We examine the effects of temperature dependence of the electrical and thermal conductivities on Joule heating of a one-dimensional conductor by solving the coupled non-linear steady state electrical and thermal conduction equations. The spatial temperature distribution and the maximum temperature and its location within the conductor are evaluated for four cases: (i) constant electrical conductivity and linear temperature dependence of thermal conductivity, (ii) linear temperature dependence of both electrical and thermal conductivities, (iii) the Wiedemann-Franz relation for metals, and (iv) polynomial fits to measured data for carbon nanotube fibers and for copper. For (i) and (ii), it is found that there are conditions under which no steady state solution exists, which may indicate the possibility of thermal runaway. For (i), analytical solutions are constructed, from which explicit expressions for the parameter bounds for the existence of steady state solutions are obtained. The shifting of these bounds due to the introduction of linear temperature dependence of electrical conductivity (case (ii)) is studied numerically. These results may provide guidance in the design of circuits and devices in which the effects of coupled thermal and electrical conduction are important.

No abstract

An electron beam in the slow wave structure of a traveling wave tube may be subjected to absolute instability at the lower and upper band edges, where the group velocity is zero. From a careful re-examination of the immediate vicinity of these band edges, we use the Briggs-Bers criterion to show that, contrary to previous findings, an absolute instability may arise at the lower band edge if the beam current is sufficiently high, even if the beam mode intersects with the circuit mode with a positive group velocity. However, the upper band edge was found to be more susceptible to absolute instability than the lower band edge. The threshold condition for the onset of absolute instabilities is derived analytically at both band edges. The Green's function shows possible transient temporal growth with an exponentiation rate proportional to t1/3, whether or not the band edge is subject to an absolute instability.

Solenoid Siberian snakes have successfully maintained polarization in particle rings below 1 GeV, but never in multi-GeV rings because the Lorentz contraction of a solenoid's B • dl would require impractically long high-field solenoids. High energy rings, such as Brookhaven's 255 GeV Relativistic Heavy Ion Collider (RHIC), use only odd multiples of pairs of transverse B-field Siberian snakes directly opposite each other. When it became impractical to use a pair of Siberian Snakes in Fermilab's 120 GeV Main Injector (see Fig. 2), we searched for a new type of single Siberian snake, which should overcome all depolarizing resonances in the 8.9-120 GeV range. We found that one snake made of one 4-twist helix and 2 short dipoles could maintain the polarization. This snake design might also be used at other rings, such as Japan's 30 GeV J-PARC, the 12-24 GeV NICA proton-deuteron collider at JINR-Dubna, and perhaps RHIC's injector, the 25 GeV AGS.

Electrical contact is an important issue to high power microwave sources, pulsed power systems, field emitters, thin film devices and integrated circuits, interconnects, etc. Contact resistance and the enhanced ohmic heating that results have been treated mostly under steady state (DC) condition. In this paper, we consider the AC contact resistance for a simple geometry, namely, that of two semi-infinite slab conductors of different thicknesses joined at z = 0, with current flowing in the z-direction. The conductivity of the two planar slabs may assume different values. We propose a procedure to accurately calculate the normalized contact resistance under the assumption σ≫ωϵ, where ω is the frequency, σ is the electrical conductivity, and ϵ is the dielectric constant of the material in either channel. We found that in the low frequency limit, the normalized AC contact resistance reduces to the DC case, which was solved exactly by Zhang and Lau. At very high frequency, we found that the normalized contact resistance is proportional to ω, in which case the resistive skin depth becomes the effective channel width, and the physical origin of the contact resistance is identified. The transition between the high and low frequency limits was explored, where, in some cases, the normalized contact resistance may become negative, meaning that the total resistance is less than the total bulk resistance expected from the two current channels. In other cases, the numerical data suggest that the normalized contact resistance is proportional to ω in the transition region. Other issues are addressed.