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Stability of the cometary ionopause
Adv. Space Res. Vol. 9, No. 3, pp. (3)305—(3)308, 1989 Printed in Great Britain. AU rights reserved.
0273—1177/89 $0.00 Copyright
+
.50
© 1989 COSPAR
STABILITY OF THE COMETARY IONOPAUSE A. I. Ershkovich,* W. I. Axford,* W. -H. Ip~and K. R. Flammer** ~ **
für Aeronomie, 3411 Katlenburg-Lindau, F.R. G. University of California, San Diego, La Jolla, CA 92093, U.S.A.
MHD stability of the cometary innopause is discussed in the context of the Giotto mission to comet Halley. A mechanism associated with the plasma compressibility is sugge8ted here as being responsible for the apparent stability of the Halley ionopause: when the phase velocity of surface waves at the ionopause approaches the fast magnetoacoustic speed the unstable surface waves are transformed into stable body waves in the whole fluid resulting in an effective damping of the instability. The effects of both mass loading (due to photoionization) and dissociative recombination are also studied.
INTRODUCTION One of the most interesting results of the Giotto mission to comet Halley was the discovery of a cavity around the nucleus in which the magnetic field strength was nearly zero /1/. The boundary of the cavity, the ionopause, located at 4470 km (4155 km) from the nucleus on the inbound (outbound) leg was apparently stable. The magnetic field B drops from about 20~yto nearly zero within a thin layer of thickness d 25 km /2/. Cravens /3/ and Ip and Axford /4/ have shown that such a magnetic field structure might result from a balance between the Lorentz body force and ion-neutral collisional drag force. For perturbations with the wavenumber lcd < 1 the ionopause of thickness d may be treated as a discontinuity surface. This is essentially a tangential discontinuity (TD) surface since both contact and rotational (or Alfvén) discontinuities require the continuity of the magnetic field magnitude across the interface, in contradiction with the Giotto measurements which found B 0 inside the cavity. As the TD interface is known to be highly unstable against various MHD instabilities the question arises: why the Halley ionopause seemed to be stable? Recent studies /5-7/ did not identify mechanism which might be responsible for effective stabilization of the Halley ionopause. One may assume that the dissociative recombination (neglected in the papers above) might stabilize the ionopause since it results in a plasma momentum loss. It will be shown below that it is unable to quench the instability, and a damping mechanism associated with the plasma compressibility might be much more effective. EFFECT OF DISSOCIATIVE RECOMBINATION The relevant set of MHD equations is as follows: Continuity equation: (1) where 6 and a are, respectively, the photoionization and recombination rate constants, p and p,~are the mass density 6p,~= ap2/M. of the plasma and neutrals, respectively, M is the ion mass. In photochemical equilibrium Momentum equation:
+(i~
=
—V(p+
f—)+
!.(~.
V)~.+pu(j~—K)+5p,~(.~,, —~)
(2)
includes the ion-neutral friction force (~ being the corresponding collision frequency) and the momentum change due to photoionization. It is easy to show that the equation of motion (2) should not depend on recombination rate constant a. induction equation: (3) where equation V . = 0 was taken into account. Standard procedure of linearization of these equations for incompressible plasma and using boundary conditions at the TD interface (cf /5/) may be shown to result in the following dispersion equation 2w
=
KV+
i(±tJ(KV)2
-
2(K.KA)2 +
(3)305
-
V2)+
L1~-
LIo)
(4)
(3)306
A. I. Ershkovich
Cr a!.
where w is the wave frequency, VA is the Alfvén velocity, i’~ ii + 6p,~/p z’ + ap/M is the effective collision frequency taking into account the ions production and loss, R is the radius of curvature of the ionopause. We arrived at equation (4) by using the facts that the plasma density p was continuous across the Halley ionopause /8/, B 0 within the cavity and choosing the frame of reference moving along the interface with the ionospheric plasma inside the cavity (then the velocity shear across the interface equals ~). The curvature effects are taken into account under the condition that KR > 1. 3 at the Halley ionopause the Alfvén With B VA ~ 201’ and the plasma number density of 2 x 1O~cm~— 4 x 1O~cm velocity ~ 1.5 kms1 — 2 kms’ and perturbations with KItE cannot grow with the velocity shear less than -~ 2.5 kms’ , due to strong stabilizing effect of the magnetic field stress. However for perturbations with KJ.B. this effect vanishes, and the interface becomes highly unstable. Neglecting small curvature effects and taking K.L,~one obtains from equation (4) for unstable branch
2lnw=~(K.~)2+~~vo>0
(5)
This expression shows that both the mass loading (due to photoionization) and recombination cannot quench the instability although these processes, naturally, slightly diminish the instability growth rate 1mw. For example, with electron temperature of 300 K /9/ a 7 x 10~cm3s’. Then tie = ti+ap/M = 8 x iø~s~with the plasma number density of 3 x iO~cm3 at the Halley ionopause and ti = 6 x 103s’ /2/. According to equation (5), dissociative recombination results in a decrease of the instability growth rate 1mw by a factor of 1.24, 1.15 and 1.065 for the velocity shear of 1 kmst,2 kms’ and 5 kms’, respectively with the wavelength A = iO~km and assuming KIli~. The plasma bulk velocity of a few kms’ at the Halley ionopause was observed during the Giotto encounter /8/. With a shear of a few kms~1the effects of photoionization and dissociative recombination become negligible. According to Ershkovich and Flaminer /10/, finite amplitude effects in incompressible plasma cannot quench the instability either. Thus we arrive at the conclusion that apparent stability of the Halley ionopause cannot be explained within the context of incompressible fluid. DAMPING MECHANISM ASSOCIATED WITH THE PLASMA COMPRESSIBILITY When the phase velocity of unstable surface waves, Rew/K approaches the fast magnetoacoustic speed U+ an effective damping of the instability is expected due to generation of MHD waves in the whole fluid. In this case the wave amplitude was shown not to decrease any more away from the interface /7,11/. Hence with Rew/K (4 the waves are no longer surface waves but body waves in the fluid. In other words, under this condition small oscillations of the interface generate MHD waves in the whole plasma thereby causing an effective damping of the instability. This mechanism, however, cannot quench the instability along all the directions K. The phase velocity is approximately given by equation (4) for incompressible plasma: Rew/K ~Vcos~bwhere ~ is the angle between K and ~. With ~ —~ ir/2 the phase velocity becomes too small to approach (4. Hence perturbations propagating along KJ-3~can grow if the magnetic field is not strong enough, and TD interface remains unstable. However the instability growth rate should decrease due to stabilizing effect of the magnetic field stress in all cases except for ~llli.(then perturbations along LL3~II~ can grow rapidly). These qualitative considerations are supported by the results of numerical calculations for compressible plasma. The corresponding dispersion equation (including the curvature effects) has been obtained by Ershkovich et al. /7/ (see equation /25/ ibid.). We solved it numerically assuming B.J.~. If ~ and ~ are not perpendicular no significant difference is expected except for the case }Lflli. mentioned above (this geometry however represents a singularity which is unlikely to occur). The instability growth rate 1mw is shown on Figures 1-3 as a function of the velocity shear for different angles ~ with the radius of curvature of the ionopause R = 4.5 x iO~km, the magnetic field B~= 207, the wavelength A = iO~km, the plasma density ratio P*/Pe = 1, the plasma temperature T~= 103K (indices i and e refer to internal and external plasmas, respectively). As V3 > (where C, is the sound velocity) these Figures change little if the temperature T~~2 x 103K which is compatible with observations /8/. They also remain practically the same with p~/p~ ~2. When the plasma number density n~ grows the Alfvén velocity VA decreases and hence the magnetoacoustic velocity (4 diminishes. Therefore the velocity shear V 5 required for stabilization due to damping 3 (Figure mechanism 1) and V under consideration decreases: V5 3 ~ U+/cos.~. (Figure 3). With The instabiliy = 0 V~growth 10 kms’ rate, with naturally, n, = 2decreases x 1O~cmwhen ~ grows due to5 stabilizing 6 kms’ effect with n~ of = the4 magnetic x iO~cm field stress. Inspection of Figures 1-3 shows that the Halley ionopause turns out to be unstable. However rapid convection of perturbations downstream may lead to an effective stabilization. The characteristic time fqr perturbations to be convected well downstream, say, at the distance ‘~ R is r~ R/V~,where V~,is the group velocity. With r~/r 1~1 (where = (Imw)’ is the instability growth time) the ionopause is effectively stable since perturbations are convected well downstream before growing substantially.
Stability ofthe Cometary lonopause
.OOS
T
I
.005
I
•
5, 1,
(3)307
I
I
I
20y 1000K 2OOOcm~’
I~
T
•
I
I000.K 3000 cm’
//;~1~J~
VELOCITY SHEAR (km/sic)
Fig. 1. The instability growth rate 1mw as a function of the velocity shear V for different angles ~ between K and .~, with the plasma number density n, = 2 x lO3cm3.B..LK is assumed, B, = 207,R = 4.5 x 10 3 km, A = i03 km, 2’, = 1o3K,p~/p.= 1.
•
VELOCITY SHEAR 1km/sic)
Fig. 2. The same as Fig. 1 but n,
=
3 x iO~cm3.
_______________________________________ .0O~.
.004
I
n
•4000cm’
VELOCITY SHEAR (km/see)
Fig. 3. The same as Fig. 1 but n,
=
4 x iO~cm3.
On the other hand, with r~/r~> 1 the ionopause should be effectively unstable. In this case penetration of the large-scale magnetic field into the cavity is expected, in contradiction with the Giotto observations. The plasma bulk velocity of a few kms’ at the Halley ionopause was observed during the Giotto mission /8/. Whereas the velocity shear V 3 — see Figure 3) seems not to be inconsistent with these 5 measurements 6 kms’ (required the shear for stabilization V with t seems n, = to 4 xbeiO~cm ruled out. With n, = 4 x io~ cm3 and 5 ~10 kms V 2s whereas 5 6 r~ kms’io~s, 1mw and —, 0 r~/r with ~ = 0, and 1mw 2.5 x iO~s’ with ~ = 30°(see Figure 3).1)Hence the group r, 4velocity x iO would be small too, and perturbations practically not be convected 1 2.5. Ifwould the shear were much smaller (say, leading 1 kms’ eventually — 2 kms to the magnetic field penetration into the cavity. Although the plasma number density n, 4 x iO~cm3 at the Halley ionopause seems not to be ruled out theoretical models (based on photochemical equilibrium) give it, -~ (1 — 2) x i03 cm3 at the ionopause /12/. Neubauer /2/ estimated it, = 2.3 x iO~cm3 based on the data obtained by Krankowsky et al. /13/. With n, = 2.3 x iO~cm3 one obtains from Figures 1 and 2 r~ 250s with Vs = 6 kms1,r~/r, 4. This value seems to be too small (i.e. the instability is not strong enough) to ensure effective penetration of the magnetic field into the cavity. Therefore the cavity should remain field-free, and indeed so far no signature of the large-scale instability has been ovserved.
A. I. Ershkovich et aL
(3)308
According to equation (4), the instability growth time r
is
1 approximately proportional to the wavelength A. Hence with smaJ.l wavelength A — 200 km one obtains r~/i-~ ~. 1, and effective instability leading to a small-scale corrugation of the ionopause is expected. According to Neubauer /14/, Halley ionopause seemed to have strong ripples with a wavelength of at least 200 km. SUMMARY
The lonopause of comet Halley was shown to undergo the MilD instability. However the instability growth rate significantly diminishes due to a damping mechanism associated with the plasma compressibility, and slightly decreases if photoionization and dissociative recombination are taken into account. As a result, perturbations with the wavelengths A .-~ iO~km cannot grow substantially before being convected well downstream, and the Halley ionopause remained effectively stable for such perturbations. With smaller wavelengths A ‘— 200 km the instability growth rate is much greater, and the ionopause becomes effectively unstable. As a result, small-scale ripples at the ionopause may occur (cf /14/). REFERENCES
1. F. M. Neubauer, K. H. Glassmeier, M. Pohi, J. Raeder, M. H. Acuna, L. F. Burlaga, N. F. Ness, G. Musmann, F. Mariani, M. K. Walls, E. Ungstrup, and H. U. Schmidt, First results from the Giotto magnetometer experiment at comet Halley, Nature 321, 352-355 (1986). 2. F. M. Neubauer, The ionopause transition and boundary layers at comet Halley from Giotto magnetic field observations, J. Geophvs. Res. 93, 7272-7281 (1988). 3. T. E. Cravens, The physics of the cometary contact surface, in: 20th ESLAB Symposium on the exploration of Halley’s comet. ed. B. Battrick, E. J. Rolfe and R. Reinhard, Europ. Space Agency Spec. Pubi., ESA SP-250, V.1, Noordwijk, the Netherlands 1986, p. 241.
4. W.-H. Ip and W. I. Axford, The formation of a magnetic field free cavity at comet Halley, Nature 325, 418-419 (1987).
5. A. I. Ershkovich and D. A. Mendis, Effects of the interaction between plasma and neutrals on the stability of the cometary ionopause, The Astrophysical Journal 302, 849-852 (1986). 6. A. I. Ershkovich, D. Prialnik, and A. Eviatar, Instability of a comet ionopause: consequences of collisions and compressibility, J. Geophys. Res. 91, 8782-8788 (1986). 7. A. I. Ershkovich, K. It. Flammer, and D. A. Mendis, Stability of the sunlit cometary ionopause, The Astrophysical Journal 311, 1031-1042 (1986). 8. H. Balsiger, K. Altwegg, F. Bühler, J. Geiss, A. G. Ghielmetti, B. E. Goldstein, It. Goldstein, W. T. Huntress, W.-H. Ip, A. J. Lazarus, A. Meier, M. Neugebauer, U. Rettenmund, H. Rosenbauer, R. Schwenn, R. D. Sharp, E. G. Shelley, E. Ungstrup, and D. T. Young, Ion composition and dynamics at comet Halley, Nature 321, 330-334 (1986). 9. W..H. Ip, It. Schwenn, H. Rosenbauer, H. Balsiger, M. Neugebauer, and E. G. Shelley, An interpretation of the ion pile-up region outside the ionospheric contact surface, Astronomy and Astrophysics 187, 132-136 (1987). 10. A. I. Ershkovich and K. R. Flammer, Nonlinear stability of the dayside cometary ionopanse, The Astroohvsical Journal 328, 967.973 (1988). 11. Z.-Y. Pu and M. G. Kivelson, Kelvin-Helmholtz instability at the magnetopause: solution for compressible plasmas, J. Geophvs. Res. 88, 841-852 (1983). 12. W.-H. Ip, H. Spinrad, and P. McCarthy, A CCD observation of the water ion distribution in the coma of comet Halley near the Giotto encounter, Astronomy and Astrophysics, in press (1988). 13. D. Krankowsky, P. Eberhardt, J. J. Berthelier, U. Dolder, It. It. Hodges, J. H. Hoffmann, J. M. llhiano, P. Lämmerzahl, W. Schulte, U. Stubbemann, and J. Woweries, Evidence for HCS+ and CH2SH+ in the inner coma of comet Halley, in: 20th ESLAB Symposium on the exploration of Halley’s comet. ed. B. Battrick, E. 3. Rolfe and It. Reinhard, Europ. Space Agency Spec. Pubi., ESA SP-250, V.1, Noordwijk, the Netherlands 1986, p. 381. 14. F. M. Neubauer, Giotto magnetic-field results on the boundaries of the pile-up region and the magnetic cavity, Aatronomv and Astroohvsics 187, 73-79 (1987).
0273—1177/89 $0.00 Copyright
+
.50
© 1989 COSPAR
STABILITY OF THE COMETARY IONOPAUSE A. I. Ershkovich,* W. I. Axford,* W. -H. Ip~and K. R. Flammer** ~ **
für Aeronomie, 3411 Katlenburg-Lindau, F.R. G. University of California, San Diego, La Jolla, CA 92093, U.S.A.
MHD stability of the cometary innopause is discussed in the context of the Giotto mission to comet Halley. A mechanism associated with the plasma compressibility is sugge8ted here as being responsible for the apparent stability of the Halley ionopause: when the phase velocity of surface waves at the ionopause approaches the fast magnetoacoustic speed the unstable surface waves are transformed into stable body waves in the whole fluid resulting in an effective damping of the instability. The effects of both mass loading (due to photoionization) and dissociative recombination are also studied.
INTRODUCTION One of the most interesting results of the Giotto mission to comet Halley was the discovery of a cavity around the nucleus in which the magnetic field strength was nearly zero /1/. The boundary of the cavity, the ionopause, located at 4470 km (4155 km) from the nucleus on the inbound (outbound) leg was apparently stable. The magnetic field B drops from about 20~yto nearly zero within a thin layer of thickness d 25 km /2/. Cravens /3/ and Ip and Axford /4/ have shown that such a magnetic field structure might result from a balance between the Lorentz body force and ion-neutral collisional drag force. For perturbations with the wavenumber lcd < 1 the ionopause of thickness d may be treated as a discontinuity surface. This is essentially a tangential discontinuity (TD) surface since both contact and rotational (or Alfvén) discontinuities require the continuity of the magnetic field magnitude across the interface, in contradiction with the Giotto measurements which found B 0 inside the cavity. As the TD interface is known to be highly unstable against various MHD instabilities the question arises: why the Halley ionopause seemed to be stable? Recent studies /5-7/ did not identify mechanism which might be responsible for effective stabilization of the Halley ionopause. One may assume that the dissociative recombination (neglected in the papers above) might stabilize the ionopause since it results in a plasma momentum loss. It will be shown below that it is unable to quench the instability, and a damping mechanism associated with the plasma compressibility might be much more effective. EFFECT OF DISSOCIATIVE RECOMBINATION The relevant set of MHD equations is as follows: Continuity equation: (1) where 6 and a are, respectively, the photoionization and recombination rate constants, p and p,~are the mass density 6p,~= ap2/M. of the plasma and neutrals, respectively, M is the ion mass. In photochemical equilibrium Momentum equation:
+(i~
=
—V(p+
f—)+
!.(~.
V)~.+pu(j~—K)+5p,~(.~,, —~)
(2)
includes the ion-neutral friction force (~ being the corresponding collision frequency) and the momentum change due to photoionization. It is easy to show that the equation of motion (2) should not depend on recombination rate constant a. induction equation: (3) where equation V . = 0 was taken into account. Standard procedure of linearization of these equations for incompressible plasma and using boundary conditions at the TD interface (cf /5/) may be shown to result in the following dispersion equation 2w
=
KV+
i(±tJ(KV)2
-
2(K.KA)2 +
(3)305
-
V2)+
L1~-
LIo)
(4)
(3)306
A. I. Ershkovich
Cr a!.
where w is the wave frequency, VA is the Alfvén velocity, i’~ ii + 6p,~/p z’ + ap/M is the effective collision frequency taking into account the ions production and loss, R is the radius of curvature of the ionopause. We arrived at equation (4) by using the facts that the plasma density p was continuous across the Halley ionopause /8/, B 0 within the cavity and choosing the frame of reference moving along the interface with the ionospheric plasma inside the cavity (then the velocity shear across the interface equals ~). The curvature effects are taken into account under the condition that KR > 1. 3 at the Halley ionopause the Alfvén With B VA ~ 201’ and the plasma number density of 2 x 1O~cm~— 4 x 1O~cm velocity ~ 1.5 kms1 — 2 kms’ and perturbations with KItE cannot grow with the velocity shear less than -~ 2.5 kms’ , due to strong stabilizing effect of the magnetic field stress. However for perturbations with KJ.B. this effect vanishes, and the interface becomes highly unstable. Neglecting small curvature effects and taking K.L,~one obtains from equation (4) for unstable branch
2lnw=~(K.~)2+~~vo>0
(5)
This expression shows that both the mass loading (due to photoionization) and recombination cannot quench the instability although these processes, naturally, slightly diminish the instability growth rate 1mw. For example, with electron temperature of 300 K /9/ a 7 x 10~cm3s’. Then tie = ti+ap/M = 8 x iø~s~with the plasma number density of 3 x iO~cm3 at the Halley ionopause and ti = 6 x 103s’ /2/. According to equation (5), dissociative recombination results in a decrease of the instability growth rate 1mw by a factor of 1.24, 1.15 and 1.065 for the velocity shear of 1 kmst,2 kms’ and 5 kms’, respectively with the wavelength A = iO~km and assuming KIli~. The plasma bulk velocity of a few kms’ at the Halley ionopause was observed during the Giotto encounter /8/. With a shear of a few kms~1the effects of photoionization and dissociative recombination become negligible. According to Ershkovich and Flaminer /10/, finite amplitude effects in incompressible plasma cannot quench the instability either. Thus we arrive at the conclusion that apparent stability of the Halley ionopause cannot be explained within the context of incompressible fluid. DAMPING MECHANISM ASSOCIATED WITH THE PLASMA COMPRESSIBILITY When the phase velocity of unstable surface waves, Rew/K approaches the fast magnetoacoustic speed U+ an effective damping of the instability is expected due to generation of MHD waves in the whole fluid. In this case the wave amplitude was shown not to decrease any more away from the interface /7,11/. Hence with Rew/K (4 the waves are no longer surface waves but body waves in the fluid. In other words, under this condition small oscillations of the interface generate MHD waves in the whole plasma thereby causing an effective damping of the instability. This mechanism, however, cannot quench the instability along all the directions K. The phase velocity is approximately given by equation (4) for incompressible plasma: Rew/K ~Vcos~bwhere ~ is the angle between K and ~. With ~ —~ ir/2 the phase velocity becomes too small to approach (4. Hence perturbations propagating along KJ-3~can grow if the magnetic field is not strong enough, and TD interface remains unstable. However the instability growth rate should decrease due to stabilizing effect of the magnetic field stress in all cases except for ~llli.(then perturbations along LL3~II~ can grow rapidly). These qualitative considerations are supported by the results of numerical calculations for compressible plasma. The corresponding dispersion equation (including the curvature effects) has been obtained by Ershkovich et al. /7/ (see equation /25/ ibid.). We solved it numerically assuming B.J.~. If ~ and ~ are not perpendicular no significant difference is expected except for the case }Lflli. mentioned above (this geometry however represents a singularity which is unlikely to occur). The instability growth rate 1mw is shown on Figures 1-3 as a function of the velocity shear for different angles ~ with the radius of curvature of the ionopause R = 4.5 x iO~km, the magnetic field B~= 207, the wavelength A = iO~km, the plasma density ratio P*/Pe = 1, the plasma temperature T~= 103K (indices i and e refer to internal and external plasmas, respectively). As V3 > (where C, is the sound velocity) these Figures change little if the temperature T~~2 x 103K which is compatible with observations /8/. They also remain practically the same with p~/p~ ~2. When the plasma number density n~ grows the Alfvén velocity VA decreases and hence the magnetoacoustic velocity (4 diminishes. Therefore the velocity shear V 5 required for stabilization due to damping 3 (Figure mechanism 1) and V under consideration decreases: V5 3 ~ U+/cos.~. (Figure 3). With The instabiliy = 0 V~growth 10 kms’ rate, with naturally, n, = 2decreases x 1O~cmwhen ~ grows due to5 stabilizing 6 kms’ effect with n~ of = the4 magnetic x iO~cm field stress. Inspection of Figures 1-3 shows that the Halley ionopause turns out to be unstable. However rapid convection of perturbations downstream may lead to an effective stabilization. The characteristic time fqr perturbations to be convected well downstream, say, at the distance ‘~ R is r~ R/V~,where V~,is the group velocity. With r~/r 1~1 (where = (Imw)’ is the instability growth time) the ionopause is effectively stable since perturbations are convected well downstream before growing substantially.
Stability ofthe Cometary lonopause
.OOS
T
I
.005
I
•
5, 1,
(3)307
I
I
I
20y 1000K 2OOOcm~’
I~
T
•
I
I000.K 3000 cm’
//;~1~J~
VELOCITY SHEAR (km/sic)
Fig. 1. The instability growth rate 1mw as a function of the velocity shear V for different angles ~ between K and .~, with the plasma number density n, = 2 x lO3cm3.B..LK is assumed, B, = 207,R = 4.5 x 10 3 km, A = i03 km, 2’, = 1o3K,p~/p.= 1.
•
VELOCITY SHEAR 1km/sic)
Fig. 2. The same as Fig. 1 but n,
=
3 x iO~cm3.
_______________________________________ .0O~.
.004
I
n
•4000cm’
VELOCITY SHEAR (km/see)
Fig. 3. The same as Fig. 1 but n,
=
4 x iO~cm3.
On the other hand, with r~/r~> 1 the ionopause should be effectively unstable. In this case penetration of the large-scale magnetic field into the cavity is expected, in contradiction with the Giotto observations. The plasma bulk velocity of a few kms’ at the Halley ionopause was observed during the Giotto mission /8/. Whereas the velocity shear V 3 — see Figure 3) seems not to be inconsistent with these 5 measurements 6 kms’ (required the shear for stabilization V with t seems n, = to 4 xbeiO~cm ruled out. With n, = 4 x io~ cm3 and 5 ~10 kms V 2s whereas 5 6 r~ kms’io~s, 1mw and —, 0 r~/r with ~ = 0, and 1mw 2.5 x iO~s’ with ~ = 30°(see Figure 3).1)Hence the group r, 4velocity x iO would be small too, and perturbations practically not be convected 1 2.5. Ifwould the shear were much smaller (say, leading 1 kms’ eventually — 2 kms to the magnetic field penetration into the cavity. Although the plasma number density n, 4 x iO~cm3 at the Halley ionopause seems not to be ruled out theoretical models (based on photochemical equilibrium) give it, -~ (1 — 2) x i03 cm3 at the ionopause /12/. Neubauer /2/ estimated it, = 2.3 x iO~cm3 based on the data obtained by Krankowsky et al. /13/. With n, = 2.3 x iO~cm3 one obtains from Figures 1 and 2 r~ 250s with Vs = 6 kms1,r~/r, 4. This value seems to be too small (i.e. the instability is not strong enough) to ensure effective penetration of the magnetic field into the cavity. Therefore the cavity should remain field-free, and indeed so far no signature of the large-scale instability has been ovserved.
A. I. Ershkovich et aL
(3)308
According to equation (4), the instability growth time r
is
1 approximately proportional to the wavelength A. Hence with smaJ.l wavelength A — 200 km one obtains r~/i-~ ~. 1, and effective instability leading to a small-scale corrugation of the ionopause is expected. According to Neubauer /14/, Halley ionopause seemed to have strong ripples with a wavelength of at least 200 km. SUMMARY
The lonopause of comet Halley was shown to undergo the MilD instability. However the instability growth rate significantly diminishes due to a damping mechanism associated with the plasma compressibility, and slightly decreases if photoionization and dissociative recombination are taken into account. As a result, perturbations with the wavelengths A .-~ iO~km cannot grow substantially before being convected well downstream, and the Halley ionopause remained effectively stable for such perturbations. With smaller wavelengths A ‘— 200 km the instability growth rate is much greater, and the ionopause becomes effectively unstable. As a result, small-scale ripples at the ionopause may occur (cf /14/). REFERENCES
1. F. M. Neubauer, K. H. Glassmeier, M. Pohi, J. Raeder, M. H. Acuna, L. F. Burlaga, N. F. Ness, G. Musmann, F. Mariani, M. K. Walls, E. Ungstrup, and H. U. Schmidt, First results from the Giotto magnetometer experiment at comet Halley, Nature 321, 352-355 (1986). 2. F. M. Neubauer, The ionopause transition and boundary layers at comet Halley from Giotto magnetic field observations, J. Geophvs. Res. 93, 7272-7281 (1988). 3. T. E. Cravens, The physics of the cometary contact surface, in: 20th ESLAB Symposium on the exploration of Halley’s comet. ed. B. Battrick, E. J. Rolfe and R. Reinhard, Europ. Space Agency Spec. Pubi., ESA SP-250, V.1, Noordwijk, the Netherlands 1986, p. 241.
4. W.-H. Ip and W. I. Axford, The formation of a magnetic field free cavity at comet Halley, Nature 325, 418-419 (1987).
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