Takashi Minoshima

The Focusing Optics X-ray Solar Imager (FOXSI)

The Focusing Optics x-ray Solar Imager (FOXSI) is a sounding rocket payload funded under the NASA Low Cost Access to Space program to test hard x-ray focusing optics and position-sensitive solid state detectors for solar observations. Todays leading solar hard x-ray instrument, the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) provides excellent spatial (2 arcseconds) and spectral (1 keV) resolution. Yet, due to its use of indirect imaging, the derived images have a low dynamic range (<30) and sensitivity. These limitations make it difficult to study faint x-ray sources in the solar corona which are crucial for understanding the solar flare acceleration process. Grazing-incidence x-ray focusing optics combined with position-sensitive solid state detectors can overcome both of these limitations enabling the next breakthrough in understanding particle acceleration in solar flares. The FOXSI project is led by the Space Science Laboratory at the University of California. The NASA Marshall Space Flight Center, with experience from the HERO balloon project, is responsible for the grazing-incidence optics, while the Astro H team (JAXA/ISAS) will provide double-sided silicon strip detectors. FOXSI will be a pathfinder for the next generation of solar hard x-ray spectroscopic imagers. Such observatories will be able to image the non-thermal electrons within the solar flare acceleration region, trace their paths through the corona, and provide essential quantitative measurements such as energy spectra, density, and energy content in accelerated electrons.

DRIFT-KINETIC MODELING OF PARTICLE ACCELERATION AND TRANSPORT IN SOLAR FLARES

Based on the drift-kinetic theory, we develop a model for particle acceleration and transport in solar flares. The model describes the evolution of the particle distribution function by means of a numerical simulation of the drift-kinetic Vlasov equation, which allows us to directly compare simulation results with observations within an actual parameter range of the solar corona. Using this model, we investigate the time evolution of the electron distribution in a flaring region. The simulation identifies two dominant mechanisms of electron acceleration. One is the betatron acceleration at the top of closed loops, which enhances the electron velocity perpendicular to the magnetic field line. The other is the inertia drift acceleration in open magnetic field lines, which produces antisunward electrons. The resulting velocity space distribution significantly deviates from an isotropic distribution. The former acceleration can be a generation mechanism of electrons that radiate loop-top nonthermal emissions, and the latter of escaping electrons from the Sun that should be observed by in situ measurements in interplanetary space and resulting radio bursts through plasma instabilities.

Dependence of the Saturation Level of Magnetorotational Instability on Gas Pressure and Magnetic Prandtl Number

A large set of numerical simulations of magnetohydrodynamic (MHD) turbulence induced by the magnetorotational instability (MRI) is presented. Revisiting the previous survey conducted by Sano et al. (2004), we investigate the gas pressure dependence of the saturation level. In ideal MHD simulations, the gas pressure dependence is found to be very sensitive to the choice of a numerical scheme. This is because the numerical magnetic Prandtl number varies according to the scheme as well as the pressure, which considerably affects the results. The saturation level is more sensitive to the numerical magnetic Prandtl number than the pressure. In MHD simulations with explicit viscosity and resistivity, the saturation level increases with the physical magnetic Prandtl number, and it is almost independent of the gas pressure when the magnetic Prandtl number is constant. This is indicative of the incompressible turbulence saturated by the secondary tearing instability.

Multi-moment advection scheme for Vlasov simulations

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one-and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.

CORONAL ELECTRON DISTRIBUTION IN SOLAR FLARES: DRIFT-KINETIC MODEL

Using a model of particle acceleration and transport in solar flares, we investigate the height distribution of coronal electrons by focusing on the energy-dependent pitch-angle scattering. When pitch-angle scattering is not included, the peak heights of loop-top electrons are constant, regardless of their energy, owing to the continuous acceleration and compression of the electrons via shrinkage of magnetic loops. On the other hand, under pitch-angle scattering, the electron heights are energy-dependent: intermediate-energy electrons are at a higher altitude, whereas lower and higher energy electrons are at lower altitudes. This implies that the intermediate-energy electrons are inhibited from following the shrinking field lines to lower altitudes because pitch-angle scattering causes efficient precipitation of these electrons into the footpoint and their subsequent loss from the loop. This result is qualitatively consistent with the position of the above-the-loop-top hard X-ray (HXR) source that is located above coronal HXR loops emitted by lower energy electrons and microwaves emitted by higher energy electrons. Quantitative agreement with observations might be achieved by considering primary acceleration before the onset of loop shrinkage and additional pitch-angle scattering via wave-particle interactions.

Multi-moment advection scheme in three dimension for Vlasov simulations of magnetized plasma

We present an extension of the multi-moment advection scheme [T. Minoshima, Y. Matsumoto, T. Amano, Multi-moment advection scheme for Vlasov simulations, Journal of Computational Physics 230 (2011) 6800-6823] to the three-dimensional case, for full electromagnetic Vlasov simulations of magnetized plasma. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, and advances them on the basis of their governing equations. Similar to the two-dimensional scheme, the three-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile with little numerical dispersion or diffusion. This is a very important property for Vlasov simulations of magnetized plasma. We apply the scheme to electromagnetic Vlasov simulations. Propagation of linear waves and nonlinear evolution of the electron temperature anisotropy instability are successfully simulated with a good accuracy of the energy conservation.

Multidimensional Vlasov–Poisson Simulations with High-order Monotonicity- and Positivity-preserving Schemes

We develop new numerical schemes for Vlasov–Poisson equations with high-order accuracy. Our methods are based on a spatially monotonicity-preserving (MP) scheme and are modified suitably so that the positivity of the distribution function is also preserved. We adopt an efficient semi-Lagrangian time integration scheme that is more accurate and computationally less expensive than the three-stage TVD Runge–Kutta integration. We apply our spatially fifth- and seventh-order schemes to a suite of simulations of collisionless self-gravitating systems and electrostatic plasma simulations, including linear and nonlinear Landau damping in one dimension and Vlasov–Poisson simulations in a six-dimensional phase space. The high-order schemes achieve a significantly improved accuracy in comparison with the third-order positive-flux-conserved scheme adopted in our previous study. With the semi-Lagrangian time integration, the computational cost of our high-order schemes does not significantly increase, but remains roughly the same as that of the third-order scheme. Vlasov–Poisson simulations on mesh grids have been successfully performed on a massively parallel computer.

Boosting magnetic reconnection by viscosity and thermal conduction

Nonlinear evolution of magnetic reconnection is investigated by means of magnetohydrodynamic simulations including uniform resistivity, uniform viscosity, and anisotropic thermal conduction. When viscosity exceeds resistivity (the magnetic Prandtl number Prm>1), the viscous dissipation dominates outflow dynamics and leads to the decrease in the plasma density inside a current sheet. The low-density current sheet supports the excitation of the vortex. The thickness of the vortex is broader than that of the current for Prm>1. The broader vortex flow more efficiently carries the upstream magnetic flux toward the reconnection region, and consequently, boosts the reconnection. The reconnection rate increases with viscosity provided that thermal conduction is fast enough to take away the thermal energy increased by the viscous dissipation (the fluid Prandtl number Pr < 1). The result suggests the need to control the Prandtl numbers for the reconnection against the conventional resistive model.