5. Discussion
5.1. Estimation of the Heliospheric Current Sheet Thickness
[22] As a bounded conductor moves across the magnetic field, charges
accumulate at its ends. In the steady state regime, current is zero. The
electric field in the conductor is determined from the Ohm's law
E+ V
B/c = j/s by substituting
j = 0. Another situation arises in the closed
current of the heliospheric current sheet, i.e., no charge accumulation
occurs, polarization field is absent, and the current density can be
estimated as
j = s V B
/c.
In an independent manner, the current density
can be obtained from Ampere's equation rot
B = 4 pj/c or
j
cB/2 pd. By
equating these expressions for
j, we get the current sheet thickness
d = (c2/2 psV)(B/B
).
By substituting plasma parameters in the current sheet
in the region of the Earth's orbit
[Smith, 2001]
- solar wind velocity in
the current sheet
V
3
107 cm s
-1,
plasma concentration
n
10 cm
-3,
magnetic field in the solar wind
B = 5 g,
Spitzer conductivity
s = 1015 s
-1 for
Te = 20 eV, and assuming the normal component of the magnetic
field in the current sheet
B
= 0.1 g, we get
d
2 mm, which contradicts
observations. The second contradiction is met in estimation of the current
density from expression
j = sV B
/c,
where there are no limitations on
the plasma density and velocity of charge carriers. The obtained value
j
2
106 CGSE corresponds to the current velocity
VC = j/ne = 3
1014 cm s
-1.
The reason for the contradiction is the use of the Spitzer conductivity
for the low-concentration plasma, when a high current density is not
provided because of deficiency of charge carriers. Apparently, the
maximum current velocity must not exceed the thermal velocity of
electrons
Vth,
otherwise an anomalous resistance will develop. By taking
the current velocity
Vth = 3
108 cm s
-1,
we obtain the maximum possible
current density in the sheet of ~1 CGSE, and the minimal possible
thickness of the current sheet of about
2
105 cm. If the electron
temperature is well above the ion one ( Te > 3Ti ),
the ion-sonic instability
can develop already at
VC
(Te/Mi)1/2 [Bernstein et al., 1960].
Then the
maximum current density will become ( Mi/me)1/2 times lower, and the
current sheet width can reach
2
107 cm.
The sheet thickness estimated in
such a manner is more than an order of magnitude lower than its
maximum thickness (10,000 km) obtained from spacecraft measurements
[Smith, 2001].
This can be explained by either a very low
B
or
development of current instability at
Vc
0.1(Te/Mi)1/2. In addition, the
sheet thickness of 10,000 km is likely to be overestimated because the
angle between the spacecraft trajectory and normal to the sheet surface at
crossing of the heliospheric current sheet can be rather large.
5.2. Possibility of Reconnection in the Heliospheric Current Sheet
[23] Reconnection above the active corona region where
b
1 is an efficient
mechanism of plasma heating. On the contrary, the reconnection in the
solar wind cannot play a significant role in its energetics because at
b=1 the temperature increases only by a factor of two even in the case of total
dissipation of the interplanetary field. As far as the heliospheric current
sheet is concerned, the flow required for reconnection cannot be
established. Indeed, reconnection occurs in the vicinity of the neutral
X line at plasma inflow from both sides of the current sheet. After
reconnection, the magnetic tension force accelerates the plasma along the
sheet in both directions. However, motion of plasma toward the Sun is
impossible in the heliospheric current sheet, because the sheet itself
exists due to the flow directed away from the Sun. Thus the flow that
must be established at reconnection is impossible in the heliospheric
current sheet.
[24] The situation in the magnetospheric tail is different. The solar wind
extends the magnetic field lines of the Earth. On the tail surface, the solar
wind generates the current that closes in the current sheet. The current
sheet of the tail plays the role of a load, while the heliospheric sheet is a
generator. Inside the current sheet of the tail, the force accelerates plasma
along the sheet rather than decelerates it. Earthward from the neutral
X line, the force
j
B/c and plasma flow are directed toward the Earth. On
the other side from the
X line, the normal component of the magnetic
field has another direction, and plasma accelerates away from the Earth
[Lui, 1987].
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