Problems and Solutions Klein, Benjamin G.; Bivens, Irl C.; King, L. R.
The College mathematics journal,
20/3/1/, Letnik:
34, Številka:
2
Journal Article
Recenzirano
Klein presents several mathematical problems and solutions for college students and teachers.
Problems and Solutions Klein, Benjamin G.; Bivens, Irl C.; King, L. R.
The College mathematics journal,
20/1/1/, Letnik:
34, Številka:
1
Journal Article
Problems and Solutions Klein, Benjamin G.; Bivens, Irl C.; King, L. R. ...
The College mathematics journal,
11/1/2002, 20021101, 2002-11-00, Letnik:
33, Številka:
5
Journal Article
We study the damping of collisionless Alfvénic turbulence by two mechanisms: stochastic heating (whose efficiency depends on the local turbulence amplitude \(\delta z_\lambda\)) and linear Landau ...damping (whose efficiency is independent of \(\delta z_\lambda\)), describing in detail how they affect and are affected by intermittency. The overall efficiency of linear Landau damping is not affected by intermittency in critically balanced turbulence, while stochastic heating is much more efficient in the presence of intermittent turbulence. Moreover, stochastic heating leads to a drop in the scale-dependent kurtosis over a narrow range of scales around the ion gyroscale.
Problems and Solutions Klein, Benjamin G.; Bivens, Irl C.; King, L. R. ...
The College mathematics journal,
20/9/1/, Letnik:
33, Številka:
4
Journal Article
Problems and Solutions Klein, Benjamin G.; Bivens, Irl C.; King, L. R. ...
The College mathematics journal,
20/5/1/, Letnik:
33, Številka:
3
Journal Article
Problems and Solutions Klein, Benjamin G.; Bivens, Irl C.; King, L. R. ...
The College mathematics journal,
20/3/1/, Letnik:
33, Številka:
2
Journal Article
Problems and Solutions Klein, Benjamin G.; Bivens, Irl C.; King, L. R. ...
The College mathematics journal,
20/1/1/, Letnik:
33, Številka:
1
Journal Article
Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in ...\(\beta_{\parallel \mathrm p}\equiv 8\pi n_{\mathrm p}k_{\mathrm B}T_{\parallel \mathrm p}/B^2\) and in \(R_{\mathrm p}\equiv T_{\perp \mathrm p}/T_{\parallel \mathrm p}\), where \(T_{\perp \mathrm p}\) and \(T_{\parallel \mathrm p}\) are the perpendicular and parallel temperatures of the protons, \(B\) is the magnetic field strength, and \(n_{\mathrm p}\) is the proton density. If the amplitude of the compressive fluctuations is large enough, \(R_{\mathrm p}\) crosses one or more instability thresholds for anisotropy-driven microinstabilities. The enhanced field fluctuations from these microinstabilities scatter the protons so as to reduce the anisotropy of the pressure tensor. We propose that this scattering drives the average value of \(R_{\mathrm p}\) away from the marginal stability boundary until the fluctuating value of \(R_{\mathrm p}\) stops crossing the boundary. We model this "fluctuating-anisotropy effect" using linear Vlasov--Maxwell theory to describe the large-scale compressive fluctuations. We argue that this effect can explain why, in the nearly collisionless solar wind, the average value of \(R_{\mathrm p}\) is close to unity.
The Arbitrary Linear Plasma Solver (ALPS) is a parallelised numerical code that solves the dispersion relation in a hot (even relativistic) magnetised plasma with an arbitrary number of particle ...species with arbitrary gyrotropic equilibrium distribution functions for any direction of wave propagation with respect to the background field. ALPS reads the background momentum distributions as tables of values on a \((p_{\perp},p_{\parallel})\) grid, where \(p_{\perp}\) and \(p_{\parallel }\) are the momentum coordinates in the directions perpendicular and parallel to the background magnetic field, respectively. We present the mathematical and numerical approach used by ALPS and introduce our algorithms for the handling of poles and the analytic continuation for the Landau contour integral. We then show test calculations of dispersion relations for a selection of stable and unstable configurations in Maxwellian, bi-Maxwellian, \(\kappa\)-distributed, and J\"uttner-distributed plasmas. These tests demonstrate that ALPS derives reliable plasma dispersion relations. ALPS will make it possible to determine the properties of waves and instabilities in the non-equilibrium plasmas that are frequently found in space, laboratory experiments, and numerical simulations.
