We propose a new mechanism of coronal heating, in which protons and minor ions are heated and accelerated by fast shocks. The interaction between network magnetic Ðelds and emerging intranetwork Ðelds may lead to the formation of thin current sheets, which triggers magnetic reconnection and microÑares. The disruption of current sheet leads to fast shocks with an Mach number In Alfve n M A \ 2. addition, fast shocks that originate in the chromosphere by magnetic reconnection of a smaller scale may produce spicules and then enter the corona. The heating and acceleration by shocks are then examined based on a theoretical model and hybrid simulations. The results show the following : (1) the near nondeÑection of ion motion across the shock ramp leads to a large perpendicular thermal velocity which (v thM ), depends on the mass/charge ratio ; (2) for subcritical shocks with the shock heating leads 1.1 ¹ M A ¹ 1.5, to a large temperature anisotropy with for O5`ions and a mild anisotropy with.2 for protons ; (3) these subcritical shocks can directly drive an outward Ðeld-aligned velocity km s~1 for protons ; (4) the large perpendicular thermal velocity of O5`ions can be D0.1V A D 240 converted to the radial outÑow velocity (u) in the diverging coronal Ðeld lines ; and (5) the heating and acceleration by shocks with can lead to km s~1 for O5`ions

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An interplanetary intermediate shock is identified from the bulk velocity, number density, and temperature of the solar wind protons and tl•e three components of the interplanetary magnetic field observed by Voyager 1 on May 1 (day 122), 1980, when the spacecraft was at a distance of about 9 AU froln the Sun. It is shown by a best fit procedure that the ineasured plasma and magnetic field on both sides of the discontinuity satisfy the Rankine-Hugoniot relations for a magnetohydrodynamic (MHD) intermediate shock.This shock satisfies the following conditions. (1) The normal Alfvtn-Mach nmnber (M^= Vn*/V ^ ) is greater than unity in the preshock state and less than unity in the postshock state. (2) Both the fast-mode Mach number (Mf= Vn*/Vf) in the preshock state and the slow-mode Mach number (Ms• = Vn*/Vs• ) in the postshock state are less than unity, but the slowqnode Mach nmnber is greater than unity in the preshock state. (3) The projected co•nponents of the magnetic fields in the shock front for the pre-and postshock states have opposite signs. (4) The magnitudes of the magnetic fields decrease from the preshock to the ptstshock states. In the above expression, V^ is the Alfvtn speed based on the inagnetic field component normal to the shock front, Vn* is the component of the bulk velocity normal to the shock front and measured in the shock frame of reference, and Vf and Vs• are the speeds of the fast-and slow-mode magnetosonic waves in the direction of the shock normal, respectively. The discontinuity event in our discussion cannot be a rotational discontinuity because the Walen's relation is not satisfied. The identified intermediate, shock has M A =1.04, 0nn =37 ø, and [• =0.56. where 0BniS the angle between the preshock magnetic field and the shock normal direction and [• is the ratio of thermal to inagnetic energy densities. Using these parameters, a numerical solution of the MHD equations for the shock is obtained. The simulated profiles of the bulk velocity, number density, temperature, and xnagnetic fields of the pre-and postshock states agree with those of the observed values. The same parameters are used to siinulate an intermediate shock using a hybrid numerical code in which full ion dynamics is retained while electron inertial force is neglected. The results of this simulation are coinpared with high-resolution magnetic field data with a time resolution of 1.92-s averages. The shock thickness of about 70 c/(Opi predicted from the hybrid code agrees with the observations. The general behavior of the magnetic field in the shock transition region is also very sinfilar for the simulated and observed results. The macro-and nficrostructures of the intermediate shock obtained from the MHD and hybrid models reseinble the observed structures. 17,443 17,444 CIqAO ET AL.' OBSERVATIONS OF AN INTERMEDIATE SHOCK

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Freshly created ions can be picked up by a moving plasma without relying on collisions. It is well known that such an ion pickup process can be accomplished via the interaction with Alfvén waves. However, it should be stressed that in general ion pickup is attributed to two distinctly different sub-processes, namely, pitch-angle diffusion and pitch-angle scattering. In this article their difference is discussed and furthermore, some new results from a recent theoretical study are reported. It is found that under some conditions the usual quasilinear theory which describes the pitch-angle diffusion process cannot be justified even when the turbulence level is low. Another significant finding is that in the presence of strong Alfvén turbulence, thermal ions can be intensely heated by a nonlinear damping of the waves, which does not depend upon the usual ion cyclotron resonance.

Contact discontinuities in a collisionless plasma are studied by hybrid simulations, in which ions are treated as particles and electrons are considered as a fluid. It is demonstrated that contact discontinuity with a stable density ramp can exist in cases with a finite electron temperature. An electron pressure gradient is present across the contact discontinuity, leading to the presence of a parallel electric field and hence field‐aligned potential increase (ΔΦ∥) in the transition region. By reflecting ions at the discontinuity, this parallel electric potential peak reduces the interpenetration between hot and cold ions and maintains a stable density ramp across the contact discontinuity. The ratio of the field‐aligned electric potential energy to ion thermal energy, eΔΦ∥/kTi, is found to be an increasing function of Te/Ti, where Te and Ti are respectively the electron and ion temperature.

A planar micromixer with rhombic microchannels and a converging-diverging element has been systematically investigated by the Taguchi method, CFD-ACE simulations and experiments. To reduce the footprint and extend the operation range of Reynolds number, Taguchi method was used to numerically study the performance of the micromixer in a L(9) orthogonal array. Mixing efficiency is prominently influenced by geometrical parameters and Reynolds number (Re). The four factors in a L(9) orthogonal array are number of rhombi, turning angle, width of the rhombic channel and width of the throat. The degree of sensitivity by Taguchi method can be ranked as: Number of rhombi > Width of the rhombic channel > Width of the throat > Turning angle of the rhombic channel. Increasing the number of rhombi, reducing the width of the rhombic channel and throat and lowering the turning angle resulted in better fluid mixing efficiency. The optimal design of the micromixer in simulations indicates over 90% mixing efficiency at both Re > or = 80 and Re < or = 0.1. Experimental results in the optimal simulations are consistent with the simulated one. This planar rhombic micromixer has simplified the complex fabrication process of the multi-layer or three-dimensional micromixers and improved the performance of a previous rhombic micromixer at a reduced footprint and lower Re.

The evolution of an initial current sheet is studied by using the set of one-dimensional (1D) magnetohydrodynamic equations. In a simulation of the 1D Riemann problem along the z direction, the initial magnetic field is chosen as B(z)=−Bx0tanh(z∕δ)x̂+Byŷ+Bzẑ, where Bx0 denotes the antiparallel component and By is called the guide field of current sheet. For the By=0 case, a pair of slow shocks is formed and propagates away from the current sheet. For By≠0 (even for a very small By), it is found that a pair of slow shocks and an additional pair of time-dependent intermediate shocks (TDISs) are formed. TDISs are not present in the By=0 case, indicating that the case with By=0 is a singular case. In this paper, an attempt is made to reconcile the By=0 case with small nonzero By cases by examining the early time evolution of TDISs and slow shocks. The early current evolutions for the By=0 case and for small By cases are found to be very similar. For By≠0 cases, the plasma density and pressure are found to increase and the magnetic field decreases across TDISs. The dependence of current sheet evolution on initial By (or ϕ∞) and the plasma beta β∞ and also examined, where ϕ∞=tan−1(By∕Bx0) is the initial angle beteween the tangential magnetic field and the x axis, and the subscript ∞ denotes the location far from the current sheet. The rotation angle (Δϕ) of tangential magnetic field across TDIS develops gradually with time and reaches the final value Δϕfinal=90°−ϕ∞. For small By (ϕ∞→0), it is found that the time reaching the final state is very long. Both pressure and temperature downstream of the slow shock decrease with ϕ∞, and increase with plasma beta β∞. With a decreasing ϕ∞ or an increasing β∞, the Alfvén Mach number (MA=Vn1∕VA) associated with slow shocks increases, and the amount of magnetic energy converted into kinetic energy also increases.