Alcances y limitaciones del marco teórico

X

Figure 14» The model of a prominence with width, Cj ,

supported by the magnetic field, which Kippenhahn & Schluter (1957) calculated and which was tested for stability to

; PROMINENCE FORMATION IN A CURRENT SHEET (Contd.) Anzer considered a thin vertical sheet of width d,' as shown in Figure(14^ page 97, containing a current

~ 7 U ~ ^ ^ A ^ L

In the limit , with ~ y.o

equation (1.97) becomes

/ = -I (( - 3 % L + %

î\

from which we find the following sufficient conditions for stability (j W > o ):

4=0

.

If the mass is supported by thelorentz force, so that 5> ■= - Ju = Bh o

Thus

and (1.99) becomes

1.9.: PROMINENCE FORMATION IN A CURRENT SHEET (Contd.) : so that for stability the current density decreases | with height. While measurements indicate that (1.98)

is correct in quiescent prominences, direct observational

proof of (lo99) is not yet available. '

Observations by Rust (1966) and Harvey (1969) that | magnetic fields in prominences apparently have no | preferred orientation with respect to the prominence

axis lèd Nakagawa to consider the possibility that the | shear between the prominence magnetic field and the 4

/ %

field below might provide support. Nakagawa & Malville Z (1969) considered an upper half plane of plasma with a

uniform magnetic field supported against $ gravity by a magnetic field (, ^ ^ o') ! in the vacuum below.

They linearized the MHD equations, neglected radiation | and thermal conduction, and investigated the stability of

the interface 2: - o as a function of the angle | between the magnetic fields in the two regions.

The fastest growing unstable mode is obtained from the -Î resulting dispersion relation and predicts a break-up |

■ I

of the prominence plasma into regular spaced sections Ï with a certain wavelength. Nakagawa & Malville suggest |

that the regular arch structure of many quiescent prominences is produced ]3y such an instability.

The angle of shear between the lower and upper field affects J the wavelength at which the instability occurs, and by I comparing this wavelength with the observed spacing, they * predict this angle to be between 60^ and 90°. 3

1.5.: PROMINENCE FORMATION IN A CURRENT 5HBET (Contd.) THE AIMS OF THE THESIS

We consider two instabilities which can occur in the solar atmosphere, the thermal instability and the

tearing mode instability. Both of these instabilities are applied to neutral current sheets in an attempt to understand the processes involved in the formation of prominences within such structures. Also we

examine the thermal instability in a magnetic arch

I

In chapter 2,we extend the work of Kuperus& Tandberg-Hanssen (1967) on the formation of quiescent prominences in a

neutral current sheet. We first set up the equilibrium for current sheet plasma under a balance between radiative

loss, constant mechanical heating and thermal conduction, and then investigate its stability. The object is to verify the order of magnitude prediction of section 1.2 that instability occurs when the current sheet length

exceeds a certain value and to obtain more accurate values for both this length and the time it takes the plasma to cool to prominence temperatures.

In their paper on the formation of prominences , Kuperus& Tandberg-Hanssen (1967) suggested that the tearing mode instability occurs along with the thermal Instability, and so we have examined, in chapter 3, this resistive instability in the neutral current sheet.

1.5.: PROMINENCE FORMATION IN A CURRENT SHEET I WliM» mi »##* ■.ni. nlfi' f—W' 1aWi'»*W'>— wwtxtog»* , i iiM<«ii iiHw*.»**i ■■■—>W W&i.M'i## ■■ (Contd.)

As described in section 1.3, Cross & Van Hoven (1971) have developed a numerical technique to calculate the growth rate of the linear stability problem for a sheared field. They search for the unique value of this growth rate which brings about convergence of the Fourier

series that describe the perturbations of a spatially periodic equilibrium configuration, We use this method

to calculate the growth rate of the tearing-mode instability * in a neutral current sheet. In addition,we investigate v

the influence of a component of the equilibrium magnetic i

k

4

flares. t

We expect some types of prominence to form in neutral î current sheets, but others may form in closed magnetic ? field configurations. In chapter 4 we consider a force-free? magnetic structure and examine the effects on the thermal ? instability of moving the feet of the arches and so ? shearing the field. We expect that, as the shearing | Increases, so the flux tubes become longer, until thermal J conduction is no longer able to prevent the occurrence i of a thermal instability. The object is then to verify

this intuitive idea and find how much shearing is necessary ; to initiate a condensation. Presumably at the onset of the ^ instability plasma is sucked up along field lines until ? enough material is present to allow a new equilibrium in |

CHAPTER 2 .