def make_dipole(pole_dimensions,
center,
length,
current=-10000,
trimesh_mode=0,
triangle_min_size=TRIANGLE_MIN_SIZE,
triangle_max_size=TRIANGLE_MAX_SIZE,
longitudinal_divisions=4):
"""
Construct a complete H-dipole made of iron.
:param pole_dimensions: (dict) Parameters describing geometry of pole piece. See `_create_point_table`.
:param center: (float) Center point of dipole in x (longitudinal center for beam frame).
:param length: (float) Length of the dipole in x
:param current: (float) Current carried by dipole coils (default: -10000)
:param trimesh_mode: (int) If 0 (default) then the pole piece is divisioned into polygons based on point ordering
from coordinate list. If != 0 then a Triangular mesh is automatically generated.
:param longitudinal_divisions: (int) Number of slices to divide up the dipole into along the x-axis (default: 4)
:return:
"""
# coil_factor increases coil size slightly to accommodate sharp corners of pole piece
coil_length_factor = 1.005
coil_height_factor = 3. / 4.
coil_or_factor = 0.85
# Geometry for the poles
table_quadrant_one = _create_point_table(**pole_dimensions)
top_coodinates = _get_all_points_top(table_quadrant_one)
bottom_coordinates = _get_all_points_bottom(top_coodinates)
top_pole = create_pole(top_coodinates,
center,
length,
mode=trimesh_mode,
triangle_min_size=triangle_min_size,
triangle_max_size=triangle_max_size)
bottom_pole = create_pole(bottom_coordinates,
center,
length,
mode=trimesh_mode,
triangle_min_size=triangle_min_size,
triangle_max_size=triangle_max_size)
# Material for the poles (uses Iron)
ironmat = rad.MatSatIsoFrm([20000, 2], [0.1, 2], [0.1, 2])
rad.MatApl(top_pole, ironmat)
rad.MatApl(bottom_pole, ironmat)
# Coils
coil_outer_radius = pole_dimensions['pole_separation'] * coil_or_factor
top_coil = make_racetrack_coil(
center=[
0, 0.0,
pole_dimensions['gap_height'] + pole_dimensions['pole_height'] / 2.
],
radii=[0.1, coil_outer_radius],
sizes=[
length * coil_length_factor,
pole_dimensions['pole_width'] * 2 * coil_length_factor,
pole_dimensions['pole_height'] * coil_height_factor
],
current=current)
bottom_coil = make_racetrack_coil(center=[
0, 0.0, -1. *
(pole_dimensions['gap_height'] + pole_dimensions['pole_height'] / 2.)
],
radii=[0.1, coil_outer_radius],
sizes=[
length * coil_length_factor,
pole_dimensions['pole_width'] * 2 *
coil_length_factor,
pole_dimensions['pole_height'] *
coil_height_factor
],
current=current)
# Visualization
rad.ObjDrwAtr(top_pole, [0, 0.4, 0.8])
rad.ObjDrwAtr(bottom_pole, [0, 0.4, 0.8])
rad.ObjDrwAtr(top_coil, [0.2, 0.9, 0.6])
rad.ObjDrwAtr(bottom_coil, [0.2, 0.9, 0.6])
# Element Division
rad.ObjDivMag(top_pole, [longitudinal_divisions, 1, 1])
rad.ObjDivMag(bottom_pole, [longitudinal_divisions, 1, 1])
return rad.ObjCnt([top_pole, bottom_pole, top_coil, bottom_coil])
def build(self):
"""Create a quadrupole with the given geometry."""
if self.solve_state < SolveState.SHAPES:
self.define_shapes()
rad.UtiDelAll()
origin = [0, 0, 0]
nx = [1, 0, 0]
ny = [0, 1, 0]
nz = [0, 0, 1]
tip_mesh = round(self.min_mesh)
pole_mesh = round(self.min_mesh * self.pole_mult)
yoke_mesh = round(self.min_mesh * self.yoke_mult)
length = self.length
# Subdivide the pole tip cylindrically. The axis is where the edge of the tapered pole meets the Y-axis.
points = rotate45(self.tip_points)
x2, y2 = points[-2] # top right of pole
x3, y3 = points[-3] # bottom right of pole
m = (y2 - y3) / (x2 - x3)
c = y2 - m * x2
pole_tip = rad.ObjThckPgn(length / 2, length, points, "z")
# Slice off the chamfer (note the indexing at the end here - selects the pole not the cut-off piece)
pole_tip = rad.ObjCutMag(pole_tip, [length - self.chamfer, 0, self.r], [1, 0, -1])[0]
n_div = max(1, round(math.sqrt((x2 - x3) ** 2 + (y2 - y3) ** 2) / pole_mesh))
# We have to specify the q values here (second element of each sublist in the subdivision argument)
# otherwise weird things happen
mesh = [[n_div, 4], [tip_mesh / 3, 1], [tip_mesh, 1]]
div_opts = 'Frame->Lab;kxkykz->Size'
# rad.ObjDivMag(pole_tip, [[tip_mesh, 1], [tip_mesh, 1], [tip_mesh, 3]], div_opts)
rad.ObjDivMag(pole_tip, mesh, "cyl", [[[0, c, 0], nz], nx, 1], div_opts)
rad.TrfOrnt(pole_tip, rad.TrfRot(origin, nz, -math.pi / 4))
pole = rad.ObjThckPgn(length / 2, length, rotate45(self.pole_points), "z")
rad.ObjDivMag(pole, [pole_mesh, ] * 3, div_opts)
rad.TrfOrnt(pole, rad.TrfRot(origin, nz, -math.pi / 4))
# Need to split yoke since Radia can't build concave blocks
points = rotate45(self.yoke_points[:2] + self.yoke_points[-2:])
# yoke1 is the part that joins the pole to the yoke
# Subdivide this cylindrically since the flux goes around a corner here
# The axis is the second point (x1, y1)
x1, y1 = points[1]
yoke1 = rad.ObjThckPgn(length / 2, length, points, "z")
cyl_div = [[[x1, y1, 0], nz], [self.width, self.width, 0], 1]
# The first (kr) argument, corresponding to radial subdivision,
# in rad.ObjDivMag cuts by number not size even though kxkykz->Size is specified.
# So we have to fudge this. It seems to require a larger number to give the right number of subdivisions.
n_div = max(1, round(2 * self.width / yoke_mesh))
rad.ObjDivMag(yoke1, [n_div, yoke_mesh, yoke_mesh], "cyl", cyl_div, div_opts)
rad.TrfOrnt(yoke1, rad.TrfRot(origin, nz, -math.pi / 4))
# For the second part of the yoke, we use cylindrical subdivision again. But the axis is not on the corner;
# instead we calculate the point where the two lines converge (xc, yc).
points = self.yoke_points[1:3] + self.yoke_points[-3:-1]
x0, y0 = points[0]
x1, y1 = points[1]
x2, y2 = points[2]
x3, y3 = points[3]
m1 = (y3 - y0) / (x3 - x0)
m2 = (y2 - y1) / (x2 - x1)
c1 = y0 - m1 * x0
c2 = y1 - m2 * x1
xc = (c2 - c1) / (m1 - m2)
yc = m1 * xc + c1
yoke2 = rad.ObjThckPgn(length / 2, length, points, 'z')
cyl_div = [[[xc, yc, 0], nz], [x3 - xc, y3 - yc, 0], 1]
n_div = max(1, round(0.7 * n_div)) # this is a bit of a fudge
rad.ObjDivMag(yoke2, [n_div, yoke_mesh, yoke_mesh], "cyl", cyl_div, div_opts)
yoke3 = rad.ObjThckPgn(length / 2, length, self.yoke_points[2:6], "z")
rad.ObjDivMag(yoke3, [yoke_mesh, ] * 3, div_opts)
steel = rad.ObjCnt([pole_tip, pole, yoke1, yoke2, yoke3])
rad.ObjDrwAtr(steel, [0, 0, 1], 0.001) # blue steel
rad.TrfOrnt(steel, rad.TrfRot(origin, ny, -math.pi / 2))
rad.ObjDrwOpenGL(steel)
rad.TrfOrnt(steel, rad.TrfRot(origin, ny, math.pi / 2))
# rad.TrfMlt(steel, rad.TrfPlSym([0, 0, 0], [1, -1, 0]), 2) # reflect along X=Y line to create a quadrant
rad.TrfZerPerp(steel, origin, [1, -1, 0])
rad.TrfZerPerp(steel, origin, nz)
steel_material = rad.MatSatIsoFrm([2000, 2], [0.1, 2], [0.1, 2])
steel_material = rad.MatStd('Steel42')
steel_material = rad.MatSatIsoFrm([959.703184, 1.41019852], [33.9916543, 0.5389669], [1.39161186, 0.64144324])
rad.MatApl(steel, steel_material)
coil = rad.ObjRaceTrk(origin, [5, 5 + self.coil_width],
[self.coil_x * 2 - self.r, length * 2], self.coil_height, 4, self.current_density)
rad.TrfOrnt(coil, rad.TrfRot(origin, nx, -math.pi / 2))
rad.TrfOrnt(coil, rad.TrfTrsl([0, self.r + self.taper_height + self.coil_height / 2, 0]))
rad.TrfOrnt(coil, rad.TrfRot(origin, nz, -math.pi / 4))
rad.ObjDrwAtr(coil, [1, 0, 0], 0.001) # red coil
quad = rad.ObjCnt([steel, coil])
rad.TrfZerPara(quad, origin, nx)
rad.TrfZerPara(quad, origin, ny)
# rad.ObjDrwOpenGL(quad)
self.radia_object = quad
self.solve_state = SolveState.BUILT
def geom(circ):
eps = 0
ironcolor = [0, 0.5, 1]
coilcolor = [1, 0, 0]
ironmat = radia.MatSatIsoFrm([20000, 2], [0.1, 2], [0.1, 2])
# Pole faces
lx1 = thick / 2
ly1 = width
lz1 = 20
l1 = [lx1, ly1, lz1]
k1 = [[thick / 4. - chamfer / 2., 0, gap / 2.],
[thick / 2. - chamfer, ly1 - 2. * chamfer]]
k2 = [[thick / 4., 0., gap / 2. + chamfer], [thick / 2., ly1]]
k3 = [[thick / 4., 0., gap / 2. + lz1], [thick / 2, ly1]]
g1 = radia.ObjMltExtRtg([k1, k2, k3])
radia.ObjDivMag(g1, n1)
radia.ObjDrwAtr(g1, ironcolor)
# Vertical segment on top of pole faces
lx2 = thick / 2
ly2 = ly1
lz2 = 30
l2 = [lx2, ly2, lz2]
p2 = [thick / 4, 0, lz1 + gap / 2 + lz2 / 2 + 1 * eps]
g2 = radia.ObjRecMag(p2, l2)
radia.ObjDivMag(g2, n2)
radia.ObjDrwAtr(g2, ironcolor)
# Corner
lx3 = thick / 2
ly3 = ly2
lz3 = ly2 * 1.25
l3 = [lx3, ly3, lz3]
p3 = [thick / 4, 0, lz1 + gap / 2 + lz2 + lz3 / 2 + 2 * eps]
g3 = radia.ObjRecMag(p3, l3)
typ = [
[p3[0], p3[1] + ly3 / 2, p3[2] - lz3 / 2],
[1, 0, 0],
[p3[0], p3[1] - ly3 / 2, p3[2] - lz3 / 2],
lz3 / ly3
]
if circ == 1:
radia.ObjDivMag(g3, [nbr, nbp, n3[1]], 'cyl', typ)
else:
radia.ObjDivMag(g3, n3)
radia.ObjDrwAtr(g3, ironcolor)
# Horizontal segment between the corners
lx4 = thick / 2
ly4 = 80
lz4 = lz3
l4 = [lx4, ly4, lz4]
p4 = [thick / 4, ly3 / 2 + eps + ly4 / 2, p3[2]]
g4 = radia.ObjRecMag(p4, l4)
radia.ObjDivMag(g4, n4)
radia.ObjDrwAtr(g4, ironcolor)
# The other corner
lx5 = thick / 2
ly5 = lz4 * 1.25
lz5 = lz4
l5 = [lx5, ly5, lz5]
p5 = [thick / 4, p4[1] + eps + (ly4 + ly5) / 2, p4[2]]
g5 = radia.ObjRecMag(p5, l5)
typ = [
[p5[0], p5[1] - ly5 / 2, p5[2] - lz5 / 2],
[1, 0, 0],
[p5[0], p5[1] + ly5 / 2, p5[2] - lz5 / 2],
lz5 / ly5
]
if circ == 1:
radia.ObjDivMag(g5, [nbr, nbp, n5[0]], 'cyl', typ)
else:
radia.ObjDivMag(g5, n5)
radia.ObjDrwAtr(g5, ironcolor)
# Vertical segment inside the coil
lx6 = thick / 2
ly6 = ly5
lz6 = gap / 2 + lz1 + lz2
l6 = [lx6, ly6, lz6]
p6 = [thick / 4, p5[1], p5[2] - (lz6 + lz5) / 2 - eps]
g6 = radia.ObjRecMag(p6, l6)
radia.ObjDivMag(g6, n6)
radia.ObjDrwAtr(g6, ironcolor)
# Generation of the coil
r_min = 5
r_max = 40
h = 2 * lz6 - 5
cur_dens = current / h / (r_max - r_min)
pc = [0, p6[1], 0]
coil = radia.ObjRaceTrk(pc, [r_min, r_max], [thick, ly6], h, 3, cur_dens)
radia.ObjDrwAtr(coil, coilcolor)
# Make container and set the colors
g = radia.ObjCnt([g1, g2, g3, g4, g5, g6])
radia.ObjDrwAtr(g, ironcolor)
radia.MatApl(g, ironmat)
t = radia.ObjCnt([g, coil])
# Define the symmetries
radia.TrfZerPerp(g, [0, 0, 0], [1, 0, 0])
radia.TrfZerPara(g, [0, 0, 0], [0, 0, 1])
return t
#Segmentation Params
nx = 2
ny = 2
n1 = [nx, ny, 3]
n2 = [nx, ny, 3]
np3 = 2
nr3 = ny
n4 = [nx, 3, ny]
np5 = ceil(np3 / 2)
print()
nr5 = ny
t0 = time()
rad.UtiDelAll()
ironmat = rad.MatSatIsoFrm([2000, 2], [0.1, 2], [0.1, 2])
g = Geom()
size = rad.ObjDegFre(g)
t1 = time()
Nmax = 10000
res = rad.Solve(g, 0.00001, Nmax)
t2 = time()
Bz = rad.Fld(g, 'Bz', [0, 1, 0]) * 1000
Iz = rad.FldInt(g, 'inf', 'ibz', [-1, 1, 0], [1, 1, 0])
Iz1 = rad.FldInt(g, 'inf', 'ibz', [-1, 10, 0], [1, 10, 0]) / 10
print('M_Max H_Max N_Iter = ', round(res[1], 4), 'T', round(res[2], 4),
'T', round(res[3]))
if (res[3] == Nmax): print('Unstable or Incomplete Relaxation')
