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DescriptionMagnetic field of an idealized quadrupole with forces.svg |
English: Magnetic field of an idealized quadrupole with forces
Русский: Магнитное поле и силы в квадрупольном магните |
Date | |
Source | python/matplotlib |
Author | Andre.holzner |
Other versions |
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xpoints = arange(-5,5,0.05)
ypoints = arange(-5,5,0.05)
X,Y = meshgrid(xpoints, ypoints)
circularMask = False
areaRadius = 4
# order of the magnet
n = 2
def func(x,y):
# the function to draw
return ((x + 1j * y)**(n)).real
func = vectorize(func)
V = func(X,Y)
# mask points which we don't want to draw
if circularMask:
# circular mask
distance = sqrt(X**2 + Y**2)
V = ma.masked_where(distance > areaRadius, V)
else:
# polygonal mask
# principal directions are at (i + 0.5) / (2n) * 2pi
#
for i in range(2*n):
angle = (i + 0.5) / float(2*n) * 2*pi
# define a straight angle perpendicular to angle
# mask all points on one side of this line
anchor_x = areaRadius * cos(angle)
anchor_y = areaRadius * sin(angle)
normal_x = cos(angle)
normal_y = sin(angle)
def acceptFunc(x,y):
value = (x - anchor_x) * normal_x + (y - anchor_y) * normal_y
return value > 0
acceptFunc = vectorize(acceptFunc)
V = ma.masked_where(acceptFunc(X,Y), V)
if True:
# levels equidistant in function value
vmax = V.max()
V /= vmax
levels = arange(-2,2,0.05)
else:
# levels equidistant on x and y axis
# determine the levels to draw from values on one of the axes
levels = float(func(x,0)) for x in arange(min(xpoints), max(xpoints),0.50) + \
float(func(0,y)) for y in arange(min(ypoints), max(ypoints),0.50)
levels = sorted(list(set(levels)))
vmax = 1
figure(figsize=(6,6));
Q = contour(X,Y, V, colors= 'black', linestyles = 'solid',
levels = levels
)
# axis([-5,5,-5,5])
xlabel("x coordinate")
ylabel("y coordinate")
# mask points which we don't want to draw
if not circularMask:
# polygonal mask
# principal directions are at (i + 0.5) / (2n) * 2pi
#
for i in range(2*n):
angle = (i + 0.5) / float(2*n) * 2*pi
if i % 2:
label = "N"
color = 'red'
else:
label = "S"
color = 'green'
anchor_x = 1.1 * areaRadius * cos(angle)
anchor_y = 1.1 * areaRadius * sin(angle)
text(anchor_x, anchor_y, label, size = 20, color = color,
horizontalalignment='center',
verticalalignment='center')
#----------------------------------------
if n == 2:
# quadrupole, draw some examples of force on charged particle
# find kth level line on axes (x = 0 and y = 0)
# the potential function is >= 0 on the x axis and <= 0 on the y axis
# for a quadrupole
lev = sorted(list(levelslevels >= 0]))[4
# find distance of this level on axis from origin
# (exploit the 90 degree symmetry of the field)
dist = fsolve(lambda x: func(x,0) / vmax - lev,3)[0
# rotation by +90 degrees
rotMatrix = array([[0,-1],[1,0]])
invRotMatrix = rotMatrix.T
arrowLength = 1.5
arrowStart = array([dist, 0])
origArrowDir = array([0, arrowLength])
bfieldLabelPosOffset = array([0.3, 0.5 * arrowLength])
forceLabelPosOffset = array([0.5 * arrowLength, -0.3])
for i in range(4):
arrowDir = origArrowDir[:]
for j in range(i):
arrowDir = rotMatrix.dot(arrowDir)
# take into account quadrupole structure
arrowDir *= (-1)**i
# draw arrow for the B field
arrow(arrowStart0],arrowStart1], arrowDir0], arrowDir1],head_width=0.3, head_length=0.3, color = 'red')
# add a label for the B field
textPos = arrowStart + (-1)**i * bfieldLabelPosOffset
text(textPos0],
textPos1], "B", size = 20, color = 'red',
horizontalalignment='center',
verticalalignment='center')
# draw the arrow for the force
arrowDir2 = invRotMatrix.dot(arrowDir)
arrow(arrowStart0], arrowStart1], arrowDir20], arrowDir21],head_width=0.3, head_length=0.3, color = 'blue')
# label for the force
textPos = arrowStart + (-1)**i * forceLabelPosOffset
text(textPos0],
textPos1], "F", size = 20, color = 'blue',
horizontalalignment='center',
verticalalignment='center')
#----------
# prepare next iteration
arrowStart = rotMatrix.dot(arrowStart)
bfieldLabelPosOffset = rotMatrix.dot(bfieldLabelPosOffset)
forceLabelPosOffset = rotMatrix.dot(forceLabelPosOffset)
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 21:12, 16 December 2012 |
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