Coupled Boltzmann calculation of mixed axion/neutralino cold dark matter production in the early universe

We calculate the relic abundance of mixed axion/neutralino cold dark matter which arises in R-parity conserving supersymmetric (SUSY) models wherein the strong CP problem is solved by the Peccei-Quinn (PQ) mechanism with a concommitant axion/saxion/axino supermultiplet. By numerically solving the coupled Boltzmann equations, we include the combined effects of 1. thermal axino production with cascade decays to a neutralino LSP, 2. thermal saxion production and production via coherent oscillations along with cascade decays and entropy injection, 3. thermal neutralino production and re-annihilation after both axino and saxion decays, 4. gravitino production and decay and 5. axion production both thermally and via oscillations. For SUSY models with too high a standard neutralino thermal abundance, we find the combined effect of SUSY PQ particles is not enough to lower the neutralino abundance down to its measured value, while at the same time respecting bounds on late-decaying neutral particles from BBN. However, models with a standard neutralino underabundance can now be allowed with either neutralino or axion domination of dark matter, and furthermore, these models can allow the PQ breaking scale f(a) to be pushed up into the 10(14) - 10(15) GeV range, which is where it is typically expected to be in string theory models.

Synthesis Methodology Applied to a Tunable Patch Filter With Independent Frequency and Bandwidth Control

A new methodology for the synthesis of tunable patch filters is presented. The methodology helps the designer to perform a theoretical analysis of the filter through a coupling matrix that includes the effect of the tuning elements used to tune the filter. This general methodology accounts for any tuning parameter desired and was applied to the design of a tunable dual-mode patch filter with independent control of center frequency and bandwidth (BW). The bandpass filter uses a single triangular resonator with two etched slots that split the fundamental degenerate modes and form the filter passband. Varactor diodes assembled across the slots are used to vary the frequency of each degenerate fundamental mode independently, which is feasible due to the nature of the coupling scheme of the filter. The varactor diode model used in simulations, their assembling, the dc bias configuration, and measured results are presented. The theory results are compared to the simulations and to measurements showing a very good agreement and validating the proposed methodology. The fabricated filter presents an elliptic response with 20% of center frequency tuning range around 3.2 GHz and a fractional BW variation from 4% to 12% with low insertion loss and high power handling with a 1-dB compression point higher than +14.5 dB.