the main system. The resulting current structures are more apparent in Fig. 3(a) where arrows of the poloidal current density J!,<,, = (,i,. 0, ,i,) behind IO in the wake are shown, lo’s outline is added for comparison. Figure 3(b) shows isosurfaces of the field-aligned current densityj,l = (J* B)/lBI. While we obtain essentially two regions with different signs when no plasma source is added, the four regions in the second case make the double structure of the poloidal current evident.

Moreover. we recognize an upward shift of the region of outward directed current (closure across IO’S surface). In order to study this effect more detailed we compare the structure of j,,,, with Fig. 4 which reveals a close connection with (a) the plasma density p as well as with (b) the angular velocity R close behind lo. We conclude that gradients in the angular velocity and the plasma density leave Jupiter’s magnetic field perturbed in the wake and thus. give rise to a current system in IO’S wake caused by mass-loading as Southwood and Dunlop (1984) as well as Ip ( 1990) already expected in analytical models.

4. Resistive instabilities of lo-induced field-aligned current sheets

In this section we concentrate on the dynamics of a single, lo-induced field-aligned current sheet due to macroscopic resistive instabilities. The train of thought here is the following: Field-aligned electric currents are the result of sheared plasma flows in the IO plasma torus that propagate along the Alfvtn characteristics (cf. Barnett, 1986). If the time scales are too short for the Jovian ionosphere to respond by a slippage of magnetic field lines, the field- aligned current densities grow and eventually the associated relative electron--ion drift velocity fly (j = IW,), which may be a diamagnetic drift velocity, exceeds a critical value. Consequently, collective plasma oscillations can be driven unstable (e.g. Papadopoulos. 1980; Kaplan and Tsytovich. 1973). which in their nonlinear evolution result in microturbulent electromagnetic or electrostatic fields. In this situation momentum transfer between the charged particles via wave-particle interaction with microturbulent fields gives rise to an anomalous electrical resistivity which is several orders of magnitude higher than the Spitzer resistivity due to Coulomb interactions. Particle acceleration arising from an anomalous resistivity in the terrestrial aurora was discussed e.g. by Kindel et uf. (1981). and in fact, there is observational evidence for turbulent wave spectra associated with field-aligned currents in the Jovian magnetosphere (Barbosa et al., I98 I ). When localized dissipative regions form in the Earth’s ionosphere macroscopic resistive instabilities (cf. Otto and Birk. I993 : Birk and Otto, 1996) may develop that result in reduction of the magnetic shear and conversion of magnetic energy in heat and bulk acceleration. The instability we consider can be regarded as a generalized tearing mode (cf. Furth et cd.. 1963) that results in a reduction of the held-aligned electric current density through partial disruption of the current layer. As a familiar feature of

A. Kopp rt ~1. : On the formation of IO-induced acceleration regions related to Jovian aurora

p at zzO.3, for >=O p at 2zO.3, for p>O

R at 2czO.3, for +O

w j, at zz0.3, for lj=O

R at 2X0.3, for p>O

j, at 2x0.3, for p>O

h c

-1

-2 -2

409

Fig. 2. Isosurfaces of (a) plasma density p, (b) angular velocity 0 and (c) perpendicular current density j, at 1~0.3. The case with plasma production added is shown on the right hand side, respectively. The color table has been reduced to five gray tones, the circle indicates lo’s surface, on the right hand side, the outer circle represents lo’s atmosphere

410 A. Kopp et cd. : On the formation of lo-induced acceleration regions related to Jovian aurora

l_Ol at y&O (behind lo), for j=O

‘1

(b) j,, at (pM” (behind lo), for +O

3

N

2

10 11 12 13 14 15 r

3. (a) The poloidal current system in the plane cp- -8” in the wake close behind IO and Fig. (b) isosurfaces of the corresponding parallel current density j, , where dark and light gray areas indicate negative and positive values, respectively. For better illustration the arrows had been set to a constant length above and omitted below a certain threshold value, respectively. In this case the circles show lo’s surface and atmosphere (cf. Figure 2) at 47 = 0

7pOr at (pz8O (behind lo), for P>O

5% -c I~“““~‘,““““‘,“““” ~eC -M._r -v..F.F.%.~ -

3

N

2

1

at 9~8' (behind lo), for rj>O

this reconnection process localized regions of enhanced generalized electric potential U = -SE,, ds form. These generalized potential structures should not be confused with electrostatic potentials that cannot lead to any net acceleration of charged particles. We will show that for realistic physical parameters the associated field-aligned electric fields can accelerate charged particles to energies high enough to result in aurora1 luminosity in the Jovian ionosphere. The local simulations carried out in order to investigate the formation of acceleration zones in consequence of resistive instabilities are performed with a 3D Cartesian version of the MHD code. As the origin of our coordinate system we consider an arbitrary point along the flux tube between IO and Jupiter in the northern hemi- sphere of Jupiter which lies at H,, = 2R, above its atmosphere corresponding to a latitude of about 45”. We note that this choice is somewhat arbitrary. In fact, even in the

well observed terrestrial context the actual locations of aurora1 acceleration regions are still a puzzle. In the sup- posed scenario these locations depend on the, fairly vari- able, local plasma parameters as well as the current densities. Anyhow, since our goal is merely order of magnitude estimations the exact location is not a crucial parameter.

Our coordinate system is sketched in Fig. 5: The Z- direction indicates the main direction of Jupiter’s dipole field which we assume to be homogeneous, the y-direction corresponds to the positive q-direction (from west to east), from which the x-direction follows. Now we take into account shear caused by the IO torus interaction. In an intermediate, cylindrical frame we see the torus plasma moving in positive and IO moving in negative cp direction, corresponding to B, < 0 at IO’S position and B, > 0 outside. In our computational box we identify 9 with I: and thus obtain a shear in positive y-direction with B, > 0

A. Kopp et a/. : On the formation of IO-induced acceleration regions related to Jovian aurora

(a) (b)

p and &,,,l at (p=8” (behind lo) R and &po, at (p=8’ (behind lo)

411

Fig. 4. Contour plots of (a) the plasma density p and (b) the angular velocity R at cpz8’ together with the poloidal current density (cf. Figure 3). where the number of arrows has been halved

L is now L = 400 km, the half-width of the field-aligned current layer. For the typical particle density we choose IZ” = 5.0 x lO’m_ (Bolin and Brenning, 1994) and for the current density Jo = B,O/p,,L = 1.0 x lo-‘A m-‘implying &, = 5.0 x IO-‘T. The main component is B=O = 2.5 x lO-5 T for the dipole field at 45” at Ho = 2R,. With these quantities we obtain an Alfven velocity and time of zlA = 150 km s-i and zA = 2.6 s, respectively. The electric field is normalized to E. = oABo = 7.7 mVm_‘. At this point we have to specify for our Lundquist number associated with the anomalous resistivity van = m,v,,ln,e2 where the anomalous collision frequency v,, is a measure for the momentum transfer of the charged particles via microturbulent electromagnetic fields. We suppose that the lower-hybrid-drift instability is excited, since it is the kind of microinstability that is excited most easily (cf. Papadopoulos, 1980) and set v,, E (m,/m,)“4q, (cf. Huba, 1985) where o,,, is the lower-hybrid frequency, from which we obtain a Lundquist number S z 100. Since the onset condition for the lower-hybrid-drift instability is un > t~,(me/m,)“4 (uD is the relative drift velocity of the charges particles associated with the current density and Vi is the ion thermal velocity) our estimations imply quite realistic ion temperatures of about Ti z 10’ K. We note that on the one hand lower ion temperatures would result in the excitation of the lower-hybrid-drift instability for lower electric current densities and on the other hand that for drift velocities significantly higher than ui(m,/mi)“4 different microinstabilities would be excited that would result in an even higher anomalous resistivity (e.g. Papadopoulos, 1980).

For numerical reasons, in the z-direction we have made use of a resealing in order to handle with the different length scales in the x-, y- and z-direction. In the normalization used, length scales in the z-direction have to be resealed by a numerical factor of 4.4.

As shown in Fig. 6 the shear flows caused by the Io- torus interaction are transported along the magnetic field lines by shear Alfven waves. Thus, we apply a velocity perturbation as an initial condition, which changes the

Fig. 5. Sketch of the coordinate system for our local simulations, the z-direction is parallel to the local direction of Jupiter’s dipole field

for x > 0 and in the opposite direction for x < 0. As an appropriate initial configuration we choose the following sheared magnetic field (cf. Otto and Birk, 1993) a force- free version of a Harris sheet (Harris, 1962) :

B = B,,tanhxe,- J B$+ 3~. (6)

In order to model a macroscopic resistive instability at altitude Ho we apply sheared plasma flows u,(x,z) at the upper boundary z = zmax. For simplicity, however we regard the shear flow as a perturbation and start with a static configuration (v = 0) with homogeneous pressure and density.

For the numerical realization we pose line symmetry as boundary conditions in the y-direction and carry out the simulations with 49 grid points in x-direction, 39 grid points in y-direction, and 105 grid points in z-direction, where we use a non-uniform numerical grid with a maximum resolution of 0.05 in the x-direction, 0.4 in the y-direction, and 0.2 in the z-direction. The dimensions of our numerical box are given by XE [ - lO,lO], YE [0,30], and z E [0,60] in normalized units. In this part we use the following quantities for normalization : The scaling length

A. Kopp rt d. : On the formation of IO-induced acceleration regions related to Jovian aurora

R at L_"=OO

Fig. 6. Is going tht

10 11 12 13 14 15

X

.osurfaces of the angular velocity R at y, = 0 (the plane rough lo’s center)

sign at x = 0. decreases which /s/ and towards Jupiter, leading to :

1:,(.X?. Z, t = 0) = L’,.,j tanh (2.~)

cosh’(.r:3) exp[- _1&,,-:)]. (7)

As a boundary condition for I > 0, ~~I(.~.:m.l,. t) = rYO tanh (2s)/cosh’(s/3) is used. These sheared flows (we choose a rather small amplitude of 5% of the Alfven velocity) lead to a further shear of the magnetic field and thereby in an increase of the field-aligned current density j,. An anomalous resistivity will be switched on if ,j, exceeds a critical value,j,’ =,jo (we start with a marginal current density), and gives rise to the macroscopic resistive instability.

The parallel current densityj increases along an arbitrary field line towards Jupiter and may finally become supercritical which results in the formation of nonideal regions. This may be seen from a strongly simplified pic- ture where we assume a stationary state. In this case the poloidal current density can be written as jp,,, = ~‘(cc)B,,,,

where I : = rB, is differentiated with respect to CC the flux function (B,,, = Vr x Vcp). Thus. the main portion of the field-aligned current density increases with the magnetic field along an arbitrary field line towards Jupiter and may finally become supercritical which results in the formation of nonideal regions. In order to attain an appropriate simulation of this situation we choose a somewhat different approach and enhance the shear flow for the current to become supercritical as described above.

If the resistive instability is excited it results in a reduction of the current density as shown in Fig. 7. This

reduction appears due to the fact that magnetic energy stored due to the shear can now be released and is con- verted into bulk kinetic energy as well as thermal energy during the instability process. Moreover, during the unstable dynamics a strong perpendicular electric field E, (see Fig. 8(a)) and a fairly localized parallel electric field Ei evolve (see Fig. 8(b)). The origin of strong perpendicular electric fields can be understood (cf. Otto and Birk. 1993)

Fig. 7. Surface plot of the field-aligned current density at : = 1600 km after t = 60~;~. The reduction of the current density t up to 20% of the initial value chosen as 100 nA m -‘) caused by the resistwe instability is evident

similar to the so-called “electrostatic shock structures” observed in the lower Earth’s magnetosphere (Weimer et rrl., 1985). Any future measurements of such electric fields. although difficult to detect by direct measurements due to their strong localization in the vicinity of the resistive instability, would obviously be in favour of our model.

The evolving parallel electric field grows up to a maximum value of 0.3 mV m-’ for the parameters chosen, which. as already mentioned, depends on the Lundquist number and critical current density. The evolving parallel electric fields can accelerate aurora1 particles in so-called “potential structures” similar to those observed in the Earth’s magnetosphere (Mozer, 1981). Figure 9 shows the generalized electric potential U evolving during the nonlinear instability dynamics. Similar to the Earth’s aur- oral acceleration regions thin elongated regions “potential” structures form. An upper limit for the generalized potential U is given by U 5 6E,,A/SSj,,, where A is the length of the acceleration region along the magnetic field lines and the factor 6/5 is due to the fact that in the simulations the critical current density during the instability process is exceeded by 20% maximum.

Even in the case of terrestrial aurora it is still only poorly known how the particles are actually accelerated (see e.g. Borovsky. 1993 for a review). Moreover the acceleration process itself is beyond the MHD description, but with we can estimate an upper boundary for the kinetic energy the particles may obtain and compare this values with observations and theoretical models. For the Jovian aurora several scenarios are discussed. Detailed dis- cussions can e.g. be found in Rego et al. ( 1994), Prangt et al. (1996) or Bisikalo et al. (1996). The first two give an energy range for electrons from 10 to 50 keV, whereas the latter discuss energies from 0.2 to 22 kW for the respective models. Assuming a central acceleration region localized at 2R,, electrons can be accelerated in our model up to energies of 9 keV. As noted before the actual location depends on the local plasma parameters allowing for localized dissipation. but already this rough estimate gives a particle energy in a reasonable range.

A. Kopp rr al. : On the formation of lo-induced acceleration regions related to Jovian aurora 413

E_x [v/ml, time = 120

‘f

10 U [kV], time = 120 F

03 = 120

&4&-P [ mv/m]l time

0.30 i

Fig. 8. Surface plots of the the x-component of the electric field at I” = 1600 km (a) and the parallel component of the electric field at y = 0 after t = 1207,. The strong perpendicular electric field - 1 Vm-’ is caused by divergent plasma flows due to the instability process. The parallel electric field may account for coherent acceleration of aurora1 particles

5. Conclusions

In this paper we suggested macroscopic instabilities as effective acceleration mechanisms in the Jovian magnetosphere-ionosphere system. These instabilities arise from supercritical current densities along the field-aligned current between 10 and Jupiter and can contribute to the so-called 10 footprint in the Jovian aurora. We used two different 3D resistive MHD simulations in order to model the generation of the current system as well as the formation of the acceleration zones in the respective appropriate geometry.

In the first part we investigated the formation of the field-aligned current system by the Io-torus interaction where plasma production from IO’S atmosphere was added. The comparison with the case without mass loading revealed significant modifications which show a close connection between flow patterns as well as density gradi-

Fig. 9. The generalized electric potential U after I = 120t,. Simi- lar to the Earth’s aurora1 acceleration regions a thin elongated structure evolves in which aurora1 particles can be accelerated up to some 9 keV giving rise to discrete bright aurora1 phenomena in the Jovian ionosphere

ents and the appearing current system at IO’S edges and especially in the wake. Thus, our results may represent a first self-consistent confirmation of earlier. analytical models about IO’S plasma wake.

When these field-aligned currents grow super-critically (due to the convergence of the Jovian dipolar magnetic field and local plasma processes that account for local dissipative regions) macroscopic resistive instabilities can operate and effectively reduce the free magnetic energy stored in the current system. In the second part we could demonstrate how during the instability process strong localized perpendicular electric fields and localized parallel electric field that may lead to aurora1 acceleration form. We conclude that macroscopic resistive instabilities may play an important role in the origin of the aurora1 luminosity at least in the IO footprint as it is probably the case in the Earth’s magnetosphere-ionosphere system.

Acknowledgements-We would like to thank Michael E. Brown and another referee for their conscientious comments which helped significantly to improve our paper and Ulrich Becker for providing Fig. 5. This work was supported by the Deutsche Forschungsgemeinschaft (Bonn) through the Sonderfor- schungsbereich SFB 191 “Physikalische Grundlagen der Nieder- temperaturplasmen” and Grant Schi 156 17-I.

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Appendix A

We start with the basic equations of resistive MHD that can be found in textbooks about plasma physics, e.g. Mitchner and Kruger ( 1973) :

+p -- = -V.(p) ?/

(Al)

?( pv)

it - -V*(pvv)-VP+jxB (AZ)

?B P=Vx(vxB-tlj) i-t (A3)

i({X)

il - -V*(psv)-P(Vv)+t/j’ (.44)

where i: denotes the inner (thermal) energy density and E is the electric field. Now we assume an ideal gas in order to establish a relation between P and I:: P = ~>k,T/nl (k, is the Boltzmann

constant). The inner energy density may nou be ~‘1 itten ;I> (( is the heat capacity) :

and Eq. (A4) may be rewritten ;IS

In order to make the set of equations ~u~t‘tl~l~ 1’0 ilumcl~ical computations we now write each quantity!/ ;I\ ,I prod LIC’I ~1 = :I$. where 9,) is the typical value (given in Scctic.bn i ;[ntl Sccrion Ai and3 is the normalized quantity which 14 uwxi ~‘oI- tht, simulation (some of the factors y,, result from the other,. ,,inc: linall\ UC

must obtain a common filctor III cd1 tclm WI-1~11 C,III h

reduced). We take the values fol- H,,. ,J,, == ..IuI.,I,,, I;, and the length scale L (used for derivations) ~‘Ix)I~ o1wr~ ation ;~nd obtain the f&wing normalization 1;ILYiOl.~ : vclocit\ o,, = P,, = B,,. ~ /,,,p,, and time sculc I,, = r ., :: I_ r,. For the :;I;

pressure we use P,, = P,,,,, = B,:$c,,. which t”\pl;un, the fact<)r I ,‘Z in the momentum b&mcc eyuarion. ThcrcforC ~hc ~OI- malized pressure P is the plasma-beta. ~vh~ch i\ Ich., tlla11 lmit\ for the configurations considered. The rcsisti\ it! i\ n~~rm~d&l with respect to P\,, = ~I,,LP,,‘S. Here, S = T,, T:, ~~ /I,;/.I , ~1 is the Lundquist number, the ratio of dilTusion and All\ en time. \vhich cannot be reduced and thus appears in the norm;llizc~I cq u;lti\ln\. Finally we replace the current densit! hl ~hc Mau\\:ii cq’.1,111on V x B = p(,j from which follows i,, = B,, 1’,,1. and 114~’ hi, I‘IIIICLL,~I~

II = (P:?), instead of P in order to simptif!; c‘quat~i~~ i \‘~a.

on the formation of io-induced acceleration regions related to jovian aurora

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