Bfield Objects¶

Bases: MachineObject, Bfield

Analytical Large Aspect Ratio magnetic field with $B(\psi_t,\theta) = 1-\sqrt{2\psi_t}\cos\theta$.

No $\psi_t$ bounds checks are performed in evaluations.

>>> bfield = dex.LarBfield()

Bases: MachineObject, Bfield

Numerical magnetic field profile reconstructed from a netCDF file.

Related quantities are computed by interpolating over the data arrays.

Parameters:

• path (str) –

  The path to the NetCDF file.

• interp_type (Interpolation2dType) –

  The 2D interpolation type.

• padding (int, default: 15 ) –

  Sets the left-right $\theta$ padding width.

  Magnetic field $\theta$ padding

  At the grid edges, the interpolator’s higher derivatives are not well defined. By left-right padding the $B$ array with extra $\psi=const$ columns, we force the interpolator to take $\theta$’s periodicity into account and therefore calculate the correct derivative values. Note that in contrast to the one-dimensional cubic spline, in a bicubic interpolation 3 columns are not enough to ensure periodicity, since the spline coefficients depend on the values of the whole array.

  According to this stack overflow thread, the effect of the $i$-th column at the $j$-th column of the spline scales as $r^{|i-j|}$, where $r=\sqrt{3}-2 \approx -0.26$. Therefore, with a padding of 10, the effect at the $\theta=0$ boundary would be of the order of $10^{-6}$.

Attributes:

• path (str) –

  The path to the netCDF file.

• netcdf_version (NetCDFVersion) –

  The netCDF file's version (SemVer).

• interp_type (Interpolation2dType) –

  The 2D interpolation type.

• baxis (float) –

  The magnetic field strength on the axis $B_0$ in $[T]$.

• padding (int) –

  The number of $\theta$ padding columns (per side).

• padding_theta (float) –

  The angle $\theta$ of the padding. This corresponds to the absolute value of the first element of the padded $\theta$ array, e.g the extends of the padding.

• shape (ArrayShape) –

  Returns the $(\psi,\theta)$ shape of the initial 1D arrays (before the padding).

• shape_padded (ArrayShape) –

  Returns the $(\psi,\theta)$ shape of the padded arrays that were used to create the interpolator.

• psit_array (Array1 | None) –

  The toroidal flux' values.

• psip_array (Array1 | None) –

  The poloidal flux' values.

• theta_array (Array1) –

  The poloidal angle $\theta$ values.

• theta_array_padded (Array1) –

  The padded $\theta$ values.

• b_array (Array2) –

  The magnetic field $B$ values.

• b_array_padded (Array2) –

  The padded $B$ values.

>>> bfield = dex.NcBfield(path, "Bicubic", padding=20)