def topple(self, point, J, cage, Bpoint, method='function', **kwargs):
# eq.Bpoint == point calculated method (slow)
# sf.Bpoint == spline interpolated method (fast)
x = {'cl': {'r': cage.coil_loop[:, 0], 'z': cage.coil_loop[:, 2]}}
if 'streamfunction' in Bpoint.__str__():
topright = Bpoint((np.max(x['cl']['r']), np.max(x['cl']['z'])),
check_bounds=True)
bottomleft = Bpoint((np.max(x['cl']['r']), np.max(x['cl']['z'])),
check_bounds=True)
if not (topright and bottomleft):
errtxt = 'TF coil extends outside Bpoint interpolation grid\n'
errtxt = 'extend sf grid\n'
raise ValueError(errtxt)
if method == 'function': # calculate tf feild as fitted 1/r function
i = np.argmax(x['cl']['z'])
ro, zo = x['cl']['r'][i], x['cl']['z'][i]
bm = ro * cage.point((ro, 0, zo), variable='feild')[1] # TF moment
elif method != 'BS': # raise error if method not 'function' or 'BS'
errtxt = 'invalid tf feild method {}\n'.format(method)
errtxt += 'select method from \'function\' or \'BS\'\n'
raise ValueError(errtxt)
if method == 'function':
b = np.zeros(3)
b[2] = -bm / point[
0] # TF feild (fast version / only good for TF cl)
elif method == 'BS': # calculate tf feild with full Biot-Savart
b = cage.point(point, variable='feild') # (slow / correct)
theta = np.arctan2(point[1], point[0])
pf_point = np.dot(geom.rotate(-theta, 'z'),
point) # rotate to PF plane
pf_b = Bpoint([pf_point[0],
pf_point[2]]) # PF feild (sf-fast, eq-slow)
b += np.dot(geom.rotate(theta, 'z'), [pf_b[0], 0, pf_b[1]]) # add PF
Fbody = np.cross(J, b) # body force
return Fbody
def point(self, s, variable='ripple'): # s==3D point vector
B = np.zeros(2)
n = np.array([0, 1, 0])
if variable == 'ripple':
planes = [0, np.pi / self.nTF] # rotate (inline, ingap)
elif variable == 'feild':
planes = [0]
else:
errtxt = '\n'
errtxt += 'point variable error, require \'ripple\' or \'feild\'\n'
raise ValueError(errtxt)
for j, theta in enumerate(planes):
sr = np.dot(s, geom.rotate(theta))
nr = np.dot(n, geom.rotate(theta))
Bo = np.zeros(3)
for tcoil in self.Tcoil:
for dy in self.dYwp: # wp pattern
for dr in self.dRwp: # wp radial pattern
Bo += self.Iturn*cc.mu_o*\
self.gfl.B(sr,theta=tcoil,dy=dy,dr=dr)/(self.ny*self.nr)
B[j] = np.dot(nr, Bo)
if variable == 'ripple':
ripple = 1e2 * (B[0] - B[1]) / np.sum(B)
return ripple
else:
return Bo
def rotate_cp(self, name, dof, theta, axis):
self.check_cp_rotation(dof, self.mpc[name]['neq'])
R = geom.rotate(theta, axis=axis) # 3x3 rotation matrix
self.mpc[name]['Cr'] = np.zeros(
(self.mpc[name]['neq'], self.mpc[name]['neq']))
self.mpc[name]['Cr'][:3, :3] = R
if self.mpc[name]['neq'] == 6:
self.mpc[name]['Cr'][3:, 3:] = R
def point(self, s, variable='ripple'): # s==3D point vector
B = np.zeros(2)
n = np.array([0, 1, 0])
if variable == 'ripple':
planes = [0, np.pi / self.nTF] # rotate (inline, ingap)
elif variable == 'feild':
planes = [0]
else:
errtxt = '\n'
errtxt += 'point variable error, require \'ripple\' or \'feild\'\n'
raise ValueError(errtxt)
for j, theta in enumerate(planes):
sr = np.dot(s, geom.rotate(theta))
nr = np.dot(n, geom.rotate(theta))
Bo = np.zeros(3)
for tcoil in np.linspace(0, 2 * np.pi, self.nTF, endpoint=False):
Bo += cc.mu_o * self.gfl.B(sr, theta=tcoil)
B[j] = np.dot(nr, Bo)
if variable == 'ripple':
ripple = 1e2 * (B[0] - B[1]) / np.sum(B)
return ripple
else:
return Bo
def plot_3D(self, ms=5, bb=12, pattern=0):
fig = pl.figure(figsize=(8, 8))
ax = fig.gca(projection='3d')
Theta = np.linspace(0, 2 * np.pi, pattern, endpoint=False)
for t in Theta:
R = geom.rotate(t, axis='y')
#X = np.dot(self.X,R)
#ax.plot(X[:,0],X[:,2],X[:,1],'o',markersize=ms,color=0.75*np.ones(3))
for i, (part, c) in enumerate(zip(self.part, color)):
D = np.dot(self.part[part]['D'], R)
ax.plot(D[:, 0], D[:, 2], D[:, 1], color=c)
ax.set_xlim(-bb, bb)
ax.set_ylim(-bb, bb)
ax.set_zlim(-bb, bb)
ax.axis('off')
def rotateX_(self,theta):
self.X_ = np.dot(self.X,geom.rotate(theta))
self.dX_ = np.dot(self.dX,geom.rotate(theta))