Multi-fluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma

We present results from the first self-consistent multi-fluid simulations of chromospheric magnetic reconnection in a weakly ionized reacting plasma. We simulate two dimensional magnetic reconnection in a Harris current sheet with a numerical model which includes ion-neutral scattering collisions, ionization, recombination, optically thin radiative loss, collisional heating, and thermal conduction. In the resulting tearing mode reconnection the neutral and ion fluids become decoupled upstream from the reconnection site, creating an excess of ions in the reconnection region and therefore an ionization imbalance. Ion recombination in the reconnection region, combined with Alfv\'{e}nic outflows, quickly removes ions from the reconnection site, leading to a fast reconnection rate independent of Lundquist number. In addition to allowing fast reconnection, we find that these non-equilibria partial ionization effects lead to the onset of the nonlinear secondary tearing instability at lower values of the Lundquist number than has been found in fully ionized plasmas.These simulations provide evidence that magnetic reconnection in the chromosphere could be responsible for jet-like transient phenomena such as spicules and chromospheric jets.Comment: 8 Figures, 32 pages tota

Disentangling the Entangled Linkages of Relative Magnetic Helicity

Magnetic helicity, $H$, measures magnetic linkages in a volume. The early theoretical development of helicity focused on magnetically closed systems in $\mathcal{V}$ bounded by $\mathcal{S}$. For magnetically closed systems, $\mathcal{V}\in\mathbb{R}^3=\mathcal{V}+\mathcal{V}^*$, no magnetic flux threads the boundary, $\hat{\boldsymbol{n}}\cdot\boldsymbol{B}|_\mathcal{S}=0$. Berger and Field (1984) and Finn and Antonsen (1985) extended the definition of helicity to relative helicity, $\mathcal{H}$, for magnetically open systems where magnetic flux may thread the boundary. Berger (1999,2003) expressed this relative helicity as two gauge invariant terms that describe the self helicity of magnetic field that closes inside $\mathcal{V}$ and the mutual helicity between the magnetic field that threads the boundary $\mathcal{S}$ and the magnetic field that closes inside $\mathcal{V}$. The total magnetic field that permeates $\mathcal{V}$ entangles magnetic fields that are produced by current sources $\boldsymbol{J}$ in $\mathcal{V}$ with magnetic fields that are produced by current sources $\boldsymbol{J}^*$ in $\mathcal{V}^*$. Building on this fact, we extend Berger's expressions for relative magnetic helicity to eight gauge invariant quantities that simultaneously characterize both of these self and mutual helicities and attribute their origins to currents $\boldsymbol{J}$ in $\mathcal{V}$ and/or $\boldsymbol{J}^*$ in $\mathcal{V}^*$, thereby disentangling the domain of origin for these entangled linkages. We arrange these eight terms into novel expressions for internal and external helicity (self) and internal-external helicity (mutual) based on their domain of origin. The implications of these linkages for interpreting magnetic energy is discussed and new boundary observables are proposed for tracking the evolution of the field that threads the boundary.Comment: 27 pages, 2 figure

Momentum transfer models of interacting dark energy

We consider two models of interacting dark energy, both of which interact only through momentum exchange. One is a phenomenological one-parameter extension to $w$CDM, and the other is a coupled quintessence model described by a Lagrangian formalism. Using a variety of high and low redshift data sets, we perform a global fitting of cosmological parameters and compare to $\Lambda$CDM, uncoupled quintessence, and $w$CDM. We find that the models are competitive with $\Lambda$CDM, even obtaining a better fit when certain data sets are included.Comment: 22 pages, 10 figures, 3 table

The Role of the Principal in Improving Student Achievement in Low-Wealth Rural Elementary Schools

Increased levels of accountability, mandated implementation of common core learning standards, and shrinking state funds for public schools have created unique challenges for principals seeking to increase student achievement levels. Schools located in states receiving Race to the Top (RTT) funds must measure teacher and principal growth by adopting evaluation systems based on student achievement measures. These issues are more significant for rural school administrators, who must pair these demands with the confining nature of small-town life; the multiple and sometimes conflicting tasks; and the lack of opportunity for professional camaraderie and growth. Although a large body of literature has identified principal behaviors that can lead to improved student achievement, few studies have focused on contextual factors in New York State rural schools. Using Leithwood’s four core leadership practices as a framework, this study examined the perspectives of principals in low-wealth New York rural elementary schools. The study used a qualitative research design including a phenomenological strategy to learn about the lived experiences of 10 New York State rural elementary school principals. Data was collected using semi-structured interviews. Analysis of transcripts identified principal core and specific practices related to improving student achievement. Understanding the impact that principals’ practices have on student achievement can provide guidance to school leaders in low-wealth rural elementary schools intent on improving