def APPLE_II(_per, _nper, _gap, _gapx, _phase, _phase_type, _lx, _lz, _cx, _cz, _air, _br, _mu, _ndiv, _bs1, _s1, _bs2, _s2, _bs3, _s3, _bs2dz, _qp_ind_mag, _qp_dz, _use_sym=False):
w = [_lx,_per/4-_air,_lz]
px = _lx/2+_gapx/2;
pz = _gap/2+_lz/2;
p1 = 0; p2 = _phase; p3 = 0; p4 = _phase
if(_phase_type < 0): p2 = -_phase
#print('w =', w)
g1 = MagnetArray(_per, _nper, _po=[px,p1,pz], _w=w, _si=1, _type=1, _cx=_cx, _cz=_cz, _br=_br, _mu=_mu, _ndiv=_ndiv,
_bs1=_bs1, _s1=_s1, _bs2=_bs2, _s2=_s2, _bs3=_bs3, _s3=_s3, _bs2dz=_bs2dz, _qp_ind_mag=_qp_ind_mag, _qp_dz=_qp_dz)
g2 = MagnetArray(_per, _nper, _po=[-px,p2,pz], _w=w, _si=1, _type=2, _cx=_cx, _cz=_cz, _br=_br, _mu=_mu, _ndiv=_ndiv,
_bs1=_bs1, _s1=_s1, _bs2=_bs2, _s2=_s2, _bs3=_bs3, _s3=_s3, _bs2dz=_bs2dz, _qp_ind_mag=_qp_ind_mag, _qp_dz=_qp_dz)
if(_use_sym):
u = rad.ObjCnt([g1,g2])
trf = rad.TrfCmbL(rad.TrfRot([0,0,0],[0,1,0],pi), rad.TrfInv())
rad.TrfMlt(u, trf, 2)
return u, g1, g2, 0, 0
g3 = MagnetArray(_per, _nper, _po=[-px,p3,-pz], _w=w, _si=-1, _type=1, _cx=_cx, _cz=_cz, _br=-_br, _mu=_mu, _ndiv=_ndiv,
_bs1=_bs1, _s1=_s1, _bs2=_bs2, _s2=_s2, _bs3=_bs3, _s3=_s3, _bs2dz=_bs2dz, _qp_ind_mag=_qp_ind_mag, _qp_dz=_qp_dz)
g4 = MagnetArray(_per, _nper, _po=[px,p4,-pz], _w=w, _si=-1, _type=2, _cx=_cx, _cz=_cz, _br=-_br, _mu=_mu, _ndiv=_ndiv,
_bs1=_bs1, _s1=_s1, _bs2=_bs2, _s2=_s2, _bs3=_bs3, _s3=_s3, _bs2dz=_bs2dz, _qp_ind_mag=_qp_ind_mag, _qp_dz=_qp_dz)
u = rad.ObjCnt([g1,g2,g3,g4])
return u, g1, g2, g3, g4
def _apply_rotation(g_id, xform):
xform = PKDict(xform)
radia.TrfOrnt(
g_id,
radia.TrfRot(
sirepo.util.split_comma_delimited_string(xform.center, float),
sirepo.util.split_comma_delimited_string(xform.axis, float),
numpy.pi * float(xform.angle) / 180.
)
)
def _apply_clone(g_id, xform):
# start with 'identity'
xf = radia.TrfTrsl([0, 0, 0])
for clone_xform in xform.transforms:
cxf = PKDict(clone_xform)
if cxf.model == 'translateClone':
txf = radia.TrfTrsl(_split_comma_field(cxf.distance, 'float'))
xf = radia.TrfCmbL(xf, txf)
if cxf.model == 'rotateClone':
rxf = radia.TrfRot(_split_comma_field(cxf.center, 'float'),
_split_comma_field(cxf.axis, 'float'),
numpy.pi * float(cxf.angle) / 180.)
xf = radia.TrfCmbL(xf, rxf)
if xform.alternateFields != '0':
xf = radia.TrfCmbL(xf, radia.TrfInv())
radia.TrfMlt(g_id, xf, xform.numCopies + 1)
def _apply_clone(g_id, xform):
xform = PKDict(xform)
# start with 'identity'
xf = radia.TrfTrsl([0, 0, 0])
for clone_xform in xform.transforms:
cxf = PKDict(clone_xform)
if cxf.model == 'translateClone':
txf = radia.TrfTrsl(
sirepo.util.split_comma_delimited_string(cxf.distance, float)
)
xf = radia.TrfCmbL(xf, txf)
if cxf.model == 'rotateClone':
rxf = radia.TrfRot(
sirepo.util.split_comma_delimited_string(cxf.center, float),
sirepo.util.split_comma_delimited_string(cxf.axis, float),
numpy.pi * float(cxf.angle) / 180.
)
xf = radia.TrfCmbL(xf, rxf)
if xform.alternateFields != '0':
xf = radia.TrfCmbL(xf, radia.TrfInv())
radia.TrfMlt(g_id, xf, xform.numCopies + 1)
def wradRotate(self, pivot_origin, pivot_vector, rot_magnitude):
'''trying to write a rotation function
# u' = quq*
#u is point
#q is quaternion representation of rotation angle ( sin (th/2)i, sin(th/2)j, sin (th/2)k, cos (th/2))'''
q = R.from_quat([
pivot_vector[0] * np.sin(rot_magnitude / 2.0),
pivot_vector[1] * np.sin(rot_magnitude / 2.0),
pivot_vector[2] * np.sin(rot_magnitude / 2.0),
np.cos(rot_magnitude / 2.0)
])
#rotate vertices
for i in range(len(self.vertices)):
u = self.vertices[i] - pivot_origin
self.vertices[i] = q.apply(u)
#rotate magnetisation vector
self.magnetisation = (q.apply(self.magnetisation)).tolist()
self.material.M = self.magnetisation
# rotate colour
q = R.from_quat([
pivot_vector[0] * np.sin(rot_magnitude / 2.0),
pivot_vector[1] * np.sin(rot_magnitude / 2.0),
pivot_vector[2] * np.sin(rot_magnitude / 2.0),
np.cos(rot_magnitude / 2.0),
])
tmpcol = [(4 * x - 2) for x in self.colour]
tmpcol = q.apply(tmpcol)
self.colour = [(2 + x) / 4.0 for x in tmpcol]
rd.ObjDrwAtr(self.radobj, self.colour, self.linethickness)
#rotate radia object
rota = rd.TrfRot(pivot_origin, pivot_vector, rot_magnitude)
rd.TrfOrnt(self.radobj, rota)
def _apply_rotation(g_id, xform):
radia.TrfOrnt(
g_id,
radia.TrfRot(_split_comma_field(xform.center, 'float'),
_split_comma_field(xform.axis, 'float'),
numpy.pi * float(xform.angle) / 180.))
def rotate(self, point, vector, angle):
"""Rotate radia object."""
if self._radia_object is not None:
self._radia_object = _rad.TrfOrnt(
self._radia_object, _rad.TrfRot(point, vector, angle))
#rad.ObjDrwOpenGL(mag01sbd)
#mag01sbd = rad.ObjDivMagPln(mag01, [[2,0.5],[3,0.2],[4,0.1]], [1,0.4,0.1], [0.4,1,0.2], [0,0,1], 'Frame->Lab')
mag01sbd = rad.ObjDivMagPln(mag01, [[2,0.5],[3,0.2],[4,0.1]])
#rad.ObjDrwOpenGL(mag01sbd)
#mag00sbd = rad.ObjDivMag(mag00, [[2,0.5],[3,0.2],[4,0.1]], 'cyl', [[2.5,4,0],[0,0,1],[8,0,0],3], 'Frame->Lab')
#mag00sbd = rad.ObjDivMagCyl(mag00, [[2,0.5],[3,0.2],[4,0.1]], [2.5,4,0], [0,0,1], [8,0,0], 3, 'Frame->Lab')
print('Volume of 3D object:', rad.ObjGeoVol(mag01sbd))
print('Geom. Limits of 3D object:', rad.ObjGeoLim(mag01sbd))
#rad.ObjDrwOpenGL(mag01)
trf01 = rad.TrfPlSym([0,10,0], [0,1,0])
trf02 = rad.TrfRot([0,10,0], [0,0,1], 1.)
trf03 = rad.TrfTrsl([30,10,0])
trf04 = rad.TrfInv()
trf05 = rad.TrfCmbL(trf01, trf04)
trf06 = rad.TrfCmbR(trf01, trf04)
#rad.TrfMlt(mag01, trf03, 3)
rad.TrfOrnt(mag01, trf06)
#rad.ObjDrwOpenGL(mag01)
matNdFeB = rad.MatStd('NdFeB')
M = rad.MatMvsH(matNdFeB, 'M', [0,0,0])
print('NdFeB material index:', matNdFeB, ' Magnetization:', M)
matLin01 = rad.MatLin([0.1,0.2],1.1)
def rotate(self, point, vector, angle):
self._radia_object = _rad.TrfOrnt(
self._radia_object, _rad.TrfRot(point, vector, angle))
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():
#Pole faces
rap = 0.5
ct = [0, 0, 0]
z0 = gap / 2
y0 = width / 2
amax = hyp * asinh(y0 / z0)
dz = z0 * (cosh(amax) - 1)
aStep = amax / np
na = int(amax * (1 + 2 / np) / aStep) + 1
qq = [[(z0 * sinh(ia * aStep / hyp)), (z0 * cosh(ia * aStep))]
for ia in range(na)]
hh = qq[np][1] + height * rap - dz
qq[np + 1] = [qq[np][0], hh]
qq[np + 2] = [0, hh]
g1 = rad.ObjThckPgn(thick / 4, thick / 2, qq)
rad.ObjDivMag(g1, n1)
#Vertical segment on top of pole faces
g2 = rad.ObjRecMag(
[thick / 4, width / 4, gap / 2 + height * (1 / 2 + rap / 2)],
[thick / 2, width / 2, height * (1 - rap)])
rad.ObjDivMag(g2, n2)
#Corner
gg = rad.ObjCnt([g1, g2])
gp = rad.ObjCutMag(gg, [thick / 2 - chamfer - gap / 2, 0, 0],
[1, 0, -1])[0]
g3 = rad.ObjRecMag([thick / 4, width / 4, gap / 2 + height + depth / 2],
[thick / 2, width / 2, depth])
cy = [[[0, width / 2, gap / 2 + height], [1, 0, 0]],
[0, 0, gap / 2 + height], 2 * depth / width]
rad.ObjDivMag(g3, [nr3, np3, nx], 'cyl', cy)
#Horizontal segment between the corners
tan_n = tan(2 * pi / 2 / Nn)
length = tan_n * (height + gap / 2) - width / 2
g4 = rad.ObjRecMag(
[thick / 4, width / 2 + length / 2, gap / 2 + height + depth / 2],
[thick / 2, length, depth])
rad.ObjDivMag(g4, n4)
#The other corner
posy = width / 2 + length
posz = posy / tan_n
g5 = rad.ObjThckPgn(thick / 4, thick / 2,
[[posy, posz], [posy, posz + depth],
[posy + depth * tan_n, posz + depth]])
cy = [[[0, posy, posz], [1, 0, 0]], [0, posy, posz + depth], 1]
rad.ObjDivMag(g5, [nr5, np5, nx], 'cyl', cy)
#Generation of the coil
Rmax = Rmin - width / 2 + gap / 2 + offset - 2
coil1 = rad.ObjRaceTrk([0, 0, gap / 2 + height / 2 + offset / 2],
[Rmin, Rmax], [thick, width - 2 * Rmin],
height - offset, 3, CurDens)
rad.ObjDrwAtr(coil1, coilcolor)
hh = (height - offset) / 2
coil2 = rad.ObjRaceTrk([0, 0, gap / 2 + height - hh / 2],
[Rmax, Rmax + hh * 0.8], [thick, width - 2 * Rmin],
hh, 3, CurDens)
rad.ObjDrwAtr(coil2, coilcolor)
#Make container, set the colors and define symmetries
g = rad.ObjCnt([gp, g3, g4, g5])
rad.ObjDrwAtr(g, ironcolor)
gd = rad.ObjCnt([g])
rad.TrfZerPerp(gd, ct, [1, 0, 0])
rad.TrfZerPerp(gd, ct, [0, 1, 0])
t = rad.ObjCnt([gd, coil1, coil2])
rad.TrfZerPara(t, ct, [0, cos(pi / Nn), sin(pi / Nn)])
rad.TrfMlt(t, rad.TrfRot(ct, [1, 0, 0], 4 * pi / Nn), int(round(Nn / 2)))
rad.MatApl(g, ironmat)
rad.TrfOrnt(t, rad.TrfRot([0, 0, 0], [1, 0, 0], pi / Nn))
return t