From e4f8071e2ee92d3d2a5e79bd5aed4d26f78e4c9a Mon Sep 17 00:00:00 2001 From: vsnever Date: Thu, 25 Apr 2024 00:28:09 +0300 Subject: [PATCH 1/9] Improve beam direction and beam density calculations. --- CHANGELOG.md | 2 ++ cherab/core/beam/node.pxd | 2 +- cherab/core/beam/node.pyx | 22 ++++++++++++++++------ cherab/core/model/attenuator/singleray.pyx | 7 ++++--- 4 files changed, 23 insertions(+), 10 deletions(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index 8156571a..caeae178 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -13,6 +13,8 @@ New: * Replace the coarse numerical constant in the Bremsstrahlung model with an exact expression. (#409) * Add the kind attribute to RayTransferPipelineXD that determines whether the ray transfer matrix is multiplied by sensitivity ('power') or not ('radiance'). (#412) * Improved parsing of metadata from the ADAS ADF15 'bnd' files for H-like ions. Raises a runtime error if the metadata cannot be parsed. (#424) +* Beam dispersion calculation has changed from sigma(z) = sigma + z * tan(alpha) to sigma(z) = sqrt(sigma^2 + (z * tan(alpha))^2) for consistancy with the Gaussian beam model. Attention!!! The results of BES and CX spectroscopy are affected by this change. (#414) +* Improved beam direction calculation to allow for natural broadening of the BES line shape due to beam divergence. (#414) Bug fixes: * Fix deprecated transforms being cached in LaserMaterial after laser.transform update (#420) diff --git a/cherab/core/beam/node.pxd b/cherab/core/beam/node.pxd index d8159bbb..8f58e0c0 100644 --- a/cherab/core/beam/node.pxd +++ b/cherab/core/beam/node.pxd @@ -47,7 +47,7 @@ cdef class Beam(Node): Vector3D BEAM_AXIS double _energy, _power, _temperature Element _element - double _divergence_x, _divergence_y + double _divergence_x, _divergence_y, _tanxdiv, _tanydiv double _length, _sigma Plasma _plasma AtomicData _atomic_data diff --git a/cherab/core/beam/node.pyx b/cherab/core/beam/node.pyx index 36877421..9fede133 100644 --- a/cherab/core/beam/node.pyx +++ b/cherab/core/beam/node.pyx @@ -30,7 +30,7 @@ from cherab.core.beam.material cimport BeamMaterial from cherab.core.beam.model cimport BeamModel from cherab.core.atomic cimport AtomicData, Element from cherab.core.utility import Notifier -from libc.math cimport tan, M_PI +from libc.math cimport tan, M_PI, sqrt cdef double DEGREES_TO_RADIANS = M_PI / 180 @@ -188,6 +188,8 @@ cdef class Beam(Node): self._element = element = None # beam species, an Element object self._divergence_x = 0.0 # beam divergence x (degrees) self._divergence_y = 0.0 # beam divergence y (degrees) + self._tanxdiv = 0.0 # tan(DEGREES_TO_RADIANS * divergence_x) + self._tanydiv = 0.0 # tan(DEGREES_TO_RADIANS * divergence_y) self._length = 1.0 # m self._sigma = 0.1 # m (gaussian beam width at origin) @@ -248,9 +250,15 @@ cdef class Beam(Node): return self.BEAM_AXIS # calculate direction from divergence - cdef double dx = tan(DEGREES_TO_RADIANS * self._divergence_x) - cdef double dy = tan(DEGREES_TO_RADIANS * self._divergence_y) - return new_vector3d(dx, dy, 1.0).normalise() + cdef double z_tanx_sqr = z * z * self._tanxdiv * self._tanxdiv + cdef double z_tany_sqr = z * z * self._tanydiv * self._tanydiv + cdef double sigma_sqr = self._sigma * self._sigma + cdef double sigma_x_sqr = sigma_sqr + z_tanx_sqr + cdef double sigma_y_sqr = sigma_sqr + z_tany_sqr + cdef double ex = x * z_tanx_sqr / sigma_x_sqr + cdef double ey = y * z_tany_sqr / sigma_y_sqr + + return new_vector3d(ex, ey, z).normalise() @property def energy(self): @@ -315,6 +323,7 @@ cdef class Beam(Node): if value < 0: raise ValueError('Beam x divergence cannot be less than zero.') self._divergence_x = value + self._tanxdiv = tan(DEGREES_TO_RADIANS * value) self.notifier.notify() cdef double get_divergence_x(self): @@ -329,6 +338,7 @@ cdef class Beam(Node): if value < 0: raise ValueError('Beam y divergence cannot be less than zero.') self._divergence_y = value + self._tanydiv = tan(DEGREES_TO_RADIANS * value) self.notifier.notify() cdef double get_divergence_y(self): @@ -501,10 +511,10 @@ cdef class Beam(Node): # radii of bounds at the beam origin (z=0) and the beam end (z=length) radius_start = num_sigma * self.sigma - radius_end = radius_start + self.length * num_sigma * drdz + radius_end = num_sigma * sqrt(self.sigma**2 + self.length**2 * drdz**2) # distance of the cone apex to the beam origin - distance_apex = radius_start / (num_sigma * drdz) + distance_apex = radius_start * self.length / (radius_end - radius_start) cone_height = self.length + distance_apex # calculate volumes diff --git a/cherab/core/model/attenuator/singleray.pyx b/cherab/core/model/attenuator/singleray.pyx index a2cfbde1..ca611d09 100644 --- a/cherab/core/model/attenuator/singleray.pyx +++ b/cherab/core/model/attenuator/singleray.pyx @@ -97,7 +97,7 @@ cdef class SingleRayAttenuator(BeamAttenuator): :return: Density in m^-3. """ - cdef double sigma_x, sigma_y, norm_radius_sqr, gaussian_sample + cdef double sigma0_sqr, sigma_x, sigma_y, norm_radius_sqr, gaussian_sample # use cached data if available if self._stopping_data is None: @@ -107,8 +107,9 @@ cdef class SingleRayAttenuator(BeamAttenuator): self._calc_attenuation() # calculate beam width - sigma_x = self._beam.get_sigma() + z * self._tanxdiv - sigma_y = self._beam.get_sigma() + z * self._tanydiv + sigma0_sqr = self._beam.get_sigma()**2 + sigma_x = sqrt(sigma0_sqr + (z * self._tanxdiv)**2) + sigma_y = sqrt(sigma0_sqr + (z * self._tanydiv)**2) # normalised radius squared norm_radius_sqr = ((x / sigma_x)**2 + (y / sigma_y)**2) From 68189f19fd1ad0e58b0180258066755d393519e8 Mon Sep 17 00:00:00 2001 From: vsnever Date: Thu, 2 May 2024 01:49:45 +0300 Subject: [PATCH 2/9] Update BES demo and beam-related pictures in the docs. --- .../emission_models/beam_emission_spectrum.py | 4 ++-- .../active_spectroscopy/BES_camera.png | Bin 4602 -> 7702 bytes .../active_spectroscopy/BES_sightline.png | Bin 24390 -> 25377 bytes .../active_spectroscopy/BES_spectrum_full.png | Bin 23734 -> 24021 bytes .../BES_spectrum_zoomed.png | Bin 36765 -> 37615 bytes .../active_spectroscopy/CXS_camera.png | Bin 5427 -> 5067 bytes .../CXS_multi_sightlines.png | Bin 58844 -> 59708 bytes .../active_spectroscopy/CXS_spectrum.png | Bin 29530 -> 24577 bytes .../plasmas/beam_attenuation.png | Bin 43674 -> 42157 bytes .../plasmas/beam_density_xz.png | Bin 31858 -> 31660 bytes .../plasmas/beam_into_plasma.png | Bin 5541 -> 4390 bytes 11 files changed, 2 insertions(+), 2 deletions(-) diff --git a/demos/emission_models/beam_emission_spectrum.py b/demos/emission_models/beam_emission_spectrum.py index f7675449..cbf5505b 100644 --- a/demos/emission_models/beam_emission_spectrum.py +++ b/demos/emission_models/beam_emission_spectrum.py @@ -69,9 +69,9 @@ beam_energy = 110000 # keV beam_current = 10 # A beam_sigma = 0.05 -beam_divergence = 0.5 +beam_divergence = 1.3 # 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Moved SingleRayAttenuator from CXS models section to Beam Attenuation section. --- cherab/core/beam/node.pyx | 17 +++++++- cherab/core/model/attenuator/singleray.pyx | 43 +++++++++++++++++++-- docs/source/models/beam/beam_attenuator.rst | 10 +++++ docs/source/models/cxs/cxs_model.rst | 9 ----- docs/source/models/emission_models.rst | 1 + docs/source/plasmas/particle_beams.rst | 2 +- 6 files changed, 67 insertions(+), 15 deletions(-) create mode 100644 docs/source/models/beam/beam_attenuator.rst diff --git a/cherab/core/beam/node.pyx b/cherab/core/beam/node.pyx index 9fede133..ec25742b 100644 --- a/cherab/core/beam/node.pyx +++ b/cherab/core/beam/node.pyx @@ -144,6 +144,7 @@ cdef class Beam(Node): :ivar float sigma: The Gaussian beam width at the origin in m. :ivar float temperature: The broadening of the beam (eV). + .. code-block:: pycon >>> # This example shows how to initialise and populate a basic beam @@ -234,7 +235,21 @@ cdef class Beam(Node): cpdef Vector3D direction(self, double x, double y, double z): """ - Calculates the beam direction vector at a point in space. + Calculates the beam direction vector at a point in beam coordinate space. + + The beam direction (non-normalised) is calculated as follows (z > 0): + + :math:`e_x = x\\frac{(ztg(\\alpha_x))^2}{\\sigma^2 + (ztg(\\alpha_x))^2}`, + :math:`e_y = y\\frac{(ztg(\\alpha_y))^2}{\\sigma^2 + (ztg(\\alpha_y))^2}`, + :math:`e_z = z`, + + where :math:`\\sigma` is the Gaussian beam deviation at origin, + :math:`\\alpha_x` and :math:`\\alpha_y` are the beam divergence angles + in the x and y dimensions respectively. + + For z <= 0 the beam direction is (0, 0, 1). + + The function returns normalised beam direction. Note the values of the beam outside of the beam envelope should be treated with caution. diff --git a/cherab/core/model/attenuator/singleray.pyx b/cherab/core/model/attenuator/singleray.pyx index ca611d09..12904524 100644 --- a/cherab/core/model/attenuator/singleray.pyx +++ b/cherab/core/model/attenuator/singleray.pyx @@ -37,6 +37,21 @@ cimport cython # todo: attenuation calculation could be optimised further using memory views etc... cdef class SingleRayAttenuator(BeamAttenuator): + r""" + Calculates beam attenuation in the single-ray approximation. + Attenuation is calculated along the beam axis and extrapolated across the beam. + + :param double step: Distance between sample points along the beam axis in meters + for beam stopping calculation. Defaults to 0.01. + :param bint clamp_to_zero: Omptimises beam density calculation. + If True, the beam density outside the clamping range is zero. Defaults to False. + :param double clamp_sigma: The clamping range as a factor of beam :math:`\sigma(z)`. + Defaults to 5. + :param Beam beam: The beam instance to which this attenuator is attached. Defaults to None. + :param Plasma plasma: The plasma instance with which this beam interacts. Defaults to None. + :param AtomicData atomic_data: The atomic data provider class for this attenuator. + Defaults to None. + """ def __init__(self, double step=0.01, bint clamp_to_zero=False, double clamp_sigma=5.0, Beam beam=None, Plasma plasma=None, AtomicData atomic_data=None): @@ -86,10 +101,30 @@ cdef class SingleRayAttenuator(BeamAttenuator): @cython.cdivision(True) cpdef double density(self, double x, double y, double z) except? -1e999: - """ - Returns the beam density at the specified point. - - The point is specified in beam space. + r""" + Returns the beam density at the specified point in beam coordinate space. + The beam density is calculated as follows: + + :math:`n(x, y, z) = \frac{R}{2\pi v_0 \sigma_x\sigma_y} exp\left(-\frac{1}{2}\left(\frac{x^2}{\sigma_x^2}+\frac{y^2}{\sigma_y^2}\right)\right)exp\left(-\int_{0}^{z}\frac{S(z')}{v_0}dz'\right)`, + + :math:`\sigma_x = \sqrt{\sigma^2 + (ztg(\alpha_x))^2}\hspace{0.5cm}\sigma_y = \sqrt{\sigma^2 + (ztg(\alpha_y))^2}`, + + where :math:`R=\frac{P}{E}` is the particle rate of the beam defined as the power + of the beam divided by the kinetic energy of the single particle, :math:`v_0=\sqrt{2E/m}` + is the particle speed, :math:`\sigma` is the Gaussian beam deviation at origin, + :math:`\alpha_x` and :math:`\alpha_y` are the beam divergence angles in the x and y + dimensions respectively, :math:`S(z)` is the composite beam attenuation coefficient due to + collisional-radiative interaction with the plasma species: + + :math:`S(z) = \sum_{i=1}^{N}Z_i n_i S_i(E_{int}, n_{i,e}^{(eq)}, T_i)`, + :math:`n_{i,e}^{(eq)} = \frac{1}{Z_i}\sum_{j=1}^{N}Z_j^2 n_j`. + + Here :math:`Z_i` is the charge of the i-th type of plasma ions, + :math:`n_i` is density of the i-th type of plasma ions, :math:`N` is the number of type of plasma + ions, :math:`E_{int}` is the kinetic energy of the beam atoms in the frame of reference where + ions of the i-th type are at rest, :math:`T_{i}` is the temperature of ions of the i-th type. + + The values of partial beam attenuation coefficients, :math:`S_i`, are provided by the atomic data source. :param x: x coordinate in meters. :param y: y coordinate in meters. diff --git a/docs/source/models/beam/beam_attenuator.rst b/docs/source/models/beam/beam_attenuator.rst new file mode 100644 index 00000000..d0cfceb7 --- /dev/null +++ b/docs/source/models/beam/beam_attenuator.rst @@ -0,0 +1,10 @@ + +Beam Attenuation +---------------- + + +Single Ray Attenuator +^^^^^^^^^^^^^^^^^^^^^ + +.. autoclass:: cherab.core.model.attenuator.singleray.SingleRayAttenuator + :members: diff --git a/docs/source/models/cxs/cxs_model.rst b/docs/source/models/cxs/cxs_model.rst index a211801c..b069c522 100644 --- a/docs/source/models/cxs/cxs_model.rst +++ b/docs/source/models/cxs/cxs_model.rst @@ -2,15 +2,6 @@ CXS models ---------- -CXS models. - - -Single Ray Attenuator -^^^^^^^^^^^^^^^^^^^^^ - -.. autoclass:: cherab.core.model.attenuator.singleray.SingleRayAttenuator - :members: - CXS Beam Plasma Intersection ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ diff --git a/docs/source/models/emission_models.rst b/docs/source/models/emission_models.rst index 3a2c3b9c..52c76e19 100644 --- a/docs/source/models/emission_models.rst +++ b/docs/source/models/emission_models.rst @@ -6,6 +6,7 @@ Cherab contains a number of independent physics models for spectroscopic emissio .. toctree:: custom_models + beam/beam_attenuator cxs/cxs_model cxs/charge_exchange_calculation bes/bes_model diff --git a/docs/source/plasmas/particle_beams.rst b/docs/source/plasmas/particle_beams.rst index 615358a3..cc9de35a 100644 --- a/docs/source/plasmas/particle_beams.rst +++ b/docs/source/plasmas/particle_beams.rst @@ -2,7 +2,7 @@ Mono-energetic Particle Beams ============================= -.. autoclass:: cherab.core.Beam +.. autoclass:: cherab.core.beam.node.Beam :members: From 70b188babca4aa58b00301e042fede09a594daaa Mon Sep 17 00:00:00 2001 From: vsnever Date: Fri, 10 May 2024 17:30:39 +0200 Subject: [PATCH 4/9] Highlighted the line about beam density and direction change in CHANGELOG.md. --- CHANGELOG.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/CHANGELOG.md b/CHANGELOG.md index caeae178..b4db5b0a 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -13,7 +13,7 @@ New: * Replace the coarse numerical constant in the Bremsstrahlung model with an exact expression. (#409) * Add the kind attribute to RayTransferPipelineXD that determines whether the ray transfer matrix is multiplied by sensitivity ('power') or not ('radiance'). (#412) * Improved parsing of metadata from the ADAS ADF15 'bnd' files for H-like ions. Raises a runtime error if the metadata cannot be parsed. (#424) -* Beam dispersion calculation has changed from sigma(z) = sigma + z * tan(alpha) to sigma(z) = sqrt(sigma^2 + (z * tan(alpha))^2) for consistancy with the Gaussian beam model. Attention!!! The results of BES and CX spectroscopy are affected by this change. (#414) +* **Beam dispersion calculation has changed from sigma(z) = sigma + z * tan(alpha) to sigma(z) = sqrt(sigma^2 + (z * tan(alpha))^2) for consistancy with the Gaussian beam model. Attention!!! The results of BES and CX spectroscopy are affected by this change. (#414)** * Improved beam direction calculation to allow for natural broadening of the BES line shape due to beam divergence. (#414) Bug fixes: From 9a9a1919ba84ad1d905cd132ba50139a26e4f881 Mon Sep 17 00:00:00 2001 From: vsnever Date: Sat, 11 May 2024 21:54:28 +0200 Subject: [PATCH 5/9] Added tests for the beam density and direction calculation. --- cherab/core/tests/test_beam.py | 156 +++++++++++++++++++++++++++++++++ 1 file changed, 156 insertions(+) create mode 100644 cherab/core/tests/test_beam.py diff --git a/cherab/core/tests/test_beam.py b/cherab/core/tests/test_beam.py new file mode 100644 index 00000000..9be75996 --- /dev/null +++ b/cherab/core/tests/test_beam.py @@ -0,0 +1,156 @@ +# Copyright 2016-2023 Euratom +# Copyright 2016-2023 United Kingdom Atomic Energy Authority +# Copyright 2016-2023 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas +# +# Licensed under the EUPL, Version 1.1 or – as soon they will be approved by the +# European Commission - subsequent versions of the EUPL (the "Licence"); +# You may not use this work except in compliance with the Licence. +# You may obtain a copy of the Licence at: +# +# https://joinup.ec.europa.eu/software/page/eupl5 +# +# Unless required by applicable law or agreed to in writing, software distributed +# under the Licence is distributed on an "AS IS" basis, WITHOUT WARRANTIES OR +# CONDITIONS OF ANY KIND, either express or implied. +# +# See the Licence for the specific language governing permissions and limitations +# under the Licence. + +import unittest + +import numpy as np + +from raysect.core import World, Vector3D, translate + +from cherab.core import Beam +from cherab.core.atomic import AtomicData, BeamStoppingRate +from cherab.core.atomic import deuterium +from cherab.tools.plasmas.slab import build_constant_slab_plasma +from cherab.core.model import SingleRayAttenuator + +from cherab.core.utility import EvAmuToMS, EvToJ + + +class ConstantBeamStoppingRate(BeamStoppingRate): + """ + Constant beam CX PEC for test purpose. + """ + + def __init__(self, donor_metastable, value): + self.donor_metastable = donor_metastable + self.value = value + + def evaluate(self, energy, density, temperature): + + return self.value + + +class TestAtomicData(AtomicData): + """Fake atomic data for test purpose.""" + + def beam_stopping_rate(self, beam_ion, plasma_ion, charge): + + return ConstantBeamStoppingRate(1, 1.e-13) + + +class TestBeam(unittest.TestCase): + + atomic_data = TestAtomicData() + + world = World() + + plasma_density = 1.e19 + plasma_temperature = 1.e3 + plasma_species = [(deuterium, 1, plasma_density, plasma_temperature, Vector3D(0, 0, 0))] + plasma = build_constant_slab_plasma(length=1, width=1, height=1, electron_density=plasma_density, + electron_temperature=plasma_temperature, + plasma_species=plasma_species) + plasma.atomic_data = atomic_data + plasma.parent = world + + beam = Beam(transform=translate(0.5, 0, 0)) + beam.atomic_data = atomic_data + beam.plasma = plasma + beam.attenuator = SingleRayAttenuator(clamp_to_zero=True) + beam.energy = 50000 + beam.power = 1e6 + beam.temperature = 10 + beam.element = deuterium + beam.parent = world + beam.sigma = 0.2 + beam.divergence_x = 1. + beam.divergence_y = 2. + beam.length = 10. + + def test_beam_density(self): + + z0 = 0.8 + x0, y0 = 0.5, 0.5 + + density_on_axis = self.beam.density(0, 0, z0) + density_off_axis = self.beam.density(x0, y0, z0) + density_outside_beam = self.beam.density(0, 0, -1) + + # validating + + speed = EvAmuToMS.to(self.beam.energy) + # constant stopping rate + stopping_rate = self.atomic_data.beam_stopping_rate(deuterium, deuterium, 1)(0, 0, 0) + attenuation_factor = np.exp(-z0 * self.plasma_density * stopping_rate / speed) + + beam_particle_rate = self.beam.power / EvToJ.to(self.beam.energy * deuterium.atomic_weight) + + sigma0_sqr = self.beam.sigma**2 + tanxdiv = np.tan(np.deg2rad(self.beam.divergence_x)) + tanydiv = np.tan(np.deg2rad(self.beam.divergence_y)) + sigma_x = np.sqrt(sigma0_sqr + (z0 * tanxdiv)**2) + sigma_y = np.sqrt(sigma0_sqr + (z0 * tanydiv)**2) + + norm_radius_sqr = ((x0 / sigma_x)**2 + (y0 / sigma_y)**2) + + gaussian_sample_on_axis = 1. / (2 * np.pi * sigma_x * sigma_y) + gaussian_sample_off_axis = np.exp(-0.5 * norm_radius_sqr) / (2 * np.pi * sigma_x * sigma_y) + + test_density_on_axis = beam_particle_rate / speed * gaussian_sample_on_axis * attenuation_factor + test_density_off_axis = beam_particle_rate / speed * gaussian_sample_off_axis * attenuation_factor + + self.assertAlmostEqual(density_on_axis / test_density_on_axis, 1., delta=1.e-12, + msg='Beam.density() gives a wrong value on the beam axis.') + self.assertAlmostEqual(density_off_axis / test_density_off_axis, 1., delta=1.e-12, + msg='Beam.density() gives a wrong value off the beam axis.') + self.assertEqual(density_outside_beam, 0, + msg='Beam.density() gives a non-zero value outside beam.') + + def test_beam_direction(self): + # setting up the model + + z0 = 0.8 + x0, y0 = 0.5, 0.5 + + direction_on_axis = self.beam.direction(0, 0, z0) + direction_off_axis = self.beam.direction(x0, y0, z0) + direction_outside_beam = self.beam.direction(0, 0, -1) + + # validating + + sigma0_sqr = self.beam.sigma**2 + z_tanx_sqr = (z0 * np.tan(np.deg2rad(self.beam.divergence_x)))**2 + z_tany_sqr = (z0 * np.tan(np.deg2rad(self.beam.divergence_y)))**2 + + ex = x0 * z_tanx_sqr / (sigma0_sqr + z_tanx_sqr) + ey = y0 * z_tany_sqr / (sigma0_sqr + z_tany_sqr) + ez = z0 + + test_direction_off_axis = Vector3D(ex, ey, ez).normalise() + + self.assertEqual(direction_on_axis, Vector3D(0, 0, 1), + msg='Beam.density() gives a wrong value on the beam axis.') + for v, test_v in zip(direction_off_axis, test_direction_off_axis): + self.assertAlmostEqual(v, test_v, delta=1.e-12, + msg='Beam.direction() gives a wrong value off the beam axis.') + self.assertEqual(direction_outside_beam, Vector3D(0, 0, 1), + msg='Beam.density() gives a non-zero value outside beam.') + + +if __name__ == '__main__': + unittest.main() From b2f4bac7905cd911877135b497347afa5b8a12fd Mon Sep 17 00:00:00 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b/docs/source/plasmas/particle_beams.rst @@ -5,4 +5,8 @@ Mono-energetic Particle Beams .. autoclass:: cherab.core.beam.node.Beam :members: +.. figure:: ./beam_direction.png + :align: center + The beam direction pattern in XZ-plane for the beam with ``sigma`` = 0.1 m + and ``divergence_x`` = 5 :math:`^{\circ}`. From e91e2a48cc93a3a527a2634c2e46d61167737862 Mon Sep 17 00:00:00 2001 From: vsnever Date: Mon, 13 May 2024 13:03:22 +0200 Subject: [PATCH 7/9] Placed the equations for the beam density and direction in the math block instead of inline. --- cherab/core/beam/node.pyx | 9 +++++--- cherab/core/model/attenuator/singleray.pyx | 27 ++++++++++++---------- 2 files changed, 21 insertions(+), 15 deletions(-) diff --git a/cherab/core/beam/node.pyx b/cherab/core/beam/node.pyx index ec25742b..9c3cff65 100644 --- a/cherab/core/beam/node.pyx +++ b/cherab/core/beam/node.pyx @@ -239,9 +239,12 @@ cdef class Beam(Node): The beam direction (non-normalised) is calculated as follows (z > 0): - :math:`e_x = x\\frac{(ztg(\\alpha_x))^2}{\\sigma^2 + (ztg(\\alpha_x))^2}`, - :math:`e_y = y\\frac{(ztg(\\alpha_y))^2}{\\sigma^2 + (ztg(\\alpha_y))^2}`, - :math:`e_z = z`, + .. math:: + e_x = x\\frac{(ztg(\\alpha_x))^2}{\\sigma^2 + (ztg(\\alpha_x))^2}, + + e_y = y\\frac{(ztg(\\alpha_y))^2}{\\sigma^2 + (ztg(\\alpha_y))^2}, + + e_z = z, where :math:`\\sigma` is the Gaussian beam deviation at origin, :math:`\\alpha_x` and :math:`\\alpha_y` are the beam divergence angles diff --git a/cherab/core/model/attenuator/singleray.pyx b/cherab/core/model/attenuator/singleray.pyx index 12904524..54672766 100644 --- a/cherab/core/model/attenuator/singleray.pyx +++ b/cherab/core/model/attenuator/singleray.pyx @@ -101,23 +101,26 @@ cdef class SingleRayAttenuator(BeamAttenuator): @cython.cdivision(True) cpdef double density(self, double x, double y, double z) except? -1e999: - r""" + """ Returns the beam density at the specified point in beam coordinate space. The beam density is calculated as follows: - - :math:`n(x, y, z) = \frac{R}{2\pi v_0 \sigma_x\sigma_y} exp\left(-\frac{1}{2}\left(\frac{x^2}{\sigma_x^2}+\frac{y^2}{\sigma_y^2}\right)\right)exp\left(-\int_{0}^{z}\frac{S(z')}{v_0}dz'\right)`, - - :math:`\sigma_x = \sqrt{\sigma^2 + (ztg(\alpha_x))^2}\hspace{0.5cm}\sigma_y = \sqrt{\sigma^2 + (ztg(\alpha_y))^2}`, - - where :math:`R=\frac{P}{E}` is the particle rate of the beam defined as the power - of the beam divided by the kinetic energy of the single particle, :math:`v_0=\sqrt{2E/m}` - is the particle speed, :math:`\sigma` is the Gaussian beam deviation at origin, - :math:`\alpha_x` and :math:`\alpha_y` are the beam divergence angles in the x and y + + .. math:: + n(x, y, z) = \\frac{R}{2\\pi v_0 \\sigma_x\\sigma_y} exp\\left(-\\frac{1}{2}\\left(\\frac{x^2}{\\sigma_x^2}+\\frac{y^2}{\\sigma_y^2}\\right)\\right)exp\\left(-\\int_{0}^{z}\\frac{S(z')}{v_0}dz'\\right), + + \\sigma_x = \\sqrt{\\sigma^2 + (ztg(\\alpha_x))^2}\\hspace{0.5cm}\\sigma_y = \\sqrt{\\sigma^2 + (ztg(\\alpha_y))^2}, + + where :math:`R=\\frac{P}{E}` is the particle rate of the beam defined as the power + of the beam divided by the kinetic energy of the single particle, :math:`v_0=\\sqrt{2E/m}` + is the particle speed, :math:`\\sigma` is the Gaussian beam deviation at origin, + :math:`\\alpha_x` and :math:`\\alpha_y` are the beam divergence angles in the x and y dimensions respectively, :math:`S(z)` is the composite beam attenuation coefficient due to collisional-radiative interaction with the plasma species: - :math:`S(z) = \sum_{i=1}^{N}Z_i n_i S_i(E_{int}, n_{i,e}^{(eq)}, T_i)`, - :math:`n_{i,e}^{(eq)} = \frac{1}{Z_i}\sum_{j=1}^{N}Z_j^2 n_j`. + .. math:: + S(z) = \\sum_{i=1}^{N}Z_i n_i S_i(E_{int}, n_{i,e}^{(eq)}, T_i), + + n_{i,e}^{(eq)} = \\frac{1}{Z_i}\\sum_{j=1}^{N}Z_j^2 n_j. Here :math:`Z_i` is the charge of the i-th type of plasma ions, :math:`n_i` is density of the i-th type of plasma ions, :math:`N` is the number of type of plasma From 753d7de67ccca95ea40fdb579d9e7882c8322997 Mon Sep 17 00:00:00 2001 From: vsnever Date: Tue, 14 May 2024 17:04:05 +0200 Subject: [PATCH 8/9] Converted docstrings to raw string format. --- cherab/core/beam/node.pyx | 10 +++++----- cherab/core/model/attenuator/singleray.pyx | 18 +++++++++--------- 2 files changed, 14 insertions(+), 14 deletions(-) diff --git a/cherab/core/beam/node.pyx b/cherab/core/beam/node.pyx index 9c3cff65..32d7291d 100644 --- a/cherab/core/beam/node.pyx +++ b/cherab/core/beam/node.pyx @@ -234,20 +234,20 @@ cdef class Beam(Node): return self._attenuator.density(x, y, z) cpdef Vector3D direction(self, double x, double y, double z): - """ + r""" Calculates the beam direction vector at a point in beam coordinate space. The beam direction (non-normalised) is calculated as follows (z > 0): .. math:: - e_x = x\\frac{(ztg(\\alpha_x))^2}{\\sigma^2 + (ztg(\\alpha_x))^2}, + e_x = x\frac{(ztg(\alpha_x))^2}{\sigma^2 + (ztg(\alpha_x))^2}, - e_y = y\\frac{(ztg(\\alpha_y))^2}{\\sigma^2 + (ztg(\\alpha_y))^2}, + e_y = y\frac{(ztg(\alpha_y))^2}{\sigma^2 + (ztg(\alpha_y))^2}, e_z = z, - where :math:`\\sigma` is the Gaussian beam deviation at origin, - :math:`\\alpha_x` and :math:`\\alpha_y` are the beam divergence angles + where :math:`\sigma` is the Gaussian beam deviation at origin, + :math:`\alpha_x` and :math:`\alpha_y` are the beam divergence angles in the x and y dimensions respectively. For z <= 0 the beam direction is (0, 0, 1). diff --git a/cherab/core/model/attenuator/singleray.pyx b/cherab/core/model/attenuator/singleray.pyx index 54672766..3c86fb06 100644 --- a/cherab/core/model/attenuator/singleray.pyx +++ b/cherab/core/model/attenuator/singleray.pyx @@ -101,26 +101,26 @@ cdef class SingleRayAttenuator(BeamAttenuator): @cython.cdivision(True) cpdef double density(self, double x, double y, double z) except? -1e999: - """ + r""" Returns the beam density at the specified point in beam coordinate space. The beam density is calculated as follows: .. math:: - n(x, y, z) = \\frac{R}{2\\pi v_0 \\sigma_x\\sigma_y} exp\\left(-\\frac{1}{2}\\left(\\frac{x^2}{\\sigma_x^2}+\\frac{y^2}{\\sigma_y^2}\\right)\\right)exp\\left(-\\int_{0}^{z}\\frac{S(z')}{v_0}dz'\\right), + n(x, y, z) = \frac{R}{2\pi v_0 \sigma_x\sigma_y} exp\left(-\frac{1}{2}\left(\frac{x^2}{\sigma_x^2}+\frac{y^2}{\sigma_y^2}\right)\right)exp\left(-\int_{0}^{z}\frac{S(z')}{v_0}dz'\right), - \\sigma_x = \\sqrt{\\sigma^2 + (ztg(\\alpha_x))^2}\\hspace{0.5cm}\\sigma_y = \\sqrt{\\sigma^2 + (ztg(\\alpha_y))^2}, + \sigma_x = \sqrt{\sigma^2 + (ztg(\alpha_x))^2}\hspace{0.5cm}\sigma_y = \sqrt{\sigma^2 + (ztg(\alpha_y))^2}, - where :math:`R=\\frac{P}{E}` is the particle rate of the beam defined as the power - of the beam divided by the kinetic energy of the single particle, :math:`v_0=\\sqrt{2E/m}` - is the particle speed, :math:`\\sigma` is the Gaussian beam deviation at origin, - :math:`\\alpha_x` and :math:`\\alpha_y` are the beam divergence angles in the x and y + where :math:`R=\frac{P}{E}` is the particle rate of the beam defined as the power + of the beam divided by the kinetic energy of the single particle, :math:`v_0=\sqrt{2E/m}` + is the particle speed, :math:`\sigma` is the Gaussian beam deviation at origin, + :math:`\alpha_x` and :math:`\alpha_y` are the beam divergence angles in the x and y dimensions respectively, :math:`S(z)` is the composite beam attenuation coefficient due to collisional-radiative interaction with the plasma species: .. math:: - S(z) = \\sum_{i=1}^{N}Z_i n_i S_i(E_{int}, n_{i,e}^{(eq)}, T_i), + S(z) = \sum_{i=1}^{N}Z_i n_i S_i(E_{int}, n_{i,e}^{(eq)}, T_i), - n_{i,e}^{(eq)} = \\frac{1}{Z_i}\\sum_{j=1}^{N}Z_j^2 n_j. + n_{i,e}^{(eq)} = \frac{1}{Z_i}\sum_{j=1}^{N}Z_j^2 n_j. Here :math:`Z_i` is the charge of the i-th type of plasma ions, :math:`n_i` is density of the i-th type of plasma ions, :math:`N` is the number of type of plasma From a433d5f5136968be2a6cd0906010e9b524e5e654 Mon Sep 17 00:00:00 2001 From: vsnever Date: Tue, 14 May 2024 17:05:17 +0200 Subject: [PATCH 9/9] Rename TestAtomicData to MockAtomicData to avoid unittest warnings. --- cherab/core/tests/test_beam.py | 4 ++-- cherab/core/tests/test_beamcxline.py | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/cherab/core/tests/test_beam.py b/cherab/core/tests/test_beam.py index 9be75996..ef10126f 100644 --- a/cherab/core/tests/test_beam.py +++ b/cherab/core/tests/test_beam.py @@ -45,7 +45,7 @@ def evaluate(self, energy, density, temperature): return self.value -class TestAtomicData(AtomicData): +class MockAtomicData(AtomicData): """Fake atomic data for test purpose.""" def beam_stopping_rate(self, beam_ion, plasma_ion, charge): @@ -55,7 +55,7 @@ def beam_stopping_rate(self, beam_ion, plasma_ion, charge): class TestBeam(unittest.TestCase): - atomic_data = TestAtomicData() + atomic_data = MockAtomicData() world = World() diff --git a/cherab/core/tests/test_beamcxline.py b/cherab/core/tests/test_beamcxline.py index 6de8ad58..ccb0c855 100644 --- a/cherab/core/tests/test_beamcxline.py +++ b/cherab/core/tests/test_beamcxline.py @@ -58,7 +58,7 @@ def evaluate(self, energy, density, temperature): return self.value -class TestAtomicData(AtomicData): +class MockAtomicData(AtomicData): """Fake atomic data for test purpose.""" def beam_cx_pec(self, donor_ion, receiver_ion, receiver_charge, transition): @@ -78,7 +78,7 @@ class TestBeamCXLine(unittest.TestCase): world = World() - atomic_data = TestAtomicData() + atomic_data = MockAtomicData() plasma_species = [(deuterium, 1, 1.e19, 200., Vector3D(0, 0, 0))] plasma = build_constant_slab_plasma(length=1, width=1, height=1, electron_density=1e19, electron_temperature=200.,