Usage
Known configurations
pyQSC has several built-in stellarator configurations that can be
called using the function Qsc.from_paper(). For example, if we
wanted to use the second order configuration from section 5.2 of
[LandremanSengupta2019], we can simply call
from qsc import Qsc
stel = Qsc.from_paper('r2 section 5.2')
pyQSC has all the first order configurations from
[LandremanSenguptaPlunk2019], all the second order configurations
from [LandremanSengupta2019], the precise quasisymmetric
configurations of [LandremanPaul2022], and the second order
configurations in [Landreman2022]. See Qsc.configurations for
the list of these available pre-defined configurations, and see the
documentation of Qsc.from_paper() for more details.
Alternatively, a configuration generated by the C++ version of QSC can be obtained using the
function
from qsc import Qsc
stel = Qsc.from_cxx(filename)
where filename is the output file of the C++ version of QSC.
New configurations
A minimal quasisymmetric configuration can be created using the following four parameters:
the cosine components of the axis radial component rc, the sine components of the axis
vertical component zs, the number of field periods nfp and the scalar parameter etabar
for the first order magnetic field.
The following example creates the r1 section 5.1 configuration using only these four
parameters:
from qsc import Qsc
stel = Qsc(rc=[1, 0.045], zs=[0, -0.045], nfp=3, etabar=-0.9)
The following example creates the second order configuration of r2 section 5.4.
As a second order configuration, besides the first order input parameters, it needs to be
specified as order="r2", and it takes one more input parameter: the scalar parameter
B2c for the second order magnetic field.
from qsc import Qsc
stel = Qsc(rc=[1, 0.155, 0.0102], zs=[0, 0.154, 0.0111], nfp=2, etabar=0.64, order='r2', B2c=-0.00322)
In the examples above, only stellarator-symmetric configurations in vacuum are created. The extra parameters
in pyQSC that need to be specified for non-stellarator-symmetric configurations are specified in
Input parameters. For a configuration with finite toroidal current on-axis, you can specify the
parameter I2 (the second derivative of the current with respect to the radial variable r).
Also, at second order, it is possible to specify a value for p2
(the second derivative of the pressure with respect to the radial variable r, usually negative)
therefore creating a finite-\(\beta\) configuration. The resolution used in pyQSC is controlled
using the parameter nphi which is set by default as nphi=61.
Simple Demo
In this demo, we create a second order configuration and evaluate a few of its parameters.
We also plot a surface shape at a constant toroidal magnetic flux (flux surface) and plot
many of the relevant parameters for the near-axis construction. The file associated with
this demo is located in the examples folder.
from qsc import Qsc
stel = Qsc(rc=[1, 0.09], zs=[0, -0.09], nfp=2, etabar=0.95, I2=0.9, order='r2', B2c=-0.7, p2=-600000.)
print(stel.iota) # Rotational transform on-axis for this configuration
print(stel.d2_volume_d_psi2) # Magnetic well V''(psi)
print(stel.DMerc_times_r2) # Mercier criterion parameter DMerc multiplied by r^2
print(stel.min_L_grad_B) # Scale length associated with the grad grad B tensor
print(stel.grad_grad_B_inverse_scale_length) # Scale length associated with the grad grad B tensor
stel.plot_boundary() # Plot the flux surface shape at the default radius r = 0.1
stel.plot() # Plot relevant near axis parameters
Input parameters
Besides the input parameters of pyQSC listed above, there are other input parameters
related to stellarator-symmetry and to the choice of vacuum or non-vacuum configurations.
By order of appearance in the Qsc function, the possible input parameters to pyQSC are:
rc: the cosine components of the axis radial component
zs: the sine components of the axis vertical component
rs: the sine components of the axis radial component
zc: the cosine components of the axis vertical component
nfp: the number of field periods
etabar: a scalar that specifies the strength of the first order magnetic field modulus
sigma0: the value of the function sigma at phi=0, which is 0 for stellarator-symmetry
B0: the strength of the magnetic field on-axis
I2: the second derivative of the current with respect to the radial variable
rsG: sign of the Boozer function G
spsi: sign of the toroidal flux function Psi
nphi: toroidal resolution specifying the number of points in a grid along the axis
B2s: a scalar that specifies the strength of the sine component of the second order magnetic field modulus, 0 for stellarator-symmetry
B2c: a scalar that specifies the strength of the cosine component of the second order magnetic field modulus
p2: the second derivative of the pressure with respect to the radial variable
r, usually negativeorder: a string that specifies the order of the expansion, “r1”, “r2” or “r3”. For “r3” only the X3c1, Y3c1 and Y3s1 components are calculated (see section 3 of [LandremanSengupta2019])
Using with SIMSOPT
An example of the usage of pyQsc with the optimization code SIMSOPT is shown
in the examples folder in the file simsopt_demo.py.
Landreman, Sengupta, and Plunk, Journal of Plasma Physics 85, 905850103 (2019).
Landreman and Sengupta, Journal of Plasma Physics 85, 815850601 (2019).
Landreman and Paul, Physical Review Letters 128, 035001 (2022).
Landreman, Journal of Plasma Physics 88, 905880616 (2022).