MHD Turbulence in Laboratory Plasmas#
Investigate turbulence in laboratory plasmas, where MHD interactions occur within controlled magnetic confinement devices such as tokamaks or stellarators.
Mathematical Model#
MHD Equations:
\[\begin{split}
\begin{align*}
\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \mathbf{v}) &= 0 \\
\rho \frac{D\mathbf{v}}{Dt} &= -\nabla p + \rho \mathbf{g} + \nabla \cdot \boldsymbol{\tau} + \mathbf{J} \times \mathbf{B} + \nu \nabla^2 \mathbf{v} \\
\frac{\partial \mathbf{B}}{\partial t} &= \nabla \times (\mathbf{v} \times \mathbf{B} - \eta \nabla \times \mathbf{B}) \\
\mathbf{J} &= \sigma (\mathbf{E} + \mathbf{v} \times \mathbf{B}) \\
\rho C_p \frac{DT}{Dt} &= -p \nabla \cdot \mathbf{v} + \nabla \cdot (k \nabla T) + \frac{1}{\sigma}(\mathbf{J} \cdot \mathbf{E})
\end{align*}
\end{split}\]
Initial and Boundary Conditions:
Initial condition: Conditions reflecting the initial state of the plasma.
Boundary conditions: Set appropriate conditions for the plasma confinement device.