High Velocity Forming Research Articles

Heat flux in a non-Maxwellian plasma.

A hybrid numerical scheme is applied to solve the Landau equation for the electron distribution function over all velocity space. At low velocities the distribution is approximated by using the Spitzer-H\"arm method [Phys. Rev. 89, 977 (1953)], while at high velocities it is described by the high-velocity form of the Landau equation. The two parts of the distribution function are then matched at a suitably chosen value of electron speed. The distribution function is determined for a thermal structure typical of an active region of the solar atmosphere or flaring solar coronal loop. The heat flux is then calculated from the distribution function and is compared with the classical Fourier law of Spitzer and H\"arm and with the models of Campbell [Phys. Rev. A 30, 365 (1984)] and Luciani et al. [Phys. Fluids 28, 835 (1985); Phys. Rev. Lett. 51, 1664 (1983)].

Heat Flux in a Non-Maxwellian Solar Coronal Plasma

AbstractWe determine the electron distribution function within a hot coronal loop using a hybrid numerical scheme which couples the Spitzer-Härm method at low velocities with the solution to the high velocity form of the Landau-Fokker-Planck equation. From this we calculate the heat flux throughout the loop and compare it with the classical fourier law of Spitzer and Härm(1953).

Non-Maxwellian distribution functions in flaring coronal loops. Comparison of Landau-Fokker-Planck and BGK solutions

The high-velocity tail of the electron distribution has been calculated by solving the high-velocity form of the Landau equation for a thermal structure representative of a flaring coronal loop. These calculations show an enhancement of the tail population above Maxwellian for electrons moving down the temperature gradient. In the transition region they also show enhancement at higher velocities for electrons with all pitch angles, except those streaming up the gradient within ≤ 45° of the vertical direction. These results have been used to test the reliability of the BGK approximation. The comparison shows that the BGK technique can estimate contributions to the heat flux from the high-energy tail, to within an order of magnitude.

Adiabatic Plastic Deformation

Adiabatic plastic may play a role in such widely diverse areas as ballistic impact, explosive fragmentation, cryogenic behavior of materials, high velocity shaping and forming, machining, grinding 0), surface frictional effects, erosion (2), and seismic faulting. All of the shearing phenomena are based on two facts: Approximately 90% of the work of plastic is converted to heat, and the flow stress of most metals is quite sensitive to temperature, decreasin g as the temperature increases. That localized temperature increases and strain concentration play a major part in high speed of metals was recognized by Zener & Hollomon (3) in 1944. The phenomenon is most clearly identified in most steels, in which heating above the transforma­ tion temperature causes the transformation of ferrite to austenite. On rapid cooling the austenite retransforms to a product that etches with difficulty and appears as a white band against the dark background of the remainder of the etched steel. These materials thus retain evidence for adiabaticity of the deformation, while in most other metals the evidence is significantly less definite. The use of the term deformation is obviously an over­ simplification in the sense that some heat always transfers out of any deforming region. Moreover, to categorize one situation as adiabatic and another not is in many instances equivalent to labeling shades of gray as black or white. It