Alcances de los objetivos

â >‘ lo^'*' j’’" e^s. ov« sec"' ^ S’

which is a little low in value at X = lO ^ K . For they take the usual expression,

where the constant, a, is determined from the coronal equilibrium condition,

L - t - t-3 * lo"-" f - ° • Thus the energy equation (1,79) becomes

’ (=-3 f L " n , which from (1,78) may be re-written

à T b 3»

P.(

X

Figure (8), The occurrence of the tearing mode instability

in the current sheet of the Kuperus & Tandberg- Hanssen (1967) model! The main effect is to reconnect magnetic field along the neutral

line (xrro) reducing the magnetic field strength in that region and forming magnetic loops as shown.

constant^determines T as a function of time. The result is that the temperature of the neutral sheet drops by a ^ factor of 10 and the density increases by the same factor

5 -

in about 10 seconds from an initial coronal temperature j of 10^ ° K . This condensation time gives good 3 agreement with the observed time for prominences to form |

(d*A%ambuja,1948). It is faster than Rajufs time

because the build-up of magnetic pressure is, in this case, ■ not considered, so that the condensation is not impeded by j magnetic forces. However, because the timescale for

the instability is greater than the resistive diffusion time, we would expect magnetic pressure to build up as the

condensation increased. However, the neutral sheet configuration is susceptible to resistive instabilities such as the tearing mode, which forms a series of magnetic loops along the neutral line (Figure (8)^ page 81) * At the same time, the magnetic pressure is reduced, allowing the condensation to continue. Also the magnetic field is

re-connected across the neutral sheet, so allowing support - for the condensing matter. This is essential, as

Hildner has shown in his - c> ^ O case, where he is unable to get reasonable condensation of the plasma when the denser matter is not supported. |

The question of support for the condensing matter in a # neutral sheet has been discussed by Kuperus & Raadu

(1974). They point out that the separate currents

(Figure(8), page 8 ij , which form in the later stages of the condensation process, due to the tearing mode instability will coalesce and form a structure shown in Figure(9)page #4

This may be regarded as the sum of a vertical field, $ supplying no vertical supporting force and a field f structure, shown in Figure (10), page 85, which will supply 9 the upward LOrentz force necessary for support. This field; structure can be thought of as being caused by two

I

' . I ' » ' ) j

where B^çis the azimuthal field at the boundary of the

condensed region which we suppose to have a radius R, Thus- to support the mass condensed into the filaments, we require,

(f- -= f TT i f ^ ,

t^V\

which, for

f

gives B ^ " G in good agreement math observations 4

(Rust, 1972).

In the calculation we take the initial background field to f be vertical. However, as suggested by Figure (8), page 81, j there may be components of the field curved downwards near the photosphere and these will tend to pull the plasma down 1 in opposition to the force F in (1,81). The plasma will j then fall if this downward force is large enough, but then n the plasma could be supported as in Kippenhahn & Schlutcr : model (Figure(13), page 94).

During the condensation process the plasma will bring in the magnetic field lines because they are frozen-ln.

Figure (9). A sketch of the expected coalescence

of the currents formed during the tearing mode instability in the current sheet of Figure (8), The magnetic field lines drawn here provide the necessary support, as shown by

h

Figure 10. The azimuthal component,0 0 , of the magnetic field shown in F i g u r e p a g e 84, which supplies the upward Lorentz

force necessary to support the condensed matter, inside the shaded region of radius R, at a height h above the photosphere.

1.5.: PROMINENCE FORMATION IN A CURRENT SHEET (Contd.)

However, these field lines are attached to the photosphere and any magnetohydrodynaraic perturbation that travels down the field line is slowed down since the Alfven speed is proportional to î/jy• Also the photosphere has a higher inertia than the coronal plasma. Thus the foot “-points of the field lines are hardly affected by the condensation process and the field lines will be bent so that Lorentz forces are set up opposing the process. Thus it may seem that this 'line-tying* effect could prevent the condensation from occuring but, as Raadu & Kuperus (1973) show, this is not the case. They consider the field

structure drawn in Figure (11), page 87, where it is ^ assumed that the frozen-in plasma pulls in the field

lines during the condensation with horizontal velocities. Now, since the field lines are tied to the photosphere

there will b® no condensation there, but there will be ' progressively more condensation the higher one goes as

the effect of line-tying is reduced. For this reason

they expected the condensation to form in a wedge (Figure (12),? page 87), so that the variables of the problem depend only on

9 ,

VJe expect the condensation to occur more slowly than the ? Alfven timescale and so the field and plasma will remain ; in horizontal force balance,

i

r

where -r ~ i ^ Eu

^ r Co:) B B ^

and, because the plasma is frozen into the field, ^/fo = ® a / 6 o

1.5.: PROMINËMCE FORMATION IM A CUHRKNT SHËET (Contd.)

/

Y

Y

Figure 12« A model for the line-tying effect of Fig

ii

Figure 11, Half of the magnetic field structure in a neutral current sheet with a neutral line at X= 0

The field lines are attached to the photosphere at y = 0 and are hardly affected as the condensation process occurs at larger y where the matter flows horizontally, in the . direction of the arrow, dragging the field lines with it*

page 87. According to Raadu & Kuperus (1973) they expect th|