Expansion of solar corona in the Sun's gravitational field...

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 times

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 approx

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 sim

10⁷ cm s ^-1, plasma concentration n sim

10 cm ^-3, magnetic field in the solar wind B = 5 g, Spitzer conductivity s = 10¹⁵ s ^-1 for T_e = 20 eV, and assuming the normal component of the magnetic field in the current sheet B = 0.1 g, we get d sim

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 sim

10⁶ CGSE corresponds to the current velocity V_C = j/n_e = 3 times

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 V_th, otherwise an anomalous resistance will develop. By taking the current velocity V_th = 3 times

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 times

10⁵ cm. If the electron temperature is well above the ion one ( T_e > 3T_i ), the ion-sonic instability can develop already at V_C sim

(T_e/M_i)^1/2 [Bernstein et al., 1960]. Then the maximum current density will become ( M_i/m_e)^1/2 times lower, and the current sheet width can reach 2 times

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 V_c sim

0.1(T_e/M_i)^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 times 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].