Decrease In Magnetic Energy Research Articles

Non-linear tearing structures in equilibrium current sheet

A family of exact analytic solutions of the time-independent Vlasov-Maxwell equations is presented. The solutions describe two-dimensional equilibrium current sheet with magnetic field structures resembling that produced by the tearing instability. In particular, the solutions presented here do not restrict the field in the magnetic island to small magnitude. It is shown that as the scale length of the magnetic island increases, the thickness of the current sheet increases while the average current and the average magnetic energy decrease. The tearing structures described by the solutions may exist in the magnetotail current sheet, the magnetopause current layer and the field-aligned auroral sheet current.

Magnetic Fields Associated with Solar Flares

An investigation of strong magnetic fields associated with flares was made with the 61 cm vacuum telescope and spectroheliograph at the San Fernando Observatory. Magnetograms of the longitudinal component of the field were made daily during the period of September 25–29, 1969. Observations were also made during this same period of the enhanced radio emission at 3.3 mm wavelength. On September 27 an importance class 3 or 4 flare occurred in the region studied. Total magnetic flux was determined for September 25, 26, 28 and 29 for the region which included the flare. In an area of about 190 arc s by 250 arc s the flux values for these dates were respectively 2.4, 2.5, 2.2 and 2.8 × 1022 Mx. Following the flare of September 27 the flux decreased significantly. Magnetic energy change in the region of the flare can be determined if an appropriate height is known. Following Howard and Severny (Astrophys. J. 137, 1242, 1963) a height of 109 cm was used. This yields a value of 5 × 1031 ergs for the decrease of magnetic energy in the longitudinal component of the field.

The magneto-caloric effect and other magnetic phenomena in iron

According to the Weiss theory a ferromagnetic body is composed of a number of “domains” each magnetized even in the absence of an external field to an intensity dependent on the temperature. At absolute zero this spontaneous magnetization (σ 0 ) is equal to the saturation intensity (σ ∞ ) whilst at any other temperature (T) the value of σ 0 /σ ∞ is dependent only on the ratio T/θ where θ is the Curie temperature. This is known as the law of corresponding states. At low temperatures the apparent increase in magnetization, accompanying the application of the external field H, is due merely to alignment of the directions of spontaneous magnetization of the various domains. As the temperature rises, however, σ 0 becomes much less than σ ∞ , and the effect of an external field is twofold—(1) an apparent increase of magnetization due to alignment, and (2) a true increase in the degree of magnetization of each domain. Magnetization of a specimen is accompanied by a decrease of magnetic energy and if the experiment is carried out adiabatically a rise in temperature results. This phenomenon is known as the magneto-caloric effect. Weiss and Forrer have shown that this temperature increase is given by the equation where ch is the specific heat at constant external field H, ρ the density, J the mechanical equivalent of heat, and σ the intensity per unit volume. This equation was arrived at thermodynamically without reference to the hypothesis of the intramolecular field. The intramolecular field theory has been attacked by Honda who develops an equation identical with (1) but in which he states that H is the total field (external + intramolecular). If this were so, equation (1) would be in complete quantitative disagreement with the experiments of Weiss and Forrer on nickel. Honda’s argument depends on the use of the equation d W = pdv + v H d σ, where v H d σ is the work done on the body by the field. Honda assumes that H is the total field, but since work can hardly be done on a body by its own internal field, it appears to the writer that the H in Honda’s formula is the external field, giving then an equation identical with that of Weiss and Forrer. Equation (1) is further justified by being in excellent agreement with the experimental results of Weiss and Forrer, and with those of the writer given below. Weiss and Forrer have further shown that the rise of temperature is related to the change in the magnetization by the equation d T = H + H'/J ρcσ d σ, (2) where H' is the internal field, c σ the specific heat at constant magnetization, and d σ the change in volume-intensity accompanying the application of an external field H. This involves no assumption as to the nature of H', but follows from the statement that the change of energy of the substance per unit volume can be expressed as d U = J ρcσ d T — H' d σ, where this equation may be considered as the definition of H'. In addition the work ( d W) done on the body by the external field is = H d σ. Since in an adiabatic process the heat d Q communicated to the specimen is zero we have d Q — d U — d W = 0 thus leading immediately to equation (2).