def randomRadiusPlotRZ():
R = 3
ms = []
rms = []
zms = []
plt.figure(figsize=(5, 5))
for _ in range(1000):
rm = R * np.random.rand()
xm = simulation.randomPointOnSphere(rm)
ms.append(xm)
rms.append((xm[0]**2 + xm[1]**2)**.5)
zms.append(xm[2])
xp = simulation.randomPointOnSphere(1)
propdir = np.cross(xm, xp)
propdir /= np.linalg.norm(propdir)
points = [
xm + i * propdir * (R**2 - rm**2)**.5
for i in np.arange(-1, 1, .05)
]
rs = [(p[0]**2 + p[1]**2)**.5 for p in points]
zs = [p[2] for p in points]
plt.plot(rs, zs, color='blue', linewidth=.1)
# plt.scatter(rms, zms, s=.5)
plt.axis('equal')
# ax.scatter(*list(zip(*ms)), color='red', s=1)
plt.show()
def randomRadiusPlot3D():
"""
Pick uniformly random r, phi, and theta in sphere as midpoint
Pick an xy vector with random angle
Take cross product with midpoint to get chord direction
Step from midpoint to boundary of circle by sqrt(r^2-m^2) in chord direction
"""
R = 3
ms = []
fig = plt.figure(figsize=(5, 5))
ax = fig.gca(projection='3d')
for _ in range(1000):
rm = R * np.random.rand()
xm = simulation.randomPointOnSphere(rm)
ms.append(xm)
xp = simulation.randomPointOnSphere(1)
propdir = np.cross(xm, xp)
propdir /= np.linalg.norm(propdir)
xstart = xm + -1 * propdir * (R**2 - rm**2)**.5
xend = xm + propdir * (R**2 - rm**2)**.5
ax.plot(*list(zip(xstart, xend)), color='blue', linewidth=.1)
# ax.scatter(*list(zip(*ms)), color='red', s=1)
_axisEqual3D(ax)
plt.axis('off')
plt.show()
def testRandomPointOnSphere():
points = np.array(
[simulation.randomPointOnSphere(10) for _ in range(1000)])
fig = plt.figure(figsize=(5, 5))
ax = fig.gca(projection='3d')
ax.scatter(points[:, 0], points[:, 1], points[:, 2])
plt.show()
def testTrajectory():
dt = 1e-11
print('dt (s):', dt)
fieldFile = 'oct30.txt'
r, z, BR = simulation.fieldGrid('fields/Brs_' + fieldFile)
_, _, BZ = simulation.fieldGrid('fields/Bzs_' + fieldFile)
BR = BR * 0 # BUG
BZ = BZ * 0
E = np.array([0., 0, 0])
qm = 9.6e7
v0 = 2.6e8
maxSteps = 30000
# Generate random point and direction
rLim = 30
x = simulation.randomPointOnSphere(rLim)
xNoField = x
direction = simulation.randomPointOnSphere(rLim) - x
direction /= np.linalg.norm(direction)
v = direction * v0
vNoField = v
xs = np.zeros((maxSteps, 3))
xNoFields = np.zeros((maxSteps, 3))
for i in range(maxSteps):
xNoField += vNoField * dt
xNoFields[i] = xNoField
# x, v = simulation.RKnext(x, v, qm, BR, BZ, r, z, dt)
B = simulation.BxyzInterpolated(x, BR, BZ, r, z)
x, v = simulation.BBnext(x, v, qm, B, E, dt)
xs[i] = x
fig = plt.figure(figsize=(10, 10))
ax = fig.gca(projection='3d')
ax.plot(xs[:, 0], xs[:, 1], xs[:, 2])
ax.plot(xNoFields[:, 0], xNoFields[:, 1], xNoFields[:, 2], '--')
_axisEqual3D(ax)
plt.show()
def testRandomDirectionCos():
fig = plt.figure(figsize=(7, 7))
ax = fig.gca(projection='3d')
axis = simulation.randomPointOnSphere(3)
ax.plot([0, axis[0]], [0, axis[1]], [0, axis[2]], color='black')
xs = []
ys = []
zs = []
for _ in range(1000):
d = simulation.randomDirectionCos(axis)
xs.append(d[0])
ys.append(d[1])
zs.append(d[2])
ax.scatter(xs, ys, zs, color='blue', alpha=.02)
_axisEqual3D(ax)
plt.show() #
def randomHomogRZ():
"""
Randomly select midpoint R and Z in order to get as uniform an R, Z grid as possible.
"""
R = 3.
zs = []
ms = []
rms = []
zms = []
plt.figure(figsize=(10, 10))
for _ in range(3000):
xm = np.array([0., 0., 4.])
while np.linalg.norm(xm) > R:
xm[2] = 2 * R * (np.random.rand() - 0.5)
rm = R * np.random.rand()**2
thetam = 2 * np.pi * np.random.rand()
xm[0] = rm * np.cos(thetam)
xm[1] = rm * np.sin(thetam)
ms.append(xm)
rms.append((xm[0]**2 + xm[1]**2)**.5)
zms.append(xm[2])
xp = simulation.randomPointOnSphere(1)
propdir = np.cross(xm, xp)
propdir /= np.linalg.norm(propdir)
points = [
xm + i * propdir * (R**2 - rm**2)**.5
for i in np.arange(-1, 1, .05)
if np.linalg.norm(xm + i * propdir * (R**2 - rm**2)**.5) < R
]
rs = [(p[0]**2 + p[1]**2)**.5 for p in points]
zs = [p[2] for p in points]
plt.plot(rs, zs, color='blue', linewidth=.1)
# plt.scatter(rms, zms, s=.5)
plt.axis('equal')
# ax.scatter(*list(zip(*ms)), color='red', s=1)
plt.show()