is there any interest in having a new mapper which, given a 2D function defined in the poloidal plane, maps such function in a 3D one which is periodic along the toroidal direction? For instance, the resulting 3D function could be alternatively zero or non-zero (and matching what one would obtain with the already existing AxisymmetricMapper) along the toridal direction. This could be useful given the usual shaping of the plasma-facing components in tokamaks and resulting emission in their proximity (see Fig. 3 of this paper for an example).
cdef class DiscreteToroidalMapper(Function3D):
"""
Performs a periodic (of period = periodicity) discrete rotation of a 2D function
(defined on the xz plane) around the z-axis. The resulting 3D function is a piece-
wise function, which is non-zero over a range of where_non_zero [rad] in each slice.
Due to the nature of this mapping, only the positive region of the x range
of the supplied function is mapped.
:param Function2D function2d: The function to be mapped.
:param float periodicity: Periodicity [rad] of the 3D mapping,
i.e. 1 / periodicity = number of slices.
:param float where_non_zero: Angle [rad] in each slice where the resulting function
is non-zero.
.. code-block:: pycon
>>> import numpy as np
>>> from cherab.core.math import DiscreteToroidalMapper
>>>
>>> def f1(r, z):
>>> return r
>>>
>>> periodicity = 2 * np.pi / 2 # 2 slices (x>0 and x<0 half-spaces)
>>> where_non_zero = periodicity / 2 # half of each slice is non-zero (1st and 3rd quadrants)
>>>
>>> f2 = DiscreteToroidalMapper(f1,
periodicity = periodicity,
where_non_zero = where_non_zero)
>>>
>>> f2(+1/np.sqrt(2), +1/np.sqrt(2), 0)
0.99999999
>>> f2(+1/np.sqrt(2), -1/np.sqrt(2), 0)
0.0
"""
def __init__(self, object function2d, double periodicity, double where_non_zero):
if not callable(function2d):
raise TypeError("Function3D is not callable.")
if where_non_zero > periodicity:
raise ValueError("where_non_zero must be smaller than periodicity.")
self.function2d = autowrap_function2d(function2d)
self.periodicity = periodicity # [rad]
self.where_non_zero = where_non_zero # [rad]
def __call__(self, double x, double y, double z):
return self.evaluate(x, y, z)
@cython.boundscheck(False)
@cython.wraparound(False)
@cython.cdivision(True)
@cython.initializedcheck(False)
cdef double evaluate(self, double x, double y, double z) except? -1e999:
"""Return the value of function2d when it is y-axis symmetrically
extended to the 3D space and falling in where_non_zero range.
Return 0 otherwise."""
cdef:
double phi, phi_dw, phi_up
int n, num
# toroidal angle [rad]
phi = atan2(y, x) + M_PI
# number of slices
num = int(2 * M_PI / self.periodicity)
# check if zero must be returned (more efficient)
for n from 0 <= n < num by 1:
phi_dw = n * self.periodicity + self.where_non_zero
phi_up = (n + 1) * self.periodicity
if phi > phi_dw and phi < phi_up:
return 0.0
return self.function2d.evaluate(sqrt(x*x + y*y), z)
Dear CHERAB team,
is there any interest in having a new mapper which, given a 2D function defined in the poloidal plane, maps such function in a 3D one which is periodic along the toroidal direction? For instance, the resulting 3D function could be alternatively zero or non-zero (and matching what one would obtain with the already existing AxisymmetricMapper) along the toridal direction. This could be useful given the usual shaping of the plasma-facing components in tokamaks and resulting emission in their proximity (see Fig. 3 of this paper for an example).
An idea of implementation could be the following: