def Bfield_CircularCurrentLoopV(I0, D, POS):
R = D / 2 #radius
N = len(D) # vector size
X, Y, Z = POS[:, 0], POS[:, 1], POS[:, 2]
RR, PHI = sqrt(X**2 + Y**2), arctan2(Y, X) # cylindrical coordinates
deltaP = sqrt((RR + R)**2 + Z**2)
deltaM = sqrt((RR - R)**2 + Z**2)
kappa = deltaP**2 / deltaM**2
kappaBar = 1 - kappa
# allocate solution vector
field_R = empty([N])
# avoid discontinuity of Br on z-axis
maskRR0 = RR == np.zeros([N])
field_R[maskRR0] = 0
# R-component computation
notM = np.invert(maskRR0)
field_R[notM] = -2 * 1e-4 * (Z[notM] / RR[notM] / deltaM[notM]) * (
ellipticKV(kappaBar[notM]) - (2 - kappaBar[notM]) /
(2 - 2 * kappaBar[notM]) * ellipticEV(kappaBar[notM]))
# Z-component computation
field_Z = -2 * 1e-4 * (1 / deltaM) * (
-ellipticKV(kappaBar) + (2 - kappaBar - 4 * (R / deltaM)**2) /
(2 - 2 * kappaBar) * ellipticEV(kappaBar))
# transformation to cartesian coordinates
Bcy = np.array([field_R, np.zeros(N), field_Z]).T
AX = np.zeros([N, 3])
AX[:, 2] = 1
Bkart = angleAxisRotationV_priv[1, 1](PHI / pi * 180, AX, Bcy)
return (Bkart.T * I0).T * 1000 # to mT
def test_ellipticSpecialCases():
X = np.linspace(0, .9999, 33)
Y = np.linspace(0, .9999, 33)[::-1]
solV = ellipticKV(X)
solC = np.array([ellipticK(x) for x in X])
assert np.amax(abs(solV - solC)) < 1e-15
solV = ellipticEV(X)
solC = np.array([ellipticE(x) for x in X])
assert np.amax(abs(solV - solC)) < 1e-15
solV = ellipticPiV(X, Y)
solC = np.array([ellipticPi(x, y) for x, y in zip(X, Y)])
assert np.amax(abs(solV - solC)) < 1e-15