J. Plasma Fusion Res. SERIES, Vol.2 (1999) 509-5ll

A New Thermodynamic Plasma Acceleration Mechanism in
the Spontaneous Fast Magnetic Reconnection
SHIMIZU Tohru and UGAI Masayuki
Department of Computer Science, Ehime University,
Matsuyama, Ehime, 790-8577 Japan(Received: 9 December 1998 / Accepted: 4 August 1999)

Abstract
The Petschek reconnection model suggests that the plasmajets cannot steadily exceed the Alfven
velocity measured in the magnetic field region. In contrast, in the spontaneous fast reconnection model,
plasma jets can steadily exceed the Alfven velocity. Actually, in our 2D MHD studies, the final steadyvelocity of the plasma jets reaches 1.4 times of the Alfven velocity. We found that this acceleration
mechanism is established by a combination of slow shocks associated with the reconnection process anda superfast (supersonic) adiabatic expansion fan. This expansion fan is similar to the Parker's solar wind

acceleration with an exception of .the gravity force. Eventually, the superfast plasma jets terminate at afast shock in the magnetic loop, giving rise to a strong plasma heating.

Keywords:
magnetic reconnection, supersonic, fast shock, adiabatic expansion

1. Introduction
Petschek [1] predicted that slow shocks in a

expansion theory. Section 4 is devoted to conclusions.

magnetic reconnection process can efficiently generate
plasma jets. Especially, when the slow shock is a switch

2. 2D MHD Simulation
This simulation starts from an anti parallel

off shock, the plasma jet can reach the maximum
magnetic field region. Actually, slow shocks aremagnetic field configuration enclosed by the upper andlower open (free) boundaries, where has no magneticfield. A current driven anomalous resistivity [3,4] isreported in many numerical studies related with themagnetic reconnection, and frequently observed inreconnection spontaneously is built up by the resistivity

velocity, which is the Alfven velocity measured in theselfconsistently set. Then, the fast magnetic

recent observations of space plasma. Also, thespontaneous fast magnetic reconnection, which isenhanced naturally at the origin [4]. Figure l(a)demonstrates magnetic field lines in a quasi-steady state
reconnection process, which has a pair of slow shocks
extended from the origin and a growing plasmoid

proposed by Ugai [2], generates slow shocks and theAlfvenic plasma jets. In addition, our recent precise(magnetic loop). The plasmoid is swelling andMHD simulations reveals that the plasma jets cansteadily exceed the Alfven velocity. The strong
acceleration process cannot be explained by thePetschek model. In section 2, the MHD simulation

propagating toward the right side (open) boundary.
Figure l(b) demonstrates profiles of plasma pressure P,
velocity U, and the local fast wave velocity C, on the.raxis. From x = 13 to 17, a rapid increase of U, (a dashresults are demonstrated. In section 3, the acceleration
mechanism is explained by the thermodynamic adiabatic
C o rre s p onding aut ho r' s e - mail : s himizu @ c s. e hime - u. acjp509@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Shimizu T. et al., A New Thermodynamic Plasma Acceleration Mechanism in the Spontaneous Fast Magnetic Reconnection

Fig.l(a)

0.

20.

40.

Fig. 1 (a): Magnetic field lines at the time, when the reconnection region becomes a steady state. The left side boundary
is symmetry, and the others are free (open).
(b): Profilesof thepressureP.plasmavelocity U,,andthelocal fastwavevelocityCt.Therightvertical solidline(X1) indicates a location of a fast shock around the x axis.

local fast wave velocity C1 and continues to expand in
the radial direction, the superfast plasma is accelerated
by the thermodynamic effect. Magnetic effects are notneeded in this mechanism. The situation is drawn in Fig.
2 with a cylindrical coordinate (r, 0, z). We assume
uniformity in the (4 3) components and plasma steadilyflows in the r direction. Between roand rb the plasma
expands by the rate 11lrs. This process is written by theline) can be seen. This strong plasma acceleratron rs
executed beyond the Alfven velocity Ve (= 1.0)
measured in the upper and lower magnetic field region.
In addition, since U, is larger than C1 in 13 < x < 17, theplasma jet is superfast. And, the rapid decrease of thepressure P means that the plasma is expanding there.
Note that, in x < 13, the plasma velocity already reaches

the Alfven velocity by slow shocks, and rapidly
decreases in X > 17 by a fast shock in front of thefollowing adiabatic fluid dynamics equation.

plasmoid. Once this reconnection process starts, theprocess is almost steadily maintained [5,6], until most ofdvldr(v2lC?-D=v/r

the magnetic field lines are reconnected.

Here, C, is the local sound velocity. According to thisequation, when the velocity D exceeds C., dvlDr > 0 is

3. Supersonic Expansion Acceleration
In general, when plasma jets largely exceed theestablished, that is an acceleration for v > 0. Thisequation can be numerically resolved and applied to the) l(,Shimizu T. et al., A New Thermodynamic Plasma Acceleration Mechanism in the Spontaneous Fast Maenetic Reconnection'.x0

4. Conclusions

IWe found that the plasma jets generated in thereconnection process steadily exceeds the Alfven
velocity measured in the magnetic field region. It is well
explained, as follows. Firstly, the plasma jets must
become superfast by accelerations in slow shocks
associated with the reconnection process. Secondly, thesuperfast plasma jets experience an expansion of theplasma jet region initiated by swelling of a plasmoid (ora magnetic loop). It results in a supersonic expansion

Fig. 2 Schematic superfast expansion acceleration

mechanism.

acceleration.

References
V.M.
Vasyliunas, Rev. Geophys. Space Phys. 13,[1]

present quasi steady state simulation result. Note that we

may ignore the magnetic effect, since p >>l B, I in t3 <

303 (1975).

< 17. In this application, r'1 - 16 is the acceleration"t2) M. Ugai and T. Tsuda, J. Plasma Phys. 17, 337

distance from.r = 13 to 17. The expansion rate rrlrs isobtained from the simulation data. As a result, rs and 11
are obtained. And, v6 and u, are assigned to the plasma(1977).

[3] T. Hayashi and T. Sato, J. Geophys. Res. 83, Al,
2r7 /1978\.
M.
t4l Ugai and T. Shimizu, Phys. Plasmas 3, 853

velocity U, at x = 13 and 17, respectively. We foundthat this equation is satisfied with the present MHD

fl996).

simulation data in error of 37o or less.

t5l M. Ugai, J. Geophys. Res. 104, A4,6929 (1999).
t6l M. Ugai, Phys. Plasmas 6,1522 (1999).

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