gkvp_f0.63

New feature: velocity-space coordinate (vl,vp)

Previous GKV code employs (vl,mu) velocity-space coordinates, namely, the parallel velocity and magnetic moment. The gkvp_f0.63 added a new choice of velocity-space coordinate (vl,vp), replacing the perpendicular velocity-space coordinate from the magnetic moment to the perpendicular velocity.

This choice is beneficial when the magnetic field strength significantly varies, like the dipole geometry.

Switching the velocity-space coordinates is done in run/gkvp_namelist:

    vp_coord = 0, # For (vl,mu) coordinates

or

    vp_coord = 1, # For (vl,vp) coordinates

In the equation, the parallel advection term is modified:

$$\frac{\partial}{\partial z}_{(z,v_\parallel,\mu)} \rightarrow \frac{\partial}{\partial z}_{(z,v_\parallel,v_\perp)} + \frac{v_\perp}{2B}\frac{\partial B}{\partial z}\frac{\partial}{\partial v_\perp}_{(z,v_\parallel,v_\perp)}$$

Note that the recent rotating flux-tube implementation, the rotating operator is unchanged,

$$\frac{\partial}{\partial t''}_{(z,v_\parallel,\mu)} - \frac{\gamma_E}{\hat{s}} \frac{\partial}{\partial z''}_{(z,v_\parallel,\mu)} \rightarrow \frac{\partial}{\partial t''}_{(z,v_\parallel,v_\perp)} - \frac{\gamma_E}{\hat{s}} \frac{\partial}{\partial z''}_{(z,v_\parallel,v_\perp)}$$

because the operators of $\partial_{v_{\perp}}$ from the first ($\partial_{t''}$) and second (\partial_{z''}) terms cancel out.

What's Changed

• Choice of (vl,vp) velocity-space coordinates by @smaeyama in #14

Full Changelog: f0.62...f0.63