数值MHD中的Biermann突变
The Biermann Catastrophe in Numerical MHD
摘要：
比尔曼电池效应经常在宇宙磁场发生中被引用，并在高能量密度实验室物理实验中进行研究。众所周知，在激波<i>后面的</i>光滑流中，由于密度和温度梯度的不对准，通过比尔曼效应产生磁场。我们表明，比尔曼效应磁场也<i>产生</i>冲击内。在MHD代码中直接实现Biermann效应并不能捕获这个物理过程，更糟糕的是，在冲击时产生非物理磁场，其值不随分辨率收敛。我们表明，这种收敛故障是由于天真的离散化，这不能占的事实，即离散无旋向量场有虚假的螺线管组件，增长没有约束附近的不连续性。我们表明，仔细考虑离子粘性冲击的动力学导致比尔曼效应，从而产生一个收敛的算法制定。我们注意到两个新的物理效应：一个<i>电阻磁前体中的冲击</i>比尔曼产生的字段“泄漏”逆流;和<i>热磁前体</i>，在该字段中产生的比尔曼效应提前的冲击前，由于冲击的电子热传导前体所产生的梯度。这两种效应似乎都可以在激光设施的实验中观察到。我们重新审视发表的研究磁在星系团形成，并得出结论，有问题的模拟分辨率不足，可靠地估计磁场产生率。校正后的估计值表明原始场值在$B\sim 10^{-22}$ G - $10^{-19}$ G乘$z=3$范围内。
英文摘要：
The Biermann Battery effect is frequently invoked in cosmic magnetogenesis and studied in High-Energy Density laboratory physics experiments. Generation of magnetic fields by the Biermann effect due to mis-aligned density and temperature gradients in smooth flow <i>behind</i> shocks is well known. We show that a Biermann-effect magnetic field is also generated <i>within</i> shocks. Direct implementation of the Biermann effect in MHD codes does not capture this physical process, and worse, produces unphysical magnetic fields at shocks whose value does not converge with resolution. We show that this convergence breakdown is due to naive discretization, which fails to account for the fact that discretized irrotational vector fields have spurious solenoidal components that grow without bound near a discontinuity. We show that careful consideration of the kinetics of ion viscous shocks leads to a formulation of the Biermann effect that gives rise to a convergent algorithm. We note two novel physical effects: a <i>resistive magnetic precursor</i> in which Biermann-generated field in the shock "leaks" resistively upstream; and a <i>thermal magnetic precursor</i>, in which field is generated by the Biermann effect ahead of the shock front due to gradients created by the shock's electron thermal conduction precursor. Both effects appear to be potentially observable in experiments at laser facilities. We re-examine published studies of magnetogenesis in galaxy cluster formation, and conclude that the simulations in question had inadequate resolution to reliably estimate the field generation rate. Corrected estimates suggest primordial field values in the range $B\sim 10^{-22}$G --- $10^{-19}$G by $z=3$.
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