磁扩散效应




磁扩散效应是由于电阻引起的感应电流的衰减,磁场从强度大的区域向强度小的区域发生扩散的效应,本质是电磁感应。在磁流体力学的磁感应方程中:


B∂t=∇×(v×B)+η2B{displaystyle {frac {partial {boldsymbol {B}}}{partial t}}=nabla times ({boldsymbol {v}}times {boldsymbol {B}})+eta nabla ^{2}{boldsymbol {B}}}{frac {partial {boldsymbol {B}}}{partial t}}=nabla times ({boldsymbol {v}}times {boldsymbol {B}})+eta nabla ^{2}{boldsymbol {B}}

如果磁雷诺数Rm=l0V0η1{displaystyle R_{m}={frac {l_{0}V_{0}}{eta }}ll 1}R_{m}={frac  {l_{0}V_{0}}{eta }}ll 1,则磁感应方程退化为扩散方程的形式


B∂t=η2B{displaystyle {frac {partial {boldsymbol {B}}}{partial t}}=eta nabla ^{2}{boldsymbol {B}}}{frac  {partial {boldsymbol  {B}}}{partial t}}=eta nabla ^{2}{boldsymbol  {B}}

磁场渗透所需要的特征时间为:


τ=L2ηL2{displaystyle tau ={frac {L^{2}}{eta }}=mu _{0}sigma L^{2}}{displaystyle tau ={frac {L^{2}}{eta }}=mu _{0}sigma L^{2}}

称为趋肤时间。该式表明,流体的电导率越大,磁场扩散得越慢。对于理想导体,σ{displaystyle sigma to infty }sigma to infty ,没有磁扩散效应。



参见



  • 磁感应方程

  • 磁雷诺数

  • 磁冻结效应




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