论文标题
通过螺旋磁场的手性不对称产生
Generation of chiral asymmetry via helical magnetic fields
论文作者
论文摘要
众所周知，螺旋磁场经历了所谓的反级联反应，由于其在经典的理想磁性水力学（MHD）中的磁螺旋性（MHD）中，其相关长度通过其相关长度而增长。但是，高能量高于$ 10 $ MEV，但是，经典的MHD必然扩展到手性MHD，然后保守的数量为$ \ langle \ nangcal \ Mathcal {h} \ rangle + 2 \langleμ5\langleμ5\ langle /λ $ \langleμ_5\ rangle $是带电费米子的平均手性化学潜力。在这里，$λ$是（现象学）手性反馈参数。在本文中，我们研究了手性MHD系统的演变，其初始条件是非零$ \ langle \ mathcal {h} \ rangle $并消失的$μ_5$。我们介绍了$ \ langle \ Mathcal {h} \ rangle $和$ \langleμ__5\ rangle $的分析推导，我们将其与一系列层状和湍流的三维直接数值模拟。我们发现，$ \ langle \ Mathcal {h} \ rangle $的后期演变取决于磁性和动力学雷诺数$ {\ rm re} _ {_ \ Mathrm {Mathrm {M Mathrm {M Mathrm {M {M {M {M}} $和$ re} $ {\ rm re} _ {_ {_ {_ {_ {_ Mathmmmath}对于高$ {\ rm re} _ {_ \ mathrm {m}} $和$ {\ rm re} _ {_ {_ \ Mathrm {k}} $，其中发生湍流，$ \ langle \ langle \ mathcal {h} \ rangle {螺旋磁场随时间$ t $作为$ k_ \ mathrm {p} \ propto t^{ - 2/3} $缩放。对于速度字段可忽略不计的低雷诺数，将缩放率更改为$ k_ \ mathrm {p} \ propto t^{ - 1/2} \ mathrm {ln} \ left（t/t/t_ \ mathrm {logrm {log}} \ right）$。迅速生成后，$ \langleμ5\ rangle $总是与$ k_ \ mathrm {p} $一起腐烂，即$ \langleμ__5\ rangle \ rangle \ langle \ langle \ of K_ \ mathrm {p Mathrm {p} $，其时间的演变取决于系统是否在限制限制或高率的数字中。
It is well known that helical magnetic fields undergo a so-called inverse cascade by which their correlation length grows due to the conservation of magnetic helicity in classical ideal magnetohydrodynamics (MHD). At high energies above approximately $10$ MeV, however, classical MHD is necessarily extended to chiral MHD and then the conserved quantity is $\langle\mathcal{H}\rangle + 2 \langleμ_5\rangle / λ$ with $\langle\mathcal{H}\rangle$ being the mean magnetic helicity and $\langleμ_5\rangle$ being the mean chiral chemical potential of charged fermions. Here, $λ$ is a (phenomenological) chiral feedback parameter. In this paper, we study the evolution of the chiral MHD system with the initial condition of nonzero $\langle\mathcal{H}\rangle$ and vanishing $μ_5$. We present analytic derivations for the time evolution of $\langle\mathcal{H}\rangle$ and $\langleμ_5\rangle$ that we compare to a series of laminar and turbulent three-dimensional direct numerical simulations. We find that the late-time evolution of $\langle\mathcal{H}\rangle$ depends on the magnetic and kinetic Reynolds numbers ${\rm Re}_{_\mathrm{M}}$ and ${\rm Re}_{_\mathrm{K}}$. For a high ${\rm Re}_{_\mathrm{M}}$ and ${\rm Re}_{_\mathrm{K}}$ where turbulence occurs, $\langle\mathcal{H}\rangle$ eventually evolves in the same way as in classical ideal MHD where the inverse correlation length of the helical magnetic field scales with time $t$ as $k_\mathrm{p} \propto t^{-2/3}$. For a low Reynolds numbers where the velocity field is negligible, the scaling is changed to $k_\mathrm{p} \propto t^{-1/2}\mathrm{ln}\left(t/t_\mathrm{log}\right)$. After being rapidly generated, $\langleμ_5\rangle$ always decays together with $k_\mathrm{p}$, i.e. $\langleμ_5\rangle \approx k_\mathrm{p}$, with a time evolution that depends on whether the system is in the limit of low or high Reynolds numbers.
