Engineering topics

Lorencz, K.

Publications and source records attributed to Lorencz, K..

3 records

NASA NTRS1993

The telegraph equation in charged particle transport

We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

Gombosi, T. I.↗

NASA NTRS1989

Combined first- and second-order Fermi acceleration in cometary environments

Two-dimensional (one velocity space and one spatial dimension), time-dependent model calculations indicate that an interplay between velocity and spatial diffusion may be responsible for the acceleration of implanted heavy ions in the cometary preshock region. Velocity diffusion (second-order Fermi acceleration) accelerates the pickup ions to moderate energies, thus creating a seed population for the more efficient diffusive-compressive shock acceleration. Solar wind convection limits the time available for diffusive-compressive acceleration. Therefore, the resulting energy spectrum above the pickup energy is a combination of an exponential decrease at lower energies (up to about 100 keV) and a power law spectrum at higher energies. The calculated energy spectra constitute a surprisingly good fit to the published Vega and Giotto energy spectra above the pickup energy.

Gombosi, T. I.↗

NASA NTRS1989

Combined first and second order Fermi acceleration at comets

Two-dimensional, time-dependent model calculations indicate that an interplay between velocity and spatial diffusion may be responsible for the acceleration of implanted heavy ions in the cometary preshock region. Velocity diffusion (second order Fermi acceleration) accelerates the pickup ions to moderate energies thus creating a seed population for the more efficient diffusive-compressive shock acceleration. Solar wind convection limits the time available for diffusive-compressive acceleration, therefore the resulting energy spectrum above 100 keV is a power law with a spectral index of 5 - 6, a value which is in reasonably good agreement with observations.

Gombosi, T. I.↗