def test_efield_vs_gauss_law():
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from math import sqrt, pi
from pytools.arithmetic_container import \
ArithmeticList, join_fields
from random import seed
from pytools.stopwatch import Job
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
seed(0)
nparticles = 10000
beam_radius = 2.5 * units.MM
emittance = 5 * units.MM * units.MRAD
final_time = 0.1 * units.M / units.VACUUM_LIGHT_SPEED()
field_dump_interval = 1
tube_length = 20 * units.MM
# discretization setup ----------------------------------------------------
from pyrticle.geometry import make_cylinder_with_fine_core
mesh = make_cylinder_with_fine_core(
r=10 * beam_radius,
inner_r=1 * beam_radius,
min_z=0,
max_z=tube_length,
max_volume_inner=10 * units.MM**3,
max_volume_outer=100 * units.MM**3,
radial_subdiv=10,
)
from hedge.backends import guess_run_context
rcon = guess_run_context([])
discr = rcon.make_discretization(mesh, order=3)
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(epsilon=units.EPSILON0, mu=units.MU0, flux_type=1)
from hedge.models.nd_calculus import DivergenceOperator
div_op = DivergenceOperator(discr.dimensions)
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units, ShapeFunctionDepositor(),
MonomialParticlePusher(), 3, 3)
# particle ic ---------------------------------------------------------
cloud_charge = -1e-9 * units.C
electrons_per_particle = abs(cloud_charge / nparticles / units.EL_CHARGE)
el_energy = 10 * units.EL_REST_ENERGY()
el_lorentz_gamma = el_energy / units.EL_REST_ENERGY()
beta = (1 - 1 / el_lorentz_gamma**2)**0.5
gamma = 1 / sqrt(1 - beta**2)
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units,
total_charge=cloud_charge,
p_charge=cloud_charge / nparticles,
p_mass=electrons_per_particle * units.EL_MASS,
radii=2 * [beam_radius],
emittances=2 * [5 * units.MM * units.MRAD],
z_length=tube_length,
z_pos=tube_length / 2,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# field ic ----------------------------------------------------------------
from pyrticle.cloud import guess_shape_bandwidth
guess_shape_bandwidth(method, state, 2)
from pyrticle.cloud import compute_initial_condition
from hedge.data import ConstantGivenFunction
fields = compute_initial_condition(rcon,
discr,
method,
state,
maxwell_op=max_op,
potential_bc=ConstantGivenFunction())
# check against theory ----------------------------------------------------
q_per_unit_z = cloud_charge / beam.z_length
class TheoreticalEField:
shape = (3, )
def __call__(self, x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
xy_unit = x / r
xy_unit[2] = 0
return xy_unit * ((q_per_unit_z) /
(2 * pi * r * max_op.epsilon))
else:
return numpy.zeros((3, ))
def theory_indicator(x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
return 1
else:
return 0
from hedge.tools import join_fields, to_obj_array
e_theory = to_obj_array(
discr.interpolate_volume_function(TheoreticalEField()))
theory_ind = discr.interpolate_volume_function(theory_indicator)
e_field, h_field = max_op.split_eh(fields)
restricted_e = join_fields(*[e_i * theory_ind for e_i in e_field])
def l2_error(field, true):
return discr.norm(field - true) / discr.norm(true)
outer_l2 = l2_error(restricted_e, e_theory)
assert outer_l2 < 0.08
if False:
visf = vis.make_file("e_comparison")
mesh_scalars, mesh_vectors = \
method.add_to_vis(vis, visf)
vis.add_data(visf, [
("e", restricted_e),
("e_theory", e_theory),
] + mesh_vectors + mesh_scalars)
visf.close()
def get_true_field():
return discr.convert_volume(
to_obj_array(mode(discr).real.astype(discr.default_scalar_type).copy()), kind=discr.compute_kind
)
def test_efield_vs_gauss_law():
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from math import sqrt, pi
from pytools.arithmetic_container import \
ArithmeticList, join_fields
from random import seed
from pytools.stopwatch import Job
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
seed(0)
nparticles = 10000
beam_radius = 2.5 * units.MM
emittance = 5 * units.MM * units.MRAD
final_time = 0.1*units.M/units.VACUUM_LIGHT_SPEED()
field_dump_interval = 1
tube_length = 20*units.MM
# discretization setup ----------------------------------------------------
from pyrticle.geometry import make_cylinder_with_fine_core
mesh = make_cylinder_with_fine_core(
r=10*beam_radius, inner_r=1*beam_radius,
min_z=0, max_z=tube_length,
max_volume_inner=10*units.MM**3,
max_volume_outer=100*units.MM**3,
radial_subdiv=10,
)
from hedge.backends import guess_run_context
rcon = guess_run_context([])
discr = rcon.make_discretization(mesh, order=3)
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(
epsilon=units.EPSILON0,
mu=units.MU0,
flux_type=1)
from hedge.models.nd_calculus import DivergenceOperator
div_op = DivergenceOperator(discr.dimensions)
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units,
ShapeFunctionDepositor(),
MonomialParticlePusher(),
3, 3)
# particle ic ---------------------------------------------------------
cloud_charge = -1e-9 * units.C
electrons_per_particle = abs(cloud_charge/nparticles/units.EL_CHARGE)
el_energy = 10*units.EL_REST_ENERGY()
el_lorentz_gamma = el_energy/units.EL_REST_ENERGY()
beta = (1-1/el_lorentz_gamma**2)**0.5
gamma = 1/sqrt(1-beta**2)
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units, total_charge=cloud_charge,
p_charge=cloud_charge/nparticles,
p_mass=electrons_per_particle*units.EL_MASS,
radii=2*[beam_radius],
emittances=2*[5 * units.MM * units.MRAD],
z_length=tube_length,
z_pos=tube_length/2,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# field ic ----------------------------------------------------------------
from pyrticle.cloud import guess_shape_bandwidth
guess_shape_bandwidth(method, state, 2)
from pyrticle.cloud import compute_initial_condition
from hedge.data import ConstantGivenFunction
fields = compute_initial_condition(
rcon,
discr, method, state, maxwell_op=max_op,
potential_bc=ConstantGivenFunction())
# check against theory ----------------------------------------------------
q_per_unit_z = cloud_charge/beam.z_length
class TheoreticalEField:
shape = (3,)
def __call__(self, x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
xy_unit = x/r
xy_unit[2] = 0
return xy_unit*((q_per_unit_z)
/
(2*pi*r*max_op.epsilon))
else:
return numpy.zeros((3,))
def theory_indicator(x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
return 1
else:
return 0
from hedge.tools import join_fields, to_obj_array
e_theory = to_obj_array(discr.interpolate_volume_function(TheoreticalEField()))
theory_ind = discr.interpolate_volume_function(theory_indicator)
e_field, h_field = max_op.split_eh(fields)
restricted_e = join_fields(*[e_i * theory_ind for e_i in e_field])
def l2_error(field, true):
return discr.norm(field-true)/discr.norm(true)
outer_l2 = l2_error(restricted_e, e_theory)
assert outer_l2 < 0.08
if False:
visf = vis.make_file("e_comparison")
mesh_scalars, mesh_vectors = \
method.add_to_vis(vis, visf)
vis.add_data(visf, [
("e", restricted_e),
("e_theory", e_theory),
]
+ mesh_vectors
+ mesh_scalars
)
visf.close()
def get_true_field():
return discr.convert_volume(to_obj_array(
mode(discr).real.astype(discr.default_scalar_type).copy()),
kind=discr.compute_kind)