Download 10 - Enea Frascati

10. EJECTION OF PLASMA TOROIDS
FROM TWISTED FLUX TUBES IN
ASTROPHYSICS
The purpose of this section is to show that in astrophysical gravity-confined systems, unstable twisted
magnetic flux tubes are able to produce, through magnetic reconnection, helically twisted toroidal
plasmoids. The fate of these toroids is to expand and to be expelled from the generating gravity-confined
parent systems. In this process the system is able to eject helicity and to shed a relevant magnetic flux, with
a negligible loss of mass. These phenomena bear a strong resemblance to the formation of the plasma in
PROTO-SPHERA, but occur at magnetic Lundquist numbers which are much larger (S~10 8-1013) than the
magnetic Lundquist number of PROTO-SPHERA (S~105). Also the range of  at which these phenomena
occur span a much larger range of values:  «in the solar corona,  =<1in collapsing magnetized clumps
inside giant molecular clouds and  »1 in protostar magnetized accretion disks. Nevertheless an accurate
study of a laboratory plasma like the one of PROTO-SPHERA could provide useful information on some
of these phenomena.
Another common feature to all these astrophysical systems is the presence of torsional Alfvén waves
(TAW). These waves act in many astrophysical systems (either being injected from the outside or being
produced inside) as current drivers. As obviously there are no externally applied electromotive forces in the
cosmos, the drivers are convective forces pushing the fluid, whose motion
u deforms B , the deformed B
creates  B and induces j . This property of TAW should encourage the use of similar mechanisms also
in laboratory plasmas and particularly in PROTO-SPHERA.
10.1 SOLAR FLARES
After the launch of the solar observatory "Yohkoh" in 1991 there is increasing evidence that X-ray toroidal
plasmoid ejection occur in both long duration events (LDE, lasting more than 1 h) as well as in short
duration impulsive solar flares. These plasmoids are helically twisted flux ropes in 3D space.
Flares seem to be triggered by the emergence of twisted flux tubes from the photosphere of the Sun R=R 
into the solar corona (see Fig. 114).
Fig. 114. Yohkoh SXT X-ray image of the solar corona. S-shaped sigmoidal structure
are contained within magnetic flux systems [94].
The twisted flux tubes are of subphotospheric origin and are produced by the solar dynamo acting at coreconvection zone interface (R~0.7•R) [95].
The magnetic helicity produced by the dynamo [76] has opposite signs in the northern and southern solar
hemispheres (and does not change sign from one 11 year period to the next). The twisted flux tubes rise
through the convection zone plasma ( »), where their twist is what opposes their fragmentation [96].
Fig. 115. In the solar convection zone the equator rotates faster than the pole. The
differential rotation injects helicity into the solar corona [76].
The electric current systems thread through the photosphere (Fig. 116) and pass into the corona ( «),
where their twist is what destabilizes kink modes [97]. The coronal field has not an infinite capacity for the
helicity, so the injected helicity must be ejected into the interplanetary space. The corona plays the role of a
helicity channel, connecting the sun and the interplanetary space.
Fig. 116. Simulation of emergence of twisted flux tube from the solar photosphere [98].
Intermittent plasmoid ejections (see Fig. 117), associated with magnetic reconnections of twisted flux
tubes, produce recurrent behavior of solar LDE flares [99] (magnetic Lundquist number S= R/A ~108 in
the solar corona).
Fig. 117. X-ray toroidal plasmoid (arrows) ejection during an LDE solar flare, observed
from YOHKOH Soft-X telescope [100].
The plasmoid induced reconnection model proposed by K. Shibata [101] postulates that an unstable
emerging twisted flux loop produces (through helicity ejection by magnetic reconnection) an X-ray toroidal
plasmoid, which triggers on its turn an increased reconnection rate: a downward jet collides with the top of
the SXR loop, producing an MHD fast shock observed in the HXR images. Thereafter the plasma toroid is
ejected into the interplanetary space.
Fig. 118. Scheme of the 'plasmoid-induced-reconnection' solar flare model ( K. Shibata).
In small scale flares [102] the plasmoid collides and reconnects with the ambient field, generating a jet of
torsional Alfvén waves (TAW), leading to X-ray jets and spinning H surges (Fig. 119).
FIG. 119. Comparison between a large scale flare, where a cusp structure remains after the
plasma loop is ejected, with a small scale flare, where the loop reconnects with the ambient
field emitting torsional Alfvén waves.
10.2 PROTOSTELLAR FLARES
There is also growing evidence that the ejection of plasma toroids from twisted flux tubes could play a role
in the star formation process, by allowing a fast shedding of the magnetic flux from the star condensation
region. Giant molecular clouds (GMCs) contain weakly ionized (10 -4-10-6) mass condensations of scale
length=<0.1pc, called clumps; they are sites of massive star formation.
The gravitational collapse of clumps is opposed by strong magnetic fields ( <1) and by Alfvén waves
turbulent energy (Alfvén Mach number mA~1). Magnetized clumps can condense via ambipolar diffusion
of the magnetic field, which decouples the ionized component of the cloud from the self gravitating
neutrals; but the ambipolar diffusive timescale for a clump is >=2•10 7 yr., longer than the lifetime of a
GMC. However the field often appears to be in filaments, with Lundquist number S~10 11: magnetic helicity
injected by torsional Alfvén waves (TAW) can drive longitudinal current instabilities [103].
Fig. 120. Evidence of twisted magnetic field jet on 0.1 pc scale length, from Hubble .
The folding of the filaments by MHD instabilities and their break-off in fast reconnection processes
(20•A), with timescales ~1-3•106 yr., can be a faster trigger of massive star formation.
Fig. 121.
Schematic picture of the interaction between a magnetic field and a
Keplerian disk [104]. Obscuring torus and high velocity bipolar jet from a
protostar (HST).
In collapsing protostars X-ray flares are observed, along with an obscuring torus ( »1, scale length=<10-3
pc) and high velocity neutral winds. High velocity collimated ionized bipolar jets ( ~1) emanates from the
central region, see Fig. 121.
One of the current explanations of what is observed around protostars is the model of the magnetically
driven jet bipolar jet. This model assumes that when an accretion disc is threaded by large scale poloidal
magnetic field, centrifugal force and magnetic pressure drive outflows, as shown in Fig. 122.
Fig. 122. Schematic picture of a magnetically driven bipolar jet.
Numerical simulations [104] of a differentially rotating cylinder with vertical magnetic field, shows the
appearance of non axisymmetric instabilities (Fig. 123). The generation and relaxation of magnetic twist is
driven by the rotation of the disk, the outflows are collimated along the rotation axis, due to the magnetic
pinch effect and the twist relaxes by emitting torsional Alfvén waves (TAW). Magnetic reconnection takes
place intermittently (S~1011). A rotating spheromak ( =<1) carries away the helicity.
Fig. 123. Structure of m=1 instability of a magnetized differentially rotating cylinder,
showing the effect of the magnetic reconnection.