Running with Diamagnetic Drift Terms

  • Diamagnetic drift terms are currently implemented in models 303, 333, 400, 500, 555, and 600.
  • To switch the terms on, set the input parameter tauIC in the namelist input file to the correct value:
\[\tau_\text{IC} = \frac{m_\text{ion}}{2e\,F_0\sqrt{\mu_0\rho_0}}\]
  • This expression assumes $T_\text{ion}=T_\text{el}$, which accounts for the factor of two in the denominator.
  • By default, the diamagnetic terms are switched off: tauIC is preset to zero.
  • According to the definition above, the tauIC input parameter is always defined as for a single-temperature model.

Examples

For an ASDEX Upgrade deuterium plasma with $n_0=10^{20}\,\mathrm{m}^{-3}$ and $F_0=4.2$, the correct value of tauIC is $3.8\times10^{-3}$:

\[\begin{aligned} \mu_0 &= 4\pi\times10^{-7}\,\mathrm{N}\,\mathrm{A}^{-2}, \\ e &= 1.6022\times10^{-19}\,\mathrm{C}, \\ m_D &= 3.344\times10^{-27}\,\mathrm{kg}, \\ \rho_0 &= 3.344\times10^{-7}\,\mathrm{kg}\,\mathrm{m}^{-3}, \\ \sqrt{\mu_0\rho_0} &= 6.5\times10^{-7}. \end{aligned}\]

For a deuterium plasma, the expression can be written as:

\[\tau_\text{IC} = \frac{1.61\times10^8}{F_0\sqrt{n_0}}.\]

Some estimates

  • The diamagnetic velocity is $\mathbf{v}\text{dia}=-(\nabla p\times\mathbf{B})/(qnB^2)$, with magnitude $v\text{dia}= \nabla p /(qnB)$, where $q$ is the particle's electric charge and $n$ is the particle density.
  • The diamagnetic frequency is given by $\tau_\text{dia}=v_D/C$, where $C\approx2\pi r$ is the poloidal circumference of the flux surface under consideration. At the edge of an ASDEX Upgrade plasma, $C\approx4\,\mathrm{m}$.