def magtrap(self):
s = system.System()
rmax = 1e3
a, b, c, d, e = -1.3, 1.3, .78, 2.5, 3.
s.append(electrode.PolygonPixelElectrode(name="rf",
rf=1., paths=[
[[rmax,0], [-rmax,0], [-rmax,a], [rmax,a]],
[[rmax,b+c], [-rmax,b+c], [-rmax,b], [rmax,b]],
]))
for cx, cy, w, n in [
(d/2+e/2, b+2*c, d, "c1"),
(0, b+2*c, e, "c2"),
(-d/2-e/2, b+2*c, d, "c3"),
(d/2+e/2, a, d, "c6"),
(0, a, e, "c5"),
(-d/2-e/2, a, d, "c4")]:
s.append(electrode.PolygonPixelElectrode(
name=n, paths=[[
[cx-w/2,cy], [cx-w/2,rmax*np.sign(cy)],
[cx+w/2,rmax*np.sign(cy)], [cx+w/2,cy],
]]))
for e in s:
e.paths = [p[::1 if o > 0 else -1]
for p, o in zip(e.paths, e.orientations())]
return s
def setUp(self):
p = np.array([[0, 0], [1, 0], [1, 2], [2, 2.]])
a = electrode.PolygonPixelElectrode(paths=[p, p + [[3, 3.]]], dc=1.)
b = electrode.PolygonPixelElectrode(paths=[p - [[3, 3]]], dc=2.)
self.s = system.System([a, b])
self.m = electrode.MeshPixelElectrode.from_polygon_system(self.s)
self.x = np.array([[1, 2, 3.]])
def test_shims(self):
x = self.x0
eln = "c1 c2 c3 c4 c5 c6".split()
s = system.System([self.s[n] for n in eln])
derivs = "x y z xx yy yz".split()
vectors = s.shims([(x, None, d) for d in derivs])
self.assertEqual(vectors.shape, (len(derivs), len(eln)))
return vectors, s, derivs
def ringtrap(self):
s = system.System()
n = 100
p = np.exp(1j*np.linspace(0, 2*np.pi, 100))
s.append(electrode.PolygonPixelElectrode(name="rf",
rf=1, paths=[np.r_[
3.38*np.array([p.real, p.imag]).T,
.68*np.array([p.real, p.imag]).T[::-1]]]
))
return s
def trap(self, tw=np.pi/4, t0=5*np.pi/8):
s = system.System()
rmax = 1e4
# Janus H. Wesenberg, Phys Rev A 78, 063410 ͑2008͒
def patches(n, tw, t0):
for i in range(n):
a = t0 + 2*np.pi/n*i
ya, yb = np.tan((a-tw/2)/2), np.tan((a+tw/2)/2)
yield np.array([[rmax, ya], [rmax, yb],
[-rmax, yb], [-rmax, ya]])
s.append(electrode.PolygonPixelElectrode(name="rf",
rf=1, paths=list(patches(n=2, tw=tw, t0=t0))))
return s
def test_pseudopotential_derivs(self):
ns = range(1, 5)
d = 1e-7
xd = self.x + [[0, 0, 0], [d, 0, 0], [0, d, 0], [0, 0, d]]
s = system.System([self.e])
self.e.rf = 1.
for n in ns:
p = s.potential(self.x, n)[0]
pd = s.potential(xd, n - 1)
pd = (pd[1:] - pd[0]) / d
for k, (i, j) in enumerate(zip(p.ravel(), pd.ravel())):
nptest.assert_allclose(i,
j,
rtol=d,
atol=d / 100,
err_msg="n=%i, k=%i" % (n, k))
def get(self, n=12, h=1/8., d=1/4., H=25/8., nmax=1, points=True):
s = system.System(electrodes=self.hextess(n, points))
for ei in s:
ei.cover_height = H
ei.cover_nmax = nmax
self.s = s
ct = []
ct.append(pattern_constraints.PatternRangeConstraint(min=0, max=1.))
for p in 0, 4*np.pi/3, 2*np.pi/3:
x = np.array([d/3**.5*np.cos(p), d/3**.5*np.sin(p), h])
r = transformations.euler_matrix(p, np.pi/2, np.pi/4, "rzyz")[:3, :3]
for i in "x y z xy xz yz".split():
ct.append(pattern_constraints.PotentialObjective(derivative=i,
x=x, rotation=r, value=0))
for i in "xx yy".split():
ct.append(pattern_constraints.PotentialObjective(derivative=i,
x=x, rotation=r, value=2**(-1/3.)))
s.rfs, self.c = s.optimize(ct, verbose=False)
self.h = h
self.x0 = np.array([d/3**.5, 0, h])
self.r = transformations.euler_matrix(0, np.pi/2, np.pi/4, "rzyz")[:3, :3]
