Vlasov simulation in multiple spatial dimensions

A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods using adaptive mesh methods [J. W. Banks et al., Physics of Plasmas 18, no. 5 (2011): 052102; B. I. Cohen et al., November 10, 2010, http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142] have recently shown promising results, in this paper we present an alternative, the Vlasov Multi Dimensional (VMD) model, that is specifically designed to take advantage of solution properties in regimes when plasma waves are confined to a narrow cone, as may be the case for stimulated Raman scatter in large optic f# laser beams. Perpendicular grid spacing large compared to a Debye length is then possible without instability, enabling an order 10 decrease in required computational resources compared to standard particle in cell (PIC) methods in 2D, with another reduction of that order in 3D. Further advantage compared to PIC methods accrues in regimes where particle noise is an issue. VMD and PIC results in a 2D model of localized Langmuir waves are in qualitative agreement

Spacecraft Observations And Analytic Theory Of Crescent-Shaped Electron Distributions In Asymmetric Magnetic Reconnection

Supported by a kinetic simulation, we derive an exclusion energy parameter $\cal{E}_X$ providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell Demon, only high energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low density separatrix. Egedal, J; Le, A; Daughton, W; Wetherton, B; Cassak, P A; Chen, L -J; Lavraud, B; Trobert, R B; Dorelli, J; Gershman, D J; Avanov, L

A correspondence of modular forms and applications to values of L-series

An interpretation of the Rogers–Zudilin approach to the Boyd conjectures is established. This is based on a correspondence of modular forms which is of independent interest. We use the reinterpretation for two applications to values of L-series and values of their derivatives

The Force Balance of Electrons During Kinetic Anti-parallel Magnetic Reconnection

Fully kinetic simulations are applied to the study of 2D anti-parallel reconnection, elucidating the dynamics by which the electron fluid maintains force balance within both the electron diffusion region (EDR) and the ion diffusion region (IDR). Inside the IDR, magnetic field-aligned electron pressure anisotropy ($p_{e\parallel}\gg p_{e\perp})$ develops upstream of the EDR. Compared to previous investigations, the use of modern computer facilities allows for simulations at the natural proton to electron mass ratio $m_i/m_e=1836$. In this high-$m_i/m_e$-limit the electron dynamics changes qualitatively, as the electron inflow to the EDR is enhanced and mainly driven by the anisotropic pressure. Using a coordinate system with the $x$-direction aligned with the reconnecting magnetic field and the $y$-direction aligned with the central current layer, it is well-known that for the much studied 2D laminar anti-parallel and symmetric scenario the reconnection electric field at the $X$-line must be balanced by the $\partial p_{exy}/ \partial x$ and $\partial p_{eyz}/ \partial z$ off-diagonal electron pressure stress components. We find that the electron anisotropy upstream of the EDR imposes large values of $\partial p_{exy}/ \partial x$ within the EDR, and along the direction of the reconnection $X$-line this stress cancels with the stress of a previously determined theoretical form for $\partial p_{eyz}/ \partial z$. The electron frozen-in law is instead broken by pressure tensor gradients related to the direct heating of the electrons by the reconnection electric field. The reconnection rate is free to adjust to the value imposed externally by the plasma dynamics at larger scales.Comment: Submitted to Physics of Plasmas, 11 October 202

Spacecraft observations and analytic theory of crescent-shaped electron distributions in asymmetric magnetic reconnection

Supported by a kinetic simulation, we derive an exclusion energy parameter $\cal{E}_X$ providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell Demon, only high energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low density separatrix.Comment: 6 pages, 3 figure

Standard Model with Cosmologically Broken Quantum Scale Invariance

We argue that scale invariance is not anomalous in quantum field theory, provided it is broken cosmologically. We consider a locally scale invariant extension of the Standard Model of particle physics and argue that it fits both the particle and cosmological observations. The model is scale invariant both classically and quantum mechanically. The scale invariance is broken cosmologically producing all the dimensionful parameters. The cosmological constant or dark energy is a prediction of the theory and can be calculated systematically order by order in perturbation theory. It is expected to be finite at all orders. The model does not suffer from the hierarchy problem due to absence of scalar particles, including the Higgs, from the physical spectrum.Comment: 13 pages, no figures significant revisions, no change in results or conclusion