simsopt.mhd package

Submodules

simsopt.mhd.boozer module

This module provides a class that handles the transformation to Boozer coordinates, and an optimization target for quasisymmetry.

class simsopt.mhd.boozer.Quasisymmetry(boozer: simsopt.mhd.boozer.Boozer, s: Union[float, Iterable[float]], m: int, n: int, normalization: str = 'B00', weight: str = 'even')

Bases: simsopt._core.optimizable.Optimizable

This class is used to compute the departure from quasisymmetry on a given flux surface based on the Boozer spectrum.

Parameters

• boozer – A Boozer object on which the calculation will be based.

• s – The normalized toroidal magnetic flux for the flux surface to analyze. Should be in the range [0, 1].

• m – The poloidal mode number of the symmetry you want to achive. The departure from symmetry B(m * theta - nfp * n * zeta) will be reported.

• n – The toroidal mode number of the symmetry you want to achieve. The departure from symmetry B(m * theta - nfp * n * zeta) will be reported.

• normalization – A uniform normalization applied to all bmnc harmonics. If "B00", the symmetry-breaking modes will be divided by the m=n=0 mode amplitude on the same surface. If "symmetric", the symmetry-breaking modes will be divided by the square root of the sum of the squares of all the symmetric modes on the same surface. This is the normalization used in stellopt.

• weight – An option for a m- or n-dependent weight to be applied to the bmnc amplitudes.

J() → numpy.ndarray

Carry out the calculation of the quasisymmetry error.

Returns

1D numpy array listing all the normalized mode amplitudes of symmetry-breaking Fourier modes of |B|.

__init__(boozer: simsopt.mhd.boozer.Boozer, s: Union[float, Iterable[float]], m: int, n: int, normalization: str = 'B00', weight: str = 'even') → None

Constructor

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(x)

This base Optimizable object has no degrees of freedom, so do nothing.

simsopt.mhd.spec module

This module provides a class that handles the SPEC equilibrium code.

class simsopt.mhd.spec.Residue(spec, pp, qq, vol=1, theta=0, s_guess=None, s_min=- 1.0, s_max=1.0, rtol=1e-09)

Bases: simsopt._core.optimizable.Optimizable

Greene’s residue, evaluated from a Spec equilibrum

J()

Run Spec if needed, find the periodic field line, and return the residue

__init__(spec, pp, qq, vol=1, theta=0, s_guess=None, s_min=- 1.0, s_max=1.0, rtol=1e-09)

spec: a Spec object pp, qq: Numerator and denominator for the resonant iota = pp / qq vol: Index of the Spec volume to consider theta: Spec’s theta coordinate at the periodic field line s_guess: Guess for the value of Spec’s s coordinate at the periodic

field line

s_min, s_max: bounds on s for the search rtol: the relative tolerance of the integrator

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

set_dofs(x)

This base Optimizable object has no degrees of freedom, so do nothing.

simsopt.mhd.vmec module

This module provides a class that handles the VMEC equilibrium code.

class simsopt.mhd.vmec.Vmec(filename: Optional[str] = None, mpi: Optional[simsopt.util.mpi.MpiPartition] = None)

Bases: simsopt._core.optimizable.Optimizable

This class represents the VMEC equilibrium code.

The input parameters to VMEC are all accessible as attributes of the indata attribute. For example, if vmec is an instance of Vmec, then you can read or write the input resolution parameters using vmec.indata.mpol, vmec.indata.ntor, vmec.indata.ns_array, etc. However, the boundary surface is different: rbc, rbs, zbc, and zbs from the indata attribute are always ignored, and these arrays are instead taken from the simsopt surface object associated to the boundary attribute. If boundary is a surface based on some other representation than VMEC’s Fourier representation, the surface will automatically be converted to VMEC’s representation (SurfaceRZFourier) before each run of VMEC. You can replace boundary with a new surface object, of any type that implements the conversion function ``to_RZFourier()`.

VMEC is run either when the run() function is called, or when any of the output functions like aspect() or iota_axis() are called.

A caching mechanism is implemented, using the attribute need_to_run_code. Whenever VMEC is run, this attribute is set to False. Subsequent calls to run() or output functions like aspect() will not actually run VMEC again, until need_to_run_code is changed to True. The attribute need_to_run_code is automatically set to True whenever set_dofs() is called. However, need_to_run_code is not automatically set to True when entries of indata are modified, or when boundary is modified.

Once VMEC has run at least once, all of the quantities in the wout output file are available as attributes of the wout attribute. For example, if vmec is an instance of Vmec, then the flux surface shapes can be obtained from vmec.wout.rmnc and vmec.wout.zmns.

Since the underlying fortran implementation of VMEC uses global module variables, it is not possible to have more than one python Vmec object with different parameters; changing the parameters of one would change the parameters of the other.

An instance of this class owns just a few optimizable degrees of freedom, particularly phiedge and curtor. The optimizable degrees of freedom associated with the boundary surface are owned by that surface object.

Parameters

• filename – Name of a VMEC input file to use for loading the initial parameters. If None, default parameters will be used.

• mpi – A simsopt.util.mpi.MpiPartition instance, from which the worker groups will be used for VMEC calculations. If None, each MPI process will run VMEC independently.

iter

Number of times VMEC has run.

s_full_grid

The “full” grid in the radial coordinate s (normalized toroidal flux), including points at s=0 and s=1. Used for the output arrays and zmns.

s_half_grid

The “half” grid in the radial coordinate s, used for bmnc, lmns, and other output arrays. In contrast to wout files, this array has only ns-1 entries, so there is no leading 0.

ds

The spacing between grid points for the radial coordinate s.

__repr__()

Print the object in an informative way.

aspect()

Return the plasma aspect ratio.

get_dofs()

This base Optimizable object has no degrees of freedom, so return an empty array

get_max_mn()

Look through the rbc and zbs data in fortran to determine the largest m and n for which rbc or zbs is nonzero.

iota_axis()

Return the rotational transform on axis

iota_edge()

Return the rotational transform at the boundary

load_wout()

Read in the most recent wout file created, and store all the data in a wout attribute of this Vmec object.

mean_iota()

Return the mean rotational transform. The average is taken over the normalized toroidal flux s.

mean_shear()

Return an average magnetic shear, d(iota)/ds, where s is the normalized toroidal flux. This is computed by fitting the rotational transform to a linear (plus constant) function in s. The slope of this fit function is returned.

run()

Run VMEC, if need_to_run_code is True.

set_dofs(x)

This base Optimizable object has no degrees of freedom, so do nothing.

vacuum_well()

Compute a single number W that summarizes the vacuum magnetic well, given by the formula

W = (dV/ds(s=0) - dV/ds(s=1)) / (dV/ds(s=0)

where dVds is the derivative of the flux surface volume with respect to the radial coordinate s. Positive values of W are favorable for stability to interchange modes. This formula for W is motivated by the fact that

d^2 V / d s^2 < 0

is favorable for stability. Integrating over s from 0 to 1 and normalizing gives the above formula for W. Notice that W is dimensionless, and it scales as the square of the minor radius. To compute dV/ds, we use

dV/ds = 4 * pi**2 * abs(sqrt(g)_{0,0})

where sqrt(g) is the Jacobian of (s, theta, phi) coordinates, computed by VMEC in the gmnc array, and _{0,0} indicates the m=n=0 Fourier component. Since gmnc is reported by VMEC on the half mesh, we extrapolate by half of a radial grid point to s = 0 and 1.

volume()

Return the volume inside the VMEC last closed flux surface.

Module contents