From 4441e95b90781c11230e3879c6a26b8a9c8ebf30 Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Wed, 22 Dec 2021 09:55:25 -0500 Subject: [PATCH 01/28] Created basic class for polynomial profiles --- src/simsopt/mhd/profiles.py | 61 +++++++++++++++++++++++++++++++++++++ tests/mhd/test_profiles.py | 26 ++++++++++++++++ 2 files changed, 87 insertions(+) create mode 100644 src/simsopt/mhd/profiles.py create mode 100755 tests/mhd/test_profiles.py diff --git a/src/simsopt/mhd/profiles.py b/src/simsopt/mhd/profiles.py new file mode 100644 index 000000000..a0dd38578 --- /dev/null +++ b/src/simsopt/mhd/profiles.py @@ -0,0 +1,61 @@ +# coding: utf-8 +# Copyright (c) HiddenSymmetries Development Team. +# Distributed under the terms of the LGPL License + +""" +This module provides classes to handle radial profiles of density, +temperature, pressure, and other quantities that are flux functions. +""" + +import logging +import numpy as np +import numpy.polynomial.polynomial as poly +import matplotlib.pyplot as plt +from .._core.graph_optimizable import Optimizable + +logger = logging.getLogger(__name__) + +class Profile(Optimizable): + """ + Base class for radial profiles. This class should not be used + directly - use subclasses instead. + """ + + def __init__(self, *args, **kwargs): + super().__init__(*args, **kwargs) + + def plot(self, ax=None, show=True, n=100): + if ax is None: + fig = plt.figure() + ax = fig.add_subplot() + + s = np.linspace(0, 1, n) + ax.plot(s, self.f(s)) + plt.xlabel('Normalized toroidal flux $s$') + if show: + plt.show() + + +class ProfilePolynomial(Profile): + """ + A profile described by a polynomial in the normalized toroidal + flux s. The polynomial coefficients are dofs that are fixed by + default. + + Args: + data: 1D numpy array of the polynomial coefficients. + The first coefficient is the constant term, the next coefficient + is the linear term, etc. + """ + def __init__(self, data): + Optimizable.__init__(self, x0=np.array(data)) + self.fix_all() + + def f(self, s): + """ Return the value of the profile at specified points in s. """ + return poly.polyval(s, self.local_full_x) + + def dfds(self, s): + """ Return the d/ds derivative of the profile at specified points in s. """ + return poly.polyval(s, poly.polyder(self.local_full_x)) + diff --git a/tests/mhd/test_profiles.py b/tests/mhd/test_profiles.py new file mode 100755 index 000000000..673c0e65b --- /dev/null +++ b/tests/mhd/test_profiles.py @@ -0,0 +1,26 @@ +import unittest +import logging +import numpy as np +from simsopt.mhd.profiles import ProfilePolynomial + +logger = logging.getLogger(__name__) +#logging.basicConfig(level=logging.DEBUG) + +class ProfilesTests(unittest.TestCase): + def test_polynomial(self): + """ + Test the value and derivative of a polynomial profile + """ + # Function: f(s) = 3 * (1 - s^3) + prof = ProfilePolynomial([3, 0, 0, -3]) + s = np.linspace(0, 1, 10) + np.testing.assert_allclose(prof.f(s), 3 * (1 - s ** 3)) + np.testing.assert_allclose(prof.dfds(s), 3 * (- 3 * s ** 2)) + + def test_plot(self): + """ + Test the plotting function. + """ + # Function: f(s) = 3 * (1 - s^3) + prof = ProfilePolynomial([3, 0, 0, -3]) + prof.plot(show=False) From 769f4dedffd085b777944d1a538dc150ac9660eb Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Thu, 23 Dec 2021 11:19:25 -0500 Subject: [PATCH 02/28] Implemented calculation of trapped fraction --- src/simsopt/mhd/profiles.py | 131 +++++++++++++++++++++++++++++++++++- tests/mhd/test_profiles.py | 85 ++++++++++++++++++++++- 2 files changed, 212 insertions(+), 4 deletions(-) diff --git a/src/simsopt/mhd/profiles.py b/src/simsopt/mhd/profiles.py index a0dd38578..4caa49e14 100644 --- a/src/simsopt/mhd/profiles.py +++ b/src/simsopt/mhd/profiles.py @@ -10,11 +10,15 @@ import logging import numpy as np import numpy.polynomial.polynomial as poly +from scipy.interpolate import RectBivariateSpline +from scipy.optimize import minimize +from scipy.integrate import quad import matplotlib.pyplot as plt from .._core.graph_optimizable import Optimizable logger = logging.getLogger(__name__) + class Profile(Optimizable): """ Base class for radial profiles. This class should not be used @@ -47,8 +51,9 @@ class ProfilePolynomial(Profile): The first coefficient is the constant term, the next coefficient is the linear term, etc. """ + def __init__(self, data): - Optimizable.__init__(self, x0=np.array(data)) + super().__init__(x0=np.array(data)) self.fix_all() def f(self, s): @@ -58,4 +63,126 @@ def f(self, s): def dfds(self, s): """ Return the d/ds derivative of the profile at specified points in s. """ return poly.polyval(s, poly.polyder(self.local_full_x)) - + + +def compute_trapped_fraction(modB, sqrtg): + """ + Compute the effective fraction of trapped particles, which enters + several formulae for neoclassical transport, as well as several + quantities that go into its calculation. The input data can be + provided on a uniform grid of arbitrary toroidal and poloidal + angles that need not be straight-field-line angles. + + The effective inverse aspect ratio epsilon is defined by + + .. math:: + \frac{Bmax}{Bmin} = \frac{1 + \epsilon}{1 - \epsilon} + + This definition is motivated by the fact that this formula would + be true in the case of circular cross-section surfaces in + axisymmetry with :math:`B \propto 1/R` and :math:`R = (1 + + \epsilon \cos\theta) R_0`. + + Args: + modB: 3D array of size (ntheta, nphi, ns) representing |B|. + sqrtg: 3D array of size (ntheta, nphi, ns) representing the Jacobian. + Returns: + 3-element tuple containing three 1D arrays, corresponding to radial grid points + Bmin: minimum of |B| on each surface + Bmax: maximum of |B| on each surface + epsilon: A measure of the inverse aspect ratio + fsa_B2: , where < > denotes a flux surface average. + f_t: The effective trapped fraction + """ + ntheta = modB.shape[0] + nphi = modB.shape[1] + ns = modB.shape[2] + fourpisq = 4 * np.pi * np.pi + dVds = np.mean(sqrtg, axis=(0, 1)) / fourpisq + fsa_B2 = np.mean(modB * modB * sqrtg, axis=(0, 1)) / (fourpisq * dVds) + + epsilon = np.zeros(ns) + f_t = np.zeros(ns) + Bmin = np.zeros(ns) + Bmax = np.zeros(ns) + + # Make a slightly enlarged version of the input array with the + # first row and column appended at the ends, for periodicity. + modB_big = np.zeros((ntheta + 1, nphi + 1, ns)) + modB_big[:ntheta, :nphi, :] = modB + modB_big[-1, :nphi, :] = modB[0, :, :] + modB_big[:, -1, :] = modB_big[:, 0, :] + + theta = np.arange(ntheta + 1) + phi = np.arange(nphi + 1) + for js in range(ns): + index_of_min = np.unravel_index(np.argmin(modB_big[:, :, js]), modB_big.shape[:2]) + index_of_max = np.unravel_index(np.argmax(modB_big[:, :, js]), modB_big.shape[:2]) + modB_spline = RectBivariateSpline(theta, phi, modB_big[:, :, js]) + soln = minimize(lambda x: np.ravel(modB_spline(x[0], x[1])), + index_of_min, + bounds=((0, ntheta), (0, nphi))) + modBmin = soln.fun + soln = minimize(lambda x: -np.ravel(modB_spline(x[0], x[1])), + index_of_max, + bounds=((0, ntheta), (0, nphi))) + modBmax = -soln.fun + Bmin[js] = modBmin + Bmax[js] = modBmax + w = modBmax / modBmin + epsilon[js] = (w - 1) / (w + 1) + + def integrand(lambd): + # This function gives lambda / : + return lambd / (np.mean(np.sqrt(1 - lambd * modB[:, :, js]) * sqrtg[:, :, js]) \ + / (fourpisq * dVds[js])) + + integral = quad(integrand, 0, 1 / modBmax) + f_t[js] = 1 - 0.75 * fsa_B2[js] * integral[0] + + return Bmin, Bmax, epsilon, fsa_B2, f_t + + +def quasisymmetry_filtered_trapped_fraction(booz, helicity_m, helicity_n): + """ + Compute quantities needed for the Redl bootstrap current formula. + + Args: + booz: An instance of :obj:`simsopt.mhd.boozer.Boozer` + helicity_m: The poloidal mode number of the desired symmetry, usually 1. + helicity_n: The toroidal mode number of the desired symmetry. + Returns: + 3-element tuple containing three 1D arrays, corresponding to radial grid points + epsilon: A measure of the inverse aspect ratio + fsa_B2: , where < > denotes a flux surface average. + f_t: The effective trapped fraction + """ + pass + + +def j_dot_B_Redl(booz, ne, Te, Ti, Zeff, R, iota): + """ + Compute the bootstrap current using the formulae in Redl et al, + Physics of Plasmas (2021). + + The quantity is computed at all surfaces s that are + available in the booz object. + + The profiles of ne, Te, Ti, and Zeff should all be Profile + objects, meaning they have ``f()`` and ``dfds()`` functions. If + Zeff==None, a constant 1 is assumed. If Zeff is a float, a + constant profile will be assumed. + + Args: + booz: An instance of :obj:`simsopt.mhd.boozer.Boozer` + ne: A + Returns: + jdotB: + """ + if Zeff == None: + Zeff = ProfilePolynomial(1.0) + if not isinstance(Zeff, Profile): + # Zeff is presumably a number. Convert it to a constant profile. + Zeff = ProfilePolynomial(Zeff) + + booz.run() diff --git a/tests/mhd/test_profiles.py b/tests/mhd/test_profiles.py index 673c0e65b..9e5d74843 100755 --- a/tests/mhd/test_profiles.py +++ b/tests/mhd/test_profiles.py @@ -1,11 +1,12 @@ import unittest import logging import numpy as np -from simsopt.mhd.profiles import ProfilePolynomial +from simsopt.mhd.profiles import ProfilePolynomial, compute_trapped_fraction logger = logging.getLogger(__name__) #logging.basicConfig(level=logging.DEBUG) + class ProfilesTests(unittest.TestCase): def test_polynomial(self): """ @@ -16,7 +17,7 @@ def test_polynomial(self): s = np.linspace(0, 1, 10) np.testing.assert_allclose(prof.f(s), 3 * (1 - s ** 3)) np.testing.assert_allclose(prof.dfds(s), 3 * (- 3 * s ** 2)) - + def test_plot(self): """ Test the plotting function. @@ -24,3 +25,83 @@ def test_plot(self): # Function: f(s) = 3 * (1 - s^3) prof = ProfilePolynomial([3, 0, 0, -3]) prof.plot(show=False) + + +class RedlBootstrapTests(unittest.TestCase): + def test_compute_trapped_fraction(self): + ns = 2 + ntheta = 15 + nphi = 7 + nfp = 3 + modB = np.zeros((ntheta, nphi, ns)) + sqrtg = np.zeros((ntheta, nphi, ns)) + + theta1d = np.linspace(0, 2 * np.pi, ntheta, endpoint=False) + phi1d = np.linspace(0, 2 * np.pi / nfp, nphi, endpoint=False) + phi, theta = np.meshgrid(phi1d, theta1d) + + sqrtg[:, :, 0] = 10.0 + sqrtg[:, :, 1] = -25.0 + + modB[:, :, 0] = 13.0 + 2.6 * np.cos(theta) + modB[:, :, 1] = 9.0 + 3.7 * np.sin(theta - nfp * phi) + + Bmin, Bmax, epsilon, fsa_b2, f_t = compute_trapped_fraction(modB, sqrtg) + # The average of (b0 + b1 cos(theta))^2 is b0^2 + (1/2) * b1^2 + np.testing.assert_allclose(fsa_b2, [13.0 ** 2 + 0.5 * 2.6 ** 2, 9.0 ** 2 + 0.5 * 3.7 ** 2]) + np.testing.assert_allclose(Bmin, [13.0 - 2.6, 9.0 - 3.7], rtol=1e-4) + np.testing.assert_allclose(Bmax, [13.0 + 2.6, 9.0 + 3.7], rtol=1e-4) + np.testing.assert_allclose(epsilon, [2.6 / 13.0, 3.7 / 9.0], rtol=1e-3) + print('f_t:', f_t) + + def test_trapped_fraction_Kim(self): + """ + Compare the trapped fraction to eq (C18) in Kim, Diamond, & + Groebner, Physics of Fluids B 3, 2050 (1991) + """ + ns = 50 + ntheta = 100 + nphi = 3 + B0 = 7.5 + epsilon_in = np.linspace(0, 1, ns, endpoint=False) # Avoid divide-by-0 when epsilon=1 + theta1d = np.linspace(0, 2 * np.pi, ntheta, endpoint=False) + nfp = 3 + phi1d = np.linspace(0, 2 * np.pi / nfp, nphi, endpoint=False) + #phi1d = np.array([0]) + phi, theta = np.meshgrid(phi1d, theta1d) + modB = np.zeros((ntheta, nphi, ns)) + sqrtg = np.zeros((ntheta, nphi, ns)) + for js in range(ns): + # Eq (A6) + modB[:, :, js] = B0 / (1 + epsilon_in[js] * np.cos(theta)) + # For Jacobian, use eq (A7) for the theta dependence, + # times an arbitrary overall scale factor + sqrtg[:, :, js] = 6.7 * (1 + epsilon_in[js] * np.cos(theta)) + Bmin, Bmax, epsilon_out, fsa_B2, f_t = compute_trapped_fraction(modB, sqrtg) + + f_t_Kim = 1.46 * np.sqrt(epsilon_in) - 0.46 * epsilon_in # Eq (C18) in Kim et al + + np.testing.assert_allclose(Bmin, B0 / (1 + epsilon_in)) + np.testing.assert_allclose(Bmax, B0 / (1 - epsilon_in)) + np.testing.assert_allclose(epsilon_in, epsilon_out) + # Eq (A8): + np.testing.assert_allclose(fsa_B2, B0 * B0 / np.sqrt(1 - epsilon_in ** 2), rtol=1e-6) + np.testing.assert_allclose(f_t, f_t_Kim, rtol=0.1, atol=0.07) # We do not expect precise agreement. + + if False: + import matplotlib.pyplot as plt + plt.figure(figsize=(14, 5)) + plt.subplot(1, 2, 1) + plt.plot(epsilon_in, f_t, label='simsopt') + plt.plot(epsilon_in, f_t_Kim, label='Kim') + plt.xlabel('epsilon') + plt.title('Trapped fraction $f_t$') + plt.legend(loc=0) + + plt.subplot(1, 2, 2) + #plt.plot(epsilon_in, (f_t_Kim - f_t) / (1 - f_t)) + plt.plot(epsilon_in, f_t_Kim - f_t) + plt.title('Relative difference in $f_c$') + #plt.plot(epsilon_in, epsilon_out, 'r') + #plt.plot(epsilon_in, epsilon_in, ':k') + plt.show() From 4846c5d3fd26d5eac8b2539d643b860286321c3d Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Thu, 23 Dec 2021 16:07:06 -0500 Subject: [PATCH 03/28] Coded up expressions in Redl paper --- src/simsopt/mhd/bootstrap.py | 286 +++++++++++++++++++ src/simsopt/mhd/profiles.py | 146 ++-------- tests/mhd/test_bootstrap.py | 104 +++++++ tests/mhd/test_profiles.py | 93 +----- tests/test_files/input.ITERModel | 34 +++ tests/test_files/wout_ITERModel_reference.nc | Bin 0 -> 99112 bytes 6 files changed, 467 insertions(+), 196 deletions(-) create mode 100644 src/simsopt/mhd/bootstrap.py create mode 100755 tests/mhd/test_bootstrap.py create mode 100644 tests/test_files/input.ITERModel create mode 100644 tests/test_files/wout_ITERModel_reference.nc diff --git a/src/simsopt/mhd/bootstrap.py b/src/simsopt/mhd/bootstrap.py new file mode 100644 index 000000000..58d379da8 --- /dev/null +++ b/src/simsopt/mhd/bootstrap.py @@ -0,0 +1,286 @@ +# coding: utf-8 +# Copyright (c) HiddenSymmetries Development Team. +# Distributed under the terms of the LGPL License + +""" +This module provides functions to compute the bootstrap current +""" + +import logging +import numpy as np +from scipy.interpolate import RectBivariateSpline, interp1d +from scipy.optimize import minimize +from scipy.integrate import quad +from .._core.util import Struct +from .profiles import Profile, ProfilePolynomial + +logger = logging.getLogger(__name__) + + +def compute_trapped_fraction(modB, sqrtg): + """ + Compute the effective fraction of trapped particles, which enters + several formulae for neoclassical transport, as well as several + quantities that go into its calculation. The input data can be + provided on a uniform grid of arbitrary toroidal and poloidal + angles that need not be straight-field-line angles. + + The effective inverse aspect ratio epsilon is defined by + + .. math:: + \frac{Bmax}{Bmin} = \frac{1 + \epsilon}{1 - \epsilon} + + This definition is motivated by the fact that this formula would + be true in the case of circular cross-section surfaces in + axisymmetry with :math:`B \propto 1/R` and :math:`R = (1 + + \epsilon \cos\theta) R_0`. + + Args: + modB: 3D array of size (ntheta, nphi, ns) representing |B|. + sqrtg: 3D array of size (ntheta, nphi, ns) representing the Jacobian. + Returns: + 3-element tuple containing three 1D arrays, corresponding to radial grid points + Bmin: minimum of |B| on each surface + Bmax: maximum of |B| on each surface + epsilon: A measure of the inverse aspect ratio + fsa_B2: , where < > denotes a flux surface average. + f_t: The effective trapped fraction + """ + ntheta = modB.shape[0] + nphi = modB.shape[1] + ns = modB.shape[2] + fourpisq = 4 * np.pi * np.pi + dVds = np.mean(sqrtg, axis=(0, 1)) / fourpisq + fsa_B2 = np.mean(modB * modB * sqrtg, axis=(0, 1)) / (fourpisq * dVds) + + epsilon = np.zeros(ns) + f_t = np.zeros(ns) + Bmin = np.zeros(ns) + Bmax = np.zeros(ns) + + # Make a slightly enlarged version of the input array with the + # first row and column appended at the ends, for periodicity. + modB_big = np.zeros((ntheta + 1, nphi + 1, ns)) + modB_big[:ntheta, :nphi, :] = modB + modB_big[-1, :nphi, :] = modB[0, :, :] + modB_big[:, -1, :] = modB_big[:, 0, :] + + theta = np.arange(ntheta + 1) + phi = np.arange(nphi + 1) + for js in range(ns): + index_of_min = np.unravel_index(np.argmin(modB_big[:, :, js]), modB_big.shape[:2]) + index_of_max = np.unravel_index(np.argmax(modB_big[:, :, js]), modB_big.shape[:2]) + modB_spline = RectBivariateSpline(theta, phi, modB_big[:, :, js]) + soln = minimize(lambda x: np.ravel(modB_spline(x[0], x[1])), + index_of_min, + bounds=((0, ntheta), (0, nphi))) + modBmin = soln.fun + soln = minimize(lambda x: -np.ravel(modB_spline(x[0], x[1])), + index_of_max, + bounds=((0, ntheta), (0, nphi))) + modBmax = -soln.fun + Bmin[js] = modBmin + Bmax[js] = modBmax + w = modBmax / modBmin + epsilon[js] = (w - 1) / (w + 1) + + def integrand(lambd): + # This function gives lambda / : + return lambd / (np.mean(np.sqrt(1 - lambd * modB[:, :, js]) * sqrtg[:, :, js]) \ + / (fourpisq * dVds[js])) + + integral = quad(integrand, 0, 1 / modBmax) + f_t[js] = 1 - 0.75 * fsa_B2[js] * integral[0] + + return Bmin, Bmax, epsilon, fsa_B2, f_t + + +def quasisymmetry_filtered_trapped_fraction(booz, helicity_m, helicity_n): + """ + Compute quantities needed for the Redl bootstrap current formula. + + Args: + booz: An instance of :obj:`simsopt.mhd.boozer.Boozer` + helicity_m: The poloidal mode number of the desired symmetry, usually 1. + helicity_n: The toroidal mode number of the desired symmetry. + Returns: + 3-element tuple containing three 1D arrays, corresponding to radial grid points + epsilon: A measure of the inverse aspect ratio + fsa_B2: , where < > denotes a flux surface average. + f_t: The effective trapped fraction + """ + pass + + +def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helicity_N): + """ + Compute the bootstrap current (specifically + :math:`\left<\vec{J}\cdot\vec{B}\right>`) using the formulae in + Redl et al, Physics of Plasmas (2021). + + The quantity is computed at all surfaces s that are + available in the booz object. + + The profiles of ne, Te, Ti, and Zeff should all be Profile + objects, meaning they have ``__call__`` and ``dfds()`` functions. If + Zeff==None, a constant 1 is assumed. If Zeff is a float, a + constant profile will be assumed. + + ne should have units of 1/m^3. Ti and Te should have units of eV. + + epsilon, f_t, iota, and R should be 1d arrays evaluated on the s grid. + + Args: + booz: An instance of :obj:`simsopt.mhd.boozer.Boozer` + ne: A + psi_edge: The toroidal flux in Webers divided by (2pi) at the boundary s=1 + Returns: + jdotB: + details: An object with intermediate quantities as attributes + """ + if Zeff == None: + Zeff = ProfilePolynomial(1.0) + if not isinstance(Zeff, Profile): + # Zeff is presumably a number. Convert it to a constant profile. + Zeff = ProfilePolynomial([Zeff]) + + # Evaluate profiles on the grid: + ne_s = ne(s) + Te_s = Te(s) + Ti_s = Ti(s) + Zeff_s = Zeff(s) + ni_s = ne_s / Zeff_s + pe_s = ne_s * Te_s + pi_s = ni_s * Ti_s + d_ne_d_s = ne.dfds(s) + d_Te_d_s = Te.dfds(s) + d_Ti_d_s = Ti.dfds(s) + + # Profiles may go to 0 at s=1, so exclude the last 2 grid points: + if np.any(ne_s[:-2] < 1e17): + logging.warning('ne is surprisingly low. It should have units 1/meters^3') + if np.any(Te_s[:-2] < 500): + logging.warning('Te is surprisingly low. It should have units of eV') + if np.any(Ti_s[:-2] < 50): + logging.warning('Ti is surprisingly low. It should have units of eV') + + # Eq (18d)-(18e) in Sauter. + # Check that we do not need to convert units of n or T! + ln_Lambda_e = 31.3 - np.log(np.sqrt(ne_s) / Te_s) + ln_Lambda_ii = 30 - np.log(Zeff_s ** 3 * np.sqrt(ni_s) / (Ti_s ** 1.5)) + logging.debug(f'ln Lambda_e: {ln_Lambda_e}') + logging.debug(f'ln Lambda_ii: {ln_Lambda_ii}') + + # Eq (18b)-(18c) in Sauter: + nu_e = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ + / (iota * Te_s * Te_s * (epsilon ** 1.5)) + nu_i = (4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ + / (iota * Ti_s * Ti_s * (epsilon ** 1.5)) + + # Redl eq (11): + X31 = f_t / (1 + (0.67 * (1 - 0.7 * f_t) * np.sqrt(nu_e)) / (0.56 + 0.44 * Zeff_s) \ + + (0.52 * 0.086 * np.sqrt(nu_e)) * (1 + 0.87 * f_t) * nu_e / (1 + 1.13 * np.sqrt(Zeff_s - 1))) + + # Redl eq (10): + Zfac = Zeff_s ** 1.2 - 0.71 + L31 = (1 + 0.15 / Zfac) * X31 \ + - 0.22 / Zfac * (X31 ** 2) \ + + 0.01 / Zfac * (X31 ** 3) \ + + 0.06 / Zfac * (X31 ** 4) + + # Redl eq (14): + X32e = f_t / ((1 + 0.23 * (1 - 0.96 * f_t) * np.sqrt(nu_e) / np.sqrt(Zeff_s) \ + + 0.13 * (1 - 0.38 * f_t) * nu_e / (Zeff_s * Zeff_s) \ + * (np.sqrt(1 + 2 * np.sqrt(Zeff_s - 1)) \ + + f_t * f_t * np.sqrt((0.075 + 0.25 * (Zeff_s - 1) ** 2) * nu_e)))) + + # Redl eq (13): + F32ee = (0.1 + 0.6 * Zeff_s) * (X32e - X32e ** 4) \ + / (Zeff_s * (0.77 + 0.63 * (1 + (Zeff_s - 1) ** 1.1))) \ + + 0.7 / (1 + 0.2 * Zeff_s) * (X32e ** 2 - X32e ** 4 - 1.2 * (X32e ** 3 - X32e ** 4)) \ + + 1.3 / (1 + 0.5 * Zeff_s) * (X32e ** 4) + + # Redl eq (16): + X32ei = f_t / (1 + 0.87 * (1 + 0.39 * f_t) * np.sqrt(nu_e) / (1 + 2.95 * (Zeff_s - 1) ** 2) \ + + 1.53 * (1 - 0.37 * f_t) * nu_e * (2 + 0.375 * (Zeff_s - 1))) + + # Redl eq (15): + F32ei = -(0.4 + 1.93 * Zeff_s) / (Zeff_s * (0.8 + 0.6 * Zeff_s)) * (X32ei - X32ei ** 4) \ + + 5.5 / (1.5 + 2 * Zeff_s) * (X32ei ** 2 - X32ei ** 4 - 0.8 * (X32ei ** 3 - X32ei ** 4)) \ + - 1.3 / (1 + 0.5 * Zeff_s) * (X32ei ** 4) + + # Redl eq (12): + L32 = F32ei + F32ee + + # Redl eq (19): + L34 = L31 + + # Redl eq (20): + alpha0 = -(0.62 + 0.055 * (Zeff_s - 1)) * (1 - f_t) \ + / ((0.53 + 0.17 * (Zeff_s - 1)) * (1 - (0.31 - 0.065 * (Zeff_s - 1)) * f_t - 0.25 * f_t * f_t)) + # Redl eq (21): + alpha = ((alpha0 + 0.7 * Zeff_s * np.sqrt(f_t * nu_i)) / (1 + 0.18 * np.sqrt(nu_i)) \ + - 0.002 * nu_i * nu_i * (f_t ** 6)) \ + / (1 + 0.004 * nu_i * nu_i * (f_t ** 6)) + + dnds_term = -G * (ne_s * Te_s + ni_s + Ti_s) * L31 * (d_ne_d_s / ne_s) / (psi_edge * (iota - helicity_N)) + dTeds_term = -G * pe_s * (L31 + L32) * (d_Te_d_s / Te_s) / (psi_edge * (iota - helicity_N)) + dTids_term = -G * pi_s * (L31 + L34 * alpha) * (d_Ti_d_s / Ti_s) / (psi_edge * (iota - helicity_N)) + jdotB = dnds_term + dTeds_term + dTids_term + + details = Struct() + variables = ['ln_Lambda_e', 'ln_Lambda_ii', 'nu_e', 'nu_i', + 'L31', 'L32', 'L34', 'alpha0', 'alpha', + 'dnds_term', 'dTeds_term', 'dTids_term'] + for v in variables: + details.__setattr__(v, eval(v)) + + return jdotB, details + + +def vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, ntheta=64, nphi=65): + """ + Evaluate the Redl bootstrap current formula for a vmec configuration. + """ + vmec.run() + + ns = len(surfaces) + nfp = vmec.wout.nfp + psi_edge = -vmec.wout.phi[-1] / (2 * np.pi) + + # First, interpolate in s to get the quantities we need on the surfaces we need. + method = 'linear' + + interp = interp1d(vmec.s_half_grid, vmec.wout.iotas[1:], fill_value="extrapolate") + iota = interp(surfaces) + + interp = interp1d(vmec.s_half_grid, vmec.wout.bvco[1:], fill_value="extrapolate") + G = interp(surfaces) + + interp = interp1d(vmec.s_half_grid, vmec.wout.gmnc[:, 1:], fill_value="extrapolate") + gmnc = interp(surfaces) + + interp = interp1d(vmec.s_half_grid, vmec.wout.bmnc[:, 1:], fill_value="extrapolate") + bmnc = interp(surfaces) + + theta1d = np.linspace(0, 2 * np.pi, ntheta, endpoint=False) + phi1d = np.linspace(0, 2 * np.pi / nfp, nphi, endpoint=False) + phi2d, theta2d = np.meshgrid(phi1d, theta1d) + phi3d = phi2d.reshape((ntheta, nphi, 1)) + theta3d = theta2d.reshape((ntheta, nphi, 1)) + + myshape = (ntheta, nphi, ns) + modB = np.zeros(myshape) + sqrtg = np.zeros(myshape) + for jmn in range(len(vmec.wout.xm_nyq)): + m = vmec.wout.xm_nyq[jmn] + n = vmec.wout.xn_nyq[jmn] + angle = m * theta3d - n * phi3d + cosangle = np.cos(angle) + sinangle = np.sin(angle) + modB += np.kron(bmnc[jmn, :].reshape((1, 1, ns)), cosangle) + sqrtg += np.kron(gmnc[jmn, :].reshape((1, 1, ns)), cosangle) + + Bmin, Bmax, epsilon, fsa_B2, f_t = compute_trapped_fraction(modB, sqrtg) + + return j_dot_B_Redl(surfaces, ne, Te, Ti, Zeff, vmec.wout.Rmajor_p, iota, G, epsilon, f_t, psi_edge, helicity_N) diff --git a/src/simsopt/mhd/profiles.py b/src/simsopt/mhd/profiles.py index 4caa49e14..9e44840cc 100644 --- a/src/simsopt/mhd/profiles.py +++ b/src/simsopt/mhd/profiles.py @@ -10,10 +10,6 @@ import logging import numpy as np import numpy.polynomial.polynomial as poly -from scipy.interpolate import RectBivariateSpline -from scipy.optimize import minimize -from scipy.integrate import quad -import matplotlib.pyplot as plt from .._core.graph_optimizable import Optimizable logger = logging.getLogger(__name__) @@ -28,7 +24,20 @@ class Profile(Optimizable): def __init__(self, *args, **kwargs): super().__init__(*args, **kwargs) + def __call__(self, *args, **kwargs): + """ Shortcut for calling f(s) """ + return self.f(*args, **kwargs) + def plot(self, ax=None, show=True, n=100): + """ + Plot the profile using matplotlib. + + Args: + ax: The axis object on which to plot. If ``None``, a new figure will be created. + show: Whether to call matplotlib's ``show()`` function. + n: The number of grid points in s to show. + """ + import matplotlib.pyplot as plt if ax is None: fig = plt.figure() ax = fig.add_subplot() @@ -65,124 +74,25 @@ def dfds(self, s): return poly.polyval(s, poly.polyder(self.local_full_x)) -def compute_trapped_fraction(modB, sqrtg): - """ - Compute the effective fraction of trapped particles, which enters - several formulae for neoclassical transport, as well as several - quantities that go into its calculation. The input data can be - provided on a uniform grid of arbitrary toroidal and poloidal - angles that need not be straight-field-line angles. - - The effective inverse aspect ratio epsilon is defined by - - .. math:: - \frac{Bmax}{Bmin} = \frac{1 + \epsilon}{1 - \epsilon} - - This definition is motivated by the fact that this formula would - be true in the case of circular cross-section surfaces in - axisymmetry with :math:`B \propto 1/R` and :math:`R = (1 + - \epsilon \cos\theta) R_0`. - - Args: - modB: 3D array of size (ntheta, nphi, ns) representing |B|. - sqrtg: 3D array of size (ntheta, nphi, ns) representing the Jacobian. - Returns: - 3-element tuple containing three 1D arrays, corresponding to radial grid points - Bmin: minimum of |B| on each surface - Bmax: maximum of |B| on each surface - epsilon: A measure of the inverse aspect ratio - fsa_B2: , where < > denotes a flux surface average. - f_t: The effective trapped fraction - """ - ntheta = modB.shape[0] - nphi = modB.shape[1] - ns = modB.shape[2] - fourpisq = 4 * np.pi * np.pi - dVds = np.mean(sqrtg, axis=(0, 1)) / fourpisq - fsa_B2 = np.mean(modB * modB * sqrtg, axis=(0, 1)) / (fourpisq * dVds) - - epsilon = np.zeros(ns) - f_t = np.zeros(ns) - Bmin = np.zeros(ns) - Bmax = np.zeros(ns) - - # Make a slightly enlarged version of the input array with the - # first row and column appended at the ends, for periodicity. - modB_big = np.zeros((ntheta + 1, nphi + 1, ns)) - modB_big[:ntheta, :nphi, :] = modB - modB_big[-1, :nphi, :] = modB[0, :, :] - modB_big[:, -1, :] = modB_big[:, 0, :] - - theta = np.arange(ntheta + 1) - phi = np.arange(nphi + 1) - for js in range(ns): - index_of_min = np.unravel_index(np.argmin(modB_big[:, :, js]), modB_big.shape[:2]) - index_of_max = np.unravel_index(np.argmax(modB_big[:, :, js]), modB_big.shape[:2]) - modB_spline = RectBivariateSpline(theta, phi, modB_big[:, :, js]) - soln = minimize(lambda x: np.ravel(modB_spline(x[0], x[1])), - index_of_min, - bounds=((0, ntheta), (0, nphi))) - modBmin = soln.fun - soln = minimize(lambda x: -np.ravel(modB_spline(x[0], x[1])), - index_of_max, - bounds=((0, ntheta), (0, nphi))) - modBmax = -soln.fun - Bmin[js] = modBmin - Bmax[js] = modBmax - w = modBmax / modBmin - epsilon[js] = (w - 1) / (w + 1) - - def integrand(lambd): - # This function gives lambda / : - return lambd / (np.mean(np.sqrt(1 - lambd * modB[:, :, js]) * sqrtg[:, :, js]) \ - / (fourpisq * dVds[js])) - - integral = quad(integrand, 0, 1 / modBmax) - f_t[js] = 1 - 0.75 * fsa_B2[js] * integral[0] - - return Bmin, Bmax, epsilon, fsa_B2, f_t - - -def quasisymmetry_filtered_trapped_fraction(booz, helicity_m, helicity_n): +class ProfileScaled(Profile): """ - Compute quantities needed for the Redl bootstrap current formula. + A Profile which is equivalent to another Profile object but scaled + by a constant. This constant is an optimizable dof, which is fixed by default. Args: - booz: An instance of :obj:`simsopt.mhd.boozer.Boozer` - helicity_m: The poloidal mode number of the desired symmetry, usually 1. - helicity_n: The toroidal mode number of the desired symmetry. - Returns: - 3-element tuple containing three 1D arrays, corresponding to radial grid points - epsilon: A measure of the inverse aspect ratio - fsa_B2: , where < > denotes a flux surface average. - f_t: The effective trapped fraction + base: A Profile object to scale + scalefac: A number by which the base profile will be scaled. """ - pass + def __init__(self, base, scalefac): + self.base = base + super().__init__(x0=np.array([scalefac]), names=['scalefac']) + self.fix_all() -def j_dot_B_Redl(booz, ne, Te, Ti, Zeff, R, iota): - """ - Compute the bootstrap current using the formulae in Redl et al, - Physics of Plasmas (2021). - - The quantity is computed at all surfaces s that are - available in the booz object. - - The profiles of ne, Te, Ti, and Zeff should all be Profile - objects, meaning they have ``f()`` and ``dfds()`` functions. If - Zeff==None, a constant 1 is assumed. If Zeff is a float, a - constant profile will be assumed. - - Args: - booz: An instance of :obj:`simsopt.mhd.boozer.Boozer` - ne: A - Returns: - jdotB: - """ - if Zeff == None: - Zeff = ProfilePolynomial(1.0) - if not isinstance(Zeff, Profile): - # Zeff is presumably a number. Convert it to a constant profile. - Zeff = ProfilePolynomial(Zeff) + def f(self, s): + """ Return the value of the profile at specified points in s. """ + return self.local_full_x[0] * self.base.f(s) - booz.run() + def dfds(self, s): + """ Return the d/ds derivative of the profile at specified points in s. """ + return self.local_full_x[0] * self.base.dfds(s) diff --git a/tests/mhd/test_bootstrap.py b/tests/mhd/test_bootstrap.py new file mode 100755 index 000000000..8f8c1d7d8 --- /dev/null +++ b/tests/mhd/test_bootstrap.py @@ -0,0 +1,104 @@ +import unittest +import logging +import os +import numpy as np +from simsopt.mhd.bootstrap import compute_trapped_fraction, vmec_j_dot_B_Redl +from simsopt.mhd.profiles import ProfilePolynomial +from simsopt.mhd.vmec import Vmec +from . import TEST_DIR + +logger = logging.getLogger(__name__) +#logging.basicConfig(level=logging.DEBUG) + + +class BootstrapTests(unittest.TestCase): + def test_compute_trapped_fraction(self): + ns = 2 + ntheta = 15 + nphi = 7 + nfp = 3 + modB = np.zeros((ntheta, nphi, ns)) + sqrtg = np.zeros((ntheta, nphi, ns)) + + theta1d = np.linspace(0, 2 * np.pi, ntheta, endpoint=False) + phi1d = np.linspace(0, 2 * np.pi / nfp, nphi, endpoint=False) + phi, theta = np.meshgrid(phi1d, theta1d) + + sqrtg[:, :, 0] = 10.0 + sqrtg[:, :, 1] = -25.0 + + modB[:, :, 0] = 13.0 + 2.6 * np.cos(theta) + modB[:, :, 1] = 9.0 + 3.7 * np.sin(theta - nfp * phi) + + Bmin, Bmax, epsilon, fsa_b2, f_t = compute_trapped_fraction(modB, sqrtg) + # The average of (b0 + b1 cos(theta))^2 is b0^2 + (1/2) * b1^2 + np.testing.assert_allclose(fsa_b2, [13.0 ** 2 + 0.5 * 2.6 ** 2, 9.0 ** 2 + 0.5 * 3.7 ** 2]) + np.testing.assert_allclose(Bmin, [13.0 - 2.6, 9.0 - 3.7], rtol=1e-4) + np.testing.assert_allclose(Bmax, [13.0 + 2.6, 9.0 + 3.7], rtol=1e-4) + np.testing.assert_allclose(epsilon, [2.6 / 13.0, 3.7 / 9.0], rtol=1e-3) + + def test_trapped_fraction_Kim(self): + """ + Compare the trapped fraction to eq (C18) in Kim, Diamond, & + Groebner, Physics of Fluids B 3, 2050 (1991) + """ + ns = 50 + ntheta = 100 + nphi = 3 + B0 = 7.5 + epsilon_in = np.linspace(0, 1, ns, endpoint=False) # Avoid divide-by-0 when epsilon=1 + theta1d = np.linspace(0, 2 * np.pi, ntheta, endpoint=False) + nfp = 3 + phi1d = np.linspace(0, 2 * np.pi / nfp, nphi, endpoint=False) + #phi1d = np.array([0]) + phi, theta = np.meshgrid(phi1d, theta1d) + modB = np.zeros((ntheta, nphi, ns)) + sqrtg = np.zeros((ntheta, nphi, ns)) + for js in range(ns): + # Eq (A6) + modB[:, :, js] = B0 / (1 + epsilon_in[js] * np.cos(theta)) + # For Jacobian, use eq (A7) for the theta dependence, + # times an arbitrary overall scale factor + sqrtg[:, :, js] = 6.7 * (1 + epsilon_in[js] * np.cos(theta)) + Bmin, Bmax, epsilon_out, fsa_B2, f_t = compute_trapped_fraction(modB, sqrtg) + + f_t_Kim = 1.46 * np.sqrt(epsilon_in) - 0.46 * epsilon_in # Eq (C18) in Kim et al + + np.testing.assert_allclose(Bmin, B0 / (1 + epsilon_in)) + np.testing.assert_allclose(Bmax, B0 / (1 - epsilon_in)) + np.testing.assert_allclose(epsilon_in, epsilon_out) + # Eq (A8): + np.testing.assert_allclose(fsa_B2, B0 * B0 / np.sqrt(1 - epsilon_in ** 2), rtol=1e-6) + np.testing.assert_allclose(f_t, f_t_Kim, rtol=0.1, atol=0.07) # We do not expect precise agreement. + + if False: + import matplotlib.pyplot as plt + plt.figure(figsize=(14, 5)) + plt.subplot(1, 2, 1) + #plt.plot(epsilon_in, f_t, label='simsopt') + #plt.plot(epsilon_in, f_t_Kim, label='Kim') + plt.plot(np.sqrt(epsilon_in), f_t, label='simsopt') + plt.plot(np.sqrt(epsilon_in), f_t_Kim, label='Kim') + plt.xlabel('sqrt(epsilon)') + plt.title('Trapped fraction $f_t$') + plt.legend(loc=0) + + plt.subplot(1, 2, 2) + #plt.plot(epsilon_in, (f_t_Kim - f_t) / (1 - f_t)) + plt.plot(epsilon_in, f_t_Kim - f_t) + plt.title('Relative difference in $f_c$') + plt.xlabel('epsilon') + #plt.plot(epsilon_in, epsilon_out, 'r') + #plt.plot(epsilon_in, epsilon_in, ':k') + plt.show() + + def test_vmec_j_dot_B_Redl(self): + ne = ProfilePolynomial(1.0e20 * np.array([1, 0, -1])) + Te = ProfilePolynomial(25e3 * np.array([1, -1])) + Ti = Te + Zeff = 1 + surfaces = np.linspace(0, 1, 5, endpoint=False) + helicity_N = 0 + filename = os.path.join(TEST_DIR, 'wout_ITERModel_reference.nc') + vmec = Vmec(filename) + jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N) diff --git a/tests/mhd/test_profiles.py b/tests/mhd/test_profiles.py index 9e5d74843..e108b639a 100755 --- a/tests/mhd/test_profiles.py +++ b/tests/mhd/test_profiles.py @@ -1,7 +1,7 @@ import unittest import logging import numpy as np -from simsopt.mhd.profiles import ProfilePolynomial, compute_trapped_fraction +from simsopt.mhd.profiles import ProfilePolynomial, ProfileScaled logger = logging.getLogger(__name__) #logging.basicConfig(level=logging.DEBUG) @@ -16,6 +16,7 @@ def test_polynomial(self): prof = ProfilePolynomial([3, 0, 0, -3]) s = np.linspace(0, 1, 10) np.testing.assert_allclose(prof.f(s), 3 * (1 - s ** 3)) + np.testing.assert_allclose(prof(s), 3 * (1 - s ** 3)) np.testing.assert_allclose(prof.dfds(s), 3 * (- 3 * s ** 2)) def test_plot(self): @@ -26,82 +27,18 @@ def test_plot(self): prof = ProfilePolynomial([3, 0, 0, -3]) prof.plot(show=False) - -class RedlBootstrapTests(unittest.TestCase): - def test_compute_trapped_fraction(self): - ns = 2 - ntheta = 15 - nphi = 7 - nfp = 3 - modB = np.zeros((ntheta, nphi, ns)) - sqrtg = np.zeros((ntheta, nphi, ns)) - - theta1d = np.linspace(0, 2 * np.pi, ntheta, endpoint=False) - phi1d = np.linspace(0, 2 * np.pi / nfp, nphi, endpoint=False) - phi, theta = np.meshgrid(phi1d, theta1d) - - sqrtg[:, :, 0] = 10.0 - sqrtg[:, :, 1] = -25.0 - - modB[:, :, 0] = 13.0 + 2.6 * np.cos(theta) - modB[:, :, 1] = 9.0 + 3.7 * np.sin(theta - nfp * phi) - - Bmin, Bmax, epsilon, fsa_b2, f_t = compute_trapped_fraction(modB, sqrtg) - # The average of (b0 + b1 cos(theta))^2 is b0^2 + (1/2) * b1^2 - np.testing.assert_allclose(fsa_b2, [13.0 ** 2 + 0.5 * 2.6 ** 2, 9.0 ** 2 + 0.5 * 3.7 ** 2]) - np.testing.assert_allclose(Bmin, [13.0 - 2.6, 9.0 - 3.7], rtol=1e-4) - np.testing.assert_allclose(Bmax, [13.0 + 2.6, 9.0 + 3.7], rtol=1e-4) - np.testing.assert_allclose(epsilon, [2.6 / 13.0, 3.7 / 9.0], rtol=1e-3) - print('f_t:', f_t) - - def test_trapped_fraction_Kim(self): + def test_scaled(self): """ - Compare the trapped fraction to eq (C18) in Kim, Diamond, & - Groebner, Physics of Fluids B 3, 2050 (1991) + Test ProfileScaled """ - ns = 50 - ntheta = 100 - nphi = 3 - B0 = 7.5 - epsilon_in = np.linspace(0, 1, ns, endpoint=False) # Avoid divide-by-0 when epsilon=1 - theta1d = np.linspace(0, 2 * np.pi, ntheta, endpoint=False) - nfp = 3 - phi1d = np.linspace(0, 2 * np.pi / nfp, nphi, endpoint=False) - #phi1d = np.array([0]) - phi, theta = np.meshgrid(phi1d, theta1d) - modB = np.zeros((ntheta, nphi, ns)) - sqrtg = np.zeros((ntheta, nphi, ns)) - for js in range(ns): - # Eq (A6) - modB[:, :, js] = B0 / (1 + epsilon_in[js] * np.cos(theta)) - # For Jacobian, use eq (A7) for the theta dependence, - # times an arbitrary overall scale factor - sqrtg[:, :, js] = 6.7 * (1 + epsilon_in[js] * np.cos(theta)) - Bmin, Bmax, epsilon_out, fsa_B2, f_t = compute_trapped_fraction(modB, sqrtg) - - f_t_Kim = 1.46 * np.sqrt(epsilon_in) - 0.46 * epsilon_in # Eq (C18) in Kim et al - - np.testing.assert_allclose(Bmin, B0 / (1 + epsilon_in)) - np.testing.assert_allclose(Bmax, B0 / (1 - epsilon_in)) - np.testing.assert_allclose(epsilon_in, epsilon_out) - # Eq (A8): - np.testing.assert_allclose(fsa_B2, B0 * B0 / np.sqrt(1 - epsilon_in ** 2), rtol=1e-6) - np.testing.assert_allclose(f_t, f_t_Kim, rtol=0.1, atol=0.07) # We do not expect precise agreement. - - if False: - import matplotlib.pyplot as plt - plt.figure(figsize=(14, 5)) - plt.subplot(1, 2, 1) - plt.plot(epsilon_in, f_t, label='simsopt') - plt.plot(epsilon_in, f_t_Kim, label='Kim') - plt.xlabel('epsilon') - plt.title('Trapped fraction $f_t$') - plt.legend(loc=0) - - plt.subplot(1, 2, 2) - #plt.plot(epsilon_in, (f_t_Kim - f_t) / (1 - f_t)) - plt.plot(epsilon_in, f_t_Kim - f_t) - plt.title('Relative difference in $f_c$') - #plt.plot(epsilon_in, epsilon_out, 'r') - #plt.plot(epsilon_in, epsilon_in, ':k') - plt.show() + prof1 = ProfilePolynomial([3, 0, 0, -3]) + scalefac = 0.6 + prof2 = ProfileScaled(prof1, scalefac) + prof2.unfix_all() + s = np.linspace(0, 1, 10) + np.testing.assert_allclose(prof2(s), scalefac * prof1(s)) + np.testing.assert_allclose(prof2.dfds(s), scalefac * prof1.dfds(s)) + newscalefac = 1.3 + prof2.x = [newscalefac] + np.testing.assert_allclose(prof2(s), newscalefac * prof1(s)) + np.testing.assert_allclose(prof2.dfds(s), newscalefac * prof1.dfds(s)) diff --git a/tests/test_files/input.ITERModel b/tests/test_files/input.ITERModel new file mode 100644 index 000000000..0a55ea483 --- /dev/null +++ b/tests/test_files/input.ITERModel @@ -0,0 +1,34 @@ +&INDATA + MGRID_FILE = 'NONE ' + LOPTIM = F + LSPECTRUM_DUMP = F + DELT = 0.9 + TCON0 = 2. + NFP = 1 + MPOL = 12 + NTOR = 0 + NITER = 1000 + + NS_ARRAY = 13 25 51 + FTOL_ARRAY = 1e-20 1e-20 1e-20 + NITER_ARRAY = 1000 1500 2000 + +! NS_ARRAY = 13 25 51 101 150 201 +! FTOL_ARRAY = 1e-20 1e-20 1e-20 1e-20 1e-20 1e-18 +! NITER_ARRAY = 1000 1500 2000 2500 3000 30000 + + NSTEP = 200 + NVACSKIP = 3 + GAMMA = 0.00000000E+00 + PHIEDGE = 67.86 + CURTOR = 1.0 + SPRES_PED = 1.0000E+00 + NCURR = 0 + AM = 0.0 + AI = 0.9 -0.65 + AC = 0.0 + RAXIS = 6.0 + ZAXIS = 0.0 + RBC(0,0) = 6.0 ZBS(0,0) = 0.0 + RBC(0,1) = 2.0 ZBS(0,1) = 2.0 +/ diff --git a/tests/test_files/wout_ITERModel_reference.nc b/tests/test_files/wout_ITERModel_reference.nc new file mode 100644 index 0000000000000000000000000000000000000000..5ee1374d1423c8fdddabb80b9d7752c9e431f2e0 GIT binary patch literal 99112 zcmeEv2Urx#wk}bE4DO#T6m{()}pcnTYKEnSE^ z2JGI6r*UByV}N65U@#t|p~1^62?}-(aSx@&`SEywn}@%11T~HeS`zH+<{cJ7jjLjJ zhEQ*RJRP@nG2nIa!Y<};_uvrkzyQa^j0IeR=Y4x7Xkp0d9S{^2>gXO3>K=ge@hsey z9|P{I1swzgduH|b4EA<&^zinhR*%a6u?)_~eT4=?Q`=r{hN|8Wxj zjQbG_f_~VIHOSvNB;=p*qp5uFz)FlEZlzNe8AEe{DT7VHu^FA$Z5ec7y`a`>+iH5IUQIkqkq6+*Z$7I zAAaQZU~v{IZ*kQ8j`}-pKbFN9;2r9|FrI#7{wQ-8=Xr;EgiuG}kF4M89>=n{{G3B} z`#U=N1$uhBI{P{PaV-5PcM9Wk`vtqZVngm<7Qi?^mYJoN@d$QzcloDfgs>tsoPNO` 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zedy4!k?nZ}d3dvP#jS;VxJaYqwZ2k3fhWnPlsZ6rta(EJ(E;$k?Rnr9v;)}3I#+i? z$>wbvme;2t*7^9H?>}Y8{uB7I-UXP$W`Zh^>)-;>pzymZLs8+ltNq%g#^tk7c_q(S ztw{!7NnPnVrQZ?-zWHo7@Rh_?S1o0BcF|~Ie~!_F3G~OiA9aoSfS-mVM!Y~8KDU4cBYmK{unvpUy}(Lm~c-x)3t4bIt7_4TqF?p|@u zx4{kO*R+}Juf01Rrv<4_ENhTQLB`wsEHp`MJske`Z7~-u*&tleVM}1aPK_LrB-rod zy*_!71h1g~#by=oi~VDp3Kc$Ym!4M~7_bcvPgH>qPil_=bHcHD?xeQ^DV|Un7l;Oz zJ5026r>%&E@m#hKWH_4Cf zA<*1?nG=`tI{^8PhXWRY_!4tJMgVEskCS+S!oc~tGoWMvv_Iiz+S}Wo_dj)9exXMB zuKiKI8K>PRMeJWRcjoKVnZWgc*G@H8e^J;UQPSaMVcTGDbUZe3kr%^$9;M=`VFnC# zPgYuf1eQDd_CDbf0p>%ysfin=Z25u)<6)IC2mv7s@IR2{9&MQmo8yub3rM_O+AEo-jovoe0 z-Xu+0t0j$LKfk2fH=7F#cF)}m-)9_P*mqE8X_7Y3{+Yrr*GmBHE7Jeo3pC%(%P1UF z(e6{a{1s%O?eA+#fE2Jj5Fr4f?LSOpui%qm+yC^(#@jEx9kf5@s$fA59rZ-rH>yiYyk2DWY10k()-ls>xTgCvtvB69~eBq@#6noKw$;|_dqnw literal 0 HcmV?d00001 From 2e4331d8483638889d4158a7b90a2c169bb68f49 Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Fri, 24 Dec 2021 16:24:46 -0500 Subject: [PATCH 04/28] Added test for bootstrap, bug fixes --- src/simsopt/mhd/bootstrap.py | 54 +++++++++++-- tests/mhd/test_bootstrap.py | 150 +++++++++++++++++++++++++++++++++-- 2 files changed, 191 insertions(+), 13 deletions(-) diff --git a/src/simsopt/mhd/bootstrap.py b/src/simsopt/mhd/bootstrap.py index 58d379da8..5f7687323 100644 --- a/src/simsopt/mhd/bootstrap.py +++ b/src/simsopt/mhd/bootstrap.py @@ -12,6 +12,7 @@ from scipy.optimize import minimize from scipy.integrate import quad from .._core.util import Struct +from ..util.constants import ELEMENTARY_CHARGE from .profiles import Profile, ProfilePolynomial logger = logging.getLogger(__name__) @@ -138,7 +139,7 @@ def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helici jdotB: details: An object with intermediate quantities as attributes """ - if Zeff == None: + if Zeff is None: Zeff = ProfilePolynomial(1.0) if not isinstance(Zeff, Profile): # Zeff is presumably a number. Convert it to a constant profile. @@ -179,7 +180,7 @@ def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helici # Redl eq (11): X31 = f_t / (1 + (0.67 * (1 - 0.7 * f_t) * np.sqrt(nu_e)) / (0.56 + 0.44 * Zeff_s) \ - + (0.52 * 0.086 * np.sqrt(nu_e)) * (1 + 0.87 * f_t) * nu_e / (1 + 1.13 * np.sqrt(Zeff_s - 1))) + + (0.52 + 0.086 * np.sqrt(nu_e)) * (1 + 0.87 * f_t) * nu_e / (1 + 1.13 * np.sqrt(Zeff_s - 1))) # Redl eq (10): Zfac = Zeff_s ** 1.2 - 0.71 @@ -223,13 +224,19 @@ def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helici - 0.002 * nu_i * nu_i * (f_t ** 6)) \ / (1 + 0.004 * nu_i * nu_i * (f_t ** 6)) - dnds_term = -G * (ne_s * Te_s + ni_s + Ti_s) * L31 * (d_ne_d_s / ne_s) / (psi_edge * (iota - helicity_N)) - dTeds_term = -G * pe_s * (L31 + L32) * (d_Te_d_s / Te_s) / (psi_edge * (iota - helicity_N)) - dTids_term = -G * pi_s * (L31 + L34 * alpha) * (d_Ti_d_s / Ti_s) / (psi_edge * (iota - helicity_N)) + # Factor of ELEMENTARY_CHARGE is included below to convert temperatures from eV to J + dnds_term = -G * ELEMENTARY_CHARGE * (ne_s * Te_s + ni_s * Ti_s) * L31 * (d_ne_d_s / ne_s) / (psi_edge * (iota - helicity_N)) + dTeds_term = -G * ELEMENTARY_CHARGE * pe_s * (L31 + L32) * (d_Te_d_s / Te_s) / (psi_edge * (iota - helicity_N)) + dTids_term = -G * ELEMENTARY_CHARGE * pi_s * (L31 + L34 * alpha) * (d_Ti_d_s / Ti_s) / (psi_edge * (iota - helicity_N)) jdotB = dnds_term + dTeds_term + dTids_term details = Struct() - variables = ['ln_Lambda_e', 'ln_Lambda_ii', 'nu_e', 'nu_i', + nu_e_star = nu_e + nu_i_star = nu_i + variables = ['ne_s', 'ni_s', 'Zeff_s', 'Te_s', 'Ti_s', + 'd_ne_d_s', 'd_Te_d_s', 'd_Ti_d_s', + 'ln_Lambda_e', 'ln_Lambda_ii', 'nu_e_star', 'nu_i_star', + 'X31', 'X32e', 'X32ei', 'F32ee', 'F32ei', 'L31', 'L32', 'L34', 'alpha0', 'alpha', 'dnds_term', 'dTeds_term', 'dTids_term'] for v in variables: @@ -238,9 +245,12 @@ def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helici return jdotB, details -def vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, ntheta=64, nphi=65): +def vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, ntheta=64, nphi=65, plot=False): """ Evaluate the Redl bootstrap current formula for a vmec configuration. + + Args: + plot: Make a plot of many of the quantities computed. """ vmec.run() @@ -283,4 +293,32 @@ def vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, ntheta=64, n Bmin, Bmax, epsilon, fsa_B2, f_t = compute_trapped_fraction(modB, sqrtg) - return j_dot_B_Redl(surfaces, ne, Te, Ti, Zeff, vmec.wout.Rmajor_p, iota, G, epsilon, f_t, psi_edge, helicity_N) + jdotB, details = j_dot_B_Redl(surfaces, ne, Te, Ti, Zeff, vmec.wout.Rmajor_p, iota, G, epsilon, f_t, psi_edge, helicity_N) + + # Add extra info to the return structure + variables = ['Bmin', 'Bmax', 'epsilon', 'fsa_B2', 'f_t', + 'modB', 'sqrtg', 'G', 'iota', 'surfaces', 'psi_edge', 'theta1d', 'phi1d'] + for v in variables: + details.__setattr__(v, eval(v)) + + if plot: + import matplotlib.pyplot as plt + plt.figure(figsize=(14, 7)) + plt.rcParams.update({'font.size': 8}) + nrows = 4 + ncols = 6 + variables = ['Bmax', 'Bmin', 'epsilon', 'fsa_B2', 'f_t', 'iota', 'G', + 'details.ne_s', 'details.ni_s', 'details.Zeff_s', 'details.Te_s', 'details.Ti_s', + 'details.ln_Lambda_e', 'details.ln_Lambda_ii', + 'details.nu_e_star', 'details.nu_i_star', + 'details.dnds_term', 'details.dTeds_term', 'details.dTids_term', + 'details.L31', 'details.L32', 'details.alpha', 'jdotB'] + for j, variable in enumerate(variables): + plt.subplot(nrows, ncols, j + 1) + plt.plot(surfaces, eval(variable)) + plt.title(variable) + plt.xlabel('s') + plt.tight_layout() + plt.show() + + return jdotB, details diff --git a/tests/mhd/test_bootstrap.py b/tests/mhd/test_bootstrap.py index 8f8c1d7d8..b73b7b45b 100755 --- a/tests/mhd/test_bootstrap.py +++ b/tests/mhd/test_bootstrap.py @@ -1,10 +1,16 @@ +# Test ideas: +# * Reproduce fig 2, 3, 4, 5, 6 from Redl paper +# * Evaluate Redl's for Wistell-A and LDRD QA configs for which I already have self-consistent SFINCS calculations + import unittest import logging import os import numpy as np -from simsopt.mhd.bootstrap import compute_trapped_fraction, vmec_j_dot_B_Redl +from simsopt.mhd.bootstrap import compute_trapped_fraction, j_dot_B_Redl, \ + vmec_j_dot_B_Redl from simsopt.mhd.profiles import ProfilePolynomial from simsopt.mhd.vmec import Vmec +from simsopt.util.constants import ELEMENTARY_CHARGE from . import TEST_DIR logger = logging.getLogger(__name__) @@ -92,13 +98,147 @@ def test_trapped_fraction_Kim(self): #plt.plot(epsilon_in, epsilon_in, ':k') plt.show() + def test_Redl_second_pass(self): + """ + A second pass through coding up the equations from Redl et al, + Phys Plasmas (2021) to make sure I didn't make transcription + errors. + """ + # Make up some arbitrary functions to use for input: + ne = ProfilePolynomial(1.0e20 * np.array([1, 0, -0.8])) + Te = ProfilePolynomial(25e3 * np.array([1, -0.9])) + Ti = ProfilePolynomial(20e3 * np.array([1, -0.9])) + Zeff = ProfilePolynomial(np.array([1.5, 0.5])) + s = np.linspace(0, 1, 20) + s = s[1:] # Avoid divide-by-0 on axis + helicity_N = 4 + G = 32.0 - s + epsilon = 0.3 * np.sqrt(s) + f_t = 1.46 * np.sqrt(epsilon) + R = 6.0 + 0.3 * s + psi_edge = 68 / (2 * np.pi) + iota = 0.95 - 0.7 * s + + # Evaluate profiles on the s grid: + ne_s = ne(s) + Te_s = Te(s) + Ti_s = Ti(s) + Zeff_s = Zeff(s) + ni_s = ne_s / Zeff_s + d_ne_d_s = ne.dfds(s) + d_Te_d_s = Te.dfds(s) + d_Ti_d_s = Ti.dfds(s) + + # Sauter eq (18d)-(18e): + ln_Lambda_e = 31.3 - np.log(np.sqrt(ne_s) / Te_s) + ln_Lambda_ii = 30.0 - np.log((Zeff_s ** 3) * np.sqrt(ni_s) / (Ti_s ** 1.5)) + + # Sauter eq (18b)-(18c): + nu_e = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ + / (iota * (Te_s ** 2) * (epsilon ** 1.5)) + nu_i = (4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ + / (iota * (Ti_s ** 2) * (epsilon ** 1.5)) + + # Redl eq (11): + X31 = f_t / (1 + 0.67 * (1 - 0.7 * f_t) * np.sqrt(nu_e) / (0.56 + 0.44 * Zeff_s) \ + + (0.52 + 0.086 * np.sqrt(nu_e)) * (1 + 0.87 * f_t) * nu_e / (1 + 1.13 * np.sqrt(Zeff_s - 1))) + + # Redl eq (10): + Zfac = Zeff_s ** 1.2 - 0.71 + L31 = (1 + 0.15 / Zfac) * X31 - 0.22 / Zfac * (X31 ** 2) \ + + 0.01 / Zfac * (X31 ** 3) + 0.06 / Zfac * (X31 ** 4) + + # Redl eq (14): + X32e = f_t / (1 + 0.23 * (1 - 0.96 * f_t) * np.sqrt(nu_e / Zeff_s) \ + + 0.13 * (1 - 0.38 * f_t) * nu_e / (Zeff_s ** 2) \ + * (np.sqrt(1 + 2 * np.sqrt(Zeff_s - 1)) + + f_t * f_t * np.sqrt((0.075 + 0.25 * ((Zeff_s - 1) ** 2)) * nu_e))) + + # Redl eq (13): + F32ee = (0.1 + 0.6 * Zeff_s) / (Zeff_s * (0.77 + 0.63 * (1 + (Zeff_s - 1) ** 1.1))) * (X32e - X32e ** 4) \ + + 0.7 / (1 + 0.2 * Zeff_s) * (X32e ** 2 - X32e ** 4 - 1.2 * (X32e ** 3 - X32e ** 4)) \ + + 1.3 / (1 + 0.5 * Zeff_s) * (X32e ** 4) + + # Redl eq (16) + X32ei = f_t / (1 + 0.87 * (1 + 0.39 * f_t) * np.sqrt(nu_e) / (1 + 2.95 * ((Zeff_s - 1) ** 2)) \ + + 1.53 * (1 - 0.37 * f_t) * nu_e * (2 + 0.375 * (Zeff_s - 1))) + + # Redl eq (15) + F32ei = -(0.4 + 1.93 * Zeff_s) / (Zeff_s * (0.8 + 0.6 * Zeff_s)) * (X32ei - X32ei ** 4) \ + + 5.5 / (1.5 + 2 * Zeff_s) * (X32ei ** 2 - X32ei ** 4 - 0.8 * (X32ei ** 3 - X32ei ** 4)) \ + - 1.3 / (1 + 0.5 * Zeff_s) * (X32ei ** 4) + + # Redl eq (12) + L32 = F32ei + F32ee + + # Redl eq (20): + alpha0 = -(0.62 + 0.055 * (Zeff_s - 1)) * (1 - f_t) \ + / ((0.53 + 0.17 * (Zeff_s - 1)) * (1 - (0.31 - 0.065 * (Zeff_s - 1)) * f_t - 0.25 * (f_t ** 2))) + + # Redl eq (21): + alpha = ((alpha0 + 0.7 * Zeff_s * np.sqrt(f_t * nu_i)) / (1 + 0.18 * np.sqrt(nu_i)) - 0.002 * (nu_i ** 2) * (f_t ** 6)) \ + / (1 + 0.004 * (nu_i ** 2) * (f_t ** 6)) + + # Redl eq (19): + L34 = L31 + + Te_J = Te_s * ELEMENTARY_CHARGE + Ti_J = Ti_s * ELEMENTARY_CHARGE + d_Te_d_s_J = d_Te_d_s * ELEMENTARY_CHARGE + d_Ti_d_s_J = d_Ti_d_s * ELEMENTARY_CHARGE + pe = ne_s * Te_J + pi = ni_s * Ti_J + p = pe + pi + Rpe = pe / p + d_ni_d_s = d_ne_d_s / Zeff_s + d_p_d_s = ne_s * d_Te_d_s_J + Te_J * d_ne_d_s + ni_s * d_Ti_d_s_J + Ti_J * d_ni_d_s + # Equation from the bottom of the right column of Sauter errata: + factors = -G * pe / (psi_edge * (iota - helicity_N)) + dnds_term = factors * L31 * p / pe * ((Te_J * d_ne_d_s + Ti_J * d_ni_d_s) / p) + dTeds_term = factors * (L31 * p / pe * (ne_s * d_Te_d_s_J) / p + L32 * (d_Te_d_s_J / Te_J)) + dTids_term = factors * (L31 * p / pe * (ni_s * d_Ti_d_s_J) / p + L34 * alpha * (1 - Rpe) / Rpe * (d_Ti_d_s_J / Ti_J)) + jdotB_pass2 = -G * pe * (L31 * p / pe * (d_p_d_s / p) + L32 * (d_Te_d_s_J / Te_J) + L34 * alpha * (1 - Rpe) / Rpe * (d_Ti_d_s_J / Ti_J)) / (psi_edge * (iota - helicity_N)) + + jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helicity_N) + + atol = 1e-13 + rtol = 1e-13 + np.testing.assert_allclose(details.nu_e_star, nu_e, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.nu_i_star, nu_i, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.X31, X31, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.L31, L31, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.X32e, X32e, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.F32ee, F32ee, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.X32ei, X32ei, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.F32ei, F32ei, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.L32, L32, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.alpha, alpha, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.dTeds_term, dTeds_term, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.dTids_term, dTids_term, atol=atol, rtol=rtol) + np.testing.assert_allclose(details.dnds_term, dnds_term, atol=atol, rtol=rtol) + np.testing.assert_allclose(jdotB, jdotB_pass2, atol=atol, rtol=rtol) + def test_vmec_j_dot_B_Redl(self): - ne = ProfilePolynomial(1.0e20 * np.array([1, 0, -1])) - Te = ProfilePolynomial(25e3 * np.array([1, -1])) + ne = ProfilePolynomial(1.0e20 * np.array([1, 0, -0.8])) + Te = ProfilePolynomial(25e3 * np.array([1, -0.9])) Ti = Te Zeff = 1 - surfaces = np.linspace(0, 1, 5, endpoint=False) + surfaces = np.linspace(0, 1, 20) helicity_N = 0 filename = os.path.join(TEST_DIR, 'wout_ITERModel_reference.nc') vmec = Vmec(filename) - jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N) + jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, plot=False) + + if False: + import matplotlib.pyplot as plt + nrows = 2 + ncols = 2 + for j in range(4): + plt.subplot(nrows, ncols, j + 1) + plt.contourf(details.phi1d, details.theta1d, details.modB[:, :, j], 25) + plt.ylabel('theta') + plt.xlabel('phi') + plt.title(f'modB, s={surfaces[j]}') + plt.colorbar() + plt.tight_layout() + plt.show() From 5f620bac2635ba116d5e8ca14a1514f0559a3677 Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Fri, 24 Dec 2021 18:09:46 -0500 Subject: [PATCH 05/28] Bootstrap test: reproducing figs 2-3 from Redl --- tests/mhd/test_bootstrap.py | 106 +++++++++++++++++++++++++++++++++++- 1 file changed, 105 insertions(+), 1 deletion(-) diff --git a/tests/mhd/test_bootstrap.py b/tests/mhd/test_bootstrap.py index b73b7b45b..fe35a3898 100755 --- a/tests/mhd/test_bootstrap.py +++ b/tests/mhd/test_bootstrap.py @@ -1,5 +1,5 @@ # Test ideas: -# * Reproduce fig 2, 3, 4, 5, 6 from Redl paper +# * Reproduce figs 4, 5, 6 from Redl paper # * Evaluate Redl's for Wistell-A and LDRD QA configs for which I already have self-consistent SFINCS calculations import unittest @@ -218,6 +218,110 @@ def test_Redl_second_pass(self): np.testing.assert_allclose(details.dnds_term, dnds_term, atol=atol, rtol=rtol) np.testing.assert_allclose(jdotB, jdotB_pass2, atol=atol, rtol=rtol) + def test_Redl_figures_2_3(self): + """ + Make sure the implementation here can roughly recover the plots + from figures 2 and 3 in the Redl paper. + """ + for Zeff in [1, 1.8]: + target_nu_e_star = 4.0e-5 + target_nu_i_star = 1.0e-5 + # Make up some profiles + ne = ProfilePolynomial([1.0e17]) + Te = ProfilePolynomial([1.0e5]) + Ti_over_Te = np.sqrt(4.9 * Zeff * Zeff * target_nu_e_star / (6.921 * target_nu_i_star)) + Ti = ProfilePolynomial([1.0e5 * Ti_over_Te]) + s = np.linspace(0, 1, 100) ** 4 + s = s[1:] # Avoid divide-by-0 on axis + G = 32.0 - s + epsilon = np.sqrt(s) + f_t = 1.46 * np.sqrt(epsilon) - 0.46 * epsilon + R = 6.0 + 0.3 * s + psi_edge = 68 / (2 * np.pi) + # Redl uses fixed values of nu_e*. To match this, I'll use + # a contrived iota profile that is chosen just to give the + # desired nu_*. + + ne_s = ne(s) + Te_s = Te(s) + Zeff_s = Zeff + + # Sauter eq (18d): + ln_Lambda_e = 31.3 - np.log(np.sqrt(ne_s) / Te_s) + + # Sauter eq (18b), but without the q = 1/iota factor: + nu_e_without_iota = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ + / (1 * (Te_s ** 2) * (epsilon ** 1.5)) + + iota = nu_e_without_iota / target_nu_e_star + # End of determining the iota profile that gives the desired nu*. + + jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, + epsilon, f_t, psi_edge, helicity_N=0) + + if False: + # Make a plot, matching the axis ranges of Redl's + # figures 2 and 3 as best as possible. + import matplotlib.pyplot as plt + plt.figure(figsize=(6.5, 5.5)) + nrows = 2 + ncols = 2 + xlim = [-0.05, 1.05] + + plt.subplot(nrows, ncols, 1) + plt.semilogy(f_t, details.nu_e_star, label=r'$\nu_{e*}$') + plt.semilogy(f_t, details.nu_i_star, label=r'$\nu_{i*}$') + plt.xlabel('f_t') + plt.legend(loc=0, fontsize=8) + + plt.subplot(nrows, ncols, 2) + plt.plot(f_t, details.L31, 'g') + plt.title('L31') + plt.xlabel('f_t') + plt.xlim(xlim) + plt.ylim(-0.05, 1.05) + + plt.subplot(nrows, ncols, 3) + plt.plot(f_t, details.L32, 'g') + plt.title('L32') + plt.xlabel('f_t') + plt.xlim(xlim) + if Zeff == 1: + plt.ylim(-0.25, 0.025) + else: + plt.ylim(-0.2, 0.05) + + plt.subplot(nrows, ncols, 4) + plt.plot(f_t, details.alpha, 'g') + plt.title('alpha') + plt.xlabel('f_t') + plt.xlim(xlim) + plt.ylim(-1.25, 0.04) + + plt.tight_layout() + plt.show() + + # Make sure L31, L32, and alpha are within the right range: + np.testing.assert_array_less(details.L31, 1.05) + np.testing.assert_array_less(0, details.L31) + np.testing.assert_array_less(details.L32, 0.01) + np.testing.assert_array_less(-0.25, details.L32) + np.testing.assert_array_less(details.alpha, 0.05) + np.testing.assert_array_less(-1.2, details.alpha) + if Zeff > 1: + np.testing.assert_array_less(-1.0, details.alpha) + assert details.L31[0] < 0.1 + assert details.L31[-1] > 0.9 + assert details.L32[0] > -0.05 + assert details.L32[-1] > -0.05 + if Zeff == 0: + assert np.min(details.L32) < -0.2 + assert details.alpha[0] < -1.05 + else: + assert np.min(details.L32) < -0.13 + assert details.alpha[0] < -0.9 + assert details.alpha[-1] > -0.1 + def test_vmec_j_dot_B_Redl(self): ne = ProfilePolynomial(1.0e20 * np.array([1, 0, -0.8])) Te = ProfilePolynomial(25e3 * np.array([1, -0.9])) From 3339787d362e52b179c21c858b034bae18fc6136 Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Sat, 25 Dec 2021 10:05:12 -0500 Subject: [PATCH 06/28] Another test for Redl bootstrap current --- tests/mhd/test_bootstrap.py | 148 +++++++++++++++++++++++++++++++++++- 1 file changed, 147 insertions(+), 1 deletion(-) diff --git a/tests/mhd/test_bootstrap.py b/tests/mhd/test_bootstrap.py index fe35a3898..7d686ae7d 100755 --- a/tests/mhd/test_bootstrap.py +++ b/tests/mhd/test_bootstrap.py @@ -1,5 +1,5 @@ # Test ideas: -# * Reproduce figs 4, 5, 6 from Redl paper +# * Reproduce fig 6 from Redl paper # * Evaluate Redl's for Wistell-A and LDRD QA configs for which I already have self-consistent SFINCS calculations import unittest @@ -322,6 +322,152 @@ def test_Redl_figures_2_3(self): assert details.alpha[0] < -0.9 assert details.alpha[-1] > -0.1 + def test_Redl_figures_4_5(self): + """ + Make sure the implementation here can roughly recover the plots + from figures 4 and 5 in the Redl paper. + """ + for Zeff in [1, 1.8]: + n_nu_star = 30 + n_f_t = 3 + target_nu_stars = 10.0 ** np.linspace(-4, 4, n_nu_star) + f_ts = np.array([0.24, 0.45, 0.63]) + L31s = np.zeros((n_nu_star, n_f_t)) + L32s = np.zeros((n_nu_star, n_f_t)) + alphas = np.zeros((n_nu_star, n_f_t)) + nu_e_stars = np.zeros((n_nu_star, n_f_t)) + nu_i_stars = np.zeros((n_nu_star, n_f_t)) + for j_nu_star, target_nu_star in enumerate(target_nu_stars): + target_nu_e_star = target_nu_star + target_nu_i_star = target_nu_star + # Make up some profiles + ne = ProfilePolynomial([1.0e17]) + Te = ProfilePolynomial([1.0e5]) + Ti_over_Te = np.sqrt(4.9 * Zeff * Zeff * target_nu_e_star / (6.921 * target_nu_i_star)) + Ti = ProfilePolynomial([1.0e5 * Ti_over_Te]) + s = np.ones(n_f_t) + G = 32.0 - s + epsilon = s # Doesn't matter + f_t = f_ts + R = 6.0 + 0.3 * s + psi_edge = 68 / (2 * np.pi) + # Redl uses fixed values of nu_e*. To match this, I'll use + # a contrived iota profile that is chosen just to give the + # desired nu_*. + + ne_s = ne(s) + Te_s = Te(s) + Zeff_s = Zeff + + # Sauter eq (18d): + ln_Lambda_e = 31.3 - np.log(np.sqrt(ne_s) / Te_s) + + # Sauter eq (18b), but without the q = 1/iota factor: + nu_e_without_iota = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ + / (1 * (Te_s ** 2) * (epsilon ** 1.5)) + + iota = nu_e_without_iota / target_nu_e_star + # End of determining the iota profile that gives the desired nu*. + + jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, + epsilon, f_t, psi_edge, helicity_N=0) + + L31s[j_nu_star, :] = details.L31 + L32s[j_nu_star, :] = details.L32 + alphas[j_nu_star, :] = details.alpha + nu_e_stars[j_nu_star, :] = details.nu_e_star + nu_i_stars[j_nu_star, :] = details.nu_i_star + #np.testing.assert_allclose(details.nu_e_star, target_nu_e_star) + #np.testing.assert_allclose(details.nu_i_star, target_nu_i_star) + + if False: + # Make a plot, matching the axis ranges of Redl's + # figures 4 and 5 as best as possible. + import matplotlib.pyplot as plt + plt.figure(figsize=(6.5, 5.5)) + nrows = 2 + ncols = 2 + xlim = [3.0e-5, 1.5e4] + + plt.subplot(nrows, ncols, 2) + for j in range(n_f_t): + plt.semilogx(nu_e_stars[:, j], L31s[:, j], label=f'f_t={f_ts[j]}') + plt.legend(loc=0, fontsize=8) + plt.title(f'L31, Zeff={Zeff}') + plt.xlabel('nu_{*e}') + plt.xlim(xlim) + if Zeff == 1: + plt.ylim(-0.05, 0.85) + else: + plt.ylim(-0.05, 0.75) + + plt.subplot(nrows, ncols, 3) + for j in range(n_f_t): + plt.semilogx(nu_e_stars[:, j], L32s[:, j], label=f'f_t={f_ts[j]}') + plt.legend(loc=0, fontsize=8) + plt.title(f'L32, Zeff={Zeff}') + plt.xlabel('nu_{*e}') + plt.xlim(xlim) + if Zeff == 1: + plt.ylim(-0.26, 0.21) + else: + plt.ylim(-0.18, 0.2) + + plt.subplot(nrows, ncols, 4) + for j in range(n_f_t): + plt.semilogx(nu_i_stars[:, j], alphas[:, j], label=f'f_t={f_ts[j]}') + plt.legend(loc=0, fontsize=8) + plt.title(f'alpha, Zeff={Zeff}') + plt.xlabel('nu_{*i}') + plt.xlim(xlim) + if Zeff == 1: + plt.ylim(-1.1, 2.2) + else: + plt.ylim(-1.1, 2.35) + + plt.tight_layout() + plt.show() + + # Make sure L31, L32, and alpha are within the right range: + if Zeff == 1: + np.testing.assert_array_less(L31s, 0.71) + np.testing.assert_array_less(0, L31s) + np.testing.assert_array_less(L31s[-1, :], 1.0e-5) + np.testing.assert_array_less(L32s, 0.2) + np.testing.assert_array_less(-0.23, L32s) + np.testing.assert_array_less(L32s[-1, :], 3.0e-5) + np.testing.assert_array_less(-3.0e-5, L32s[-1, :]) + np.testing.assert_array_less(L32s[0, :], -0.17) + np.testing.assert_array_less(alphas, 1.2) + np.testing.assert_array_less(alphas[0, :], -0.58) + np.testing.assert_array_less(-1.05, alphas) + np.testing.assert_array_less(0.8, np.max(alphas, axis=0)) + np.testing.assert_array_less(L31s[:, 0], 0.33) + assert L31s[0, 0] > 0.3 + np.testing.assert_array_less(L31s[0, 1], 0.55) + assert L31s[0, 1] > 0.51 + np.testing.assert_array_less(L31s[0, 2], 0.7) + assert L31s[0, 2] > 0.68 + else: + np.testing.assert_array_less(L31s, 0.66) + np.testing.assert_array_less(0, L31s) + np.testing.assert_array_less(L31s[-1, :], 1.5e-5) + np.testing.assert_array_less(L32s, 0.19) + np.testing.assert_array_less(-0.15, L32s) + np.testing.assert_array_less(L32s[-1, :], 5.0e-5) + np.testing.assert_array_less(0, L32s[-1, :]) + np.testing.assert_array_less(L32s[0, :], -0.11) + np.testing.assert_array_less(alphas, 2.3) + np.testing.assert_array_less(alphas[0, :], -0.4) + np.testing.assert_array_less(-0.9, alphas) + np.testing.assert_array_less(1.8, np.max(alphas, axis=0)) + np.testing.assert_array_less(L31s[:, 0], 0.27) + assert L31s[0, 0] > 0.24 + np.testing.assert_array_less(L31s[0, 1], 0.49) + assert L31s[0, 1] > 0.45 + np.testing.assert_array_less(L31s[0, 2], 0.66) + assert L31s[0, 2] > 0.63 + def test_vmec_j_dot_B_Redl(self): ne = ProfilePolynomial(1.0e20 * np.array([1, 0, -0.8])) Te = ProfilePolynomial(25e3 * np.array([1, -0.9])) From d4e509854795fd7ed6792798163e96e86d5b49f9 Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Mon, 27 Dec 2021 09:42:56 -0500 Subject: [PATCH 07/28] bootstrap tests: comparing Redl to sfincs --- src/simsopt/mhd/bootstrap.py | 8 +- tests/mhd/test_bootstrap.py | 176 +++++++++++++++++++++++++++++++++-- 2 files changed, 172 insertions(+), 12 deletions(-) diff --git a/src/simsopt/mhd/bootstrap.py b/src/simsopt/mhd/bootstrap.py index 5f7687323..33f32ded7 100644 --- a/src/simsopt/mhd/bootstrap.py +++ b/src/simsopt/mhd/bootstrap.py @@ -173,10 +173,10 @@ def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helici logging.debug(f'ln Lambda_ii: {ln_Lambda_ii}') # Eq (18b)-(18c) in Sauter: - nu_e = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ - / (iota * Te_s * Te_s * (epsilon ** 1.5)) - nu_i = (4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ - / (iota * Ti_s * Ti_s * (epsilon ** 1.5)) + nu_e = np.abs((6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ + / ((iota - helicity_N) * Te_s * Te_s * (epsilon ** 1.5))) + nu_i = np.abs((4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ + / ((iota - helicity_N) * Ti_s * Ti_s * (epsilon ** 1.5))) # Redl eq (11): X31 = f_t / (1 + (0.67 * (1 - 0.7 * f_t) * np.sqrt(nu_e)) / (0.56 + 0.44 * Zeff_s) \ diff --git a/tests/mhd/test_bootstrap.py b/tests/mhd/test_bootstrap.py index 7d686ae7d..d988b3840 100755 --- a/tests/mhd/test_bootstrap.py +++ b/tests/mhd/test_bootstrap.py @@ -134,10 +134,10 @@ def test_Redl_second_pass(self): ln_Lambda_ii = 30.0 - np.log((Zeff_s ** 3) * np.sqrt(ni_s) / (Ti_s ** 1.5)) # Sauter eq (18b)-(18c): - nu_e = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ - / (iota * (Te_s ** 2) * (epsilon ** 1.5)) - nu_i = (4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ - / (iota * (Ti_s ** 2) * (epsilon ** 1.5)) + nu_e = abs((6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ + / ((iota - helicity_N) * (Te_s ** 2) * (epsilon ** 1.5))) + nu_i = abs((4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ + / ((iota - helicity_N) * (Ti_s ** 2) * (epsilon ** 1.5))) # Redl eq (11): X31 = f_t / (1 + 0.67 * (1 - 0.7 * f_t) * np.sqrt(nu_e) / (0.56 + 0.44 * Zeff_s) \ @@ -468,17 +468,62 @@ def test_Redl_figures_4_5(self): np.testing.assert_array_less(L31s[0, 2], 0.66) assert L31s[0, 2] > 0.63 - def test_vmec_j_dot_B_Redl(self): - ne = ProfilePolynomial(1.0e20 * np.array([1, 0, -0.8])) - Te = ProfilePolynomial(25e3 * np.array([1, -0.9])) + def test_Redl_sfincs_benchmark(self): + """ + Compare the Redl to a SFINCS calculation for a tokamak. + + The SFINCS calculation is on Matt Landreman's laptop in + /Users/mattland/Box Sync/work21/20211225-01-sfincs_tokamak_bootstrap_for_Redl_benchmark + """ + ne = ProfilePolynomial(5.0e20 * np.array([1, 0, 0, 0, -1])) + Te = ProfilePolynomial(8e3 * np.array([1, -1])) Ti = Te Zeff = 1 - surfaces = np.linspace(0, 1, 20) + surfaces = np.linspace(0.01, 0.99, 99) helicity_N = 0 filename = os.path.join(TEST_DIR, 'wout_ITERModel_reference.nc') vmec = Vmec(filename) jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, plot=False) + jdotB_sfincs = np.array([-577720.30718026, -737097.14851563, -841877.1731213, -924690.37927967, + -996421.14965534, -1060853.54247997, -1120000.15051496, -1175469.30096585, + -1228274.42232883, -1279134.94084881, -1328502.74017954, -1376746.08281939, + -1424225.7135264, -1471245.54499716, -1518022.59582135, -1564716.93168823, + -1611473.13548435, -1658436.14166984, -1705743.3966606, -1753516.75354018, + -1801854.51072685, -1850839.64964612, -1900546.86009713, -1951047.40424607, + -2002407.94774638, -2054678.30773555, -2107880.19135161, -2162057.48184046, + -2217275.94462326, -2273566.0131982, -2330938.65226651, -2389399.44803491, + -2448949.45267694, -2509583.82212581, -2571290.69542303, -2634050.8642164, + -2697839.22372799, -2762799.43321187, -2828566.29269343, -2895246.32116721, + -2962784.4499046, -3031117.70888815, -3100173.19345621, -3169866.34773162, + -3240095.93569359, -3310761.89170199, -3381738.85511963, -3452893.53199984, + -3524079.68661978, -3595137.36934266, -3665892.0942594, -3736154.01439094, + -3805717.10211429, -3874383.57672975, -3941857.83476556, -4007909.78112076, + -4072258.58610167, -4134609.67635966, -4194641.53357309, -4252031.55214378, + -4306378.23970987, -4357339.70206557, -4404503.4788238, -4447364.62100875, + -4485559.83633318, -4518524.39965094, -4545649.39588513, -4566517.96382113, + -4580487.82371991, -4586917.13595789, -4585334.66419017, -4574935.10788554, + -4555027.85929442, -4524904.81212564, -4483819.87563906, -4429820.99499252, + -4364460.04545626, -4285813.80804979, -4193096.44129549, -4085521.92933703, + -3962389.92116629, -3822979.23919869, -3666751.38186485, -3493212.37971975, + -3302099.71461769, -3093392.43317121, -2867475.54470152, -2625108.03673121, + -2367586.06128219, -2096921.32817857, -1815701.10075496, -1527523.11762782, + -1237077.39816553, -950609.3080458, -677002.74349353, -429060.85924996, + -224317.60933134, -82733.32462396, -22233.12804732]) + + # The relative error is a bit larger at s \approx 1, where the + # absolute magnitude is quite small, so drop those points. + np.testing.assert_allclose(jdotB[:-5], jdotB_sfincs[:-5], rtol=0.1) + + if False: + import matplotlib.pyplot as plt + plt.plot(surfaces, jdotB, '.-', label='Redl') + plt.plot(surfaces, jdotB_sfincs, '.-', label='sfincs') + plt.xlabel('s') + plt.title('J dot B') + plt.legend(loc=0) + plt.show() + if False: import matplotlib.pyplot as plt nrows = 2 @@ -492,3 +537,118 @@ def test_vmec_j_dot_B_Redl(self): plt.colorbar() plt.tight_layout() plt.show() + + @unittest.skip("") + def test_Redl_sfincs_WistellA(self): + """ + Compare the Redl to a SFINCS calculation for a tokamak. + + The SFINCS calculation is on Matt Landreman's laptop in + /Users/mattland/Box Sync/work21/20211225-01-sfincs_tokamak_bootstrap_for_Redl_benchmark + """ + ne = ProfilePolynomial(0.9e20 * np.array([1, 0, 0, 0, 0, -1])) + #Te = ProfilePolynomial(1.3e3 * np.array([1, -1])) + #Te = ProfilePolynomial(2.5e3 * np.array([1, -1])) + Te = ProfilePolynomial(3.5e3 * np.array([1, -1])) + Ti = Te + Zeff = 1 + helicity_N = 4 + #filename = os.path.join(TEST_DIR, 'wout_ITERModel_reference.nc') + #filename = '/Users/mattland/Box Sync/work19/20191229-01-wistell_self_consistent_current_profiles/wout_wista_15_beta_0.71.00000.nc' + #filename = '/Users/mattland/Box Sync/work19/20191229-01-wistell_self_consistent_current_profiles/wout_wista_15_beta_1.39.00000.nc' + filename = '/Users/mattland/Box Sync/work19/20191229-01-wistell_self_consistent_current_profiles/wout_wista_15_beta_1.97.00000.nc' + vmec = Vmec(filename) + surfaces = vmec.s_full_grid[1:-1] # Drop points on the axis and edge to avoid divide-by-0 + jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, plot=False) + + # The current profile in this vmec file was computed using SFINCS: + jdotB_sfincs = vmec.wout.jdotb[1:-1] + + # The relative error is a bit larger at s \approx 1, where the + # absolute magnitude is quite small, so drop those points. + #np.testing.assert_allclose(jdotB[:-5], jdotB_sfincs[:-5], rtol=0.1) + + if True: + import matplotlib.pyplot as plt + plt.plot(surfaces, jdotB, '.-', label='Redl') + plt.plot(surfaces, jdotB_sfincs, '.-', label='sfincs') + plt.legend(loc=0) + plt.xlabel('s') + plt.title('J dot B') + plt.show() + + @unittest.skip("") + def test_Redl_sfincs_precise_QA(self): + """ + Compare the Redl to a SFINCS calculation for the precise QA. + + The SFINCS calculation is on cobra in + /ptmp/mlan/20211226-01-sfincs_for_precise_QS_for_Redl_benchmark/20211226-01-012_QA_Ntheta25_Nzeta39_Nxi60_Nx7_manySurfaces + """ + ne = ProfilePolynomial(4.13e20 * np.array([1, 0, 0, 0, 0, -1])) + Te = ProfilePolynomial(12.0e3 * np.array([1, -1])) + Ti = Te + Zeff = 1 + helicity_N = 0 + filename = os.path.join(TEST_DIR, 'wout_new_QA_aScaling.nc') + vmec = Vmec(filename) + surfaces = np.linspace(0.025, 0.975, 39) + jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, plot=False) + + jdotB_sfincs = np.array([-2164875.78234086, -3010997.004258, -3586912.40439179, -4025873.78974165, + -4384855.40656673, -4692191.91608418, -4964099.33007648, -5210508.61474677, + -5442946.68999908, -5657799.82786579, -5856450.57370037, -6055808.19817868, + -6247562.80014873, -6431841.43078959, -6615361.81912527, -6793994.01503932, + -6964965.34953497, -7127267.47873969, -7276777.92844458, -7409074.62499181, + -7518722.07866914, -7599581.37772525, -7644509.67670812, -7645760.36382036, + -7594037.38147436, -7481588.70786642, -7299166.08742784, -7038404.20002745, + -6691596.45173419, -6253955.52847633, -5722419.58059673, -5098474.47777983, + -4390147.20699043, -3612989.71633149, -2793173.34162084, -1967138.17518374, + -1192903.42248978, -539990.088677, -115053.37380415]) + + if True: + import matplotlib.pyplot as plt + plt.plot(surfaces, jdotB, '.-', label='Redl') + plt.plot(surfaces, jdotB_sfincs, '.-', label='sfincs') + plt.legend(loc=0) + plt.xlabel('s') + plt.title('J dot B') + plt.show() + + @unittest.skip("") + def test_Redl_sfincs_precise_QH(self): + """ + Compare the Redl to a SFINCS calculation for the precise QH. + + The SFINCS calculation is on cobra in + /ptmp/mlan/20211226-01-sfincs_for_precise_QS_for_Redl_benchmark/20211226-01-019_QH_Ntheta25_Nzeta39_Nxi60_Nx7_manySurfaces + """ + ne = ProfilePolynomial(4.13e20 * np.array([1, 0, 0, 0, 0, -1])) + Te = ProfilePolynomial(12.0e3 * np.array([1, -1])) + Ti = Te + Zeff = 1 + helicity_N = -4 + filename = os.path.join(TEST_DIR, 'wout_new_QH_aScaling.nc') + vmec = Vmec(filename) + surfaces = np.linspace(0.025, 0.975, 39) + jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, plot=False) + + jdotB_sfincs = np.array([-1086092.9561775, -1327299.73501589, -1490400.04894085, -1626634.32037339, + -1736643.64671843, -1836285.33939607, -1935027.3099312, -2024949.13178129, + -2112581.50178861, -2200196.92359437, -2289400.72956248, -2381072.32897262, + -2476829.87345286, -2575019.97938908, -2677288.45525839, -2783750.09013764, + -2894174.68898196, -3007944.74771214, -3123697.37793226, -3240571.57445779, + -3356384.98579004, -3468756.64908024, -3574785.02500657, -3671007.37469685, + -3753155.07811322, -3816354.48636373, -3856198.2242986, -3866041.76391937, + -3839795.40512069, -3770065.26594065, -3649660.76253605, -3471383.501417, + -3228174.23182819, -2914278.54799143, -2525391.54652021, -2058913.26485519, + -1516843.60879267, -912123.395174, -315980.89711036]) + + if True: + import matplotlib.pyplot as plt + plt.plot(surfaces, jdotB, '.-', label='Redl') + plt.plot(surfaces, jdotB_sfincs, '.-', label='sfincs') + plt.legend(loc=0) + plt.xlabel('s') + plt.title('J dot B') + plt.show() From 8a5f719b6093b51473264be0585f38454665a2b8 Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Mon, 27 Dec 2021 13:55:15 -0500 Subject: [PATCH 08/28] Redl j_bootstrap: better way to compute effective R --- src/simsopt/mhd/bootstrap.py | 31 ++++++++++++------- tests/mhd/test_bootstrap.py | 60 ++++++++++++++++++++---------------- 2 files changed, 53 insertions(+), 38 deletions(-) diff --git a/src/simsopt/mhd/bootstrap.py b/src/simsopt/mhd/bootstrap.py index 33f32ded7..45b7537dc 100644 --- a/src/simsopt/mhd/bootstrap.py +++ b/src/simsopt/mhd/bootstrap.py @@ -45,6 +45,7 @@ def compute_trapped_fraction(modB, sqrtg): Bmax: maximum of |B| on each surface epsilon: A measure of the inverse aspect ratio fsa_B2: , where < > denotes a flux surface average. + fsa_1overB: <1/B>, where < > denotes a flux surface average. f_t: The effective trapped fraction """ ntheta = modB.shape[0] @@ -53,6 +54,7 @@ def compute_trapped_fraction(modB, sqrtg): fourpisq = 4 * np.pi * np.pi dVds = np.mean(sqrtg, axis=(0, 1)) / fourpisq fsa_B2 = np.mean(modB * modB * sqrtg, axis=(0, 1)) / (fourpisq * dVds) + fsa_1overB = np.mean(sqrtg / modB, axis=(0, 1)) / (fourpisq * dVds) epsilon = np.zeros(ns) f_t = np.zeros(ns) @@ -93,7 +95,7 @@ def integrand(lambd): integral = quad(integrand, 0, 1 / modBmax) f_t[js] = 1 - 0.75 * fsa_B2[js] * integral[0] - return Bmin, Bmax, epsilon, fsa_B2, f_t + return Bmin, Bmax, epsilon, fsa_B2, fsa_1overB, f_t def quasisymmetry_filtered_trapped_fraction(booz, helicity_m, helicity_n): @@ -113,7 +115,7 @@ def quasisymmetry_filtered_trapped_fraction(booz, helicity_m, helicity_n): pass -def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helicity_N): +def j_dot_B_Redl(s, ne, Te, Ti, Zeff, G, R, iota, epsilon, f_t, psi_edge, helicity_N): """ Compute the bootstrap current (specifically :math:`\left<\vec{J}\cdot\vec{B}\right>`) using the formulae in @@ -173,10 +175,11 @@ def j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helici logging.debug(f'ln Lambda_ii: {ln_Lambda_ii}') # Eq (18b)-(18c) in Sauter: - nu_e = np.abs((6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ - / ((iota - helicity_N) * Te_s * Te_s * (epsilon ** 1.5))) - nu_i = np.abs((4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ - / ((iota - helicity_N) * Ti_s * Ti_s * (epsilon ** 1.5))) + geometry_factor = abs(R / (iota - helicity_N)) + nu_e = geometry_factor * (6.921e-18) * ne_s * Zeff_s * ln_Lambda_e \ + / (Te_s * Te_s * (epsilon ** 1.5)) + nu_i = geometry_factor * (4.90e-18) * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ + / (Ti_s * Ti_s * (epsilon ** 1.5)) # Redl eq (11): X31 = f_t / (1 + (0.67 * (1 - 0.7 * f_t) * np.sqrt(nu_e)) / (0.56 + 0.44 * Zeff_s) \ @@ -267,6 +270,9 @@ def vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, ntheta=64, n interp = interp1d(vmec.s_half_grid, vmec.wout.bvco[1:], fill_value="extrapolate") G = interp(surfaces) + interp = interp1d(vmec.s_half_grid, vmec.wout.buco[1:], fill_value="extrapolate") + I = interp(surfaces) + interp = interp1d(vmec.s_half_grid, vmec.wout.gmnc[:, 1:], fill_value="extrapolate") gmnc = interp(surfaces) @@ -291,13 +297,16 @@ def vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, ntheta=64, n modB += np.kron(bmnc[jmn, :].reshape((1, 1, ns)), cosangle) sqrtg += np.kron(gmnc[jmn, :].reshape((1, 1, ns)), cosangle) - Bmin, Bmax, epsilon, fsa_B2, f_t = compute_trapped_fraction(modB, sqrtg) + Bmin, Bmax, epsilon, fsa_B2, fsa_1overB, f_t = compute_trapped_fraction(modB, sqrtg) - jdotB, details = j_dot_B_Redl(surfaces, ne, Te, Ti, Zeff, vmec.wout.Rmajor_p, iota, G, epsilon, f_t, psi_edge, helicity_N) + # There are several ways we could define an effective R for shaped geometry: + R = (G + iota * I) * fsa_1overB + #R = vmec.wout.RMajor_p + jdotB, details = j_dot_B_Redl(surfaces, ne, Te, Ti, Zeff, G, R, iota, epsilon, f_t, psi_edge, helicity_N) # Add extra info to the return structure - variables = ['Bmin', 'Bmax', 'epsilon', 'fsa_B2', 'f_t', - 'modB', 'sqrtg', 'G', 'iota', 'surfaces', 'psi_edge', 'theta1d', 'phi1d'] + variables = ['Bmin', 'Bmax', 'epsilon', 'fsa_B2', 'fsa_1overB', 'f_t', + 'modB', 'sqrtg', 'G', 'I', 'iota', 'surfaces', 'psi_edge', 'theta1d', 'phi1d'] for v in variables: details.__setattr__(v, eval(v)) @@ -307,7 +316,7 @@ def vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, ntheta=64, n plt.rcParams.update({'font.size': 8}) nrows = 4 ncols = 6 - variables = ['Bmax', 'Bmin', 'epsilon', 'fsa_B2', 'f_t', 'iota', 'G', + variables = ['Bmax', 'Bmin', 'epsilon', 'fsa_B2', 'fsa_1overB', 'f_t', 'iota', 'G', 'I', 'R', 'details.ne_s', 'details.ni_s', 'details.Zeff_s', 'details.Te_s', 'details.Ti_s', 'details.ln_Lambda_e', 'details.ln_Lambda_ii', 'details.nu_e_star', 'details.nu_i_star', diff --git a/tests/mhd/test_bootstrap.py b/tests/mhd/test_bootstrap.py index d988b3840..c1e0b34e1 100755 --- a/tests/mhd/test_bootstrap.py +++ b/tests/mhd/test_bootstrap.py @@ -36,9 +36,10 @@ def test_compute_trapped_fraction(self): modB[:, :, 0] = 13.0 + 2.6 * np.cos(theta) modB[:, :, 1] = 9.0 + 3.7 * np.sin(theta - nfp * phi) - Bmin, Bmax, epsilon, fsa_b2, f_t = compute_trapped_fraction(modB, sqrtg) + Bmin, Bmax, epsilon, fsa_b2, fsa_1overB, f_t = compute_trapped_fraction(modB, sqrtg) # The average of (b0 + b1 cos(theta))^2 is b0^2 + (1/2) * b1^2 np.testing.assert_allclose(fsa_b2, [13.0 ** 2 + 0.5 * 2.6 ** 2, 9.0 ** 2 + 0.5 * 3.7 ** 2]) + np.testing.assert_allclose(fsa_1overB, [1 / np.sqrt(13.0 ** 2 - 2.6 ** 2), 1 / np.sqrt(9.0 ** 2 - 3.7 ** 2)]) np.testing.assert_allclose(Bmin, [13.0 - 2.6, 9.0 - 3.7], rtol=1e-4) np.testing.assert_allclose(Bmax, [13.0 + 2.6, 9.0 + 3.7], rtol=1e-4) np.testing.assert_allclose(epsilon, [2.6 / 13.0, 3.7 / 9.0], rtol=1e-3) @@ -66,7 +67,7 @@ def test_trapped_fraction_Kim(self): # For Jacobian, use eq (A7) for the theta dependence, # times an arbitrary overall scale factor sqrtg[:, :, js] = 6.7 * (1 + epsilon_in[js] * np.cos(theta)) - Bmin, Bmax, epsilon_out, fsa_B2, f_t = compute_trapped_fraction(modB, sqrtg) + Bmin, Bmax, epsilon_out, fsa_B2, fsa_1overB, f_t = compute_trapped_fraction(modB, sqrtg) f_t_Kim = 1.46 * np.sqrt(epsilon_in) - 0.46 * epsilon_in # Eq (C18) in Kim et al @@ -76,6 +77,7 @@ def test_trapped_fraction_Kim(self): # Eq (A8): np.testing.assert_allclose(fsa_B2, B0 * B0 / np.sqrt(1 - epsilon_in ** 2), rtol=1e-6) np.testing.assert_allclose(f_t, f_t_Kim, rtol=0.1, atol=0.07) # We do not expect precise agreement. + np.testing.assert_allclose(fsa_1overB, (2 + epsilon_in ** 2) / (2 * B0)) if False: import matplotlib.pyplot as plt @@ -113,11 +115,11 @@ def test_Redl_second_pass(self): s = s[1:] # Avoid divide-by-0 on axis helicity_N = 4 G = 32.0 - s + iota = 0.95 - 0.7 * s + R = 6.0 - 0.1 * s epsilon = 0.3 * np.sqrt(s) f_t = 1.46 * np.sqrt(epsilon) - R = 6.0 + 0.3 * s psi_edge = 68 / (2 * np.pi) - iota = 0.95 - 0.7 * s # Evaluate profiles on the s grid: ne_s = ne(s) @@ -134,9 +136,9 @@ def test_Redl_second_pass(self): ln_Lambda_ii = 30.0 - np.log((Zeff_s ** 3) * np.sqrt(ni_s) / (Ti_s ** 1.5)) # Sauter eq (18b)-(18c): - nu_e = abs((6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ + nu_e = abs(R * (6.921e-18) * ne_s * Zeff_s * ln_Lambda_e \ / ((iota - helicity_N) * (Te_s ** 2) * (epsilon ** 1.5))) - nu_i = abs((4.90e-18) * R * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ + nu_i = abs(R * (4.90e-18) * ni_s * (Zeff_s ** 4) * ln_Lambda_ii \ / ((iota - helicity_N) * (Ti_s ** 2) * (epsilon ** 1.5))) # Redl eq (11): @@ -199,7 +201,7 @@ def test_Redl_second_pass(self): dTids_term = factors * (L31 * p / pe * (ni_s * d_Ti_d_s_J) / p + L34 * alpha * (1 - Rpe) / Rpe * (d_Ti_d_s_J / Ti_J)) jdotB_pass2 = -G * pe * (L31 * p / pe * (d_p_d_s / p) + L32 * (d_Te_d_s_J / Te_J) + L34 * alpha * (1 - Rpe) / Rpe * (d_Ti_d_s_J / Ti_J)) / (psi_edge * (iota - helicity_N)) - jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, epsilon, f_t, psi_edge, helicity_N) + jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, G, R, iota, epsilon, f_t, psi_edge, helicity_N) atol = 1e-13 rtol = 1e-13 @@ -233,11 +235,12 @@ def test_Redl_figures_2_3(self): Ti = ProfilePolynomial([1.0e5 * Ti_over_Te]) s = np.linspace(0, 1, 100) ** 4 s = s[1:] # Avoid divide-by-0 on axis - G = 32.0 - s + helicity_N = 0 epsilon = np.sqrt(s) f_t = 1.46 * np.sqrt(epsilon) - 0.46 * epsilon - R = 6.0 + 0.3 * s psi_edge = 68 / (2 * np.pi) + G = 32.0 - s # Doesn't matter + R = 5.0 + 0.1 * s # Doesn't matter # Redl uses fixed values of nu_e*. To match this, I'll use # a contrived iota profile that is chosen just to give the # desired nu_*. @@ -249,15 +252,15 @@ def test_Redl_figures_2_3(self): # Sauter eq (18d): ln_Lambda_e = 31.3 - np.log(np.sqrt(ne_s) / Te_s) - # Sauter eq (18b), but without the q = 1/iota factor: - nu_e_without_iota = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ - / (1 * (Te_s ** 2) * (epsilon ** 1.5)) + # Sauter eq (18b), but without the iota factor: + nu_e_without_iota = R * (6.921e-18) * ne_s * Zeff_s * ln_Lambda_e \ + / ((Te_s ** 2) * (epsilon ** 1.5)) iota = nu_e_without_iota / target_nu_e_star - # End of determining the iota profile that gives the desired nu*. + # End of determining the qR profile that gives the desired nu*. - jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, - epsilon, f_t, psi_edge, helicity_N=0) + jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, G, R, iota, + epsilon, f_t, psi_edge, helicity_N) if False: # Make a plot, matching the axis ranges of Redl's @@ -346,10 +349,11 @@ def test_Redl_figures_4_5(self): Ti_over_Te = np.sqrt(4.9 * Zeff * Zeff * target_nu_e_star / (6.921 * target_nu_i_star)) Ti = ProfilePolynomial([1.0e5 * Ti_over_Te]) s = np.ones(n_f_t) - G = 32.0 - s + helicity_N = 0 + G = 32.0 - s # Doesn't matter + R = 5.0 + 0.1 * s # Doesn't matter epsilon = s # Doesn't matter f_t = f_ts - R = 6.0 + 0.3 * s psi_edge = 68 / (2 * np.pi) # Redl uses fixed values of nu_e*. To match this, I'll use # a contrived iota profile that is chosen just to give the @@ -363,14 +367,14 @@ def test_Redl_figures_4_5(self): ln_Lambda_e = 31.3 - np.log(np.sqrt(ne_s) / Te_s) # Sauter eq (18b), but without the q = 1/iota factor: - nu_e_without_iota = (6.921e-18) * R * ne_s * Zeff_s * ln_Lambda_e \ - / (1 * (Te_s ** 2) * (epsilon ** 1.5)) + nu_e_without_iota = R * (6.921e-18) * ne_s * Zeff_s * ln_Lambda_e \ + / ((Te_s ** 2) * (epsilon ** 1.5)) iota = nu_e_without_iota / target_nu_e_star - # End of determining the iota profile that gives the desired nu*. + # End of determining the qR profile that gives the desired nu*. - jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, R, iota, G, - epsilon, f_t, psi_edge, helicity_N=0) + jdotB, details = j_dot_B_Redl(s, ne, Te, Ti, Zeff, G, R, iota, + epsilon, f_t, psi_edge, helicity_N) L31s[j_nu_star, :] = details.L31 L32s[j_nu_star, :] = details.L32 @@ -468,7 +472,7 @@ def test_Redl_figures_4_5(self): np.testing.assert_array_less(L31s[0, 2], 0.66) assert L31s[0, 2] > 0.63 - def test_Redl_sfincs_benchmark(self): + def test_Redl_sfincs_tokamak_benchmark(self): """ Compare the Redl to a SFINCS calculation for a tokamak. @@ -606,13 +610,14 @@ def test_Redl_sfincs_precise_QA(self): -4390147.20699043, -3612989.71633149, -2793173.34162084, -1967138.17518374, -1192903.42248978, -539990.088677, -115053.37380415]) - if True: + if False: import matplotlib.pyplot as plt plt.plot(surfaces, jdotB, '.-', label='Redl') plt.plot(surfaces, jdotB_sfincs, '.-', label='sfincs') plt.legend(loc=0) plt.xlabel('s') - plt.title('J dot B') + plt.ylabel('J dot B [SI units]') + plt.title('Bootstrap current for the precise QA (Landreman & Paul (2021))') plt.show() @unittest.skip("") @@ -644,11 +649,12 @@ def test_Redl_sfincs_precise_QH(self): -3228174.23182819, -2914278.54799143, -2525391.54652021, -2058913.26485519, -1516843.60879267, -912123.395174, -315980.89711036]) - if True: + if False: import matplotlib.pyplot as plt plt.plot(surfaces, jdotB, '.-', label='Redl') plt.plot(surfaces, jdotB_sfincs, '.-', label='sfincs') plt.legend(loc=0) plt.xlabel('s') - plt.title('J dot B') + plt.ylabel('J dot B [SI units]') + plt.title('Bootstrap current for the precise QH (Landreman & Paul (2021))') plt.show() From 205ba8e5053032b05b91020be4592d00d1c15a52 Mon Sep 17 00:00:00 2001 From: Matt Landreman Date: Wed, 29 Dec 2021 06:05:10 -0500 Subject: [PATCH 09/28] Bootstrap tests: comparing to sfincs for precise QA and QH --- tests/mhd/test_bootstrap.py | 17 +- ...t.LandremanPaul2021_QA_reactorScale_lowres | 155 ++++++++++++++++++ ...t.LandremanPaul2021_QH_reactorScale_lowres | 150 +++++++++++++++++ ...ul2021_QA_reactorScale_lowres_reference.nc | Bin 0 -> 1055848 bytes ...ul2021_QH_reactorScale_lowres_reference.nc | Bin 0 -> 1055848 bytes 5 files changed, 314 insertions(+), 8 deletions(-) create mode 100644 tests/test_files/input.LandremanPaul2021_QA_reactorScale_lowres create mode 100644 tests/test_files/input.LandremanPaul2021_QH_reactorScale_lowres create mode 100644 tests/test_files/wout_LandremanPaul2021_QA_reactorScale_lowres_reference.nc create mode 100644 tests/test_files/wout_LandremanPaul2021_QH_reactorScale_lowres_reference.nc diff --git a/tests/mhd/test_bootstrap.py b/tests/mhd/test_bootstrap.py index c1e0b34e1..cf8711d7d 100755 --- a/tests/mhd/test_bootstrap.py +++ b/tests/mhd/test_bootstrap.py @@ -545,10 +545,7 @@ def test_Redl_sfincs_tokamak_benchmark(self): @unittest.skip("") def test_Redl_sfincs_WistellA(self): """ - Compare the Redl to a SFINCS calculation for a tokamak. - - The SFINCS calculation is on Matt Landreman's laptop in - /Users/mattland/Box Sync/work21/20211225-01-sfincs_tokamak_bootstrap_for_Redl_benchmark + Compare the Redl to a SFINCS calculation for Wistell-A. """ ne = ProfilePolynomial(0.9e20 * np.array([1, 0, 0, 0, 0, -1])) #Te = ProfilePolynomial(1.3e3 * np.array([1, -1])) @@ -581,7 +578,6 @@ def test_Redl_sfincs_WistellA(self): plt.title('J dot B') plt.show() - @unittest.skip("") def test_Redl_sfincs_precise_QA(self): """ Compare the Redl to a SFINCS calculation for the precise QA. @@ -594,7 +590,8 @@ def test_Redl_sfincs_precise_QA(self): Ti = Te Zeff = 1 helicity_N = 0 - filename = os.path.join(TEST_DIR, 'wout_new_QA_aScaling.nc') + # filename = os.path.join(TEST_DIR, 'wout_new_QA_aScaling.nc') # High resolution + filename = os.path.join(TEST_DIR, 'wout_LandremanPaul2021_QA_reactorScale_lowres_reference.nc') vmec = Vmec(filename) surfaces = np.linspace(0.025, 0.975, 39) jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, plot=False) @@ -620,7 +617,8 @@ def test_Redl_sfincs_precise_QA(self): plt.title('Bootstrap current for the precise QA (Landreman & Paul (2021))') plt.show() - @unittest.skip("") + np.testing.assert_allclose(jdotB[1:-1], jdotB_sfincs[1:-1], rtol=0.1) + def test_Redl_sfincs_precise_QH(self): """ Compare the Redl to a SFINCS calculation for the precise QH. @@ -633,7 +631,8 @@ def test_Redl_sfincs_precise_QH(self): Ti = Te Zeff = 1 helicity_N = -4 - filename = os.path.join(TEST_DIR, 'wout_new_QH_aScaling.nc') + #filename = os.path.join(TEST_DIR, 'wout_new_QH_aScaling.nc') # High resolution + filename = os.path.join(TEST_DIR, 'wout_LandremanPaul2021_QH_reactorScale_lowres_reference.nc') vmec = Vmec(filename) surfaces = np.linspace(0.025, 0.975, 39) jdotB, details = vmec_j_dot_B_Redl(vmec, surfaces, ne, Te, Ti, Zeff, helicity_N, plot=False) @@ -658,3 +657,5 @@ def test_Redl_sfincs_precise_QH(self): plt.ylabel('J dot B [SI units]') plt.title('Bootstrap current for the precise QH (Landreman & Paul (2021))') plt.show() + + np.testing.assert_allclose(jdotB, jdotB_sfincs, rtol=0.1) diff --git a/tests/test_files/input.LandremanPaul2021_QA_reactorScale_lowres b/tests/test_files/input.LandremanPaul2021_QA_reactorScale_lowres new file mode 100644 index 000000000..2bc2ea401 --- /dev/null +++ b/tests/test_files/input.LandremanPaul2021_QA_reactorScale_lowres @@ -0,0 +1,155 @@ +!----- Runtime Parameters ----- +&INDATA + DELT = 9.000000000000E-001 + NITER = 10000 + NSTEP = 200 + TCON0 = 2.000000000000E+000 + +! NS_ARRAY = 12 25 50 75 +! 100 150 201 +! FTOL_ARRAY = 1.000000E-17 1.000000E-17 1.000000E-17 1.000000E-17 +! 1.000000E-17 1.000000E-17 2.000000E-17 +! NITER_ARRAY = 1200 2000 3000 4000 +! 5000 6000 20000 + + NS_ARRAY = 12 50 + FTOL_ARRAY = 1.000000E-17 1.000000E-15 + NITER_ARRAY = 1000 5000 + + PRECON_TYPE = 'none' + PREC2D_THRESHOLD = 1.000000E-19 +!----- Grid Parameters ----- + LASYM = F + NFP = 0002 +! MPOL = 0016 +! NTOR = 0012 + MPOL = 008 + NTOR = 008 + PHIEDGE = 5.048228826746E+001 + NTHETA = 0000 + NZETA = 0000 +!----- Free Boundary Parameters ----- + LFREEB = F +!----- Pressure Parameters ----- + GAMMA = 0.000000000000E+000 + BLOAT = 1.000000000000E+000 + SPRES_PED = 1.000000000000E+000 + PRES_SCALE = 3.446233666638E+001 + PMASS_TYPE = 'power_series' + AM = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 +!----- ANI/FLOW Parameters ----- + BCRIT = 1.000000000000E+000 + PT_TYPE = 'power_series' + AT = 1.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 + PH_TYPE = 'power_series' + AH = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 +!----- Current/Iota Parameters ----- + CURTOR = 0.000000000000E+000 + NCURR = 1 + PIOTA_TYPE = 'power_series' + AI = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 + PCURR_TYPE = 'power_series' + AC = 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 +!----- Axis Parameters ----- + RAXIS_CC = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 + ZAXIS_CS = 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 +!----- Boundary Parameters ----- + RBC( 000,000) = 1.012658382028E+001 ZBS( 000,000) = 0.000000000000E+000 + RBC( 001,000) = 1.656442246637E+000 ZBS( 001,000) = -1.269527884010E+000 + RBC( 002,000) = 1.168065396338E-001 ZBS( 002,000) = -1.157570635450E-001 + RBC( 003,000) = 1.681848906918E-003 ZBS( 003,000) = -1.859955209758E-003 + RBC( 004,000) = -4.344142209654E-004 ZBS( 004,000) = 6.460740786144E-004 + RBC( 005,000) = -7.178092442796E-005 ZBS( 005,000) = 6.506076688604E-005 + RBC(-005,001) = -1.250523900045E-005 ZBS(-005,001) = 1.671593720258E-005 + RBC(-004,001) = 5.960412998346E-004 ZBS(-004,001) = 7.845776908340E-004 + RBC(-003,001) = 1.192612929656E-002 ZBS(-003,001) = 8.879234742430E-003 + RBC(-002,001) = 6.194886954255E-002 ZBS(-002,001) = 7.005027786691E-002 + RBC(-001,001) = 3.742783485244E-001 ZBS(-001,001) = 3.400206123943E-001 + RBC( 000,001) = 1.679774143201E+000 ZBS( 000,001) = 2.181203441748E+000 + RBC( 001,001) = -1.102571811326E+000 ZBS( 001,001) = 8.105522673578E-001 + RBC( 002,001) = -2.155805264092E-001 ZBS( 002,001) = 1.966385492229E-001 + RBC( 003,001) = -2.329273845974E-002 ZBS( 003,001) = 2.069175208826E-002 + RBC( 004,001) = -2.661237318218E-004 ZBS( 004,001) = 9.636272685192E-004 + RBC( 005,001) = -3.670631879823E-005 ZBS( 005,001) = 2.265932688630E-005 + RBC(-005,002) = 3.473389706292E-006 ZBS(-005,002) = 3.699307142425E-005 + RBC(-004,002) = 4.912086813127E-004 ZBS(-004,002) = 2.613952319580E-004 + RBC(-003,002) = -1.650091111779E-004 ZBS(-003,002) = 9.372934311218E-004 + RBC(-002,002) = 6.572506820813E-003 ZBS(-002,002) = 4.002721688287E-003 + RBC(-001,002) = 3.489234562081E-004 ZBS(-001,002) = -1.348294789692E-002 + RBC( 000,002) = 1.602596115905E-001 ZBS( 000,002) = 1.581142854112E-001 + RBC( 001,002) = 2.579026786227E-001 ZBS( 001,002) = 8.515829474462E-004 + RBC( 002,002) = 3.635432233409E-002 ZBS( 002,002) = -7.253576144831E-002 + RBC( 003,002) = 2.048904025366E-002 ZBS( 003,002) = -1.644076893936E-002 + RBC( 004,002) = 1.351013065632E-003 ZBS( 004,002) = -2.171973960015E-003 + RBC( 005,002) = 7.590720843726E-005 ZBS( 005,002) = -3.080501850148E-005 + RBC(-005,003) = 2.628832174986E-005 ZBS(-005,003) = 7.641923854311E-006 + RBC(-004,003) = -2.787430121400E-004 ZBS(-004,003) = -1.310287213145E-004 + RBC(-003,003) = -6.968320714789E-004 ZBS(-003,003) = -1.161154377680E-003 + RBC(-002,003) = 1.874492796226E-003 ZBS(-002,003) = 2.060514452732E-003 + RBC(-001,003) = -9.619402016515E-003 ZBS(-001,003) = -1.209237167999E-002 + RBC( 000,003) = 6.875154340249E-003 ZBS( 000,003) = 2.101177453522E-002 + RBC( 001,003) = 1.294437252868E-003 ZBS( 001,003) = 1.472181704879E-002 + RBC( 002,003) = 1.232040919148E-003 ZBS( 002,003) = 1.774116385019E-002 + RBC( 003,003) = -8.936328881911E-003 ZBS( 003,003) = 4.338128864939E-003 + RBC( 004,003) = -8.395399281403E-004 ZBS( 004,003) = 1.378423434210E-003 + RBC( 005,003) = -7.822252591332E-005 ZBS( 005,003) = 8.626413411417E-005 + RBC(-005,004) = -4.582548539172E-006 ZBS(-005,004) = -4.076195898557E-006 + RBC(-004,004) = -3.813191053140E-005 ZBS(-004,004) = -5.155484031027E-005 + RBC(-003,004) = 1.319411647064E-004 ZBS(-003,004) = 2.976111360202E-005 + RBC(-002,004) = -9.599663502253E-004 ZBS(-002,004) = -2.272484918867E-004 + RBC(-001,004) = 2.292855397569E-003 ZBS(-001,004) = -2.552760624864E-004 + RBC( 000,004) = -3.191042298440E-003 ZBS( 000,004) = 9.438118148131E-004 + RBC( 001,004) = 3.338606495371E-003 ZBS( 001,004) = -2.067893160914E-004 + RBC( 002,004) = 3.749381751266E-003 ZBS( 002,004) = 4.116238480522E-004 + RBC( 003,004) = 1.409401250244E-003 ZBS( 003,004) = -1.378509756730E-004 + RBC( 004,004) = 6.773407011029E-005 ZBS( 004,004) = -6.692016011567E-004 + RBC( 005,004) = 1.356208853860E-004 ZBS( 005,004) = -4.442280007640E-005 + RBC(-005,005) = -4.663415942586E-006 ZBS(-005,005) = -1.943134303013E-006 + RBC(-004,005) = 4.764896732353E-005 ZBS(-004,005) = 4.097168014316E-005 + RBC(-003,005) = -3.956686227747E-005 ZBS(-003,005) = 1.491783071001E-005 + RBC(-002,005) = 1.584781052977E-005 ZBS(-002,005) = -4.756691784527E-005 + RBC(-001,005) = 1.531874445946E-004 ZBS(-001,005) = 2.751071776720E-004 + RBC( 000,005) = 2.719607218643E-004 ZBS( 000,005) = 4.061345747065E-004 + RBC( 001,005) = -6.606905059771E-004 ZBS( 001,005) = 1.644012364749E-004 + RBC( 002,005) = -3.582600862273E-004 ZBS( 002,005) = -3.555595686945E-004 + RBC( 003,005) = 3.385254893765E-004 ZBS( 003,005) = 2.382197572763E-004 + RBC( 004,005) = -9.869119751268E-005 ZBS( 004,005) = 1.658366920165E-005 + RBC( 005,005) = -2.001537004214E-005 ZBS( 005,005) = 4.555704877329E-007 +/ +! RMIN = 6.210434530466387 +! RMAX = 13.168885503102558 +! ZMIN = -3.9363076554911123 +! ZMAX = 3.936307655491112 +! PHIMIN = 0.0 +! PHIMAX = 3.141592653589793 diff --git a/tests/test_files/input.LandremanPaul2021_QH_reactorScale_lowres b/tests/test_files/input.LandremanPaul2021_QH_reactorScale_lowres new file mode 100644 index 000000000..2dcbc7529 --- /dev/null +++ b/tests/test_files/input.LandremanPaul2021_QH_reactorScale_lowres @@ -0,0 +1,150 @@ +!----- Runtime Parameters ----- +&INDATA + DELT = 9.000000000000E-001 + NITER = 10000 + NSTEP = 200 + TCON0 = 2.000000000000E+000 + +! NS_ARRAY = 12 25 50 75 +! 100 150 201 +! FTOL_ARRAY = 1.000000E-17 1.000000E-17 1.000000E-17 1.000000E-17 +! 1.000000E-17 1.000000E-17 2.000000E-17 +! NITER_ARRAY = 1200 2000 3000 4000 +! 5000 6000 20000 + + NS_ARRAY = 12 50 + FTOL_ARRAY = 1.000000E-17 1.000000E-15 + NITER_ARRAY = 1200 5000 + PRECON_TYPE = 'none' + PREC2D_THRESHOLD = 1.000000E-19 +!----- Grid Parameters ----- + LASYM = F + NFP = 0004 + MPOL = 0008 + NTOR = 0008 + PHIEDGE = 4.186387773208E+001 + NTHETA = 0000 + NZETA = 0000 +!----- Free Boundary Parameters ----- + LFREEB = F +!----- Pressure Parameters ----- + GAMMA = 0.000000000000E+000 + BLOAT = 1.000000000000E+000 + SPRES_PED = 1.000000000000E+000 + PRES_SCALE = 7.129296562972E+000 + PMASS_TYPE = 'power_series' + AM = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 +!----- ANI/FLOW Parameters ----- + BCRIT = 1.000000000000E+000 + PT_TYPE = 'power_series' + AT = 1.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 + PH_TYPE = 'power_series' + AH = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 +!----- Current/Iota Parameters ----- + CURTOR = 0.000000000000E+000 + NCURR = 1 + PIOTA_TYPE = 'power_series' + AI = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 + PCURR_TYPE = 'power_series' + AC = 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 +!----- Axis Parameters ----- + RAXIS_CC = 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 0.00000000000000E+00 + 0.00000000000000E+00 + ZAXIS_CS = 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 0.000000000000E+000 + 0.000000000000E+000 +!----- Boundary Parameters ----- + RBC( 000,000) = 1.367375147766E+001 ZBS( 000,000) = 0.000000000000E+000 + RBC( 001,000) = 2.458811088284E+000 ZBS( 001,000) = 2.087809952337E+000 + RBC( 002,000) = 2.372329091047E-001 ZBS( 002,000) = 2.551979044092E-001 + RBC( 003,000) = 3.523944757399E-002 ZBS( 003,000) = 1.640455405466E-002 + RBC( 004,000) = -2.239610058463E-003 ZBS( 004,000) = 9.550219792542E-004 + RBC( 005,000) = -3.316302012241E-004 ZBS( 005,000) = -3.484833707189E-004 + RBC(-005,001) = -1.172891142384E-003 ZBS(-005,001) = 2.796952906580E-004 + RBC(-004,001) = -4.613589269547E-003 ZBS(-004,001) = 6.900936651125E-003 + RBC(-003,001) = -4.979105145863E-002 ZBS(-003,001) = 5.172083717870E-002 + RBC(-002,001) = -3.343003913181E-001 ZBS(-002,001) = 3.319884811820E-001 + RBC(-001,001) = -1.193959494238E+000 ZBS(-001,001) = 6.176721078449E-001 + RBC( 000,001) = 1.887511629365E+000 ZBS( 000,001) = 1.792585070922E+000 + RBC( 001,001) = 3.969748602910E-001 ZBS( 001,001) = 4.471578733064E-001 + RBC( 002,001) = 9.401042030899E-002 ZBS( 002,001) = 9.303041096194E-002 + RBC( 003,001) = 1.114488176302E-002 ZBS( 003,001) = 1.175169476452E-002 + RBC( 004,001) = -3.888445102044E-004 ZBS( 004,001) = -1.609774846436E-004 + RBC( 005,001) = 2.500873812304E-004 ZBS( 005,001) = -2.208606573753E-004 + RBC(-005,002) = 2.991444392846E-004 ZBS(-005,002) = -1.011921788627E-003 + RBC(-004,002) = 1.147708525686E-002 ZBS(-004,002) = -6.131141323267E-003 + RBC(-003,002) = 2.696174566065E-002 ZBS(-003,002) = -4.341286997869E-002 + RBC(-002,002) = 7.205801299407E-002 ZBS(-002,002) = -9.726361389574E-002 + RBC(-001,002) = 2.894642478614E-001 ZBS(-001,002) = 2.550978449509E-001 + RBC( 000,002) = 2.100364675213E-001 ZBS( 000,002) = 1.292325414648E-001 + RBC( 001,002) = -1.609502453632E-002 ZBS( 001,002) = -6.008853156679E-003 + RBC( 002,002) = 1.778839808673E-002 ZBS( 002,002) = 1.397982953330E-002 + RBC( 003,002) = 3.756695795525E-004 ZBS( 003,002) = -8.614906220464E-004 + RBC( 004,002) = 1.276351022476E-003 ZBS( 004,002) = 8.959625788496E-004 + RBC( 005,002) = -7.681122004966E-005 ZBS( 005,002) = -2.528069567306E-006 + RBC(-005,003) = 3.930144897455E-005 ZBS(-005,003) = 1.075890317063E-003 + RBC(-004,003) = -2.603315575112E-003 ZBS(-004,003) = 5.035365770564E-004 + RBC(-003,003) = 3.036129934725E-004 ZBS(-003,003) = 8.589410639810E-003 + RBC(-002,003) = -1.480145412461E-002 ZBS(-002,003) = 8.813872115569E-003 + RBC(-001,003) = 8.799578974345E-004 ZBS(-001,003) = 1.560654534427E-002 + RBC( 000,003) = 1.462294459199E-003 ZBS( 000,003) = 5.199929737940E-003 + RBC( 001,003) = 6.814970719862E-003 ZBS( 001,003) = 9.358252016759E-003 + RBC( 002,003) = 4.546887392291E-003 ZBS( 002,003) = 3.274915427664E-003 + RBC( 003,003) = -1.145935652702E-003 ZBS( 003,003) = -3.908787494710E-005 + RBC( 004,003) = 1.116974368241E-003 ZBS( 004,003) = 5.235215882911E-004 + RBC( 005,003) = -1.603874518889E-004 ZBS( 005,003) = -3.510808935320E-006 + RBC(-005,004) = 2.639941928257E-004 ZBS(-005,004) = 7.997384801817E-005 + RBC(-004,004) = 8.087263486072E-004 ZBS(-004,004) = -1.336953822527E-003 + RBC(-003,004) = -2.099839582050E-003 ZBS(-003,004) = -2.691620048604E-003 + RBC(-002,004) = 1.265505108246E-003 ZBS(-002,004) = -1.715979913932E-003 + RBC(-001,004) = 3.032178576699E-003 ZBS(-001,004) = 9.753931940415E-004 + RBC( 000,004) = 6.322332213688E-003 ZBS( 000,004) = 4.561763184144E-003 + RBC( 001,004) = -6.610823086742E-004 ZBS( 001,004) = -2.713711235770E-004 + RBC( 002,004) = 1.982117968414E-003 ZBS( 002,004) = 4.711445679698E-004 + RBC( 003,004) = -7.370713133332E-004 ZBS( 003,004) = -8.263510173517E-004 + RBC( 004,004) = -3.767350282858E-004 ZBS( 004,004) = -4.422365940715E-004 + RBC( 005,004) = -1.410486346676E-004 ZBS( 005,004) = -1.141331244167E-004 + RBC(-005,005) = -1.125394635239E-004 ZBS(-005,005) = -6.785534181825E-006 + RBC(-004,005) = -5.856768005525E-004 ZBS(-004,005) = 3.493202560578E-004 + RBC(-003,005) = 9.806370018962E-005 ZBS(-003,005) = 6.032755666345E-004 + RBC(-002,005) = 2.305942363495E-004 ZBS(-002,005) = -7.998114339313E-005 + RBC(-001,005) = -4.247530107429E-005 ZBS(-001,005) = 2.022420756102E-005 + RBC( 000,005) = -4.248290092659E-004 ZBS( 000,005) = -6.229177562600E-004 + RBC( 001,005) = -2.894739047193E-004 ZBS( 001,005) = 6.774144048711E-005 + RBC( 002,005) = 1.920402595905E-005 ZBS( 002,005) = 3.994646750689E-005 + RBC( 003,005) = -2.038807166485E-004 ZBS( 003,005) = -1.828397894803E-004 + RBC( 004,005) = -1.452176687737E-004 ZBS( 004,005) = -1.420015297700E-004 + RBC( 005,005) = -4.178619587655E-005 ZBS( 005,005) = -3.596593433452E-005 +/ +! RMIN = 8.975629164617695 +! RMAX = 17.826308553121798 +! ZMIN = -4.285189611385015 +! ZMAX = 4.285189611385015 +! PHIMIN = 0.0 +! 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